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"SESOIL"
A SEASONAL SOIL COMPARTMENT MODEL
by
Marcos Bonazountas
Janet M. Wagner
Arthur D. Little, Inc.
Cambridge, Massachusetts 02140
617/864-5770
(see section 1.0)
This Model Version Prepared for
United States Environmental Protection Agency
Office of Toxic Substances
Washington, D.C. 20460
202/755-8068
Task Manager: Annette Nold
EPA Contract No. 68-01-6271
December 1981
Arthur D Little, Inc
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ABSTRACT
Bonazountas, M. and J. Wagner (1981); "SESOIL: A Seasonal Soil Compartment
Model," Arthur D. Little, Inc., Cambridge, Massachusetts 02140
Prepared for U.S. Environmental Protection Agency, Office of Toxic Substances
Contract No. 68-01-6271
SESOIL is a "user-friendly" statistical mathematical model designed for long-
term environmental pollutant fate simulations that can describe: water
transport (quality/quantity); sediment transport (quality/quantity); pollutant
transport/transformation; and soil quantity. Simulations are performed for a
user specified soil column (designated as compartment), extending between the
ground surface and the lower part of the saturated soil zone of a region. The
simulation is based upon a three-cycle rationale, each cycle being associated
with a number of processes. The three cycles are the: (1) water cycle which
takes account of rainfall, infiltration, exfiltration, surface runoff, evapo-
transpiration, groundwater runoff, snow pack/melt and interception, (2) sediment
cycle which takes account of sediment resuspension (because of wind) and sediment
washload (because of rain storms), and (3) pollutant cycle which takes account of
convection, diffusion, volatilization, adsorption/desorption, chemical degra-
dation/decay, biological transformation/uptake, hydrolysis, photolysis, oxi-
dation, complexation of metals by organics and nutrient cycles. Model
development has been sponsored by the U.S. Environmental Protection Agency and
has been validated—as an unsaturated soil zone pollutant transport model—at
waste land treatment disposal sites. The entire model development has not yet
been accomplished; however, certain model features are operational.
Key words; SESOIL, mathematical modeling, pollution, soil quality, ground-
water, pathways, land treatment, waste disposal, multi-media
modeling.
Dec. 1981
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TABLE OF CONTENTS
Page
Abstract
1.0 INTRODUCTION 1-1
2.0 THE SESOIL MODEL 2-1
3.0 USER'S MANUAL 3-1
APPENDICES
HY ' Hydrologic Cycle HY-1
SW Soil Washload SW-1
SR Soil Resuspension SR-1
VO Diffusion and Volatilization VO-1
AD Adsorption and Desorption AD-1
DE Degradation and Decay DE-1
HD Hydrolysis of Organic Compounds HY-1
CE Cation Exchange CE-1
CM Complexation of Metals CM-1
PH Photolysis (not in this documentation) PH-1
FX Fixation (not in this documentation) FX-1
BI Biologic Activities (not in this documentation) BI-1
NU Nutrient Cycles NU-1
PT Pollutant Transport Cycle PT-1
ID Input Data Compilation ID-1
DF Data Files and Arrays DF-1
FC FORTRAN Code FC-1
AP Application Samples AP-1
RE References RE-1
MI Miscellaneous MI-1
Dec. 31, 1981 iii
Arthur DLittfelhc
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DISTRIBUTION LIST
(of Dec. 31, 1981)
M. Callahan (EPA/OTS)
G. Contos (Versar)
J. Dragun (EPA/OTS)
P. Eagleson (MIT)
G.R. Foster (Purdue Univ.)
G. Harris (ADL)
R. Kickert (EPA/CERL)
A. Nold (EPA/OTS)
M. Slimak/J. Segna (EPA/MDSD)
W. Wood (EPA/OTS)
Dec. 31, 1981 iv
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1.0 INTRODUCTION
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TABLE OF CONTENTS
Page
1.0 INTRODUCTION 1-2
1.1 Preamble Notes 1-2
1.2 Organization of this Documentation 1-3
1.3 Raison d'Etre of SESOIL 1-4
1.4 Acknowledgements 1-6
1.5 References 1-7
Dec. 81 1-1
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1.0 INTRODUCTION
1.1 Preamble Notes
• This modeling effort and its documentation have been accomplished
at an expense (professional time, all other expenses) of less than
$70,000 and, as such, they should be evaluated or criticized
correspondingly.
• This documentation is a preliminary draft and has not been publicly
released by the U.S. Environmental Protection Agency; however, it
has been circulated to scientists for comments on its technical
approach. Since model developers have not published their original
work, quotations related to SESOIL or the processes described in
this documentation must be referenced (Bonazountas and Wagner
1981) as indicated in the abstract.
• All models are good as long as: (i) users are aware of the
assumptions upon which they have been developed; and (ii) they are
employed and applied appropriately.
• SESOIL is a "user-friendly" model that can be operated with very few
input data, mostly available from government records or other
literature (e.g., handbooks). This has been achieved with a
sophisticated mathematical description of all SESOIL processes, a
task that has exceeded previous similar efforts of the literature.
However, "amateur (modelers) can do more harm than city fellers on
a farm" (Groundwater 1981); therefore, potential users should be
careful when employing this friendly and easy to use package.
• Most environmental models of the literature can be "forced" by
their developers to predict almost exactly what their developers
desire to predict—via calibration coefficients; this is not a
secret among modelers. In that respect, SESOIL is at an ad-
vantageous position because no calibration coefficients accompany
its theory; however, users should validate model predictions with
available data as far as possible. (See also Section 3.4.)
• The authors intend to continue improving SESOIL—both in its newly
developed scientific basis and its range of applicability—and to
update this documentation as appropriate. In that respect, they:
(a) solicit any critical review, and (b) kindly ask users to make
sure to have the latest version of the model code.
• SESOIL has been carefully developed and its software has been
tested; however, the ultimate responsibility for its use rests with
the user, since this is the first version of the model, and
developers have not repeatedly applied the model to the real world.
However, developers intend to correct any errors which users may
report.
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• This SESOIL version presents only a subset of all model features.
The computer code, therefore, contains control nodes and dummy
statements and loops that will facilitate potential future de-
velopment. It would be inappropriate for a user to modify the code
without notifying model developers, because this may result in
incorrect calculations.
• Roughly speaking, this version of SESOIL can be employed as: (i) a
hydrologic basin model (watershed, unsaturated soil zone, ground-
water recharge); and (ii) a pollutant transport model of the
unsaturated soil zone, however, interacting (for mass balance
purposes) with both the watershed and the groundwater of a soil
environment. (See Section 2.0.)
• Strong appreciation is given by model developers to all the people
who have supported this effort. (See Section 1.4.)
• Users are advised to read this documentation carefully and, in case
of questions, to contact developers. The authors would be happy to
provide assistance—as far as possible—to potential users.
1.2 Organization of this Documentation
The main intentions while drafting this documentation have been: sim-
plicity, clarity and expandability; therefore, it has been structured
around two major parts containing:
(1) an overall presentation, and
(2) twenty appendices
It is believed that this documentation format allows:
(1) readers to clearly understand both the various scientific
areas modeled (described in the appendices) and the SESOIL
operations, and
(2) users to efficiently apply SESOIL following knowledge gained
after reading the entire documentation.
The overall presentation is covered in three main sections:
• Section 1.0 - Introduction
• Section 2.0 - SESOIL Description
• Section 3.0 - User's Manual
The 20 appendices are self-contained, short documents and give both
background information, and mathematics employed for the various areas
of science (hydrology, sedimentation, chemistry, other) modeled via
SESOIL. Each appendix is designated with two characteristic letters as
shown in the Table of Contents of this documentation. References are
given in each section or each appendix and are aggregared in Appendix RE.
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It is believed that this format permits expansion, improvement and
substitution of the background and parts of the theory given in this
documentation without affecting the overall model presentation. This
loose-leaf binder version also provides the possibility of single-page
substitutions in the near future. The latest version of a page is
printed with a date next to the page number; if no date is given, the date
of the first page of the section of appendix is assumed. The appendix
format facilitates reading because the same text is not to be found in
two different chapters; it also facilitates users who do not actually
care for the background during an application.
A potential user, however, is advised to read all sections of the report,
namely, from the Introduction to the last appendix (Appendix MI,
Miscellaneous). A user who desires to only use a few aspects of the model
operation (e.g., pollutant cycle) would have to refer only to the
corresponding appendix (i.e., Appendix PT, Pollutant Transport Cycle).
In the computer code, reference is made to the equations of individual
appendices.
1.3 Raison d'Etre of SESOIL
SESOIL is the acronym for a jSEasonal SOIL compartment model, a de-
velopment motivated by the individual needs of various technical and
regulatory offices within the U.S. Environmental Protection Agency.
SESOIL was designed to be an integrated package of a "user-friendly" tool
for modeling hydrologic, sediment and pollutant cycles in soil "com-
partments." Many reasons supported this development as described below.
First, in reference to a soil compartment (see cover figure), we have
today a variety of excellent watershed simulation (e.g., Johanson et al
1979) models, a variety of unsaturated soil zone numerical (e.g., Adams
et al 1976) models, a variety of stochastic soil moisture models, or a
number of watershed erosion and sediment transport models (e.g., Leytham
et al 1979). However, we do not have an integrated, and developed from
"scratch," soil compartment mathematical model, designed for long-term
(defined below) environmental process simulations that can describe
simultaneously water transport (quantity/quality), sediment transport
(quantity/quality), pollutant fate (transport/transformation) and soil
quality. SESOIL has been designed to fill this need.
Second, current regulations (e.g., the Resource Conservation Recovery
Act) require that decision makers consider the environment as a con-
tinuum. Thus, pollutant fate must be modeled in this continuum—
encompassing air, soil and water compartments—rather than in single
medium. This request brought model users to the dilemma of "which model
to interface with what model" in order to create a useful continuous
package (Fiksel et al 1981). In many cases, data requirements and time
resolutions of the various models were so different, that interfacing
requirements necessitated the writing of complicated or lengthy data
management computer programs. In addition, separate calibration pro-
cedures may have to be followed for different submodels (e.g., watershed
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submodel, unsaturated soil zone submodel) of one and the same environ-
mental compartment (i.e., soil compartment), resulting in much dupli-
cation of effort.
In response to the above regulations, an immediate need for integrated
modeling packages has emerged, leading to a boom in environmental
modeling and the use of models as decision mechanisms. This immediate
necessity has not left enough time to model developers to "sit back" and
develop truely "integrated" approaches. The difficulties created by
employing and interfacing incompatible submodels is analogous, for
example, to the industry where in an attempt to quickly release a new
product, manufacturers assemble—not always successfully—a new product
with parts desinged for other similar situations. With SESOIL, an
attempt is made to better integrate certain model categories and provide
an efficient interfacing module between air and water compartmental
models of the literature toward a formulation of an environmental
continuum.
Third, a characteristic of the existing environmental models is the
simulation time step. Most of the watershed soil models consist of a set
of equations solved after each storm event. Therefore, hydrology,
sedimentation and pollution mass transport at the end of a season (e.g.,
month, year) is estimated by summing up distribution estimates after
each storm event. This necessitates lengthy data inputs of hydrologic
records, a fact that makes use of models very time consuming, and may not
necessarily lead to more accurate cycle (hydrology, sediment, pollutant)
estimates. The SESOIL seasonality provides a different and flexible
approach to this issue.
Principally, SESOIL is intended to be a model that:
(1) is seasonal—provision is also made for storm-by-storm sim-
ulations ;
(2) is independent from the size and the shape of the soil column,
i.e., independent from the numerical discretization mathe-
matical problems of some models;
(3) is user-friendly and requires a minimum number of hydrologic
and other input data;
(4) can study the hydrologic cycle, the sediment cycle, pollutant
fate and soil quality of the compartment in one integrated
effort;
(5) is operational at various "levels" depending on users' needs
and data availability;
(6) is operational either as a self-standing soil compartment
model or as a.model to be interfaced with an atmospheric and a
fresh water body model toward the format.ion of a mathematical
environmental continuum;
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(7) does not require calibration of coefficients that do not
describe physical or chemical parameters, yet it might be
calibrated via its basic parameters if field data are avail-
able;
(8) a user can operate with data obtained from existing data
bases (even on-line) or from handbooks;
(9) is expandable in logic and capabilities; and
(10) can be operated at minimum expense (time, cost) and by uses
who may or may not exactly follow all the theoretical back-
ground of the various processes/subroutines modeled.
The attempt to accomplish the above 10 desires/needs is the "raison
d'etre" of SESOIL. It is hoped that it will become a valuable tool in
environmental quality planning. The fact that SESOIL is user-friendly,
comprehensive and inexpensive to run should stimulate users to take
advantage of its benefits.
1.4 Acknowledgements
This report has been submitted by Arthur D. Little, Inc., in partial
fulfillment of the requirements of EPA Contract No. 68-01-6271. The
study was performed for the U.S. Environmental Projection Agency, Office
of Toxic Substances, Washington, D.C. The authors would like to extend
their graditude to all the contributors to this project.
Special thanks are extended to the Arthur D. Little, Inc., staff members
who have contributed extensively to this report: Warren Lyman (Ap-
pendices HD, CE, CM), Diane Gilbert (Appendices SR, ID), Joo Hooi Ong
(Appendix NV), Kate Scow (Appendix DE), Irene Rickabaugh (report
coordination), Linda Nazaretian and Emma Wood (general support).
The authors extend their thanks to all scientists within EPA who have
assisted them on this and the previous SESOIL contracts.
Dr. Annette Nold of the Office of Toxic Substances (OTS) has been the
Project Officer of this first finalized model version (1981). She has
assisted the authors in the improvement of the model over the past
versions, she has been patient with developmental problems, and she was
always ready to compile scientific and other information for us. We have
appreciated our collaboration with her.
Dr. William Wood, at the head of OTS Modeling Group, has been the Project
Officer and Mrs. Joan Leffler supervised in 1979 the EPA contract which
lead to the conceptualization of SESOIL (Aravamudan et al 1979). The
authors appreciate both the scientific advice and the support received
for the SESOIL concept.
Jan. 82 1-6
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Following its conceptualization in 1979, a model improvement and an
application were sponsored in 1980 by the EPA, Monitoring and Data
Support Division (MDSD). Mr. Michael Slimak, at the head of MDSM, has
been the Project Officer and Mr. John Segna supervised that task. The
authors appreciate the overall advice of Mike Slimak, the technical
advice of John Segna and the ongoing support received from this office.
The authors would like to extend their appreciation to: Mr. Michael
Callahan, head of the Exposure Assessment Branch, EPA/OTS; Dr. James
Dragun, EPA/OTS, for his participation in the model development in 1979
and for reviewing the chemistry aspects of the model and insisting on
valuable improvements; and Dr. Ronald Kickert, EPA/Corvallis Research
Laboratory for requesting detailed information regarding the model and
making substantial comments.
The authors express their graditude to Professor Peter S. Eagleson,
Massachusetts Institute of Technology, Ralph M. Parsons Laboratory for
Water Resources and Hydrodynamics, who has voluntarily reviewed and has
made suggestions for the application of his annual water balance theory
(Eagleson 1978) in respect to the long-term (averaged) estimates of
pollutant concentrations in the unsaturated soil zone of SESOIL.
Appreciation is expressed to Professor George R. Foster, Purdue Uni-
versity, Agricultural Engineers Department, for his generosity in re-
leasing his sedimentation theory (Foster et al 1980) and its computer
code to the authors, although integration of his theory (Appendix SW)
into the SESOIL framework has not yet been initiated.
Finally, we would like to thank Ms. Gayaneh Contos at Versar, Inc., and
Dr. George Harris, at Arthur D. Little, Inc., who have managed this
contract with the EPA; Dr. Alfred Wechsler, Dr. Alan Eschenroeder, Dr.
Philip Levins; and Dr. Frank Feeley who have supported us in many
different ways.
1.5 References
Adams, R.T. and F.M. Jurisu (1976). Simulation of pesticide, movement on
small agricultural watersheds. U.S. EPA, Athens Environmental Research
Laboratory, Georgia 30605. EPA-600/3-76-066, NTIS PB-259933.
Aravamudan, K.; M. Bonazountas; A. Eschenroeder; D. Gilbert; L. Nelken;
K. Scow; R. Thomas; W. Tucker; and C. Unger (1979). An Environmental
Partitioning Model for Risk Assessments of Chemical. Arthur D. Little,
Inc., report, prepared for U.S. EPA, Office of Toxic Substances, under
Contract No. 68-01-3857.
Eagleson, P.S. (1978). Climate, Soil and Vegetation (1-7). Water
Resource Research, Vol. 14, No. 5, pp. 705-776.
Jan. 82 1-7
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Fiksel, J.; M. Bonazountas; H. Ojha; and K. Scow (1981). An Integrated
Geographic Approach to Developing Toxic Substances Control Strategies.
Report by Arthur D. Little, Inc., for U.S. EPA, Office of Policy and
Resource Management, Contract No. 68-01-6160.
Foster, G.R.; L.J. Lane; J.D. Wowlin; J.M. Laflen; and R.A. Young (1980).
A Model to Estimate Sediment Yield from Field-sized Areas: Development
of Model. USDA, Purdue Agricultural Experiment Station. Purdue Journal
Paper No. 7781.
Groundwater (1981). Journal of Groundwater Technology Division, Na-
tional Water Well Association, p. 56 (quotation from Burma Shave, circa
1940).
Johanson, R.C.; J.C. Imhoff; and H.H. Davis (1979). Hydrologic Simu-
lation Program-Fortran (HSPF). U.S. EPA, Athens Environmental Research
Laboratory, Georgia 30605. EPA Grant No. R804971-01.
Leytham, K.M. and R.C. Johnson (1979). Watershed Erosion and Sediment
Transport Model. U.S. EPA, Athens Environmental Research Laboratory,
Georgia 30605. EPA-600/3-79-028.
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2.0 THE SESOIL MODEL
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2.0 THE "SESOIL" MODEL
This section contains only an executive summary of all appendices
presented in this documentation, and as such it does not offer anything
new to model readers or users.
The model developers have purposely kept this section brief because;
(1) They feel that users of this first SESOIL version should
read/consult—for their own benefit—the entire theory of each
major area of science presented in each appendix separately,
in order to appreciate both the capabilities of SESOIL and the
limitations or assumptions supporting this model version.
(2) SESOIL development has not yet been completed and since the
model is limited to simulating the unsaturated soil zone of
the soil compartment, the developers do not want to give the
impression of having accomplished all their goals.
The executive summary of SESOIL is presented in the following pages.
Please contact the authors with any questions regarding this model
version and/or questions as to potential (future) capabilities of the
model.
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"SESOIL"
A SEASONAL SOIL COMPARTMENT MODEL
By
Marcos Bonazountas
Janet Wagner
Arthur D. Little, Inc.
Cambridge, Massachusetts 02140
617/864-5770
GENERAL INFORMATION
SESOIL is a newly developed "user-friendly" mathematical model for long-
term environmental pollutant fate simulations that has been designed to
describe:
• water transport (quality/quantity),
• sediment transport (quality/quantity),
• pollutant fate (transport/transformation), and
• soil quality
within a user specified soil column (designated as compartment) ex-
tending between the ground surface and the lower part of the saturated
soil zone of a region. (See figure 2-1.)
SESOIL is designated as "seasonal" because it statistically estimates
the pollutant distribution in the soil column after a season (e.g., year,
month) "directly." It does not estimate pollutant distribution in-
directly (i.e., by summing up pollutant distribution estimates in the
soil column after each major storm event) as do existing models described
in the literature.
SESOIL has been designed to become, in the long run: (1) a watershed
model; (2) an unsaturated soil zone model; and (3) a groundwater model.
However, the current SESOIL version can only simulate processes of an
unsaturated soil zone of a compartment and can roughly account for
certain watershed aspects of the compartment. The groundwater aspects
of SESOIL are part of the long-range plans of the developers. As such,
SESOIL is designed to simulate point or nonpoint pollution from major
land use categories, and soil-column pollution originating on the
watershed (future development), in the soil column (presently) and in
groundwater (ultimate development).
SESOIL is designed as: (1) a self-standing soil compartment model, and
(2) a compartment model to be interfaced with other atmospheric and water
body models towards the formation of a mathematical environmental
continuum (multi-media environmental modeling). The current version can
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(Rgin, Snow.)
A ' * '"
-V-N/*
Evaporation
Figure 2-1 SCHEMATIC PRESENTATION OF THE SESOIL COMPARTMENT
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be easily interfaced with a groundwater model toward the formulation of
an unsaturated/saturated soil compartment model.
SESOIL simulations do not require the extensive and time consuming
calibration procedures of other models, although it may be easily calibrated
to agree with field records. The model employs theoretically derived
equations driven by climatic, soil property, geometric and chemical
compound property data. In addition, simulations are performed for the
entire compartment (i.e., watershed, unsaturated and saturated soil
zones) in one effort in order to circumvent the known calibration
difficulties of simulation models. As such, SESOIL may be employed as a
precalibration model for other simulation models.
There exist no artifically imposed limitations in: (1) timing and sizing
the soil compartment (cell) and (2) the shape of the compartment per se.
If the soil column is chosen small enough (i.e., finite approach), SESOIL
encompasses the concept of the numerical models (e.g., finite dif-
ference/element models); if the soil column is chosen large enough
(e.g., a river basin), SESOIL becomes a sophisticated one-compartment
model. The unsaturated soil zone of the model can be discretized to
account for more than one soil layer in order to best meet simulation
needs.
SESOIL is designed to provide great flexibility to the user who can
execute various "levels" of model operation, the criterion for a level
selection being data availability and study objectives. The major
advantage of SESOIL is that it can be executed with easily obtainable
input data because this information can be compiled from existing data
bases (e.g., NOAA) and known references for the pollutant and soil
properties. A data management structure accompanies SESOIL. If the
model is not linked to existing data bases, then the number of input data
can be less than 50 as contrasted to the other numerical models which may
require more than 500, because: (a) the model employs theoretically
derived equations which "may not require calibration, and (b) the
statistical simulation does not take place after each major storm event.
Potential applications of SESOIL include long-term leaching studies from
waste disposal sites, acid rain, pesticide and sediment transport on
watersheds, contaminant exposure assessments, pre-calibration runs for
other simulation models, hydrologic cycles of soil compartments, etc.
This model version has been developed on behalf of the U.S. Environmental
Protection Agency, Office of Toxic Substances, Washington, D.C. A model
application at industrial land treatment sites has been sponsored for a
slightly different model version by the Monitoring and Support Data
Division, EPA, Washington, D.C.
SDIULATION CYCLES
The simulation is structured around three cycles, each cycle being
associated with a number of processes. These are the:
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• Hydrologic cycle which takes account of:
rainfall, infiltration, soil moisture, surface runoff, ex-
filtration, evapotranspiration, groundwater runoff, capillary
rise, snow pack/melt (not operational in this version) and
interception (not operational).
. Sediment cycle which takes account of:
sediment resuspension (due to wind) and sediment washload (due
to rain storms), not operational in this version.
• Pollutant cycle which can take account of:
advection, diffusion, volatilization, adsorption/desorption,
chemical degradation/decay, biological transformation and
uptake, hydrolysis, photolysis, oxidation, cation exchange,
complexation chemistry (metals by organics) and nutrient
cycles (not operational).
The hydrologic cycle controls the sediment cycle, whereas both previous
cycles control the pollutant cycle. Cycles, processes, mathematical
modeling, application and validation issues are summarized in the
following paragraphs.
(1) The hydrologic cycle is based on a statistical dynamic formulation
of vertical water budget at a land-atmosphere interface (Eagleson
1978), adapted to account for monthly simulations. Uncertainty of
the hydrologic cycle simulation is expressed via probability
density functions of the independent climatic variables and yields
derived probability distributions of the dependent water balance
elements: surface runoff, evapotranspiration, and groundwater
runoff. Some details of the hydrologic analysis are (Eagleson
1978):
Seasonal point precipitation is represented by Poisson arrivals of
rectangular gamma distributed intensity pulses that have random
depth and duration. Infiltration and exfiltration are described by
the Philip equation (Philip 1969), which assumes the medium to be
effectively semi-infinite, and the internal soil moisture at the
beginning of each storm and inter-storm period to be uniform at its
long-term space-time average. Gravitation and percolation to
groundwater is assumed to be steady throughout the time step of a
simulation and at a rate determined by the long-term space-time
average seasonal soil moisture. Capillary rise from the water
table is assumed to be steady throughout the season and to take
place to a dry surface. Soil properties, soil moisture, climate and
functional relationships derived by Brooks and Corey (1966) de-
scribe the wetting drying soil intrinsic permeability temporal
variation.
Seasonal bare soil evaporation and vegetal transpiration are
calculated for the interstorm periods as functions of properties of
the climate, the storm sequence, the surface, the soil and the
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average rate of a derived potential evapotranspiration. The work
of Penman (1963), Van den Honert (1948), Cowan (1965) is employed
(Eagleson 1978). The distribution of surface runoff volume is
derived from the distribution of rainstorm intensity and duration
and the use of the previously discussed infiltration equation.
Specific subroutines of the model have been validated in the
literature. The annual dynamic water balance of the model has been
validated by Eagleson (Eagleson 1978). The monthly dynamic water
balance of the model has been applied; however, it was not validated
as a hydrologic routine per se. Validation of the routine was
undertaken in connection with pollutant migration in the unsatu-
rated soil zone (Bonazountas and Wagner 1981).
(2) The sediment cycle accounts for both sediment washload due to
precipitation and sediment (dust) resuspension due to wind. Two
sediment washload routines are accounted by SESOIL: (a) an annual
sediment yield equation based on the Universal Soil Loss Equation
(USLE) as developed and documented by the U.S. Department of
Agriculture (Wischmeier and Smith 1978) and employed by other
watershed models of the literature; and (b) a monthly sediment
washload routine based on theoretically derived equations and first
physical principles (Foster et al 1980).
The theoretical monthly sediment routine can account for: (a)
various sizes and shapes of watersheds (e.g., overland flow,
channel flow, impoundment, pond); (b) detachment of soil particles,
transport and deposition of soil particles, rill and inter-rill
erosion on the watershed; (c) sediment characteristics and other
fundamental relationships of precipitation energy and erosion
sediment transport. The sediment washload model is based on the
fundamental theoretical models of Yalin (1963), Foster et al
(1980), and Cooley (1980). The sediment routine has not been
validated with SESOIL's hydrologic cycle.
The dust resuspension routine estimates the losses from the surface
of the SESOIL soil column of any pollutants associated with surface
particles. The losses due to physical removal of the particles that
have an associated pollutant load are calculated as a function of
particle characteristics (chemical composition, diameter, etc.)
and weather conditions. Variables such as soil moisture and wind
speed are utilized; however, this routine has not been validated
yet with SESOIL's hydrologic cycle.
(3) The pollutant cycle accounts for more than 12 chemical processes.
(See previous section.) There exists no single equation that can
optimally describe each of the pollutant processes under all all
conditions, so some alternative simulation options are possible;
for example, adsorption is modeled as sorption to soil particles,
partitioning to soil organic carbon, or as an ion exchange process
simply by varying the input parameters. Another example is
volatilization from soil to air that can be modeled with more than
one user specified equation (theoretical, experimental).
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The pollutant cycle is simulated in more than one soil sub-
compartments, each one consisting of three phases: soil-air, soil-
moisture and soil-solids. The pollutant cycle routine has been
rederived from a pollutant mass balance equation that can be
expanded or modified easily in order to account for additional
processes and model improvements.
MODEL VALIDATION
A pollutant transport application/validation study was undertaken to
assess the long-term predictive pollutant pathway capabilities of SESOIL
using field monitoring data and supporting background information
already collected as part of another study (monitoring program). The
model has been employed as (1) an upper unsaturated soil zone model at
two industrial land treatment waste sites, and (2) as an exposure
assessment model for fictitious environmental soil compartments. The
behavior of two organic pollutants (napthalene, anthracene) and four
inorganic pollutants (copper, chromium, nickel, sodium) at two sites was
simulated and analyzed. Predicted concentrations and laboratory mea-
sured concentrations agreed within expected limits. Calibrated and non-
calibrated model runs have been compared (Bonazountas et al 1981).
SESOIL has been also employed as a mathematical tool for exposure
assessment studies for predicting the behavior of pollutants in soil
compartments, and it proved to be an interesting application for
screening, analyzing and prioritizing pollutant behaviors in soil
systems (Bonazountas and Wagner 1982).
REFERENCES
Wagner, J. and M. Bonazountas (1982). Buried Halogenated Solvent
Simulations via SESOIL. Arthur D. Little, Inc., study in progress,
performed for U.S. EPA, Office of Toxic Substances. EPA Contract No. 68-
01-6271.
Bonazountas, M. ; J. Wagner; and B. Goodwin (1981). Evaluation of
Seasonal Soil/Groundwater Pollutant Pathways. Arthur D. Little, Inc.,
Final Report, prepared for U.S. EPA, Monitoring and Data Support
Division. EPA Contract No. 68-01-5949/9.
Bonazountas, M.; J. Wagner; and B. Goodwin (1981). Seasonal Cycles of
Pollutants Originating from Land Treatment Practices. Proceedings
Environmetrics '81 Conference, SIAM/SIMS, Virginia.
Brooks, R.H. and A.T. Corey (1966). Properties of Porous Media Affecting
Fluid Flow. Proc. ASCE Journal of the Irrigation and Drainage Division,
No. IR 2, Paper 4855, pp. 61-68.
Cooley, R.K. (1980). Erosivity "R" for Individual Rain Storms, (in
Knisel, p. 386).
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Cowan, J.R. (1965). Transport of Water in the Soil-Plant-Atmosphere
System. J. App. Ecology, (2) pp. 221-239.
Eagleson, P.S. (1978). Climate, Soil, and Vegetation (1-7). Water
Resources Research, Vol. 14, No. 5, pp. 705-776.
Foster, G.R.; L.J. Lane; J.D. Nowlin; J.M. Laflen; and R.A. Young (1980).
A Model to Estimate Sediment Yield from Field-Sized Areas: Development
of Model. Purdue Agricultural Experiment Station. Purdue Journal No.
7781.
Knisel, W.G. (1980). CREAMS: A Field Scale Model for Chemicals Runoff
and Erosion for Agricultural Management Systems. USDA Conservation
Research Report No. 26.
NOAA (National Oceanographic and Atmospheric Administration), Local
Climatological data files, Monthly Climatologic data.
Penman, H.L. (1963). Natural Evaporation from Open Water, Bare Soil, and
Grass. Proc. Roy. Soc. (London), Ser. A, Vol. 193, 1948, pp. 120-145.
Philip, J.R. (1969). Theory of Infiltration, in Advances in Hydro-
science, Vol. 5, edited by V.T. Chow, pp. 215-296. Academic Press, New
York.
Van den Honert, T.H. (1948). Water Transport in Plants as a Catenary
Process. Discuss. Faraday Soc., (3), pp. 146-153 (cited fromk Eagleson
1978).
Yalin, Y.J. (1963). An Expression for Bedcover Transportation. Journal
of the Hydraulics Division. Proceedings of the ASCE 89(HY3): 221-250.
Wischmeier, W.H. and D.D. Smith (1978). Predicting Rainfall Erosion
Losses. U.S. Department of Agriculture, Agriculture Handbook No. 537.
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3.0 USER'S MANUAL
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SECTION 3.0
USER'S MANUAL
3.1 INTRODUCTION
3.1.1 General Capabilities
3.1.2 Phenomenology in the Soil Compartment
3.1.3 Mathematical Modeling Issues
3.1.A Levels of SESOIL Operations/Capabilities
3.1.4.1 General
3.1.4.2 LEVELO
3.1.4.3 LEVEL1
3.1.4.4 LEVEL2
3.1.4.5 LEVEL3
3.1.4.6 Other Levels
3.1.5 Problem Identification/Level Selection
3.1.6 Canonical/Scenario's Chemical Fate Modeling
3.2 DATA STRUCTURE/MANAGEMENT
3.2.1 General
3.2.2 SESOIL Program Structure
3.2.3 Model Execution Philosophy
3.2.4 Input Data Files
3.2.4.1 GE DATA File
3.2.4.1.1 General
3.2.4.1.2 Data Input
3.2.4.2 LO DATA File
3.2.4.2.1 General
3.2.4.2.2 Data Input
3.2.4.3 LI DATA File
3.2.4.3.1 General
3.2.4.3.2 Data Input
3.2.4.4 L2 DATA File
3.2.4.4.1 General
3.2.4.4.2 Data Input
3.2.4.5 L3 DATA File
3.2.4.6 EXEC DATA File
3.2.5 Summary of Data Input
3.3 MODEL EXECUTION
3.3.1 Data Requirements
3.3.2 Execution Statement
3.3.3 Examples of Execution (Output)
3.4 MODEL "VALIDATION"
3.4.1 General
3.4.2 Model Application
3.4.3 Model Calibration
3.4.4 Model Validation
Page
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3.4.5 Model Sensitivity Analysis
3.4.6 Model Limitation
3.4.7 Discussion
3.5 REFERENCES
Page
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FIGURES
3-1 Environmental Pathways of Toxic Substances
3-2 Ultimate Developmental Features of SESOIL
3-3 Complete Disaggreation; LEVELO, LEVEL1,
and LEVEL2 Operations
3-4 Conceptual Compartment Discretization for the
LEVELS Operation
3-5 Schematic Presentation of SESOIL Operations
3-6 GE DATA File
3-7 LO DATA File
3-8 LI DATA File
3-9 L2 DATA File
3-10 L3 DATA File
3-11 EXEC DATA File
3-12 Schematic of Model Application/Calibration/
Validation
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TABLES
J-l GE DATA File 3-51
3-2 LO DATA File 3-52
3-3 LI DATA File 3-53
3-4 L2 DATA File 3-54
3-5 L3 DATA File 3-55
3-6 Soil Modeling Major Input 3-60
Parameter Categories
3-7 References of Current Research in Calibration/ 3-63
Validation Procedures for Soil/Groundwater Models
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3.1 INTRODUCTION
3.1.1 General Capabilities
This version of SESOIL can be used as:
(1) a hydrologic cycle model for the watershed and the
unsaturated soil zone of the compartment
(2) as a hydrologic and pollutant cycle model for the
unsaturated soil zone of the compartment.
SESOIL is still under development, therefore the following sections only
guide a user through details and the input/output data of this version
of the model. This section (User's Manual) might be expanded in the
future to a self-contained document with guidelines for problem identi-
fication, problem structure, optimal compilation of input data, model
validation and calibration procedures.
3.1.2 Phenomenology in the Soil Compartment
A soil "compartment" (or cell) is defined as a soil column extending
between the ground surface and the bottom of the "upper" saturated soil
zone. As such, the soil compartment interacts with the air and the
water compartments of an environment as schematically shown in the cover
figure of this document (also Figure 2-1). It is evident that the upper
saturated soil zone might be underlain by impermeable soil layers and
other saturated soil zones (or aquifers); however, these zones are not
part of the soil compartment as previously defined.
Physical and chemical processes or phenomena of importance to the quality
of a soil compartment are the hydrologic cycle, the sediment cycle, the
biologic cycle, and the pollutant cycle. Processes important to each
cycle are described in the appendices HY through PT of this documentation.
When released into the environment, pollutants move by a number of fate
(transport/transformation) mechanisms. For some pollutants such as
phosphorus, ammonia and certain pesticides, surface runoff, soil wash
and dust particles might be the primary carriers to the final place of
deposition. Other pollutants are directly applied to plants and reach
the soil through drift, wash-off or when the plant decays. Many pollu-
tants are transported through the hydrologic cycle or the hydrologic
mechanisms of watersheds and have a final destination in the water
compartment of an environment. The figure of the next page (Figure 3-1)
is a generalized pathway diagram of toxic substances in the environment;
from source-to-receiver. The SESOIL model deals with processes inter-
acting and related to the soil compartment of the environment; the "elliptic"
subcompartment in this figure.
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Surface
ioff (#
— —•
Soil Wash (22)
Near/Far Field Paths
Near
Far*-
#1 Direct discharge pathways.
#2-4 Intermedia discharge pathways (primary, secondary, potential).
Degradation of substances can take place in any compartment.
Out-of and into basin transfers are not shown.
Source: 'Fiksel et al (1981).
FIGURE 3-1: ENVIRONMENTAL PATHWAYS OF TOXIC SUBSTANCES
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The manner in which pollutants enter the hydrologic cycle of the com-
partment depends on the characteristics of the pollutant source, such as
location, time and physical or chemical form of pollutant. Gaseous,
emulsified and dispersed airborne pollutants enter water by precipitation
and/or dry fallout. Soluble pollutants and/or pollutants merely mixed
in the water may then enter the soil. Relatively insoluble pollutants
discharged to water or soil either are dispersed or are transported by
stormwater runoff or are entrained by wind and subsequently redeposited.
Pollutants are also adsorbed and desorbed by soil particles and then can
be transported by the water cycle in either state.
A major characteristic of a soil compartment — as contrasted to a water
or an air compartment — is that the temporal physical and the chemical
behavior of the compartment is governed by both; out-compartmental forces
such as precipitation, air temperature, solar radiation, and in-compart-
mental forces/features such as soil structure and biology. This charac-
teristic is also one of the main reasons why soil compartmental
mathematical modeling is much more complex than water or air modeling.
When dealing with mathematical modeling of pollutant transport in soil
compartments, it is a natural way to study pollution migration in the
hierarchical order: (1) hydrologic cycle, (2) sediment cycle, which is
primarily governed by the first cycle, and (3) pollutant cycle, which
is primarily governed by the two previous cycles. It has been, however,
a frequent practice to model pollutant migration based upon soil-moisture
migration, so that no soil moisture presence results in no pollutant
migration. Although the latter is not the case in SESOIL (eg. appendix VO) ,
the logical hierarchy hydrologic cycle, sediment cycle, pollutant cycle
has been followed in this modeling effort.
3.1.3 Mathematical Modeling Issues
Environmental mathematical models can be classified in general into:
Deterministic models which_describe the system as ransp/pf
t.Ttnefa-jLncorporate the conrpp*
yiubalUIitv, or nt-hor measures jaf uncertainty. Deterministic and stochas-
ric models may be developed from: observation, semi-empirical approaches,
and theoretical approaches. In developing a model, scientists attempt to
reach an optimal compromise among the above approaches given the level of
detail justified by both the data availability and model objectives.
Beterministic models can j>e__classified into simulation models which
employj a^jall accepted empirical tjquaLlon. that is torced via_calibra-
'^t-torT'coefficients. to describe a system^ and_analytic_models in~which
-EhenTferivefl equation describesthe physics/cliejnistry^of_a' sys£Effl7~^Soth__
the simulation aruTthe analytic models can emploV namericaT"solution
procedures ror tneir equations^ Although the above terminology is ^iot
standard in the literature, it has been used here as a means of outlining
some 'of the concepts of modeling.
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This SESQIL^ version employs the stochastic approach for the hydrologic
cyclgj. and the deterministic approach^Fbr the -£gJigr^hysical^rcK§mlgal
projess^s. The sediment evcle oi this model will also emDioy~the sto-
chastic approach. Parameters of simulation or empirical models are
.determined by calibrating the model output against ^ar^e jnassee of
^gbservatioiial dataT This procedure involves curve-fitting and least-
squares analyses, and requires extensive field data information. _In____
order to by-pass many calibration HI f fixities. SESQIL employ^ primarily
theoretically developed stochastic or deterministic routines^ Thus,
model input variables describe physical or chemical parameters and can
be determined or obtained independently either from laboratory analyses,
field investigation, handbooks or data bases.
The choice of theoretical pi-r^pci-if— f»i- qjQgTyr-i^ deterministic models ^
— of course — that these models are always superior__£p
or Simulation model_s.(" The rigs-ire rnr an aifprnarg approach
was of importance, therefore a "modular" structure has been employed for
SESOIL, so that a substitution of a particular equation, theory, or sub-
routine (modules) can be undertaken at any time — along the course of
a model improvement — and in a straightforward manner. To achieve
effectiveness in the modular approach a new, efficient and chemistry
strong concept has been employed for the pollutant transport cycle
(appendix PT) of SESOIL.
3.1.4 Levels of SESOIL Operations/Capabilities
3.1.4.1 General
Discussions in the following sections are oriented towards the conceptual
approaches employed in this methodology and are not intended to fully
describe the fundamentals of all the cycles — hydrologic, sediment,
pollutant. For detailed information the reader is referred to the indi-
vidual appendices.
— SESOIL encompasses — by design — many features. It_can be, for example,
•a~vgatershed model - an nnsatiirated soil zone hvdrologic model^ a sediment:
__ transportation model, a soil chemistry model, etc. It can also be
operated at annual or monthly time steps, for onp-, run- , nr Three-soil
layers. In the future it may be expanded to incorporate the fate of second
' pRsrse chemicals in the soil column, or nutrient cycles and sedimentation
after each storm event. Many SESOIL potential features are schematically
presented on the next page (Figure 3-2); however, only a few features are
operational at the present time, and these features are focused around the
unsaturated soil zone and are offered to users in "integrated" packages
designed as "levels" of operation.
In this model version, the four different levels of operation are LEVELO,
LEVEL1, LEVEL2 and LEVEL3. Each level is associated with certain temporal
and Spatial resolution characteristics, and each has different specific
input requirements.
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ScsoiL features
uesoluti.o'ns
C tu»«*n.
sf ; • • "&.}-'« x /-
C^i^ frj
tVLLfe or 6ESo'u OPIRATION4 --THJ&
Colo avoilob. t, 1 o.^ i)uci. okfi((s , MaUi . qfvxii'oi nfimlrt.ine W
FIGURE 3-2 CURRENT AND POTENTIAL SESOIl, RESOLUTIONS, FEATURES, AND CAPABILITIES
re
n
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3.1.4.2 LEVELO
LEVELO is the simplest operational version of the model and_^djaes not
require knowledge of the hydrology of the compartment; (area"modeled).
""SESOIL is employed as^an unsaturated soil zone model interacting hydro-
logically (for mass balance purposes) with both the watershed and the
groundwater table.
Ihis ley_el caiL be employed for pollutant- rrangpnrr-ffimnlarjsns in
^'fictitious" <• omjaartments. The unsaturated soil zone compartment
consists of two distinct layers, as shown in Figure 3-3, namely the
upper unsaturated soil zone (or watershed zone), and the lower unsatu-
rated soil zone. T£e_j»aj:urated soil zone (groundwater) is not part of
iration of this moHelTersionr
The simulation is performed annually and for only one year. The user
has to input : (1) the annual averaged values of rainfall depth, soil
moisture- (unsaturated soil zones) , infiltration and grnnnHwat-gr rprhargp
depths-;- (2) the total annual pollution^ loltd~nCpT3]xLutaTi£jma^sy to the
compartment; (3) chgmiGal/^ompound relatejLjaa£ameters..;. and (4) soil
4?e4ated_p3xameters . The output""fTom the^model is: (1) the_j3p_llutant
d_isrribution (i.e. concentrations, mass distribution) in the compartment,
and (2) the annual jgollut ion contribution (transport} to gj:her_enviroQs_
comparjLmentspy means ot surface runoff. volatilization. leaching^
Additional information for use of this level is
provided in section PT-3.2. Details of input data formats are given in
section 3-3.2. Details of the output are given in section 3-3.3.
LEVELO should be employed with care and only if "real" climatological
and field data are^ available, because~rthe~hydr61oglT"parameters (eg.
rainfall vs. soil moisture content) are always correlated, though
independency is assumed for these input data.
Thi.«i_lg^el has specialized applications, for example: scj^pn\nj of a
large numbers of chemicals that have to be compared for their environ-
mental effects wheia released into non-site specific (fictitious) compart-
ents.
.1.4.31 LEVEL1
philosophically like LEVELO; however, it has been designed for
region specitlc simulations.Tne simulation is performed annually and
for only one year and yg^niT-og^the^ knowledge of few annual ^averaged
'' imate
climaticand soil datafor the area, in_arder tor'the modejto^
' ""^ hydrulogiC parameters relating to the compartment which have
>een a user input to LEVELO. • • •—"
The user has to input: (1) climatic/storm parameters, (2) soil para-
meters which may vary in the two layers, OT" chemical parameters, and
T4) simulation SpeCrlic parSmeterT:—-These data are readily available
from the literature (eg. NOAA reports, handbooks). The output from the
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FIGURE 3-3: COMPARTMENT DISAGGREGATION; LEVELO. LEVEL1,
AND LEVEL2 OPERATIONS
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\
model is: (1) the hydrologic cycle components of the annual compart-
mental water balance, (2) the annual pollution distribution (eg. concen-
trations, mass to groundwater.)
As in LEVELO simulations are performed in two unsaturated soil zone
layers (Figure 3-3) and are of use for specialized applications.
Additional information for this level is provided in section PT-3.2.
Details of input/output data formats are given in sections 3-3.2 and
3-3.3.
3.1.4.4 LEVEL 2
LEVEL2 resembles LEVEL1
he input data required
33);
can be simulated.
^ ^ . Jie-^-ser nasHEeL-kaow.: (1) thejnonj
di,s££ibju.tion_af rainfall depths and—othpr r 1 jmaf-jir paramete:
param
and (2) the monthly distribution of input pollution (pollutant mass) to
—t-he-eomjiartinejiL. MostotTFier input data are~similar' to LEVEL1. The
monthly output from the model resembles the LEVEL1 •dtnroaT'Sutput.
Simulations performed with LEVEL2 may reflect site specificity, both in
time (averages over month) and area (reflected in the compartment charac-
teristics). Input data are easily compiled from existing data sources
(eg. NOAA, handbook, this documentation); however, for -&4te—specific
sinnilafinnjiiodel outpu£_has to be^cottreg-Eed to actual field da£a^
both_h>'drglogy_and che'mjs.try), and eventuaJLLy-saljbrated.. Validation
of final output is essential. ''
Additional information for this level is provided in section PT-3.3. De-
tails of input/output data formats are given in sections 3-3.0 and 3-3.4.4.
3.1.4.5 LEVEL3
LEVEL3 resembles LEVEL2 in philosophy (monthly simulations): however.
input_dAfca_required b£_LEVEL27~tKe~user has
fore, i
c° inBuJt^pollutant mass and__soil characteristics for_an addlt±ona-l— 1-a-ygr.
This fact increases spatial resolution, but also user's required effort.
This level has been developed for the needs of this contract and can
become a subset of the N- layered monthly SESOIL version (Figure 3-4).
Additional information for this level is provided in section PT-3.3.
Details of input/output data formats are given in sections 3-3.2 and 3-3.3.
3.1.4.6 Other Levels
The authors intend to develop^ additional levels such as:
(1) a storm-by-storm temporal resolution and a
N-layered compartment that may handle release
of a second phase (insoluble) chemical spill on
the soil surface, or
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FIGURE 3-4: CONCEPTUAL COMPARTMENT DISCRETIZATION FOR
THE LEVEL3 OPERATION
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(2) a statistical version to handle pollutant
(eg. pesticide) transport on the watershed.
Authors have conceptualized these versions but have not proceeded in ed
any real developmental effort. Their main goal will always be a "user
friendly" model accepting calibration of parameters describing physical
or chemical rate processes (eg. intrinsic permeability of soil, cm^).
3.1.5 Problem Identification/Level Selection
This section will be expanded in the future to contain information
regarding: (1) how to identify a problem suitable for modeling via
SESOIL, (2) how to select the compartment's temporal and spatial resolution
(i.e., level), and (3) how to proceed with the actual modeling (single
medium, multimedia).
3.1.6 Canonical/Scenario's Chemical Fate Modeling
Recent concerns related to environmental quality require a methodology
to relate sources and quantities of chemical releases into the environ-
ment to the actual amounts of these chemicals to which humans and other
biota are exposed. SESOIL is extremely well suited for such environmental
exposure studies, which are based on "canonical" environmental compartments
and employ typical scenarios (single medium or multimedia). This section
will discuss such issues in the future. It has to be emphasized that the
selection/compilation of typical/canonical compartments is not an easy
issue, and has to involve consideration of statistical techniques (eg.
kriging, see section 3.4.3) to optimally/appropriately design the com-
partments.
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3.2 DATA STRUCTURE/MANAGEMENT'
3.2.1 General
For a user it is important to understand the model data structure and
management, the model execution philosophy of the version accompanying
this documentation, and the content of the input data files.
3.2.2 SESOIL Program Structure
A generalized flow chart of SESOIL data files and operation is shown on
the next page (Figure 3-5). The executive program of operations, desig-
nated as SE81, calls the main program designated as SESOIL, and the
latter calls the two basic data subroutines RFILE (read data file),
PFILE (print data file), and one of the four operational basic subroutines
LEVELO (level "0" operations), LEVEL1, LEVEL2 or LEVEL3. Consequently,
each of the basic operational routines calls a number of secondary rou-
tines such as HYDROA (annual hydrologic cycle), HYDROM (monthly hydrologic
cycle), TRANSA (annual pollutant transport routine), TRANSM (monthly pol-
lutant transport routine; two soil layers) or TRANS3 (three soil layers).
Finally, each of the secondary routines calls a variety of functional
routines, as presented in appendix FC (FORTRAN Code).
A major emphasis is placed into the data management aspects and the easy
input of data. Data are read by the model from 6 data files GE (general),
LO (level 0), LI (level 1), L2, L3 and EXEC (executive operation).
In the IBM system data files are accessed via the file name and a "DATA"
designation; therefore, reference is made in the following sections to
the 5 files GE DATA, LO DATA, LI DATA, L2 DATA, and EXEC DATA (Figure 3-5) ,
which are all expandable in size.
GE DATA file (see section 3.2.4.1) contains: (1) climatologic data of
regions, areas or cities, (2) soil data for various soil types, and
(3) chemistry specific data and pollutant parameters.
LO DATA data file (see section 3.2.4.2) contains geometric and simulation
related information for the LEVELO applications. LI DATA contains informa-
tion (see section 3.2.4.3) for using LEVELl of the model, and L2 DATA contains
the LEVEL2 information/data (see section 3.2.4.4). Information
data or parameters that are used for both LEVELl and LEVEL2 operations
are given twice (double-input), one in each data file, in order to make each
level of operation self-standing and self-contained.
EXEC DATA (see also section 3.2.4.6) contains executive simulation data
and information for each actual execution of SESOIL, such as "what level
of operation is desired?", "where is the area of simulation?", "what type
of a soil or chemical compound is involved?".
Detailed information regarding the "loading" of these files is presented
in section 3.2.4 and in appendix DF (Data Files).
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either printout
or a file
FIGURE 3-5: SCHEMATIC PRESENTATION OF SESOIL OPERATIONS
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3.2.3 Model Execution Philosophy
Model execution is accomplished with the following steps:
(1) The SESOIL user selects/decides for a level of
operation (i.e. LEVEL//).
(2) The user "edits" his basic data files (section 3.2.3.A)
GE DATA, L# DATA and EXEC DATA
• either through an interactive process via a
screen terminal (eg. IBM VM-CMS system), or
• by inserting or changing computer cards from
his deck.
Editing of the basic data files involves either
the input of non-existing values (eg. new clima-
tological data) in the data files, or the up-
dating of the previous information (eg. another
region).
Above files have unlimited expansion capabilities
so that data from previous simulations may be saved
for future comparative runs.
(3) The user asks for program execution via the statement :
SE81
3.2.A Input Data Files
The following 6 sections (3.2.4.1-3.2.4.6) give the information contained
in the 6 data files:
GE DATA File of general information to be employed
by all levels of operations
LO DATA File containing data for LEVELO executions
LI DATA File containing data for LEVEL1 executions
L2 DATA File containing data for LEVEL2 executions
L3 DATA File containing data for LEVELg executions
EXEC DATA Executive data file of operations
At this point, the reader may find the program/data logic expressed
previously to be somewhat confusing; however, this program/data/execu-
tion rationale will become clearer after reading the coming sections
and paragraphs and the more detailed description of the data files;
appendix DF.
3-15
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3.2.4.1 GE DATA File
3.2.4.1.1 General
This file (Figure 3-6) contains information applicable to all levels of
SESOIL operations: LEVELO, LEVEL1, LEVEL2 and LEVEL3. The file is
permanent and self expandable with the insert of new data.
Information contained in the file includes:
(1) Regional Descriptions: climatic, storm data, for
areas where the model might be applied,
(2) Soil Classifications: soil, sediment data of typical or
specific soil compartments, and
(3) Chemistry Data: related to various pollutants whose
fate might be simulated.
Regional Description data are not required for a LEVELO operation; how-
ever, soil and chemistry data are required.
The file is designed to be self explanatory and provision is made for
non-readable (by the computer) statements in order to aid the user.
The user can input into the file blocks of annual or monthly climatic
data in anv sequence. The program can "spot" the correct areal climate
via a user specified index (eg. "17" SITE A (KANSAS), Figure 3-6). This
index does not have to be sequentially numbered. Only the actual input
data sets (blocks) have to be correctly given to the file. Most of the
other labels and text are designed for the user's aid. However, appro-
priate labeling and numbering is a good practice.
GE data is the largest file, and as such a new user may find this
documentation to be intimidating. However, as the input procedures
are easier to do than described, users will find that data input is
easy once one becomes familiar with the use of the model.
Note: The SESOIL data files are formatted and thus
it is important that data be entered in the
appropriate columns, with decimals if real
numbers, right justified if integer etc.
The last page of Figure 3-6 presents some
sample input data as coded for entry.
The model is delivered with a small input data file, so that section
headings and labels of each file — though described as inputs in the
following pages — do not have to be inserted again by users.
Section 3.2.5 presents a summary of all data entries for all files.
Readers familiar with data entries may consult only that section.
3-16
Arthur D Little. Inc
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3.2.4.1.2 Data Input
The following data information is entered into the GE file in the
following order in the file:
(1) Climatologic Data
(1.1) Annual
(1.2) Monthly
(2) Soil Data
(3) Chemistry Data
(4) End of File
Note: Annual and monthly data sets can be interspersed.
In this documentation the following symbols are used:
***** indicates repetition of data lines, or data sets
!!!!! indicates important comments
..." indicates an emphasis in the word or sentence in quotation
Input parameters for each line, data format, units, and sample input
for each line follow.
The line numbers used below (refer to Figure 3-6) are employed for demon-
stration purposes only and do not appear in the data file.
(1) Climatologic Data
Line 1 FORMAT(I1,5X.12A4)
contains the heading
1 REGIONAL DESCRIPTIONS; CLIMATIC STORM DATA;
The index "1" must appear in the first column (#1, see
circled number Figure 3-6) of this statement, because it
controls the reading of the climatic data.
The user is not concerned with such an entry, since it is
delivered with the SESOIL-code.
!!!!!! Following the above statement, either annual or_ monthly,
climatic sets can be given to the file.
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Arthur D Little. Inc
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(1.1) Annual Climatic Data Inserts
Only one year of data is contained in an annual
data set (lines 2-6) below, since the annual data
are used for LEVELS 0 and 1 which run for one year
only.
Line 2 FORMAT(2X,I3,1X,12A4)
contains the heading of an area where the model may be
applied
1 CLINTON, MA (SUB-HUMID)
The above is not an executable statement. The number "1"
before the area has to appear in the statement.
Line 3 FORMAT(38,6F7.2)
contains the numerical data sets of
• either
L [°N] latitude of the area (eg. 42.50)
TA [°C] temperature of area at surface (eg. 8.40)
NN [fraction] fraction of sky covered by clouds
(eg. 0.35)
S [fraction] relative humidity of the area
(eg. 0.70)
A [-] shortwave albedo of the surface (eg. 0.30)
REP [cm/day] evapotranspiration rate of the area
(eg. 0.15)
• or
"both" above sets if the user desires so; however, the
program will assume the evapotranspiration rates in the
area as "known" and will "not" estimate it from the first
data set L, TA, NN, S, A.
Note:
- Above data is stored in array CLIMAl(6);
see appendix DF
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Arthur D Little, Inc
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- Only the temperature is required for a LEVELO
model execution; however:
- If line 2 above is inserted, then this data
(line 3) must be given even with 0.00 values.
Line 4 FORMAT(38X.4F7.2)
contains the numerical values of:
MPA[cm] annual depth of rain (eg. 94.10)
MTR[day] annual mean storm duration (eg. 0.32)
MN[-] number of storm events per year (eg. 109.00)
MT[days] mean length of rainy season (eg. 365.00)
Note:
- Above data is stored in the array spaces
CLIMAl(6); see appendix DF, figure DF-2.
- This data is not required for a LEVELO
execution.
- If line 2 is inserted, then this data
(line 4) must be given, even with 0.00
values.
Line 5 FORMAT(38X.6F7.2)
contains the numerical values of:
MPM[cm] mean monthly (M) depth of rain of
the first six months of the year
(October through March) starting with
the month of October (M=l); eg. 10.36,
8.96, etc.
Note:
- Above data is stored in the array spaces
CLIMA3U-6).
- This data set is not required for the LEVELO
and LEVEL1 executions; however:
- If line 2 is inserted, then this data set
(line 5) must be given, even with 0.00 values
(required by LEVELO and LEVEL1).
3-23
Arthur D Little. Inc
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Line 6 FORMAT(38X.6F7.2)
contains the numerical value of:
MPM[cm] mean monthly (M) depth of rain of the
remaining six months of the year (April
through September) starting with the
month of April (M=7); eg. 8.38, 7.82, etc.
Note:
- Above data is stored in the array spaces
CLIMA3(7-12).
- This data set is not required for the LEVELO
and LEVEL1 executions; however:
If line 4 is inserted, then this data set must
be given, even with 0.00 values (for LEVELO).
!!!!! Data in lines 5 and 6 are not used in this form and
are usually centered as zero. These lines have been
left in this version for future use, and to be com-
patible with previous versions.
A**** Above data entries (lines 2-6) can be repeated as
necessary for multiple sites in this permanent and
expandable data file (eg. 2 SITE B (MONTANA),..., etc),
(1.2) Monthly Climatic Data Inputs
Note: It is not necessary to input annual climatic
data sets before monthly sets; the two types of
data sets may be interspersed.
The line numbers used are from Figure 3-6. In
the actual file these line numbers may change,
although their contents will not. The line
numbers are for reference only, they are not
used by the code.
Line 27 FORMAT(2X,I3,1X,12A4,I5)
contains the heading of an area/region where the
model may be applied
17 SITE A (KANSAS) Oct. '79-Sept '80 10
This is not an executable statement. However, the
numbers "17" and "10" have to appear in the statement
and at the correct place in the file. The "17" is
3-24
Arthur D Little. Inc
-------
Lines 29
to 38
the index of the site. The "10" is the index of how
many years of data follow this first statement of
SITE A (KANSAS) Oct. '79-Sept. '80 (i.e. 10 years).
Following the above statement numerical input data
for the climatic parameters for each month and year
can be inserted.
Line 28 FORMAT(8X.1F6. 2)
This line contains the numerical value of:
L[°N] latitude of area (eg. 39.00)
FORMAT(8X,12F6.2) for each line
These lines contain the monthly values of the
parameter, starting with the October value in
column 1 and ending with the following September
value in column 12.
29 TA[°C] temperature of the area (eg. 12.80)
30 NN[£raction] fraction of sky covered by clouds (eg. '0.30)
31 S[fraction] relative humidity of area (eg. 0.60)
32 A[-] shortwave albedo of the surface (eg. 0.10)
33 REP[cm/day] daily evapotranspiration or 0.0 (see Line 3)
34 MPM[cm] monthly precipitation (eg. 0.91)
35 MTR[days] mean time of rain (eg. 0.22)
36 MN[//] mean number of storm events (eg. 1.00)
37 MT[days] mean length of rain season (i.e. days
in a month). If it rains almost every
3-4 days in a week during the entire month,
then MT=365/12=30.50 (eg. 30.50).
38 This is an empty line for visual purposes. It
indicates end of year.
***** Above lines (28-38) can be repeated for the same area
for up to 10 years (by indexing; eg. "10")jic L is given 10-times.
***** The above data set (lines 27-38) can be repeated for
any number of areas (by indexing; eg. "17").
Above data is stored in arrays CLIMM1(6,12,10) and
CLIMM2(6,12,10); see appendix DF, figure DF-2.
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Arthur D Little, Inc
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(2) Soil Data Inserts
Following the climatological input entries, the soil data must be given.
In Figure 3-6 climatological entries end in line 137. For this documen-
tation, soil data entry starts therefore with line 138 (circled "2").
Note: Lines 137 and 138 are not the real line #s. Thev onlv corre.sponH
to Figure 3-6.
Line 138 FORMAT(11,5X.12A4)
This line contains the indexed alphanumeric statement
2 SOIL CLASSIFICATIONS; SOIL, SEDIMENT DATA:
The index "2" has to appear in the first column of the
statement. Following this statement, numerical input
data for the various soil types are given.
Line 139 FORMAT(2X,13,IX,12A4)
contains the description of the indexed soil type whose
data follow; eg.
1 CLAY
Note:
- The index should always appear (eg. "1")
- This type of data is required by all levels of
operation (LEVELO - LEVELS); therefore, at least
one soil-type data set has to be given to acti-
vate the program.
- The alphanumeric title is stored in the array
spaces TITLES (5,12); see appendix DF.
Line 140 FORMAT(38X.6F7.2)
contains the numerical values of:
RS[g/cm2] soil density (eg. 1.32)
Kl[cm2]
OC[%oc]
CC[%cc]
soil intrinsic permeability
(eg. 1.00 X 10~10)
soil disconnectedness index (see
appendix HY) (eg. 12.00)
effective soil porosity (eg. 0.45)
organic content of soil (eg. 1.46)
clay content of soil (eg. 3.0)
3-26
Arthur D Little, Inc
-------
Note:
- Above values are stored in the array spaces
SOIL1(6)
- If line 140 is inserted in this file, then this line
must be given, even with 0.00 values.
Line 141 FORMAT(38X,4F7.2)
contains the numerical values of:
CEC[me/100 g soil] soil cation exchange capacity (eg. 15.00)
^] intrinsic permeabilities of upper
soil layer
^] intrinsic permeabilities of middle
soil layer
n
KlLfcm ] intrinsic permeabilities of lower
soil layer
Note:
- K1U, KIM, K1L are used for LEVEL3; therefore, they
do not have to be inserted for other levels.
If both Kl and the set of K1U, KIM and K1L are
given, the program will ignore the later values and
will use the value of Kl for all layers.
- This data is stored in array SOIL2(6); see
appendix DF, figure DF-3
- If line 140 is inserted in this file, then this
line must be input (even with 0.00 values.
***** Lines 139-141 can be inserted for an "unlimited"
number of soils. As such they create the soil-part
of the GE DATA base. Note: "indexing" (eg. "1" CLAY)
is necessary.
!!!!! Assume that the soil entries have reached line 150,
figure 3-6, 3rd page. Chemistry data inputs will
follow in line 151.
(3) Chemistry Data Inserts
Following the soil entries, the chemistry data must be given. In
Figure 3-6 soil entries end with line 150. For this documentation
chemistry data entry starts with line 151.
3-27
Arthur DLittlelnc
-------
Line 151 FORMAT(II,3X.12A4)
contains the headings of the next category of input data.
3 CHEMISTRY DATA:
Following this statement, chemical descriptions and
numerical input data are given. The "3" has to appear
in the first column of this line.
Line 152 FORMAT(2X,13,IX,12A4)
contains the name of the compound whose data follow
(lines 153-155), eg.
1 l,i-TRICHLOROETHANE
Note:
- The index of the compound (eg. "1") should
always appear in this statement.
- This type of input is required for all levels
of operation, LEVELO-LEVEL3; therefore, at
least one chemical data set should be given
into the GE DATA base (even with 0.0 values).
The name of the chemical is stored in the
spaces of the alphanumeric array TITLE(5,12).
Line 153 FORMAT(38X.6F7.2)
contains the index and the name of the chemical
compound and numerical values of parameters asso-
ciated with it. These parameters are:
SL[ug/mL] compound solubility in water
(eg. 1100)
KOC[(ug/goc)/(ug/mL)] adsorption coefficient of the
compound on organic carbon
(eg. 180.00)
f\
DA[cm /sec] diffusion coefficient in air
(eg. 0.04)
KDE[day~l] biodegradation rate of the compound
(eg. 0.00)
3-28
Arthur D Lit tie, Inc
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H[m3-atm/°K-mol] Henry's law constant (eg. 3.93E-3)
K[ (ug/g)/(ug/mL) ] averaged adsorption coefficient
for the compound on the soil
(eg. 0.0)
Note:
Above data are stored in the array CHEM(18).
If K is given (different from 0.0) then the
program uses as an adsorption coefficient this
K, otherwise it uses the KOC.
Line 154 FORMAT(38X,5F7. 2)
This line contains the numerical values of:
MWT[g/mol] molecular weight of compound
VAL[-] valence of compound
KNH[day~l] neutral hydrolysis constant
KBH[L/mol-day] base hydrolysis constant
KAH[L/mol'day] acid hydrolysis constant
All above entries in Figure 3-6 are 0.0.
This data is stored in array CHEM1(18); see
appendix DF, figure DF-3
Line 155 FORMAT(38X.3F7.2)
This line contains the numerical value of:
SK[-] stability constant of compound-
ligand complex
B[JT] number of moles of ligand per mole
of compound complexed
MWTLIG[g/mol] molecular weight of ligand
Above entries in Figure 3-6 have 0.0 values.
This data is stored in array CHEM1(18).
***** Lines 152-155 can be repeated for an "unlimited" number
of chemicals. Indexing (eg. "1") is essential. For
example, lines 156-159 contain "2"; COPPER values.
3-29
Arthur D Little, Inc
-------
(4) End of File
Following creation of the chemistry section of the GE DATA file, we
designate the "End of File" with (Figure 3-6, 3rd page).
Line 160 FORMAT(II,5X.12A4)
(End of
File) 9 END FILE
This is the last line of the GE DATA file, and should
be identified by the number 9 in the first column
(#1, Figure 3-6, 4th page).
A summary of all previously discussed data entries is given in one
table in section 3.2.5 (Table 3-1).
3-30
Arthur D Little, Inc
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3.2.4.2 LO DATA File
3.2.4.2.1 General
This file (Figure 3-7) contains information applicable to the LEVELO
operations. This file is used in conjunction with the GE DATA file
and contains:
(1) Geometric and other parameters related to a region
(2) Information relating components of the hydrologic
cycle of the area and pollutant transport of the
LEVELO simulation.
(3) Pollutant (and other chemical) loadings.
Because the LO DATA file is used in conjunction with the GE file, it is
Assumed that the user is familiar with the presentation of the input
data of the previous section 3.2.4.1 (GE DATA File), and therefore
input data descriptions are only briefly presented. A reminder: the
SESOIL code is delivered with a basic data base that facilitates addi-
tional data entry in terms of format.
As was done for the GE DATA file, a summary of all inputs of the LO DATA
file is presented in section 3.2.5 of the user's manual. Users familiar
with the input data concepts of SESOIL may consult only the summary
section.
3.2.4.2.2 Data Input
Spacing and format of data are shown in the 2nd page of Figure 3-7.
The content of each line is described below. For clarity, input data
to this file are described with reference to the figure; line 1 below
does not have to be the first line in the file.
Line 1 FORMAT(2X,I3,1X,12A4)
contains the heading of the first region of the
file, eg.
1 TEST LOCATION
Note:
- The index of the region (eg. "1") must appear.
The title is stored in the first line of the
array TITLES(5,12); see appendix DF.
3-31
Arthur D Little Inc
-------
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Line 2 FORMAT(38X.5F7.2)
contains the numerical data of:
2
AR[cm ] surface area of the compartment (eg. 1.00)
Z[m] depth to groundwater table for this appli-
cation (eg. 50.00 meters)
DU[cm] depth of upper unsaturated soil zone for
this application (eg. 0.7576 centimeters)
PH[-] pH of the upper unsaturated soil zone (eg. 8.00)
APH[-] ratio of pH lower/upper unsaturated soil
zone (eg. 0.875)
Note:
- Above data is stored in the array spaces GEOM(20);
see appendix DF.
Line 3 FORMAT(38X,6F7.2)
contains the numerical data of:
AKDE[-] ratio: biodegradation rate of
compound in lowe'r soil zone to
upper unsaturated soil zone (eg. 1.10)
AOC[-] ratio: organic carbon content in
soil in lower soil zone to upper
unsaturated soil zone (eg. 1.26)
ACC[-] ratio: clay content in soil in
lower soil zone to upper unsatu-
rated soil zone (eg. 1.30)
ISRA[-] index of surface runoff participation
in pollutant transport
ISRA = 0 no participation
ISRA ^ 0, any participation
ISRA = 1 pollutant in surface runoff
ASL[-] ratio of pollutant concentration in rain
to maximum solubility in water (eg. 0.40)
ACEC [-] ratio of CEC, lower/upper soil zone
(eg. 0.001)
Note:
Above data is stored in array spaces of GEOM(20).
3-34
Arthur D Little Inc
-------
Line 4 FORMAT(38X,4F7.2)
contains the numerical data:
POLINU[ug/cm2] total pollution load (mass) per unit
area (cm2) per year, entering the
compartment in the upper zone (eg. 200.00)
POLINL[ug/cm2] total pollution load (mass) per unit
area (cm2) per year, entering the
compartment in the lower zone (eg. 1000.0)
LIGU[ug/cm2] ligand input mass to upper zone (ug/cm2)
(eg. 10.00)
LIGL[ug/cm2] ligand input mass to lower zone (ug/cm2)
(eg. 2000.0)
Note:
- This data is stored in array LOAD(6); see
appendix DF.
Line 5 FORMAT(38X.4F7.2)
contains the numerical data:
THA[-] soil moisture content (%) (eg. 9.76)
IA[cm] infiltration (eg. 67.A3)
RGA[cm] groundwater recharge (eg. 19.03)
RSA[cm] surface runoff (eg. 35.12)
Note:
- Above data is stored in array RUNLO(6); see
appendix DF.
***** Lines 1-5 can be repeated for an unlimited number
of entries by "indexing" each time the new region
(eg. "4" TEST LOCATION)
Line 21 FORMAT(II,5X.12A4)
(End File)
This is the last statement of the LO DATA file, given as
9 END FILE
3-35
Arthur D Little, Inc
-------
3.2.4.3 LI DATA File
3.2.4.3.1 General
This file (Figure 3-8) contains information required to perform a LEVELl
simulation. This file is used in conjunction with the GE DATA file, and
may contain information existing in other files (eg. GE DATA), in order
to make this level of operation a self-contained section for the user.
As such, LI DATA contains:
(1) Geometric and other parameters related to a region.
(2) Pollutant (and other chemical) loadings.
It has been assumed again that the user is familiar at this point with
the data entry presentation of the previous section; therefore, only
brief statements are given below.
3.2.4.3.2 Data Input
Spacing (format) of data and parameter descriptions (Figure 3-8) is
described below. For clarity, input data to this file is described with
reference to the figure. Line 1 below does not have to be necessarily
the first line of the file.
Line 1 FORMAT(2X,I3,1X,12A4)
contains the heading:
1 CLINTON, MASS
Note:
- The index (eg. "1") must appear.
- The title is stored in alphanumeric array
spaces TITLES(5,12); see appendix DF.
Line 2 FORMAT(38X.5F7.2)
contains the numerical data of:
l\ f\
ARfcnr] surface area of the compartment (eg. 1.00 cm )
Z[m] depth to groundwater table for this application
(eg. 100.00 meters)
DUfcm] depth of upper unsaturated soil zone for this
application (eg. 15.00 centimeters)
3-36
Arthur D Little Inc
-------
I- i L - :
LI DATA
I .
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Ll. -ir
i ur. CLNT : ;
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o
-------
PH[-] pH of the upper soil zone (eg. 8.00)
APH[-] ratio of pH, lower/upper soil zone (eg.
0.875)
Note:
- This data is stored in spaces of array GEOM(20);
see appendix DF.
Line 3 FORMAT(38X.6F7.2)
contains the numerical data of:
AKDE[-] ratio: biodegradation rate of compound in
lower soil zone to upper unsaturated soil
zone (eg. 0.10)
AOC[-] ratio: organic carbon content of soil in
lower soil zone to upper unsaturated soil
zone (eg. 0.10)
ACC[-] ratio: clay content of soil in lower soil
zone to upper unsaturated soil zone (eg. 0.10)
ISRA[-] index for pollutant participation in surface
runoff
ISRA = 0.00; no surface runoff participation
ISRA ^ 0.00; any participation (eg. 1.4)
ISRA = 1.00; surface runoff participation
ASL[-] ratio of pollutant concentration in rain to
maximum pollutant solubility in water
ACECf-] ratio: lower/upper cation exchange capacity
of soil (eg. 0.01)
Note:
- Above data is stored in the array spaces GEOM(20)
Line 4 FORMAT(38X.4F7.2)
contains the numerical data of:
2
POLINU[ug/cm ] total pollution load (mass) per unit
area (cm2) per year, entering the
compartment in the upper zone (eg. 10.00)
POLINL[ug/cm2] total pollution load (mass) per unit
area (cm2) per year, entering the
compartment in the lower zone (eg. 5.00)
3-38
Arthur D Little, Inc
-------
LIGU[ug/cm2] pollutant input mass per unit are in
upper zone (eg. 10)
r\
LIGL[ug/cm ] pollutant input mass per unit are in
lower zone (eg. 20)
Note:
- This data is stored in array LOAD(6); see
appendix DF.
***** Lines 1-4 can be inserted for an unlimited number
of data sets. Area has to be indexed (eg. "1"
CLINTON, MA).
Line 17 FORMAT(I1,5X,12A4)
(End of
File) This is the last statement of this file, given as
9 END OF FILE
A summary of all data entries is presented in Table 3-3 of section 3.2.5.
3.2.A.4 L2 DATA File
3.2.4.4.1 General
This monthly data file (Figure 3-9) contains information required to
perform a LEVEL2 simulation. This file is used in conjunction with
the GE DATA file. L2 DATA contains:
(1) Soil quality and soil moisture quality data (input)
for the months of a year, and
(2) Pollutant input/transformation data for each month
of a year.
In the following sections it is assumed that the user is familiar
with data entries in the previous files, GE DATA, LO DATA, LI DATA;
therefore, data entries are described only briefly.
3.2.4.4.2 Data Input
Spacing and format of data are shown in Figure 3-9 and is described
below. For clarity, data input is described by means of an example;
line 1 does not need to be the first line of the file.
3-39
Arthur D Little, Inc
-------
L2 DATA
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3-^
L^ OfttA
o
-------
Line 1 FORMAT(2X,I3,1X,12A4,I5)
contains the heading related to the region/application
for which data follow, eg.
1 KANSAS-COPPER (OCT '78-SEP '80) 2
Note:
- the index "1" of the region (or description)
must be given
no"
"2" represents the number of years for which
a simulation will be performed (2=IYRS). This
number may be 1-10.
- the title is stored in the alphanumeric array
TITLES(5,12); see appendix DF.
Line 2 FORMAT(38X.5F7.2)
contains the numerical geometric and other data of:
ARfcm^] surface area of the compartment
(eg. 1.00)
Z[m] depth to groundwater table for this
application (eg. 100.00 meters)
DU[cm] depth of upper unsaturated soil zone
for this application (eg. 15.00 centimeters)
PH[-] pH of upper soil zone layer(eg. 8.00)
APH[-] ratio of pH for lower/upper soil layer(eg. 0.875)
Note:
- This data is stored in the array spaces GEOM(20);
see appendix DF.
Line 3 FORMAT(38X.5F7.2)
contains the numerical data of:
AKDE[-] ratio: biodegradation rate of compound
in lower soil zone to upper unsaturated
soil zone (eg. 0.00)
AOC[-] ratio: organic carbon content of soil
in lower soil zone to upper unsaturated
soil zone (eg. 1.00)
3-41
Arthur D Little, Inc
-------
ACC[-] ratio: clay content of soil in lower
soil zone to upper unsaturated soil
zone (eg. 0.00)
FRN[-] Freundlich equation exponent (eg. 1.00)
ACECf-] ratio: lower/upper soil zone cation
exchange capacity (eg. 0.00)
Note:
- Above data are stored in the array GEOM(20); Appendix DF
Line 4 FORMAT(8X,12F6.2)
contains the numerical data:
CUM(Oct-Sept)[ug/mL] concentration of pollutant in
soil moisture of upper zone. If an
application is to start with an already
polluted column, this concentration should
be entered in the month before any loading
is specified.
Note:
- These data are stored in the 1st line of the array
RUNM1(10,12); see appendix DF.
Line 5 FORMAT(8X.12F6.2)
contains the numerical data:
CLM(Oct-Sept)[ug/mL] concentration of pollutant in
soil moisture of lower zone. If an
application is to start with an already
polluted column, this concentration should
be entered in the month before any loading
is specified.
Note:
- These data are stored in the 2nd line of the array
RUNM1(10,12); see appendix DF.
Line 6 FORMAT(8X.12F6.2)
contains the numerical data:
3-42
Arthur D Little Inc
-------
POLINU(Oct-Sept)[ug/cm2]; monthly pollution load
(mass) per unit area (cm2) entering
the upper soil zone.
Note:
- These data are stored in the 4th line of the
array RUNM1(10,12); see appendix DF.
Line 7 FORMAT(8X.12F6.2)
contains the numerical data:
POLINL(Oct-Sept)[ug/cm2]; monthly pollution load
(mass) per unit area (cm2) entering
the lower soil zone.
Mote:
- These data are stored in the 6th line of the
array RUNM1(10,12); see appendix DF.
Line 8 FORMAT(8X.12F6.2)
contains the numerical data:
ISRM(Oct-Sept)[ug/cm2]; monthly index for
pollutant appearance in surface runoff.
ISRM=0 no surface runoff participation
ISRMj^O any runoff participation
ISRM=1 pollutant in surface runoff
Note:
- These data are stored in the 7th line of the array
RUNM1(10,12); see appendix DF.
Line 9 FORMAT(8X.12F6.2)
contains the numerical data:
ASL(Oct-Sept)[-] monthly ratio: concentration of
pollutant in rain to maximum solubility
in water.
Note:
These data are stored in the 1st line of the array
RUNM2(10,12); see appendix DF.
3-43
Arthur D Little Inc
-------
Line 10 FORMAT(8X.12F6. 2)
contains the numerical data:
TRANSU(Oct-Sept)[ug/cm2] monthly amount of pollutant
transformed (chemically, biologically
or other) in upper soil zone, and not
accounted by individually existing model
processes.
Note:
- These data are stored in the 2nd line of the array
RUNM2(10,12); see appendix DF.
Line 11 FORMAT(8X.12F6.2)
contains the numerical data:
TRANSL(Oct-Sept)[ug/cm ] monthly amount of pollutant
transformed (chemically, biologically
or other) in lower soil zone, and not
accounted individually.
Note:
- These data are stored in the 4th line of the array
RUNM2(10,12); see appendix DF.
Line 12 FORMAT(8X.12F6. 2)
contains the numerical data:
n
SINKU(Oct-Sept)[ug/cm ] monthly amount of pollutant
"lost" by processes not directly
described by the model (eg. plant
uptake) in the upper soil zone.
Note:
- These data are stored in the 5th line of the array
RUNM2(10,12); see appendix DF.
Line 13 FORMAT(8X.12F6.2)
contains the numerical data:
r\
SINKL(Oct-Sept)[ug/cm ] monthly amount of pollutant
"lost" by processess not directly
described by the model in the lower
soil zone.
3-44
Arthur D Little Inc
-------
Note:
- These data are stored in the 7th line of the array
RUNM2(10,12); see appendix DF.
Line U FORMAT(8X,12F6.2)
contains the numerical data:
LIGU(Oct-Sept)[ug/cm2] ligand mass input to the
upper soil zone
Note:
- These data is stored in the 8th line of the array
RUNM2(10,12); see appendix DF.
Line 15 FORMAT(8X.12F6.2)
contains the numerical data:
n
LIGL(Oct-Sept)[ug/cm ] ligand mass input to the
lower soil zone
Note:
- These data is stored in the 10th line of the array
RUNM2(10,12); see appendix DF.
*****
Line 43
(End of
file)
Lines 4-15 can be repeated up to 10 times (10 years)
for multi-annual applications of the same site. The
number of sets of lines 4-15 should be specified as IYRS
in line 1 (eg. IYRS=2).
Lines 1-15 can be repeated for an unlimited number of site-
applications by "indexing" (eg. 2 KANSAS, SODIUM)
the region/application).
FORMAT(II,5X.12A4)
This is the last statement of this file (line 43,
figure 3-9)
9 END OF FILE
The previous information is summarized also in Table 3-4 of section 3.2.5.
3-45
Arthur D Little Inc
-------
3.2.A.5 L3 DATA File
This monthly data file contains (Figure 3-10) information required to
perform a LEVEL3 application. This file is used in conjunction with
the GE DATA file. This file is in structure almost identical to L2
DATA with the exception of additional entries for the third (middle)
soil layer.
A user who desires to employ both levels 2 and 3 should load both files,
or should load file L3 DATA, copy it into L2 DATA, and consequently
eliminate from the L2 DATA the lines he doesn't need for the level 2
simulation.
Because data files L2 and L3 are almost identical, only a file output is
presented in this section (Figure 3-10). The user is referred to
section 3.2.4.5 for the units of the input parameters or to section 3.2.5
where input information for all files is summarized.
3.2.A.6 EXEC DATA File
This file is used with all -levels of operation and controls the execution
of the program, as well as the reading of the various data files. As
such, EXEC DATA is employed in conjunction with one or more of the previ-
ously described data files.
Each line of the EXEC DATA file corresponds to one run of SESOIL. An
unlimited number of runs can be specified. Each line of the file con-
tains 8 integer (control) numbers (Fiugre 3-11). Format and description
of these parameters are as follows:
Line 1 FORMAT(8I5)
controls the control variables:
JRUN[-] incremental number of the run (i.e. 1,2,...)
LEVEL[-] SESOIL level of operation (i.e. 0-3)
JRE[-] index of area of application (eg. 17,
i.e. CLINTON, MASS from data file EXEC DATA)
JSO[-] soil type (eg. 8, i.e. CLAY-LOAM)
JCH[-] chemical compound (eg. 20, i.e. TCE)
JNUT[-] nutrient cycle participation (for later use,
enter as 0 now)
JAPPL[-] application area (eg. 21, i.e. CLINTON, MASS
'79-'80)
JYRS[-] number of years to be simulated (eg. 1)
3-46
Arthur D Little; Inc
-------
L3 DATA
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c
3-U
J)/»-TA
-------
***** Multiple runs are specified with multiple run/line
entries.
END OF FILE The number 999 [FORMAT(I5)] indicates end of file.
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3.2.5 Summary of Data Input
Table 3-1 summarizes all input data of the GE DATA file.
Table 3-2 summarizes all input data of the LO DATA file.
Table 3-3 summarizes all input data of the LI DATA file.
Table 3-4 summarizes all input data of the L2 DATA file.
Table 3-5 summarizes all input data of the L3 DATA file.
Note: Only 1 region, 1 soil type, 1 chemical and 1 application area
are shown in the following tables. Following his familiariza-
tion with SESOIL, the user may consider consulting only the
following tables to load data.
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TABLE 3-1
GE DATA FILE
Line
Section 3.2.4.1.2
1
2
3
4
5
6
27
28
29
30
31
32
33
34
35
36
37
38
138
139
140
141
151
152
153
154
155
160
Input Parameter/Variable
Clj Regional Data
fl |~ 1 Regional Title
* L TA NN S A (REP)1)
•£ MPA MTR MN MT
| MPM(OCT) MPM(MAR)
L MPM(APR) MPM(SEP)
2 Regional Title (lYRs)
L
TA(OCT) TA(SEP)
NN(OCT) NN(SEP)
S(OCT) S(SEP)
A(OCT) A(SEP)
IYRS REp(OCT)l .... REP (SEP)
(Sets) MpM(OCT) .... MPM(SEP)
g MTR(OCT) .... MTR(SEP)
MN(OCT) MN(SEP)
MT(OCT) MT(SEP)
Empty Line
{2J Soil Data
1 Soil Title
RS Kl C N OC CC
CEC K1U KIM K1L
( 3j Chemical Data
1 Chemical Title
SL KOC DA KDE H K
MWT VAL KNH KBH KAH
SK B MWTLIG
MM End of File
FORTRAN Format
I1,5X,12A4
2X,I3,1X,12A4
38X.6F7.2
38X.4F7.2
38X.6F7.2
38X.6F7.2
2X,I3,1X,12A4,I5
8X.1F6.2
8X.12F6.2
8X.12F6.2
8X.12F6.2
8X.12F6.2
8X.12F6.2
8X.12F6.2
8X.12F6.2
8X.12F6.2
8X.12F6.2
1)
I1,5X,12A4
2X,I3,1X,12A4
38X.6F7.2
38X.4F7.2
I1.5X.12A4
2X,I3,1X,12A4
38X.6F7.2
38X.5F7.2
38X.3F7.2
I1,5X,12A4
1)
see section 3.2.4.1.2.
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TABLE 3-2
LO DATA file
Line
Section 3.2.4.2.2
1
2
3
4
5
21
u
V
CO
ctl
0)
f
Input Parameter/Variable
-(j)Application Area / Title
AR Z DU PH APH
AKDE AOC ACC ISRA ASL ACEC
POLINU POLINL LIGU LIGL
_ THA INF RGA RSA
End of File
FORTRAN Format
2X,I3,1X,12A4
38X.5F7.2
38X.6F7.2
38X.4F7.2
38X.4F7.2
I1.5X.12A4
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TABLE 3-3
LI DATA file
T.inp
Section 3.2.A.2.2
1
2 u
*• QJ
CO
3 a
17
Input Parameter/Variable
i
f (^Application Area / Title
AR Z DU PH APR
AKDE AOC ACC ISRA ASL ACEC
L POLINU POLINL LIGU LIGL
-------
TABLE 3-4
L2 DATA file
Line Input* Parameter/
Section 3.2.4.4.2
1
2
3
4
5
6
7
8
9
10 a!
en
11 «
QJ
12 <
13
14
15
~ M.J Application Area / 1
AR Z DU PH
AKDE AOC ACC
|— CUM(OCT) . . .
CLM(OCT) . . .
POLINU(OCT) .
POLINL(OCT) .
ISRM(OCT . . .
8 5 ASL(OCT) . . .
H -5 TRANSU (OCT) .
TRANSL(OCT) .
SINKU(OCT) . .
SINKL(OCT) . .
LIGU(OCT) . .
__ l_ LIGL(OCT) . .
APH
FRN
. CU*
. CU
. .POI
. .POI
. ISI
. ASI
. .TR/
. .TR/
. Sll
. SIN
. LIC
. LIC
SINKU(SEP)
SINKL(SEP)
43
©
End of File
FORTRAN Format
2X,I3,1X,12A4,I5
38X.5F7.2
38X.5F7.2
8X.12F6.2
8X,12F6.2
8X.12F6.2
8X.12F6.2
8X.12F6.2
8X.12F6.2
8X.12F6.2
8X.12F6.2
8X.12F6.2
8X.12F6.2
8X.12F6.2
8X.12F6.2
I1.5X.12A4
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TABLE 3-5
L3 DATA file
Line
Figure 3-10
1
2
3
4
5
6
7
8
9
10
11
12
3
14 S
15 „
0)
16 £
17
18
19
20
21
22
(0
HI
(0
en
OS
Input Parameter/Variable
Application Area/Title
AR Z DU DM FRN
PH A2PH APH
A2KDE AKDE A20C AOC A2CC ACC
A2CEC ACEC
CUM
CMM
CLM
POLINU
POLINM
POLINL
ISRM
ASL
TRANSU
TRANSM
TRANSL
SINKU
SINKM
SINKL
LIGCU
LIGCM
LIGCL
FORTRAN Format
2X,I3,1X,12A4,I5
38X.5F7.2
38,3F7.2
38X.6F7.2
38X.2F7.2
8X.12F6.2
57
End of File
I1.5X.12AA
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3.3 MODEL EXECUTION
3.3.1 Data Requirements
Input of data to the model consists of "adding to" and "editing" the
various data files previously described. The following data files and
corresponding lines (blocks of data) have to be included for a simula-
tion run (see Tables 3-1 through 3-5).
LEVELO Operations
• GE DATA
Lines 1, 138, 151, 160 — Titles
Lines 2, 3 (only TA), and 4, 5, 6 with 0.00 ~ Climate
Lines 139, 140, 141 — Soil
Lines 152-155 (B=l) « Chemistry
• LO DATA
• EXEC DATA
LEVEL1 Operations
t GE DATA
• LI DATA
• EXEC DATA
LEVEL2 Operations
• GE DATA
o L2 DATA
at least 1 set (5 lines)
at least 1 line
Lines 1,138, 151, 160 — Titles
Lines 2, 3, 4, and 5, 6 (with 0.0) — Climate
Lines 139, 140, 141 — Soil
Lines 152-155 (B=l) — Chemistry
at least 1 set (4 lines)
at least 1 line
Lines 1, 27, 138, 151, 160 — Titles
Lines 28-38
Lines 139, 140, 141
Lines 152-155
at least 1 set (15 lines)
V56
— Climate
— Soil
— Chemistry
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• EXEC DATA at least 1 line
LEVELS Operations
• GE DATA
as in LEVEL2 operations
• L3 DATA
at least one set (22 lines)
• EXEC DATA
at least one line
3.3.2 Execution Statement
The user has to give the statement SE81, via a terminal or a card to
start the model execution.
3.3.3 Examples of Execution (Output)
The output is intended to be self explanatory and presently it provides
information on
(1) all simulation input data (application, climatic,
chemical, soil, other) employed in a particular
run/execution
(2) the hydrologic cycle components (estimated or
assumed in LEVELO), and the monthly or annual
pollutant cycle in two or three zones of the
compartment, depending upon the level of
operation
(3) pollutant concentrations (in soil-moisture, soil-
air and adsorbed on soil) in the various soil zones
modeled
(4) pollutant masses in the various phases and zones
within the soil compartment and released to air
and groundwater
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(5) averaged and/or totaled behavior of above cycles
over a year of tiionthly simulations via LEVEL2 or
LEVEL3.
The SES01L code is released (upon request) with four pre-programmed
runs (see editing of data file EXEC). The user can give the statement
SE81 and receive an output for levels 0,1,2 and 3. Periodically
developers undertake aesthetic improvements of the output. If neces-
sary they will notify receivers of their tape, and/or provide updated
model versions.
A typical input/output is presented in appendix AP (Applications)
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3.4 MODEL "VALIDATION"
3.4.1 General
Model output validation is essential to any modeling effort. However,
model "validation" is a very broad term and may include model verifica-
tion, application, calibration, validation and frequently sensitivity
and model capabilities. The definition of these terms and the pro-
cedures needed to accomplish these objectives is discussed in
this section.
Model verification is defined as "the action during which model computer
code is run to extremes and model equations are applied to boundary con-
ditions to assure proper code operation" under all potential climatic,
soil and other input parameters. Such an action has been undertaken by
the developer (see also section 1.1) and users should not be extremely
concerned with it. Therefore, only the remaining issues are discussed
below.
3.4.2 Model Application
Once a verified model has been obtained, data have to be compiled and
input to the model for the "first" application (i.e. model application).
Input data can be compiled from:
• site specific investigations and analyses (eg.
leaching rates of pollutants, soil permeability);
• national data bases (eg. climatological data from
the NOAA); and
• other sources (eg. diffusion rate of pollutants
from handbooks).
Compilation of input data for site specific computer runs are model
specific, geohydrology and chemistry specific. Some data categories
are pollutant source data, climatological data, geographic data,
particulate transport data and biological data. Table 3-6 presents
some parameters associated with each category.
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TABLE 3-6
SOIL MODELING MAJOR INPUT PARAMETER CATEGORIES
CLIMATE:
Evapotranspiration
Temperature
Latitude
Sunlight
Plant Cover
Humidity
Cloud Cover
Wind Precipitation
SOIL:
Porosity
Density
Hydraulic Conductivity
Permeability
Adsorption Capacity
Organic Carbon Content
Clay Content
GEOGRAPHY:
Slope
Surface Storage
Terrain
Area Coordinates
SOURCES:
Leaching Rates
Release Mechanisms
Patterns of Operation (continuous, batch)
Locations
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Compilation of input data can be relatively straightforward for SESOIL,
since SESOIL employs parameters with a physical/chemical meaning.
However, time and spatial resolution input data are user-decision input
parameters and have to be determined with a previous understanding of
the hydrogeology, soil and pollutant characteristics.
Expected outputs from the SESOIL model are:
• temporal and spatial pollutant concentration
distributions in soil-air, soil-moisture;
• temporal and spatial pollutant concentration
distributions on soil particles; and
• leachate (pollutant mass) migration from the
unsaturated soil zone to groundwater.
However, the first application of SESOIL can not be expected to match
monitoring records. The common procedure prior to seeking "final" model
output is the performance of a number of model runs associated with model
applications, model calibrations and a final model validation. This is
an iterative operational procedure as discussed in the following sections.
3.4.3 Model Calibration
The calibration, or identification, of a model is the process in which
the various model parameters (and that may also include its geometry,
inputs, etc.) are redetermined — although knowledge of them is avail-
able from the application stage — or verified (if such information is
available).
The calibration is based on data obtained from observation of the
behavior of the simulated "regime" (eg. water balance of basin) in the
past. Such data usually include:
• soil moisture, soil infiltration or percolation rates; and
• water levels at gaging station of the basin.
As discussed in Appendix FT, unsaturated models are mathematically
structured by:
• developing a flow (moisture movement) submodel;
• developing a quality (pollutant transport) sub-
model; and
• interfacing the above two submodels.
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Calibration procedure, in the context of SESOIL, applies to the flow
model part of a code and, therefore, is defined as "the effort (para-
meter estimation) towards a historical matching of the climate, soil
and water balance of a basin."
The calibration procedure is often referred to as the "inverse problem."
Methods of solving this problem are discussed in the literature.
Table 3-7 lists a number of current research efforts that are oriented
towards calibrating mainly groundwater models. The same techniques might
be applied for unsaturated soil zone models, although unsaturated soil
zone modeling is complicated and no single mathematical method can
optimally be applied. The following general discussion presents the
concept of calibration as applicable to the SESOIL model.
When performing simulations, two different systems are being compared:
(1) soil column and (2) the (conceptual) model. Data are taken from the
first system, say, on basin annual yield (Eagleson 1978), in order to
calibrate the latter. Roughly speaking, the calibration procedure for
the model consists of finding a parameter set (intrinsic permeability,
porosity) that minimizes deviations between observed and calculated
values of annual yields. Least square's deviation is one of the methods
employed in the literature. Other methods are linear programming,
quadratic programming, and dynamic optimization. The least square's
criterion may be written as:
Minimize [Y <*.y,V _y (x,y t) 2
. . observed calculated i
where i = 1, . . . n, and n is the number of observed yield values.
The statistical analysis of parameter estimates and model predictions
are very promising areas of current research. The mathematics involved,
unfortunately, tend to be rather advanced and may be beyond the scope
or needs of this modeling effort. Many of the parameter estimation
techniques require both initial estimates of the soil cell parameters
and their statistical properties. This has stimulated an interest in
obtaining the statistical properties directly from field data. One of
the more promising procedures is "kriging," which is a stochastic interpo-
lation technique (Delhomme 1979), the developers are planning to use.
Calibration is not a single process, neither is it a process that can
be designed step by step ja priori. As more data become available, the
calibration process should be repeated leading to improved model para-
meters. A schematic of the proposed calibration procedure is shown
in Figure 3-12.
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Table 3-7
References of Current Research in
Calibration/Validation Procedures for Soil/Groundwater Hodels
Aguado, E. ; N. Sitar; and I. Reinson (1977). Sensitivity Analysis in
Aquifer Studies. Journal of Geophysical Research, Vol. 13, No. 4, p.
733.
Bachmat, Y. and A. Dax (1979). An Iterative Method for Calibrating a
liulticcll Aquifer Model. Water Resources Research.
Brakensiek, D.L. and C.A. Onstad (1977). Parameter Estimation of the
Green and Ampt Infiltration Equation. Water Resources Research, Vol.
13, No. 6, p. 1009.
Cooley, R.L. (1977). A Method of Estimating Parameters and Assessing
Reliability for Models of Steady State Groundwater Flow. 1. Theory and
Numerical Properties. Water Resources Research, Vol. 13, No. 2, pp. 318-
324.
Cooley, R.L. (1979). A Method of Estimating Parameters and Assessing
Reliability for Models of Steady State Groundwater Flow. 2. Application
of Statistical Analysis. '.Jater Resources Research, Vol. 15, No. 3, pp.
603-617.
Cooley, R.L. and P.J. Sinclair (1976). Uniqueness of a Model of Steady-
State Groundwater Flow. Journal of Hydrology, Vol. 31, pp. 245-269.
Delhomme, J.P. (1979). Spatial Variability and Uncertainty in Ground-
water Flow Parameters: A Geostatistical Approach. Water Resources
Research, Vol. 15, No. 2, pp. 269-280.
Delhomme, J.P. (1978). Kriging in the Hydrosciences. Advances in Water
Resources, Vol. 1, No. 5, p. 251-266.
Dettinger, M.D. and J.L. Wilson (1981). First Order Analysis of
Uncertainty in Numerical Models of Groundwater Flow. 1. Mathematical
Development. Water Resources Research, Vol. 17, No. 1, pp. 149-161.
Gambolati, G. and G. Volpi (1979). A Conceptual Deterministic Analysis
of the Kriging Technique in Hydrology. Water Resources Research, Vol.
15, No. 3, pp. 625-629.
Haverkamp, R. and M. Vauclin (1979). A Note on Estimating Finite
Difference Interblock Hydraulic Conductivity Values for Transient Un-
saturated Flow Problems. Water Resources Research, Vol. 15, No. 1, p.
181.
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Table 3-7 (continued)
Hayhoe, H.N. (1978). Study of the Relative Efficiency of Finite
Difference and Galerkin Techniques for Modeling Soil-Water Transfer.
Water Resources Research, Vol. 14, No. 1, p. 97.
Hefez, E.; U. Shamir; and J. Bear (1975). Identifying the Parameters of
an Aquifer Cell Model. Water Resources "Research, Vol. 11, No. 6, p. 993.
Kohberger, R.C.; D. Scavia; and J.W. Wilkinson (1978). A Method for
Parameter Sensitivity Analysis in Differencial Equation Models. Water
Resources Research, Vol. 14, No. 1, p. 25.
McElwee, C.D. and M.A. Yukler (1978). Sensitivity of Groundwater Models
with Respect to Variations in Transmissivity and Storage. Water Re-
sources Research, Vol. 14, No. 3, pp. 451-459.
Murty, V.V.N. and V.H. Scott (1977). Determination of Transport Model
Parameters in Groundwater Aquifers. Water Resources Research, Vol. 13,
No. 6, p. 941.
Navarro, A. (1977). A Modified Optimization Method of Estimating
Aquifer Parameters. Water Resources Research, Vol. 13, No. 6, p. 935.
Nutbrown, D.A. (1975). Identification of Parameters in a Linear
Equation of Groundwater Flow. Water Resources Research, Vol. 11, No. 4,
p. 581.
Sagar, B.; S. Yakowitz; and L. Duckstein (1975). A Direct Method for the
Identification of the Parameters of Dynamic Nonhomogeneous Aquifers.
Water Resources Research, Vol. 11, No. 4, p. 563.
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f Start J
4*» Model
Application
Output
Evaluation
Model
Application
Initial Parameter
Estimates
New Parameter
Estimates
no
Model
Calibration
alibrstion
chieved
Figure 3-12 SCHEMATIC OF MODEL APPLICATION/CALI3RATION/VALIDATIO-;
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Calibration of unsaturated soil zone models can be uncertain and diffi-
cult because climate, soil moisture, soil infiltration and percolation
are strongly interrelated parameters that can be difficult and/or
expensive to measure in the field. Therefore, calibration of unsatu-
rated soil zone models is frequently associated with a model validation
(described in the next section).
For the available version of SESOIL that employs Eagleson's (1978) annual
water balance theory (as expanded to monthly simulations and with moisture
transfer budget in the course of the months), authors recommend model
calibration by varying the intrinsic permeability (k), the pore disconnected-
ness index (c) and the porosity (n) of the soil; all input parameters to
the model (see appendix ID, section 3.0).
The outlining of steps for the calibration procedure of SESOIL is a
feasible task; however such a task would require a thoughtful elabora-
tion of this issue by the authors prior to outlining it in this document.
3.4.A Model Validation
Frequently, the definitions of calibration and validation are synonymously
employed in the literature because of the large number of nonvalidated but
calibrated groundwater models and the limited number of noncalibrated but
validated unsaturated soil zone models. For SESOIL , model validation is
defined as "the process which analyzes the validity of final model output."
In SESOIL, the validity of the predicted pollutant concentrations would be
compared to available knowledge of measured pollutant concentrations from
monitoring data (field sampling).
A disagreement in absolute levels of concentration (predicted versus
measured) does not necessarily indicate that either method of obtaining
data (modeling, field sampling) is incorrect or that either data set
needs revision. Field sampling approaches and modeling approaches rely
on two different perspectives of the same situation.
Field data give concentrations at points in time and space, models
predict "average" concentrations for a particular assumed set of
conditions. Thus, field and model results may differ and still both
be correct. Some possible reasons for a discrepancy are:
o The field sample was taken from a spot with atypical
concentrations (eg. a water sample may be close to
an unidentified confounding source, and so give
abnormally high readings).
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• The sample was taken under a typical conditions
(eg. on the one day/month that it rained); model
results were calculated for average conditions,
which may rarely occur (eg. at the "average" soil
moisture content which occurred only for a short
period).
• The sample contained interactive compounds (eg. a
water sample contained some sodium that may have
resulted in increased soil permeabilities).
• The extraction procedure for the sample was under or
over efficient (eg. it not only extracted all organic
pollutants from a soil sample but also dissolved
the soil).
Mathematically, the available model validation procedures and techniques
are similar to those presented in the previous section. Following a
validation procedure with good field data, "no better model predictions"
can be made. This will be the "best possible" output.
For SESOIL, the approach — at the present time — would be to:
• apply simplified mathematical techniques (as described
above for calibration);
• exercise the professional experience, gained from
original model application work to refine the results;
and
• document the validation logic for the SESOIL level
employed.
A schematic figure of the previously discussed processes is shown in
Figure 3-12.
3.4.5 Model Sensitivity Analysis
It is frequently worthwhile to perform sensitivity analyses to determine
the effect on the predicted concentrations caused by a change in the
input parameters. These sensitivity analyses are particularly important
when data gaps or uncertain input values exist. It may also be useful
to rerun SESOIL to estimate the impact of various site management or
design strategies on pollutant distribution and concentrations in the
environment. Two main techniques are widely used to perform sensitivity
analyses:
• model simulations; and
e analytic techniques.
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Model simulations are performed by running and rerunning the model,
simultaneously varying the value of one or more parameters following
a "scenario" logic. Model concentration predictions may be compared
to monitoring data as described in the previous section.
Analytic techniques of linear systems theory (Dooge 1973) and optimiza-
tion theory (Haimes 1977) may correlate sensitivity of model input
(eg. leaching quantity) to model output (eg. soil concentrations)
"without" performing multiple model reruns (simulations). An example
is given below for an analytic technique (Fiksel et al 1981).
Assume a SESOIL column receiving pollutant input quantifies I in all
layers (cells). Assume SESOIL accounting for a linear Freundlich
adsorption coefficient and assume that average predicted adsorbed
concentrations in the N cells are the c(N). Then the following matrix,
linear response function F(N) can be written:
F(N) • c(N)
where F(N) a low triangular (f,0) matrix:
0
F(N) =
From the first relation, we have:
from which all elements N of F can be estimated. Given a possible
linearity of c versus I, we are at a position now to vary input sources
of the model and estimate concentration "without" having to run and
rerun SESOIL. This approach has not been exercised by the developers;
however, they may consider it in the future for certain processes and
parameters.
3. A. 6 Model Limitation
Any mathematical model is "as good as its weakest link"; therefore,
limitations of the model are correlated with the limitations of each
of the routines and processes coded (see also section 1.1). In general,
limitations can be due to:
• data availability,
• inoptimal single medium model application
to a particular site,
• omission of important chemistry reactions, and
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• lack of appropriate model validation opportunity
Data availability refers to environmental data (eg. climatic, soil,
water resource), source data (eg. pollutant leaching from the site),
chemistry data (eg. chemical properties of pollutants) and monitoring
data (eg. ambient concentrations). It is not appropriate, for example,
to drive any soil model without a proper set of weather records and then
attempt to validate the model output with available monitoring data.
Omitting certain important pathways or chemistry reactions or processes
(eg. volatilization) because of lack of data can become an issue of
concern. Such pathways should be evaluated outside the model or, at
certain times, another modeled via SESOIL as far as possible. A model
sensitivity analysis of omitted (or to be omitted) processes is essential.
3.4.7 Discussion
During the SESOIL development a number of verifications, calibration,
validation and sensitivity steps have been performed to one degree
or another.
The model code has been verified by extensive testing and under extreme
conditions of input data. Each level of operation has been run multiple
times and the results have been compared and rectified with sample hand
calculations and by other models.
On an earlier contract to the EPA, SESOIL has been applied to two actual
land treatment sites at which considerable monitoring data were available.
Good agreement was obtained between monitoring data and model results.
This study provided to model developer the only validation of SESOIL.
These sites were also used for a sample calibration effort where the
soil parameters of intrinsic permeability and adsorption coefficients
(K,KOC) were calibrated/validated to field records (Bonazountas et al
1981).
One short study for metals has been performed (Bonazountas et al 1981)
and another short study for halogenated solvents is underway (Wagner
& Bonazountas 1982), both aimed to evaluate the overall fate of pollu-
tants in the soil compartment, including losses to the air and to
groundwater. In both studies, canonical/scenario environments were
designed by combining a range of climates, soils and pollutants, in
order to trace sensitivity of various parameters upon the long-term
overall pollutant fate.
In the future model developers hope to extend these efforts, particularly
to include increased calibrations and validations with actual field data,
an essential task for model improvement and validity.
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3.5 References
Aguado, E. ; N. Sitar; and I. Rein son (1977). Sensitivity Analysis in
Aquifer Studies. Journal of Geophysical Research, Vol. 13, No. 4, p.
733.
Bachmat, Y. and A. Dax (1979). An Iterative Method for Calibrating a
Multicell Aquifer Model. Water Resources Research.
Bonazountas, M.; J. Wagner; and B. Goodwin (1981). Evaluation of
Seasonal Soil/Groundwater Pollutant Pathways. U.S. EPA, Data and
Monitoring Support Division, EPA Contract No. 68-01-5949, Task 9,
Arthur D. Little, Inc., report.
Brakensiek, D.L. and C.A. Onstad (1977). Parameter Estimation of the
Green and Ampt Infiltration Equation. Water Resources Research, Vol.
13, No. 6, p. 1009.
Cooley, R.L. (1977). A Method of Estimating Parameters and Assessing
Reliability for Models of Steady State Groundwater Flow. 1. Theory
and Numerical Properties. Water Resources Research, Vol. 13, No. 2,
pp. 318-324.
Cooley, R.L. (1979). A Method of Estimating Parameters and Assessing
Reliability for Models of Steady State Groundwater Flow. 2. Appli-
cation of Statistical Analysis. Water Resources Research, Vol. 15,
No. 3, pp. 603-617.
Cooley, R.L. and P.J. Sinclair (1976). Uniqueness of a Model of
Steady-State Groundwater Flow. Journal of Hydrology, Vol. 31, pp.
245-269.
Delhomme, J.P. (1979). Spatial Variability and Uncertainty in Ground-
water Flow Parameters: A Geostatistical Approach. Water Resources
Research, Vol. 15, No. 2, pp. 269-280.
Delhomme, J.P. (1978). Kriging in the Hydrosciences. Advances in
Water Resources, Vol. 1, No. 5, p. 251-266.
Dettinger, M.D. and J.L. Wilson (1981). First Order Analysis of Un-
certainty in Numerical Models of Groundwater Flow. 1. Mathematical
Development. Water Resources Research, Vol. 17, No. 1, pp. 149-161.
Dooge, J.C. (1973). Linear Theory of Hydrologic Systems. U.S. De-
partment of Agriculture, Washington, D.C. 20402, Technical Bulletin
No. 1468.
Eagleson, P.S. (1978). Climate, Soil, and Vegetation (1-7). Water
Resources Research, Vol. 14, No. 5, pp. 705-776.
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Fiksel, J.; M. Bonazountas, H. Ojha; and K. Scow (1981). An Inte-
grated Geographic Approach to Developing Toxic Substance Control
Strategies. Arthur D. Little, Inc., Report for the U.S. Environmental
Protection Agency, Office of Policy and Resource Management. EPA Con-
tract No. 68-01-6160.
Haimes, Y.Y. (1977). Hierarchiacal Analyses of Water Resource Sys-
tems. McGraw Hill International Book Company, New York. ISBN 007-
025507-5.
Gambolati, G. and G. Volpi (1979). A Conceptual Deterministic Analy-
sis of the Kriging Technique in Hydrology. Water Resources Research,
Vol. 15, No. 3, pp. 625-629.
Haverkamp, R. and M. Vauclin (1979). A Note on Estimating Finite
Difference Interblock Hydraulic Conductivity Values for Transient Un-
saturated Flow Problems. Water Resources Research, Vol. 15, No. 1, p.
181.
Hayhoe, H.N. (1978). Study of the Relative Efficiency of Finite Dif-
ference and Galerkin Techniques for Modeling Soil-Water Transfer.
Water Resources Research, Vol. 14, No. 1, p. 97.
Hefez, E.; U. Shamir; and J. Bear (1975). Identifying the Parameters
of an Aquifer Cell Model. Water Resources Research, Vol. 11, No. 6,
p. 993.
Kohberger, R.C.; D. Scavia; and J.W. Wilkinson (1978). A Method for
Parameter Sensitivity Analysis in Differencial Equation Models. Water
Resources Research, Vol. 14, No. 1, p. 25.
McElwee, C.D. and M.A. Yukler (1978). Sensitivity of Groundwater
Models with Respect to Variations in Transmissivity and Storage. Water
Resources Research, Vol. 14, No. 3, pp. 451-459.
Murty, V.V.N. and V.H. Scott (1977). Determination of Transport Model
Parameters in Groundwater Aquifers. Water Resources Research, Vol.
13, No. 6, p. 941.
Navarro, A. (1977). A Modified Optimization Method of Estimating
Aquifer Parameters. Water Resources Research, Vol. 13, No. 6, p. 935.
Nutbrown, D.A. (1975). Identification of Parameters in a Linear Equa-
tion of Groundwater Flow. Water Resources Research, Vol. 11, No. 4,
p. 581.
Sagar, B.; S. Yakowitz; and L. Duckstein (1975). A Direct Method for
the Identification of the Parameters of Dynamic Nonhomogeneous Aqui-
fers. Water Resources Research, Vol. 11, No. 4, p. 563.
Wagner, J. and M. Bonazountas (1982). Buried Halogenated Solvent
Simulations via "SESOIL." U.S. EPA, Office of Toxic Substances, EPA
Contract No. 68-01-6271, Arthur D. Little, Inc., report.
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HY • hydrologic cycle
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APPENDIX HY
HYDROLOGIC CYCLE
To the Reader/User:
Information contained in this appendix is not well documented at all,
for reasons explained below, and authors fully recognize this fact.
For the authors - although the hydrologic cycle governs the model ^
operations -- the full and accurate hydrologic cycle documentation
has not been of primary importance because:
• Hydrologic cycle development of SESOIL has not
been accomplished yet.
• The hydrocycle of SESOIL is primarily based on
Eagleson's annual "Climate, Soil, and Vegetation
theory, which is excellently documented in the
literature (Eagleson 1978; other publications).
Therefore, the author would have spent appreciable
effort in representing Eagleson's work.
• Budget constraints of this contract (see section 1.1)
led the authors to prioritize documentation of
chemistry related and other issues of SESOIL, i.e.
original information generated for SESOIL.
• This SESOIL documentation is not to be released in
the public domain, therefore, a tentative draft
regarding the hydrologic cycle would be sufficient^
for a reader/user to understand the basic "concept
adapted for the hydrologic cycle; i.e. Eagleson s
theory adaptation.
• The hydrologic cycle documentation is of secondary
importance to a reader or a user, contrasted to the
documentation of other processes, because of the
simplicity of input data (and here lies the sophisti-
cation and elegancy of Eagleson's theory) required
to drive this part (hydrology) of SESOIL.
However: Eagleson's annual theory has been adapted to SESOIL needs by
cpanding the work into monthly hydrocycles,
ext
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• accounting of moisture storage transfer from
month-to-month in the entire compartment,
• not fully employing the vegetational aspects
of the basic theory, because the watershed
aspects of SES01L have not been developed yet,
• accounting for zero rain (depth, number of storm
events, etc)
• accounting for a "smooth" heterogeneity along
the soil column (soil type stratification)
• omitting vegetational and soil surface moisture
retention for reasons related to SESOIL needs
under the current contract (i.e. a model for
overall fate of pollutants) at non-vegetated
areas rather than a model for basin-specific
pollutant transport on the watershed.
• presenting (model output) only expected values
of the statistical distributions of the hydro-
logic processes model.
The above adaptation issues are not always clearly documented in this
appendix. The authors are aware of the deficiencies of this document
that was drafted in 1980 (see page HY-1) when SESOIL was conceptua-
lized; however, they intend to improve it when possible.
The SESOIL authors appreciate that Eagleson's work might have been
frequently misquoted, paraphrased and mis-duplicated. The issue is
not so much of credit given to Eagleson by citing his work, but rather
it is one of possible misunderstanding and misuse of his theory. There-
fore, readers or users are advised to consult Eagleson's original theory.
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APPENDIX HY
HYDROLOGIC CYCLE
CONCEPTUAL
DRAFT
(see section 1.1)
1.0 INTRODUCTION
1.1 General
1.2 Hydrologic Processes Involved
1.3 Modeling Background
2.0 LEVELO - ANNUALLY "KNOW" HYDROLOGIC COMPONENTS
3.0 LEVEI.1 - ANNUALLY "ESTIMATED" HYDROLOGIC CYCLE
3.1 General
3.2 Definitions
3.3 Annual Mathematical Analysis
3.3.1 Assumptions
3.3.2 Theoretical Overall Approach
3.3.2.1 The Water Balance Equation
3.3.2.2 Precipitation
3.3.2.3 Soil Infiltration
3.3.2.4 Annual Infiltration and
Surface Runoff
3.3.2.5 Potential Evaportranspiration
3.3.2.6 Annual Evaportranspiration
3.3.2.7 Groundwater Runoff
3.3.2.8 Annual Hydrologic Water
Balance
3.3.2.9 Depth Dependent Infiltration
3.4 Model Variables/Parameters
3.5 Water Balance Sensitivity
3.6 Subroutine HYDROA
3.6.1 Equation Summary
3.6.2 Input/Output Variables
3.6.3 Step-by-Step Calculation Procedure
4.0 LEVEL2 - MONTHLY "ESTIMATED" HYDROLOGIC CYCLES
4.1 General
4.2 Definitions
4.3 Monthly Mathematical Analysis
4.3.1 Principal Assumptions
4.3.2 Theroethical Overall Approach
4.4 Input/Output Variables
HY-1
Page
HY-2
HY-2
HY-2
HY-5
HY-7
HY-8
HY-8
HY-8
HY-10
HY-10
HY-11
HY-11
HY-14
HY-17
HY-20
HY-23
HY-25
HY-26
HY-2 7
HY-28.1
HY-29
HY-37
HY-41
HY-41
HY-49
HY-51
HY-5 2
HY-5 2
HY-52
HY-52
HY-52
HY-52
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5.0 MODEL EXTENSION HY-55
5.1 General HY-55
5.2 Snow Pack/Melt HY-56
5.3 Interception HY-57
6.0 REFERENCES HY-58
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1.0 INTRODUCTION
1.1 General
The hydrology of the soil compartment can be:
(1) Assumed annually known (LEVELO),
(2) Simulated annually (LEVELl), or
(3) Simulated monthly (LEVEL2, LEVEL3).
Simulations* (LEVELl, LEVEL2, LEVEL3) are performed via two hydrologic
cycle subroutines, designed as HYDROA (Annually) and HYDROM (Monthly),
the latter being an extention of the first.
1.2 Hvdrologic Processes Involved
The two hydrologic subroutines (HYDROA and HYDROM) simulate the atmosphere,
surface and subsurface hydrologic processes shown in Figure HY-1. The
hydrologic processes are the main governing factors of pollutant movement
in the soil compartment.
Precipitation encompasses rainfall and snow. Snowpack and snowmelt
affect pollutant movement first by reducing erosion and secondly by
causing less polluted runoff than the corresponding rain runoff.
Infiltration is the movement of water through the soil surface into
the soil column. Infiltration rates are variable and change with the
moisture content of the soil profile. During a storm event, the rate
of infiltration decreases as the soil voids become filled. Usually more
than half of the water which infiltrates is retained in the soil until
it is returned to the atmosphere by evapotranspiration. Some infiltrated
water may move laterally through the upper soil through the stream
channel as interflow, and some may enter temporary storages and be later
discharged into the stream channel as base or groundwater flow. The
infiltration capacity is a function of the plant cover and of variable
hydrogeologic characteristics, primarily soil moisture content.
*In this appendix the word simulation is equivalent to modeling.
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Precipitation r- 'fa*Atmospheric
(Rain, Snow) , V^* Fallout
Pollution
Load
Evap'otranspiration
___.-_-^-
-.of jys/t/*y*im fy*y *yr^y7r
Exfiltration
•Infiltration
Erosion
Biologic Uptake
Capillary
rise
4-
Percolation
Groundwater
Runoff
Upper Unsaturated Soil Zone
Lower Unsaturated Soil Zone
Saturated Soil Zone
Figure HY-1
Atmosphere, Land, Surface, Subsurface,
Biotic and Pollutant/Processes
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Evapotranspiration is the transfer of water from land, vegetative
cover and water bodies to the atmosphere. The term involves two dis-
tinct processes, exfiltration and transpiration. The volume of water
leaving the watershed through evapotranspiration is greater than the
total contribution to the base streamflow of most systems. All surfaces
that are exposed to precipitation are considered to have a potential for
evapotranspiration. Transpiration is a function of a vapor pressure
gradient between air and leaf cells and occurs when leaf pores are
stimulated by light. Deeply rooted plants continue to transpire even
in periods of infrequent rainfall.
Interception is the amount of precipitation remaining on leaves,
branches, and stems. This volume may or may not return to the atmosphere
through transpiration. Intercepted water quantities during a single
storm are relatively minor. However, they can have a significant effect
on long term surface runoff volumes. Interception is a function of the
type and extent of vegetation, land and meteorologic characteristics of
the area (wind, temperature, solar radiation, precipitation, etc.)
Percolation results in groundwater runoff. Percolation rates depend
mainly upon the infiltration rate, the moisture storage in the unsaturated
soil zone and the depth to groundwater. During dry seasons percolation
may become negative (upward) due to capilarity.
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1.3 Modeling Background
Previous efforts to model combined hydrologic, soil and vegetational
systems of an area have been in two noteworthy directions (Eagleson, 1979;
p. 924):
(1) Empirical studies that provide validated interrelation-
ships among the principle variables but that, due to their
weak physical basis, lack both the generality and the
parametric incorporation of climate, soil and vegetal
properties that are necessary for general insight into
soil processes. Prominent among these studies are the
works of Lettan (1973) and Thornthwaite (1948); and
(2) Numerical studies—that utilize detailed formulations
of the physics at the microprocess scale but that, due
to their complexity, impose infeasible validation data
requirements and impede the generation of overall behavioral
insight. Prominent among these studies are the works of
Adams and Jurisa (1976), Donigian, et al (1977), and
Novotny, et al (1978).
It is beyond the scope of this study to review the literature and
describe the physics and mathematics of the previous studies.
SESOILdoes not employ either an empirical or a numerical hydrologic routine;
instead it employs the statistical analytic "annual water balance" model
of Eagleson (1978), which couples atmosphere, soil and vegetation systems.
In SESOIL, however, Eagleson's model is modified to perform both
annual and monthly simulations. The scientific background of the annual
model has been presented and discussed in various journals since 1978.
Therefore, this appendix (HY) is intended to presently only an "extracted"
outline of the model as previously given in Eagleson's publications.
The following paragraphs intend only to inform the reader about the nature
of the hydrologic routine employed and not to give a thorough background
of it. To maintain a consistent approach, Eagleson's notation is followed.
Readers interested in the derivation of the annual equations presented
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in the following sections, are referred to the original publications.
The work of Eagleson presents a "generalized" annual water balance
model based upon simplified physics of the component proceses. The model
is detailed enough to capture the "essential" system dynamics yet simple
enough to permit analytical (as opposed to numerical) solution. It pro-
duces valuable insights into the role of soil moisture in environmental
compartments, of which moisture is one of the most important factors
governing pollutant transport and decay in the soil cell. Eagleson1s
model has a unique statistical approach in coupling systems and represents
the state of the art in environmental modeling. The model is easy to use
because of the limited number of input parameters required. The latter
is fully justified by the sophisticated mathematical approach developed
by Eagleson.
Section 2.0 of this appendix provides the hydrologic cycle background for
the LEVELO model operation, dealing with "known" hydrologic components
of the soil compartment. The following two main sections (Sections 3.0
and 4.0) outline the theoretical background for the "annual" hydrologic
cycle subroutine (HYDROA) and the "Monthly" hydrologic cycle subroutine
(HYDROM), the latter being developed based upon the theory of the first.
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2.0 LEVELO - ANNUALLY "KNOWN" HYDROLOGIC COMPONENTS
2.1 Input Data
The following parameters must be known (input) for the LEVELO operation
of SESOIL.
I. = annual infiltration; (cm)
A
R = annual surface runoff; (cm)
R - annual groundwater runoff; (cm)
gA
0 = mean annual soil moisture content; (mL/mL)
2.2 Discussion on Soil Water Models
Recent developments of soil water models based on column mass balance
provide an alternative to directly or indirectly measuring soil moisture
in the field. Figure HY-1 is a schematic diagram of the physical system
and the driving forces that must be considered in modeling the system.
Based upon conservation of mass, the soil moisture in the system at any
time can be determined using the relationship:
PA = ETA+ A'o + V + RsA
where:
P = total annual precipitation
A
R . = total annual surface runoff
sA
E = total annual evapotranspiration
X A
= s (t)-so(t-l); annual change in the soil moisture storage.
R . = total annual groundwater runoff
gA
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Four of the above variables are user supplied input, the fifth is
estimated. A standard practice in annual soil water budget modeling
is to estimate As from the above equation, using site-specific estimates
of the other parameters. Consequently SQ = SQ(t) is estimated from
the relationship SQ(t) •= ASQ - so(t-l), given the historical moisture
storage s (t-1).
Various references (e.g., National Water Atlas, Gerapty & Miller, Inc.)
can be consulted for the annual averages of PA> ETA> RGA and RSA»
for various locations in the U.S.
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3.0 LEVEL1 - ANNUALLY "ESTIMATED" HYDROLOGIC CYCLE
3.1 General
The theory for the "annual" hydrologic cycle routine is presented by Peter S.
Eagleson, in Water Resources Research (WRR), Volume 14, October 1978,
Number 5, pages 705 through 776 and in a number of other publications. In
this report, reference is mainly made to the above publication by
indicating the page number and the equation number of the equations
employed.
3.2 Definitions
It is the writer's feeling that the reader of this documentation and
of Eagleson's publications might be confused with the
definitions:annual, seasonal, monthly, long-term, etc., unless they
are thoroughly acquainted with the theoretical background of the
hydrologic cycles presented in this documentation. Therefore, it is
worthwhile to clarify at this point the following expressions applicable
to both the "annual" (Section 3.0) and the "monthly" (Section 4.0)
hydrologic cycle routines.
(1) For the "annual" hydrologic cycle routine the "simulation
period" or simulation time (or time step) equals a period
of "one year" (i.e. 12 months). Within this year we have
a rainy "season" which can be shorter or equal
to one year ( 12 months) depending on the climate of the
area.
(2) For the "monthly" hydrologic cycle routine, the "simulation
period" or simulation time equals a period of "one month".
Within this month we have a rainy "season"
which can be shorter or equal to one month ( 1 month)
depending on the climate of the area.
HY-9
Arthur D Little Inc
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Eagleson employs both expressions "annual/seasonal" while presenting
his "annual" water balance theory [e.g.,WRR,p.749,eq.(1)1. This is
fully justified from his perspective, however, to avoid confusion
(e.g. seasonal for annual vs. seasonal for monthly simulation) in the
following section we will standardize our definitions as discussed
above, and will explicitly define the terms.
Nov. 80 HY-9.a
-------
3.3 Annual Mathematical Analysis
3.3.1 Assumption
The principal assumptions made are [Eagleson, 1977]:
(1) No consideration of heavy snow or ice precipitation
(2) Consideration of vegetation only as it affects surface
albedo and roughness
(3) One-dimensional analysis, involving vertical processes only
(4) All processes are stationary in their long-term (annual/
seasonal) average
(5) First-order analysis, namely, long-term averaged behavior,
is used to represent relationships between seasonal
averages.
Nov. 80 HY-10
-------
3.3.2 Theoretical Overall Approach
3.3.2.1 The Water Balance Equation
The analysis of subroutine HYDROA is based upon:
(1) The volumetric water balance equation per unit area of the
soil column over time [WRR,p.706,eq.(1)]:
t t t
f[i(t)-eT(t)-vs(t)]dt = \[rs(t)+rg(t)]dt = \y(t)dt
where:
t = time
s = soil moisture concentration
i(t) = precipitation
eT(t) = potential evapotranspiration rate
v (t) = rate of moisture storage in soil,
vegetation, snow, ice, lakes, etc.
r (t) - surface runoff rate
S
r (t) = groundwater runoff rate
g
y(t) = yield rate
(2) The surface infiltration conservation equation over time
[WRR,p.706,eq.(3)]:
t t t t
(i(t)dt - (vss(t)dt - (fi(t)dt = \rs(t)dt (HY-2)
ooo o
Nov. 80 HY-11
Arthur D Little, Inc
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where:
v = rate of capture of precipitation in surface storage
ss
(i.e., on the soil and vegetal surface)
f.(t) = infiltration rate
Assuming all evapotranspiration comes from soil moisture and considering
only systems which are steady-state in long-term average, Eagleson
[WRR,p.706,eq.(2)] developed the water balance equation:
E[PA] - E[ETA] = E[RsA] + E[RgA]
where :
E[x] = mr ,, expected value or mean of a variable x
LXJ
P = annual precipitation; (depth, cm)
A
R . = annual surface runoff; (depth, cm)
sA
R = annual groundwater runoff; (depth, cm)
gA
E = annual total evaporation; (depth, cm)
L A
Y = annual yield; (depth, cm)
A
Rearranging the above equation and by omitting the E[ ] designations
LWRR,p.707,eq.(4)]:
Nov. 80 HY-12
-------
Surface
Precipitation Runoff
i J V I
RsA(PA) (HY-4)
Infiltration
ETA(PA>
Evapotranspiration Groundwater
Runoff
(Recharge
and Loss)
The following sections present a summary of the mathematical ex-
pressions developed by Eagleson for the various terms of the above
equation. This equation is designated later on as "soil moisture (so)"
equation because factors become soil-moisture dependent. It must
also be noted that the above equation involves the implicit assump-
tion of constant water storage over the given water season. This is
only an approximation of reality; it is closest in nature to an arid,
seasonal climate with ephemeral streams because the end-of-year moisture
storage is there only at its annual minimum, and therefore very small.
Significant snowfall may have large interception losses, theoreti-
cally invalidating the above. However, the authors believe that the
employment of Eagleson's model — a discussion for snow pack/melt and
interception is made in a later section — is strongly desired because
of its advantages in its formulation that is based on a relatively few
physical parameters and very few input data.
Nov. 80 HY~ 13
Arthur D Little, Inc
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3.3.2.2 Precipitation
The storm sequence is represented in the model by Poisson arrivals
of rectangular pulses, as shown in Figure HY-2.
The cumulative distributive function for normalized annual point pre-
cipitation is [WRR,p.715,eq.(36)]:
Prob
"PA
>
-MB
= e
oo (um )
117
1+E . v!
v=l
V
• "P r \l^ /ilTYl ^ 7 1
i [ V K j U) ffl K 2 J
(HY-5)
where :
P = total seasonal precipitation (cm)
A
IIL. = average seasonal precipitation (cm)
U = storm arrival rate (days )
m = average length of rainy season (days)
K - shape parameter of Gamma distribution of
storm depth (h)
v = number of storms
P[ ] = Pearson's incomplete Gamma function
z
P
= value of annual rainfall (taken on by
the random variables PA).
The Gamma distribution of storm depth is given by [TOR,p.714,eq.(15)]
K-l
fR(h) = G(.c,X) =
with mean [WRR,p.714,eq.(16)]:
X(Xh)
-Xh
(HY-6)
(HY-7)
Nov. 80
HY-14
Arthur D Little Inc
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RAINFALL
INTENSITY
..-..- • •
(o) ACTUAL
RAINFAL
i
i
L
INTENSITY
CLIMATIC
PARAMETERS
HI-"!
STORM
' i
i i.
t,
i
i
f
ta — J
tfc
•• *•
-
* • • •
»,.
r
hT STORM ,
GENERATING^-** «
PROCESS
T ,
f
DE
^H n = i • tr
• • • t •
i
(b) MODEL
Figure HY-2
Precipitation Event Model
Source: [TOR,p.707,Figure 5]
HY-15
Arthur D Little, Inc.
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and variance [WRR.p. 714, eq. (17) ] :
K/002 (HY-8)
in which:
h = storm depth (cm)
X = parameter of Gamma distribution of storm
depths, equal to K/n (erf )
Equation HY-6 is shown to accurately reproduce the observed
annual precipitation probability relationship in applications to both
humid and arid-seasonal climates using only a few years (e.g., five) of
storm data.
HY-16
Arthur D Little Inc
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3.3.2.3 Soil Infiltration
The following assumptions were made for deriving statistical equa
tions for capillary rise from the water table (dry seasons), infiltra-
tion, exfi. tration (i.e., desorption against gravity), and percolation
to groundwater table [P.Eagleson, 1977]:
(1) Homogeneous soil
(2) No vegetation, snow or ice presence
(3) Movement of water vapor negligible
(4) Soil column is effectively semi-infinite concerning
surface processes of infiltration and exfiltration
(i.e., the water table or other boundary is deeper
than the penetration depth of the surface processes)
(5) Soil moisture is spatially uniform at the beginning
of each storm and interstorm period with a value SG,
given by the long-term temporal and spatial average
(6) Infiltration processes (infiltration, exfiltration,
gravitational percolation and capillary rise) are
considered as separable superimposable processes
(7) Infiltration is described by the Phillip equation.
The derived soil moisture velocity equations are:
Capillary Rise from the Water Table [WRR,p.728,eq.(59)]:
w = I „„ i I »A-"-y I 7 I
mc-1 J L ^ J
11/2
fv r_s_i3
Y k(l)+(c)
w i- J
(HY-10)
Nov. 80 HY-17
Arthur D Little Inc
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in which:
w = apparent velocity of capillary rise; (cm/sec)
m
pore size distribution index; (-)
3 3
n = effective medium porosity; (cm /cm )
c = pore disconnectedness index; (-)
K(l) = saturated effective hydraulic conductivity (cm/sec) ,
k(l) = spatial average effective soil permeability at
2
saturation; (cm )
¥(1) = saturated matrix potential; (cm)
Z = depth to groundwater table; (cm)
a = surface tension of pore liquid; (dynes/cm)
<|> = pore shape parameter; (-)
3
Y = specific weight of liquid; (dynes/cm )
= dynamic viscosity of pore fluid ; (poises)
w
Infiltration [TOR,p.726,eq.(42);p.723,eq.(16)]:
.n1'2
(HY-U)
= 10(0.66 + 0.55/m + 0.14/m2) (HY-12)
Nov. 80 HY-18
-------
where :
f. = apparent infiltration velocity; (cm/sec)
n = soil effective porosity; (-)
= infiltration diffusivity function; (-)
d = c - 1 - (1/m); [WRR,p.723,eq.(12)]
Exfiltration [WRR,p. 727, eq. (44)] , simplified for no vegetation:
f«>s> - S - + « (HT-13)
e>o
where:
fg = apparent exfiltration velocity; (cm/sec)
e = dimensionless exfiltration diffusivity; (-)
Percolation to Water Table [WRR,p.729,eq. (62) ] :
v(sQ) = K(l)soC - w (HY-1A)
where:
v = apparent percolation velocity (cm/sec)
Nov. 80 HY-19
Arthur D Little Inc
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3.3.2.4 Annual Infiltration and Surface Runoff
The principal assumptions made are [Eagleson, 1977]:
(1) No evaporation from surface storage at any time
(2) No infiltration from surface storage following cessation
of precipitation
(3) No surface inflows from outside region
(A) Soil moisture is uniform at s at the beginning of each
storm
(5) Precipitation intensity, i, and duration, tr, are
statistically independent.
The probability density function of storm surface runoff is
determined and gives the:
Frequency of Flood Volume [WRR,p.746,eq. (72) ] :
v r(o + l)/o° (HY-15)
ii*
Annual Average Surface Runoff. E[RcAl ; [WRR,p.746,eq. (68) ] :
° (HY-16)
in which [WRR,p.746,eq. (69) ] :
T = recurrence interval of flood of depth, R.
6ir6m
Nov. 80 HY-20
Arthur D Little Inc
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and [WRR,p.746,eq.(70)]:
G = oKd) [1 + s ° ] - aw (HY-18)
where:
n = mean storm depth, nu ; (cm)
6"1 = mean storm duration, mtr ; (sec)
and
a"1 = mean storm intensity = mH/mtr» (cm/sec)
For representative soil properties Equation HY-16 illustrates the
range of observed surface runoff values. A graphical presentation of
the surface runoff function is shown in Figure HY-3.
Net Infiltration
Based upon Equation HY-16 and because [WRR,p.747,eq. (7A) ] :
(HY'19)
the expected seasonal net infiltration as a function of precipitation
equals [above equation and WRR,p.746,eq. (68) ] :
r(o + l)/o° = 1-5
This also represents the fraction of all storms which do not produce
surface runoff.
Nov. 80 H*'21
Arthur D Little, Inc
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O.I
h = 0
t-
G
E[PA]
.. f .
-2.7
r
I
5nT?2K(l)>F(l)(l-s0)
G =
WET SOIL
0.
Source: [WRR,p.7A6, Figure 6]
Figure HY-3
Surface Runoff Function [Eagleson, 1979]
Nov. 80
HY-22
Arthur D Little, Inc
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3.3.2.5 Potential Evaportranspirat ion
The "potential" evapotranspiration of an area can be estimated based
on the following assumptions [Eagleson, 1977]:
(1) The energy balance equation may be time averaged by
replacing variables by their time averages
(2) The average rates of energy advection and storage are zero
(3) Difference between surface and atmospheric temperatures
may be neglected in estimating net outgoing longwave
radiation.
The modified Penman energy balance equation can be used to estimate
the average rate of potential evapotranspiration.
, (1 - A) - q. + H
in which:
q\ = average rate of insolation (ly/min)
q, = average rate of net outgoing longwave
radiation (ly/min)
H = average sensible heat flux residual (ly/min)
A = shortwave albedo of surface
3
p = mass density of evaporating water (g/cm )
e
L = latent heat of vaporization (cal/g)
e
Y/A = atmospheric parameter (a function of temperature)
Empirical values of q". , q"b and H are presented by Eagleson (1977)
in a form suitable for practical use. (Table HY-1) . The potential
evapotranspiration can be either an input variable to SESOIL or can
be estimated using the above equation.
HY-23
Arthur D Little. Inc
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TABLE HY-1
Observed Values of Annual Potential Evapotranspiration
Observed
Calculated
^ocation Ref. ^
in/vr
Mesllld. N.M.
Pecos, N.M.
Sangamon R. , 111.
Green K. , Ky.
Tallapuosti R, Cj.
Had R. . Ohio
Skunk R. , lova
W.Fork.White R..Ko.
K. Platce R., Neb.
Black R.. Vis.
Cyprus Crk., Tex.
Wagon Uhcel Cap, Col.
Herrlnac R. . Ma.
Vest R. , Vt.
•Lake Cochltuate^ln.
Swift R., Ma.
* Phoenix, Arlx.
*Davls. Cal.
•Fresno, Cal.
•Grand Junction, Ci-l
•Boise, Idaho
•Dodge C: ty, Kans.
•Clascov, Hon.
•Great F.ills, Men
•tly. Ncv.
•BisnarcV , N.Dak.
•Stillwater, Ck.
•Astoria, Ore.
•Hedford. Ore.
•Rapid Cltv , S.I>.
•Brownsville, Tex.
•Fort Worth, lex.
•MidlanJ, Tex.
•Spokane, Wash.
•Lander, Wyo.
50
50
50
50
50
50
50
50
50
50
50
50
50
50
50
50
(5
45
i5
45
:5
'.5
-5
45
«'i
i5
45
i5
i->
4!»
•-5
45
'.'i
-j
ij
34.0
35.3
29.2
31. i
33.0
25.8
27.0
31.0
23.8
22.2
36.2
15.6
21.5
21.5
23.2
23.1
71.6
50.0
60.0
35.6
33.4
62.6
38 0
35.0
66.0
34.1
57.0
20.0
33.0
40.6
56.0
57.2
71 3
38.4
35.0
; 1
•N
32.27
35.57
40.02
37.90
32.50
40.00
40.70
37.00
42.00
43.93
32.00
37.77
43.20
42.98
42.50
42.50
33.43
38.37
36.77
39.12
43.57
37.77
48.22
47.48
39.28
48.77
36.13
46.15
42.37
44.03
?5.90
32.82
31. "3
47.62
42.80
A r
0.26
C.26
0.26
0.26
0.26
0.26
0.26
0.26
0.26
0.26
0.26
0.40
0.30
0.30
0.30
0.26
0.05
0.05
0.05
0.05
0.05
0.05
0.05
0 05
0.05
0.05
0.05
0.05
n.05
0.05
0.05
0.05
0.05
0.05
0.05
V
14.6
13. B
11.5
13.1
15.4
10.8
9.4
13.4
9.0
8.0
17.9
5.3
7.6
7.6
10.7
8.4
21.3
15.7
16.8
11.5
10.5
12.7
5.3
7.2
6.7
5.2
15.6
10.3
11.7
e.i
.'3.2
18.6
17.7
8.5
6.9
K fc
0.18
0.18
0.34
0.46
0.36
0.40
0.34
0.33
0.30
0.40
0.20
0.25
0.47
0.67
0.33
0.33
0.20
0.30
0.25
0.30
0.35
0.27
0.25
0.25
0.28
0.30
0.35
0.50
0.50
0.35
0.40
0.40
0.25
0.40
0.25
S 5
0.53
0.45
0.70
0.73
0.77
0.72
0.70
0.72
0.60
0.74
0.75
0.60
0.78
0.78
0.70
0.70
0.63
0.52
0.43
0.34
0.37
0.50
0.54
0.50
0.36
0.63
0.50
0.80
O.bfi
0.56
0.77
0.63
0.50
0.42
0.42
/*
n/sec
4.2
6.1
3.8
3.0
2.3
3.0
6.0
6.0
6.2
3.5
S.O
3.8
2.5
2.5
4.9
3.9
2.7
3.9
2.8
3.4
3.8
6.0
6.8
5.9
4.7
6 4
5.5
4.0
2.2
4.6
5.2
4.8
4.5
3.9
3.2
Ta X '0
mln/cn
5.5
6.4
4.2
6.6
8.7
8.6
4.3
4.6
7.0
7.9
3.5
7.2
7.0
7.0
3.7
5.9
4.8
5.2
3.4
5.0
3.7
1.8
3.0
3.9
5.4
3.2
1.8
-
-
3.7
3.9
4.6
2.0
4.5
14.3
* Water surface
1 Lbtirnted f rcr •11.1*
A • 0.26 choscr IIM rectal =uilac<.s> (slightly preu.er for seasonal snow or
A • 0.05 chuser icr water hurt BITS
J Average annual • iljv Uilcii I"rcr 't.n.i»p.,l Weather Service Clir.Btologic.il Sumnr\ at
nearest scaticn
11 Fron CliratolCRicil Si-rrar; at nearest station
• Awerapc frora Cli -.-,:. lc-iic.il Surrar .11 :>r.-.r«'.t station
Source: P. Eagleson (1977)
Nov. 80
HY-24
Arthur DLittklnc
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3.3.2.6 Annual Evapotranspiration
The previous background and the following assumptions lead to the
estimation of the "expected annual" evapotranspiration E[ETA]:
(1) No evaporation except from water which has first
infiltrated
(2) No effect of vegetation in bringing soil moisture to
surface
(3) Soil moisture is uniform at s at the beginning of each
interstorm period
(A) Variance of average annual rate of potential evapotran-
spiration is negligible
(5) e~p » w .
The annual average evapotranspiration E[ETA] is given by [WRR,p.736,
eq.(A5)]:
J(E) = !-[! + 21/2E]e~E + (2E)1/2 T [f ,E] (HY-22)
"PA
in which [WRR,p.762,eq.(70),(71)]:
2&nK(lWl) (d)
s
,— ,.2 o
irm(e - w)
P
/TTW
(HY-
where:
= mean time between storms, mtu» (sec)
= exfiltration parameter
Nov. 80 HY-25
Arthur D Little, Inc
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3.3.2.7 Groundwater Runoff
The annual groundwater runoff is defined as the "net" groundwater
recharge from the unsaturated soil zone, namely the percolation flow
reduced by the capillary rise flow.
The following assumptions are associated with the potential seasonal
groundwater runoff estimate:
(1) Percolation to water table is steady throughout the wet
season at value determined by the average soil moisture,
s , and is zero during the dry season
(2) Capillary rise from the water table is steady throughout
the entire year at the rate given by a dry surface
(3) Water table elevation, z = Z, is constant .
The annual non-dimensional average groundwater runoff, E[R .] is
gA
given by [WRR,p.751,eq.(20)]:
E[R ] m
n g = - sc - -S- (HY-24)
"PA
Assuming that no groundwater storage occurs within a season, the total
groundwater runoff will recharge adjacent surface waters.
Nov. 80 HY-26
Arthur D Little Inc
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3.3.2.8 Annual Hydrologic Water Balance
The annual water budget (HY-4) is given by:
E[IA(so)]
+E[RgA(so)]
(HY-25)
Equations HY-20, HY-22 and HY-24 contribute to the first-order dimension
less water budget equation [WRR,p.766,eq.(6)]:
Groundwater:
Infiltration Recharge Loss
c Tw
PA S° " PA
A A
(HY-26)
Precip. Surface Runoff Evapotran- Groundwater Runoff
spiration
A graphic presentation of function J(E), equation HY-22, is shown in
Figure HY-4 [WRR,p.737, Figure 5].
The above equation is used to define the dependent variable, s ,
which can be used, in turn, to define the separate terms of the water
budget in terms of the independent climate and soil variables and para-
parameters.
The annual water yield, Y , is determined in this way as
A
W - RBA(8o(PA» + VW = *(PA>
(HY-27)
and is used to transform the CDF of annual precipitation tYA(pA)] into the
CDF of annual yield according to
Prob
•"PA
-urn
= e
a (urn )v
I I «• ' Til
v=l V'
nTg 1(z)]
(HY-28)
Nov. 80
HY-27
Arthur D Little Inc
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Figure HY-4
Base Soil Evaporation Function (w/e «1)
P
Source: Eagleson (1978); WRR,p.737, Figure 5
Nov. 80
HY-28
Arthur D Little, Inc
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3.3.2.9 Depth Dependent Infiltration
In the previous sections the infiltration (I) is defined as the total
depth of rainfall infiltrating the ground surface (see Figure HY-4.1).
Consequently the groundwater runoff (R ) is defined as the excess of
o
water in the soil column percolating the ground, namely reaching the
saturated soil zone.
SESOIL is designed to estimate pollution distribution in the upper, middle
and lower unsaturated soil zone of the compartment. It is, there-
fore, required to have a seasonal averaged estimate of the infiltration
at a depth z of the soil column as shown in Figure HY-4.1. This estimate
(Iz) is required for both the annual and the monthly simulations of the
pollutant transport.
Based upon the geometry of the soil compartment we may make the assumption
that the annual (A) — section 3.3 of this appendix — and monthly (M) ~
section 3.4 of this appendix — variations are given by:
IZ(A,M) = R (A,M) + di • tana =
d,
= R (A,M) + 1 [I(A,M) - R (A,M)] (HY-28.1)
B u 1 °
where du and d^ the depths of the upper and the lower unsaturated soil
zones respectively. The Iz values estimated by the above equation are
employed by the pollutant transport routines, Appendix PT, equations
PT-6, PT-13, PT-28 and PT-31.
The layered averaged intrinsic permeability of the compartment is approxi-
mated to
kz = (du + dM + dL)/(du/ku + dM/kM + W (HY-28.2)
and each infiltrating quantity (depth) is given by
I(A,M) = Iz(A,M) (HY-28.2)
where
, 2 - 3 • kz (HY-28.2)
Dec. 80 HY-28.1
Arthur D Little Inc
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'
T3.fA,H) *
Uuoet
T
7/7777^7
Figure HY-4.1
Depth Dependent Infiltration in the Soil Column
Dec. 80
HY-28.2
Arthur D Little Inc
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3.4 Model Variables/Parameters
The full set of twenty (20) parameters and variables governing the
previous equations are:
nip = mean annual precipitation; (cm)
E[Ep.] = mean annual potential evapotranspiration; (cm)
e = mean annual rate of potential evapotranspiration; (cm)
P
m = 6 = mean storm duration; (days)
m , = B~ = mean time between storms; (days)
m.. = n = mean storm depth; (cm)
m. = a~ = mean storm average intensity; (cm/sec)
m = mean length of rainy season; (days)
T = duration of capillary rise from watertable ; (days)
k(l) = spatial average effective soil permeability at
2
saturation; (cm )
T = normal annual temperature of surface soil moisturn; (°c)
3.
c = soil conductivity index; (-)
m = soil matrix potential index ; (-)
d = soil diffusivity index; (-)
3 3
n = effective soil porosity; (cm /cm )
*(1) = spatial average soil matrix potential at saturation;
(cm)
Z = depth to watertable; (cm)
$ = exfiltration diffusivity function: (-)
. = infiltration diffusivity function; (-)
s = spatial and temporal average soil moisture within the
soil boundary layer; (-)
Nov. 80 HY-29
Arthur D Little. Inc
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Introducing a twenty-first parameter,
m = mean number of storms per season, (//)
we have ten supplementary relations in addition to the water budget
equation (HY-26) :
m.. = TCLp./m (definition)
m = m (m ,+ HI ) , m > 1 (definition)
T v tb tr v —
m. = m-j/m (assuming independence of i and tr)
E[EpA] = mvmtbep (definition)
d = (c + l)/2 (semi-empirical) (HY-29)
m = 2/(c-3) (semi-empirical)
T = one year (definition)
I'd) = nn,k(l), T); t^R, P- 724, eq. (17)]
<(.i = i(d,so) (Figure HY-5)
e = <()e(d) (Figure HY-6)
To solve the water budget relation for the dependent variable,
s , we must therefore specify the values of ten parameters (i.e., 21
variables minus 11 equations). Thus:
(1) INPUT parameters to the model are:
Soil system:
k(l), c, n, fflf and Z (HY-30)
Climate System; Five independent parameters may be chosen
from the set of six:
"PA' V V mtr' V mT
(HY"31)
Nov. 80 HY-30
Arthur D Little Inc
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FOR INTEGER VALUES OF d
Figure HY-5
Dimensionless Infiltration Diffusivity
Source: [Eagleson, TOR,p.727, Figure 9]
Nov. 80 HY-31
Arthur D Little, Inc
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X
V
FOR INTEGER VALUES OF d
n
•o
3 -—
2LE*<
10
10"
fre (d!
Figure HY-6
Dimensionless Exfiltration Diffusivity
Source: [Eagleson, WRR,p.727, Figure 10]
Nov. 80
HY-32
Arthur D Little, Inc
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(2) OUTPUT parameters from the model are:
so' PA' ETA' SA' RSA' RgA'
An example of input and other climatic data for sub-humid (Clinton,
Massachusetts) and an arid (Santa Paula, California) climate-soil
system is shown in Table HY-2.
Representative independent soil properties nominal values
covering a range of observations (Eagleson 1977) are given in
Table HY-3. It is important to notice that there is no unique
association of the particular c and n values with the tabulated
value of k(l) for each soil. Derived (Eagleson 1979) climate-soil
parameters for indicated climatic and soil input are given, as an
example, in Table HY-4. The latter values are derived using
Table HY-3 values.
Note: Model users should validate their model output based upon
"water balance" data from a given site, and they should never rely
upon the derived parameters of Tables HY-3 and HY-4. These tables
should not give the impression, for example, that they contain all
one needs to know about soil. That is, if the soil is clay it has
the properties of the first column of Table HY-3. This is not the
case of course, since soil stratification properties are of paramount
importance and may drastically alter the k(l), n and c values of a
site. The soil properties are critical to the moisture fluxes and
are tremendously variable spatially. Use of point measured soil
properties can yield results of only local (and hence not really
averaged) character.
HY-33
Arthur D Little Inc
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TABLE HY- 2
Independent Soil and Climate Parameters
for a Sub-Humid and an Arid Climate Soil System
Location
Parameter
n
c
\
¥P
mtr
m_
"V
mH
Z
Units
-
cm2
cm
cm/day
days
days
-
cm
m
Clinton, Mass.
0.35
2.8X10"10
10
94.1
0.15
0.32
365
109
1.0
00
Santa Paula , Ca .
0.35
1.2X10"9
51)
54.4
0.27
1.4
212
15.7
3.0
oo
8.4
13.8
"tb
days
3.0
ic - 0.50
h0 cm 0.1
oj day"1 0.30
Source: Eagleson [WRR,p.717, Table 1]
comment on Table HY-3.
Nov. 80
HY-34
10.4
0.25
0.1
1
0.084
Arthur D Little Inc.
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TABLE HY-3
INDEPENDENT SOIL PROPERTIES1' FOR VARIOUS SOIL TYPES
Property
(Variable)
k{1) [cm2]
n
c
Soil Type2)
Clay
1X10"10
0.45
12
Clay-Loam
2.8X10'10
0.35
10
Silty-Loam Sandy-Loam
1.2X10'9 2.5X1
0.35 0.25
c3) 4
0-9
Source: Eagleson 1977, p. 256.
'See limitation discussion in previous pageS.
^Derived by using Table HY-4 values and the
corresponding .environments.
^Personal communication with Eagleson. In his
publications c(silty-loam) = 6; however, later
investigations indicated c = 4.5-5.5. An average
value c = 5 is given here.
Nov. 80
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Arthur D Little Inc
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TABLE HY-4
DERIVED CLIMATE-SOIL PARAMETERS
FOR A CLIMATE AND RELATED SOIL TYPES (OF TABLE HY-2)
Climate: a =1.5
e = 7
mT = 365
T = 15
a
x 104 sec/m ;
x 10"3 hr"1 ;
days ;
°C
6 = 10"1 hr"1
m.. = 2.54 cm
m = 75 events
Derived Climate-Soil Parameters
Derived Parameter
m
d
Yd), cm
K(l), cm/sec
*e(d)
^(d.O)
*±(d,l)
G(0)
G(l)
a(0)
a(l)
F(a(0) +1)
r(a(l) +1)
ocor°<0>
1/2
S.(0), cm/ sec ' ]
1 1 1">
S.(l), cm/sec '
Clay
0.222
6.5
25
8.2 x 10"6
0.0385
0.122
0.6
0.0621
0.124
0.432
0
0.886
1
1.44
L.04 x 10~2 1
0
Clay-Loam
0.286
5.5
19
2.32 x 10~5
0.0494
0.140
0.6
0.174
0.348
0.482
0
0.886
1
1.42
.27 x 10~2
0
Silty-Loam Sandy-Loam
0.667 2
3.5 2.5
166 200
9.94 x 10~5 2.08 x 10~4
0.0920 0.1430
0.194 0.240
0.6 0.6
0.746 1.560
1.490 3.120
1.340 1.220
0 0
1.200 1.110
1 1
0.68 0.79
5.97 x 10"2 5.15 x 10"2
0 0
1/2
0
Se(0), cm/sec
, cm/sec1/2 4.54 x 10~3 5.82 x 10~3
3.19 x 10
-2
3.08 x 10
-2
Source: Eagleson [1978, 1979]
Nov. 80 HY-36
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3.5 Water Balance Sensitivity
Equation HY-26 and its component equations were used by Eagleson
(1979) in studying the sensitivity of the model to variation of the
climatic or soil parameters. For the climatic parameters of Table HY-2
the sensitivity of the average annual water budget components is presented
as a function of the soil permeability and soil porosity in Figures HY-7
and HY-8 for both locations, Clinton, Massachusetts and Santa Paula,
California.
According to Eagleson, by comparing the two columns of Figure HY-7
we see contrasting behavior only in evapotranspiration and soil moisture.
Beginning with the former, we see insensitivity of ETA to soil proper-
ties in the sub-humid climate except when the soil gets very permeable.
For the arid climate, however, E_. is sensitive to the soil properties
over their full range.
In the humid case, the supply of water is adequate and the soil
moisture will be largest where the permeability readily admits water
(and holds it against gravity). This requires a small a which occurs
for small k and large m (i.e., small c).
In the arid case where the evapotranspiration is controlled by the
moisture supply to the surface, s will be largest where the moisture
movement to the surface, as given by E, is smallest. This will occur
for small k(l) and large d (i.e., large d).
The runoff behavior is qualitatively the same in both climates.
For small k(l), the total yield is predominantly surface runoff because
the water cannot enter the soil. This component increases with c due
Nov. 80 HY-37
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•««.•. ?»
*e
O CLIMATE
-------
I'"0'"
a CLINTON CLIMATE
t CLINTON CLIMATE WITH SANTA PAULA
Figure HY-8
Effect on Annual Budget Due to
Decreasing Mean Annual Precipitation
Source: Eagleson (1979)
Nov. 80
HY-39
Arthur D Little, Inc
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to decreasing permeability and it decreases with increasing k(l) due
to increasing permeability. The groundwater component also increases
with k(l). The "saddle" in the Santa Paula groundwater component with
increasing c results from the behavior of the factor s where s is
o o
less than one and is increasing with c.
For additional information regarding the sensitivity analysis the
reader is referred to the original publication of P. Eagleson [WRR,
p.749].
Nov. 80 HY-40
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3.6 Subroutine HYDROA
3.6.1 Equation Summary
The water balance model, as presented previously, has two distinc-
tive working-steps:
(1) Based upon climatic data, the soil moisture, s , is
determined;
(2) Based upon the soil moisture value, s , any desired
seasonal water balance component is obtained.
Therefore:
(1) The soil moisture, s , is estimated by the first order
conservation equation
Groundwater:
Infiltration Recharge Loss
J(E) + . - - CBY-32)
"PA "PA ° "PA
Precip. Surface Runoff Evapotran- Groundwater Runoff
spiration
in which:
G = f K(l)[l + S(jC] -
-------
J(E) = l-( + VT • E) • e~ + ^2E • r[3/2,E] (HY-35)
w = K(l) [l+(mc-D] [ni)/Z]mC (HY-36)
2BnK(imi)<|> (d) ...
E -- ^ - s d+2 (HY-37)
/~ \ 2 o
irm(e -w)
The values of any desired seasonal water balance component are
estimated by substituting a value for s in Equations H-32 through H-36,
namely for:
Infiltration
I /P = i . e'" F(o + Do'0 (HY-38)
A A
Surface Runoff
R /P = e-G~2a p(o + l)a"° (HY-39)
sA A
Evapotranspiration
ETA/PA = J(E) (HY-40)
Groundwater Runoff
mTK(1) c Tw
R /P —= c - —
RgA/PA- PA So PA
Annual Yield
YA/PA " -^ ^ " i-EpA^A
A A P. PA A
Nov. 80 HY-42
Arthur D Little Inc
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Precipitation
PA = E[EpA] J(E) + mT K(l) sQC - T • w
1 -
where: £= e 2o.r(o+l)
Equation HY-43 is another form of the water balance equation HY-32,
that is employed in the step-by-step calculation procedure, section
3.6.3.
Nov. 80 HY-43
Arthur D Little Inc
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where:
E[ ] = expected value of [ ]
T( ) = Gamma function of ( ) (see Table HY-5)
E[E ] = long-term expected (average) annual
i. C\
potential evapotranspiration (cm)
a. = average annual precipitation (cm)
G = gravitational infiltration parameter
(Equation HY-33)
o - capillary infiltration parameter (Equation HY-34)
J( ) = evaporation function (Equation HY-35)
E = evaporation parameter (Equation HY-37)
w = apparent velocity of capillary rise from
water table (cm/sec)
c = pore disconnectedness index = ln[K(s )/K(l)]/lns
o o
T = time (year)
m = long-term average length of annual rainy season (days)
K(l) = saturated effective hydraulic conductivity
(cm/sec)
s = long-term average effective soil moisture
o
concentration in the unsaturated soil zone
a = reciprocal of mean storm intensity = m.
(sec/cm)
Nov. 80 HY-44
Arthur D Little Inc
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Table HY-5
Values of the Gamma Function
1.00
1.01
1.02
1.03
1.04
1.05
1.06
1.07
1.08
1.09
1.10
1.11
1.12
1.13
1.14
1.15
1.16
1.17
1.18
1.19
1.20
1.21
1.22
1.23
1.24
1.25
1.26
1.27
1.28
1.29
1.30
1.31
1.32
1.33
1.000
0.994
0.989
0.984
0.978
0.974
0.969
0.964
0.960
0.955
0.951
0.947
0.944
0.940
0.936
0.933
0.930
0.927
0.924
0.921
0.918
0.916
0.913
0.911
0.909
0.906
0.904
0.903
0.901
0.899
0.897
0.896
0.895
0.893
1.34
1.35
1.36
1.37
1.38
1.39
1.40
1.41
1.42
1.43
1.44
1.45
1.46
1.47
1.48
1.49
1.50
1.51
1.52
1.53
1.54
1.55
1.56
1.57
1.58
1.59
1.60
1.61
1.62
1.63
1.64
1.65
1.66
1.67
0.892
0.891
0.890
0.889
0.889
0.888
0.887
0.887
0.886
0.886
0.886
0.886
0.886
0.886
0.886
0.886
0.886
0.887
0.887
0.888
0.888
0.889
0.890
0.890
0.891
0.892
0.894
0.895
0.896
0.897
0.899
0.900
0.902
0.903
1.68
1.69
1.70
1.71
1.72
1.73
1.74
1.75
1.76
1.77
1.78
1.79
1.80
1.81
1.82
1.83
1.84
1.85
1.86
1.87
1.88
1.89
1.90
1.91
1.92
1.93
1.94
1.95
1.96
1.97
1.98
1.99
2.00
O.<»05
0.907
0.909
0.911
0.913
0.915
0.917
0.919
0.921
0.924
0.926
0.929
0.931
0.934
0.937
0.940
0.943
0.946
0.9^9
0.952
0.955
0.958
0.962
0.965
0.969
0.972
0.976
0.980
0.984
0.988
0.992
0.996
1.000
Source: Eagleson, 1977
HY-45
Arthur D Little Inc
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= effective soil porosity = volume of active
voids/total volume
= reciprocal of mean storm depth = HL. (cm )
= saturated soil moisture potential (cm)
[equation HY-10]
°w r n ,1/2 ^n-O.ee-O.SS/m-O.U/m2 )1/2
= Y~ kTlT ^
w
o = surface tension of pore water (dynes/cm)
w
3
•y = specific weight of pore water (dynes/cm )
w
k(l) = spatial average saturated effective intrinsic
permeability of soil (cm) = K(!)UW/YW (see
Table HY-3)
= dynamic viscosity of pore fluid (poises)
w
(> (
<(> (d,§0)= dimensionless infiltration diffusivity (see
Figure HY-5)
<5 = reciprocal of mean storm duration (days )
E mt"r
m = 2/(c-3) pore size distribution index (Brook,
R.H., et al; 1964)
B = reciprocal of mean interstorm period = mtr
(ft (d) = dimensionless exfiltration diffusivity (see
Figure HY- 6 )
e" = potential rate of evaporation from a bare
soil surface (cm/sec)
Nov. 80 HY-46
Arthur D Little Inc
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= (c + l)/2 = diffusivity index
f\
= e~ a • p(o + l)a~°; surface runoff function
(see Figure HY-3)
With Equations HY-32 through HY-42 the average seasonal water
balance can be displayed graphically in a variety of ways, one of which
is illustrated in Figure HY-10 for an annual water cycle.
Nov. 80
HY-47
Arthur Dbttklnc
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LU
13
Z
Q
_J
LD
2
POTENTIAL
EVAPOTRANSPIRATION
J
RgA
GROUNDWATER
RUNOFF
EVAPOTRANSPIRATION
EVAPOTRANSPIRATION DEFICIT
ANNUAL PRECIPITATION, PA
Figure HY-9
Climatic Influence of Annual Water Balance
Source: Eagleson (1979)
HY-48
Arthur D Little, Inc
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3.6.2 Input/Output Variables
INPUT data to HYDROA are categorized into the three groups of:
(1) Climatic data:
either: ep (cm/day)
or: the data set
S (fractional)
A (-)
NN (fractional)
(2) Storm data:
T = 365 (days)
(cm)
m (day)
m (*)
v
m (days)
(3) Soil data:
k(l) (cm2)
c (-)
n (-)
Above variables are stored in arrays CLIMA1, CLIMA2 and SOIL1 of the
SESOIL Data Base; see Appendix DF, Data Files.
OUTPUT data from HYDROA is the data set.
HY-49
Nov. 80
Arthur DLittklnc
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so
PA=mPA
IA (cm)
ETA (cm)
RsA (cm)
V (cm)
Y (cm)
Nov. 80 HY-50
Arthur DUttlelnc
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3.6.3 General Calculation Procedure .
The calculation of the annual water balance has the following
major steps.
(1) Estimation of initial parameters
1.1 Estimation of climate parameters
1.2 Estimation of soil parameters
1.3 Estimation of potential evapotranspiration
1.4 Estimation (or input) of annual evapotranspiration
(2) Solution of the annual water balance equation HY-32
2.1 Solution of the water balance equation HY-32 (i.e.
estimation of s ) is best accomplished by employing
an iterative procedure for s increments, that is by
assuming an SQ and consequently estimating P via
eq. HY-43.
2.2 Estimation of water balance components for the assumed
s value.
o
2.3 Comparison of estimated P versus assumed rL.
to obtain the solution.
Nov. 80 HY-51
Arthur DLttleJnc
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4.0 LEVEL2 - MONTHLY "ESTIMATED" HYDROLOGIC CYCLES
4.1 General
Subroutine HYDROM estimates the monthly (M) hydrologic cycle components
of the soil compartment. HYDROM is based upon the theory of HYDROA
discussed in the previous section.
4.2 Definitions
See Section 3.2.
4.3 Monthly Mathematical Analysis
4.3.1 Principal Assumptions
The principal assumptions made are:
(1) The assumptions made for the annual warer balance
(see Section HY-3.3.1); and
(2) The response of the environment (eg. moisture content)
at the end of a month with "constant" and "continuous"
rain MPA is "similar" to the response of this environ-
ment at the end of a year with constant and continuous
rain of the 12 (MPA). Mathematical Linearity of
Processes (Dooge 1973) is assumed.
4.3.2 Theoretical Overall Approach
To reduce the averaging time of a simulation from a year to a
month or shorter, traditionally modelers develop a numerical, finite-
difference solution to the basic equations, thus "scaling down" the
temporal resolution of equations.
To by-pass the numerical discretization difficulties of the literature,
in SESOIL the temporal resolution of the equations is "scaled up."
That is, the monthly subroutine HYDROM employs subroutine HYDROA which
is now run 12 times in a year for 12 "typical" years. Each typical
year has, for example, an annual precipitation that equals 12 times
the precipitation of the month to be simulated. At the end of the
"typical" year simulation, the annual output variables PA IA> ETA, RSA,
R A are divided by 12 in order to estimate the monthly values of the
Dec. 81 HY-52
Arthur DLittleJnc
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month under consideration, while the annual output value so (moisture
content) is kept at the typical annual year output value. However,
because of the new time resolution issue, the change in soil moisture
storage from month-to-month becomes important. To account for this
moisture budget transfer (from time t-1 to time t) in the entire
column, a moisture storage term As0 = Z-n(so(t)-s (t-1)) has been added
to the denominator of equation (HY-43) to balance (via precipitation) the
deficit or surplus of moisture in the course of the months. The mathe-
matical derivation of this logic can be traced from equation (HY-3)
in conjunction with equation (HY-0) and will be documented in the
future in this section.
In addition to the soil moisture storage issue, the authors had to
retrieve solutions of equation HY-43 when nip =0 (no rain) because in
the original Eagleson theory, when m_ =0, m =0 and in that case many
parameters (eg. a, 6, a, G) tend to «. The designed scheme will be presented
in the revised documentation, but principally when m =o, the a(t-l),
G(t-l) function of a previous time step (t-1) have been used for time
step (t).
Finally the authors have accounted for a "smooth" soil anisotropy along
the soil column by employing the theoretical background given in
Freeze & Cherry (1979, p. 32). Documentation will also be presented
in the near future.
Averaged annual estimates of the soil moisture content (s0) calculated
with both the subroutines HYDKOA and HYDROM, gave an excellent correla-
tion, thus leaving the authors to believe that the accuracy obtained
from HYDROM is satisfactory.
HY-53
Arthur D Little Inc
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4.4 Input/Output Variables
INPUT data to HYDROM are the:
(1) Input data to HYDROA, and
(2) The 12 monthly storm depths m (M); (cm)
Above variables are stored in arrays CLIMA1, CLIMA2 and SOILI
of the SESOIL Data Base; see Appendix DF (Data Files).
OUTPUT data from HYDROM are 12 data sets (one for each month)
SO(M), P(M), KM), RS(M), Rg(M), Y(M)
M = 1 through 12; October through September
This data is stored in array HYDBAL.
HY-54
Arthur D Little Inc
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5.0 MODEL EXTENSION
5.1 General
The hydrologic cycle routines (HYDROA, HYDROM) are based upon on analytic
solution (versus numerical) approach and can be operated for monthly and
annual simulations. The routines employ Eagleson's annual water balance
model, the state of the art in analytic hydrologic research, which
provides excellent theoretical insight to the coupling of the water
balance components. This model is very easy to operate with a minimum
of inputs. In addition the hydrologic cycle routines provide the feature
of not requiring calibration procedure of non-physically based parameters
(i.e. coefficients). Their hydrologic routines are suitable, for the
time being, for:
• Seasonal (i.e. annual or monthly) simulations;
• Omission of snow or ice phenomena;
• Omission of energy and surface moisture storage
in soil processes;
• Omission of vegetal influence on soil moisture
movement;
• Linear superposition of moisture phenomena.
To remove the above constraints and reduce the seasonal period to less
than a month (eg. storm-by-storm event), theoretically, it is necessary
to formulate a finite difference solution to the basic equations.
However, authors have a different approach to this issue, encompassing
the use of the developed monthly routine (HYDROM) and the use of a
finite difference moisture movement model. The latter will be "self-
calibrational" based upon input information received from HYDROM.
For either vegetated or bare soils (but particularly the former), the
effect of surface retained water and of moisture fluctuations to the
fluctuations of the groundwater table is of importance and should be
Included in this model development. In certain climates, such as the
Dec. 84 HY-5b
Arthur D Little, Inc
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Pacific Northwest where the rain is intermittent drizzle with broken
spells of sunshine, this fluctuation can be quite a significant iteii in
the annual/monthly water balance estimates (Personal communication with
Eagleson).
The phenomena of snow pack/melt and interception might be handled by
assuming (in the future, however), in a semi-theoretical way, an increase
(snow melt) or decrease (snow pack, interception) in precipitation.
These water quantities can be separately estimated (see subsequent
sections) and added or subtracted from the unit-term of equation HY-32.
The snow pack/melt phenomenon might be also treated mathematically as
increased "soil permeability," but additional thinking is required for
this approach. A short discussion regarding above processes is given
in the following sections.
5.2 Snow Pack/Melt
Two well known methods for modeling snow pack/melt phenomena are:
(1) the Heat Balance Method; and (2) the Temperature Index, or
Degree-Day Method. The first was developed by the U.S. Army Corps
of Engineers and has been successfully applied in numerous cases.
The Heat Balance Method requires extensive calculations, taking
account of phenomena such as radiation, melt, condensation-convection
melt, rain melt, snow density and compaction parameters, areal
coverage, snow evaporation, snow pack heat and snow pack liquid
water storage. The Temperature Index Method is extremely simple,
but it has been reported to provide estimates which are of the same
accuracy as those of the detailed Heat Balance Method (Novotny, 1976).
SESOIL might employ, for example, the Temperature Index Method,
adopted, however, to SESOIL1S theoretical needs:
S = abs(k *T ) (HY-44)
1Q S a
Dec. 81 HY-56
Arthur D Little, Inc
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in which:
S = snowmelt intensity(cm/day)
T = mean daily air temperature (°C); input variable
O
T <_ 0°C (snow pack), T > 0°C (snow melt)
kg = snowmelt coefficient (cm/°C.day); input variable
abs = absolute value (i.e., S > 0)
m —
When the average daily temperature is below freezing temperature
(i.e., T _<_ 0°C), precipitation becomes snowfall and accumulates as
snow pack providing a minimum runoff. Conversely, when the average
daily temperature is above freezing (i.e., T > 0), the snowmelt
quantity is added to rainfall runoff (if any) for that period.
A simplified calculation procedure might be as follows:
Subtract (when T < 0) or add (when T > 0) the quantity S* = S . P./At
— m m A
from the unit term on the left-hand side of Equation HY-32 (where At
the simulation time step); and use the hydrologic cycle subroutines
as previously described.
5.3 Interception
Interception is a function of the type and extent of vegetation,
land use and meteorologic characteristics (wind, temperature, solar
radiation, precipitation, etc.). In nature, all precipitation is
assumed to enter interception storage until it is filled to capacity.
Water is removed from the interception storage by transpiration, which
may occur even during rain. For, soil interception is modeled as a
"one way" phenomenon, namely as a precipitation volume retained by
vegetation, which for a particular season equals (Novotny et al, 1976);
Ir(A,M) = 2.54 (a + b-(P/2.54))m £ c-P(A,M)/2.54 (HY-45)
Dec. 81 HY-57
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where:
Ir(A,M) = intercepted rainfall; annual, monthly (cm)
P=P(A,M) = average seasonal precipitation (cm);
a,t>friL = constants (Table HY-6)
c = % coefficient of average interception (Table HY-6)
A simplified calculation procedure might be as follows:
Subtract the quantity c of the above equation from the unit pre-
cipitation term on the left-hand side of Equation HY-32 and use the
hydrologic routines (annual, monthly) as described in a previous
section.
6.0 REFERENCES
References of this section only are given in appendix RE.
Dec. 81 HY-58
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TABLE HY-6
Constants a, b, m of the Interception Equation (H-52)
Vegetal cover
Orchards
Ash, In vouds
Beech, in woods
Oak, in woods
Kaple, ici woods
Willow, shrubs
Hemlock and pine woods
0.04
0.02
•0.04
0.05
0.04
0.02
' O.OS
0.18
0.18
0.18
0.18
0.18
0.40
0.20
1.00
1.03
1.00
1.00
1.30
1.00
o.sot -,...
Beans, potatoes, cabbage
and other snail hilled
crops 0.02h O.lSh 1.00
Clover and meadow grass O.OOSh O.OSh 1.00
Forage, alfalfa, vetch,
aillet, etc. O.Olh O.lOh 1.00
Sea 11 grains, rye, wlic.it.
barley O.OOSh O.OSh 1.00
Corn O.OOSh O.OOSh 1.00
* This approximation is reasonable for the sole purpose of using
the equation (HY-45); I = c.P(A,M)/2.54
** The symbol h refers to the height of the plant (h in m)
Source: Novotny, et al, 1978.
Dec. 80 HY-59
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SW • soil washload
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APPENDIX SW
TERRESTRIAL SOIL WASHLOAD SIMULATION
1.0 INTRODUCTION
2.0 "ANNUAL" SEDIMENT YIELD SIMULATIONS
2.1 General
2.2 Universal Soil Loss Equation (USLE)
2.2.1 General
2.2.2 Rainfall and Runoff Factor (R)
2.2.3 Soil Erodibility Factor (K)
2.2.A Topographic Factor (LS)
2.2.5 Cover and Management Factor (C)
2.2.6 Support Practice Factor (P)
2.2.7 Sediment Delivery Factor (D)
2.3 Subroutine SEDIMA
2.3.1 General
2.3.2 Input/Output Parameters
2.3.3 Parameter Units
2.4 Numerical Example
2.5 Discussion
3.0 "MONTHLY" WASHLOAD SIMULATIONS**
3.1 Objective
3.2 Background/Acknowledgments
3.3 Overview of the Monthly Washload Model
3.4 Model Mathematics
3.4.1 Basic Concepts and Equations
3.4.2 Modeling Issues
3.4.3 Sediment Characteristics
3.4.4 Overland Flow Element
3.4.5 Channel Element
3.4.6 Impoundment Element
3.4.7 Discussion
3.5 Subroutine SEDIMM
3.6 Sensitivity Analysis of SEDIMM
3.7 Conclusions
4.0 REFERENCES
SW-4
SW-5
SW-5
SW-6
SW-9
SW-13
SW-17
SW-31
SW-33
SW-35
SW-35
SW-35
SW-35
SW-37
SW-39
SW-41
SW-41
SW-41
SW-4 3
SW-47
SW-47
SW-52
SW-53
SW-58
SW-64
SW-68
SW-68
SW-70
SW-70
SW-70
SW-71
**
n
This subroutine is not operational in this version; therefore, little
emphasis has been placed in its accurate documentation.
Information abstracted from Foster et al (1980). The authors appreciate
his contribution (see sections 1.4 Acknowledgements and SW-3.2 of this
appendix).
SW-01
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LIST OF FIGURES
Figure No. • page
SW-1 Average Annual Rainfall Erosion (R) Values SW-7
SW-2 Annual Rainfall Erosion (R) Values, Hawaii SW-8
SW-3 K-Values SW-12
SW-4 LS-Values SW-1A
SW-5 Delivery Ratio Relationship to the Watershed Size SW-34
SW-6 Relation of Sediment Delivery Ratio to Storm
Characteristics SW-34
SW-7 Typical Field Elements SW-40
SW-8 Schematic Representation of Typical Field Systems
in the Field-Scale Erosion/Sediment Yield Model SW-45
SW-9 Flow Chart for Detachment-Transport-Deposition
Computations Within a Segment of Overland Flow
or Concentrated Flow Elements SW-48
SW-10 Schematic Representation of Convex Slope Profile
for Overland Flow SW-63
SW-02
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LIST OF TABLES
Table No.
SW-1 Computed K Values for Soils on Erosion
Research Stations
SW-2 Approximate Values of the Soil Erodibility
Factor, K, for 10 Benchmark Soils in Hawaii
SW-3 Values of the Topographic Factor, LS, for
Specific Combinations of Slope Length and
Steepness
SW-4 Estimated Relative Soil Losses from Successive
Equal-Length Segments of a Uniform Slope
SW-5 Adjustment of LS-Factor, Irregular Slopes
SW-6 Ratio of Soil Loss from Cropland to Corresponding
Loss from Continuous Fallow
SW-7 Approximate Soil Loss Ratios for Cotton
SW-8 Soil Loss Ratios for Conditions not Evaluated
in Table SW-5
SW-9 Soil Loss Ratios (Percent) for Cropstage 4
When Stalks are Chopped and Distributed
Without Soil Tillage
SW-10 Factors to Credit Residual Effects of Turned Sod
SW-11 Percentage of the Average Annual El which
Normally Occurs Between January 1 and the
Indicated Dates
SW-12 Mulch Factors and Length Limits for Construction
Slopes
SW-13 Factor C for Permanent Pasture, Range, and Idle
Land
SW-14 Factor C for Undisturbed Forest Land
SW-15 Factor C for Mechanically Prepared Woodland Sites
SW-16 P Values and Slope-Length Limits for Contouring
SW-17 P Values, Maximum Strip Widths, and Slope-Length
Limits for Contour Stripcropping
Page
SW-10
SW-11
SW-15
SW-15a
SW-16
SW-18,19,20
SW-21
SW-2 2
SW-23
SW-24
SW-2 5
SW-2 6
SW-2 7
SW-2 9
SW-30
SW-32
SW-32
SW-03
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LIST OF TABLES (Continued)
Table No. Page
SW-18 P Values for Contour-Farmed Terraced Fields SW-32
SW-19 Summary of Available Sediment Transport Formulas SW-42
SW-20 Possible Elements and Their Calling Sequence
Used to Represent Field-Sized Area SW-46
SW-21 Sediment Characteristics Assumed for Detached
Sediment Before Deposition; Assumed Typical of
Many Midwestern Silt Loam Soils SW-54
SW-22 Equations Employed to Describe Particle Size
Distribution SW-55
SW-23 Assumed Typical Diameters of Particle Sizes
I
SW-24 Equations Employed for Particle Composition of
Sediment Load SW-56
SW-25 Overland Flow Element Equations SW-59,60
SW-26 Dimensionless Sediment Transport Capacity
Equation of S. Yalin [1963] SW-61,62
SW-1
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1.0 INTRODUCTION
The SESOIL terrestrial washload simulation provides a quantitative
seasonal prediction of soil sediment transport because of rainfall
erosion.
Soil washload is the overland sediment transport of fine particles
carried by surface runoff. Nutrients and pollutants can be adsorbed
readily on fine soil particles and carried to receiving water bodies.
In addition, sediment itself is a serious pollutant of surface water
resources. The washload magnitude can be related to the available
supply of solid particles in a watershed.
Washload is usually caused by land erosion and is defined by the
American Geophysical Union (Konrad, et al. 1978) as the part of the
sediment load composed of particles smaller than those found in appre-
ciable quantities in the shifting portion of the streambed. The bed-
load portion is composed mostly of larger particles—sand and gravel—
which originate from gulley and river bank erosion. It does not possess
the high adsorptive capacity characteristic of clay and fine soil
particles and may not be a significant nutrient or pollutant carrier.
Increased awareness of the ecological and financial consequences
of severe erosion and resulting sedimentation on both urban and
agricultural lands has increased the need for better methods of esti-
mation deposition and sediment yield. Section 208 of Public Law 92-500
requires planning Agencies to develop plans for evaluating and con-
trolling pollution, including sediment from nonpoint sources. Prediction
equations for sediment yields are desirable in all these plans.
[Neibling, W.H. and G.R. Foster, 1977.]
The mechanics of washload are very comples and it is impossible to
formulate a realistic "all purpose" mathematical model at the micro-
level, that will account for all variables describing the physics of
transport. However, numerous mathematical algorithms for estimating
sediment yield are available in the literature. The choice of an
algorithm depends on the watershed characteristics, input data and
objectives of the modeling effort, but in general, sediment washload
can be estimated using: (1) empirical models; or (2) theoretically
developed models.
May 81 sw_2
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Well known and widely used empirical models, formulated employing
statistical techniques to measured sediment transport yields, are the
Universal Soil Loss Equation (USLE) developed by the US Department of
Agriculture [Wischmeier, W.H. and D.D. Smith, 1978], and the Raiting
Curves Sediment Method (RCSM) [Novotny e_t _al. ]. Excellent discussions
of such models have been presented in the literature by Novotny
[Novotny, V., 1980] and Foster [Foster, G.R., 198 ].
Theoretically-developed sediment yield models can be categorized
into stochastic yield models [Murota and Hashino, 1969; Woolhister and
Todonivic, 1974], models using kinetic wave theory [Madsen and Grant,
1976] and models using the continuity mass transport equation [Foster
and Meyer, 1972, and Adams, et al., 1976]. It is beyond the scope of
this appendix to present a review of all models, rather an effort is
made to shortly document employed models to performing "annual" and
"monthly" sediment simulation. SESOIL employs: (1) USLE for annual
simulations; and (2) two theoretically developed sediment yield models
for monthly simulations.
May 81
SW-3
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2.0 "ANNUAL" SEDIMENT YIELD SIMULATIONS
2.1 General
Subroutine SEDIMA (Sediment Annual) of the model simulates annual
sediment (soil) losses for a particular area. SEDIMA is employed by
both LEVELO and LEVEL1 SESOIL simulations. Simulations are performed
via the Universal Soil Loss Equation (USLE) as developed and documented
by the US Department of Agriculture. [Wischmeier and Smith, 1978.]
The USLE initially developed for areas (regions) east of the Rocky
Mountains has been applied to the entire United States for both urban
and agricultural areas. The USLE enables planners to predict the
average rate of soil erosion for each feasible alternative combination
of crop systems and management practices in association with a specified
soil type, rainfall pattern, and topography. The equation has been also
applied to construction sites and other non-agricultural uses.
The USLE does not predict deposition, does not estimate sediment
yields from gully, streambank and streambed erosion; it is applicable only
for annual sediment transport predictions mainly originating from small
watersheds subject to sheet and rill erosion. In case the USLE has to
be applied to specific storm events or time periods, less than a year,
two recent reports [Foster, G.R. £t _al., 1977; Oustand, C.A. et al.,
1975] are recommended by the equation developers [Wischmeier and Smith,
1978]. SESOIL, however, does not employ for monthly or after-each-
rainfall-event sediment simulations the USLE; therefore, above issue
is not of concern.
In the following sections a summary of the USLE theory is presented
in order to make this appendix a self-contained document for SESOIL
users. Additional details regarding the USLE are to be found in the
original publication.
SW-A
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2.2 Universal Soil Loss Equation (USLE)
2.2.1 General
The USLE is
A=RKLSCP (SW-1)
Several studies [Roehl, 1962; Denfro, 1975; Novotny, 1980] have shown
that the upland erosion estimated either by an erosion model or extra-
polated from measurements on small plots, does not equal the sediment
nor pollutant yield measured at the watershed outlet. This fact is
applicable to the USLE theory as well. To overpass these differences,
a sediment delivery ratio factor D, was introduced by Novotny [Novotny,
£t _al., 1978] to account for resettling of particulate matter after or
during the overland flow. Thus, the USLE equations is formulated as:
SYA=RKLSCPD (SW-2)
where
SYA = annual sediment yield of basin
A = estimated soil loss by the USLE
R = rainfall and runoff factor
K = soil erodibility factor
L = slope-length factor
S = slope-steepness factor
C = cover and management factor
P = support practice factor
D = sediment delivery factor
Above factors, their units, and their numerical values for practical
application (related to LEVELO and LEVEL1 simulations) are discussed
in the following sections. A numerical example for sediment yield
delivered by an agricultural small watershed in Clinton, Massachusetts
is presented in section 2.4.
SW-5
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2.2.2 Rainfall and Runoff Factor (R)
The factor R encompasses a rainfall erosion index unit factor and
a factor for runoff from snowmelt or applied water where such runoff is
significant.
Data have shown that the rainfall factor used to estimate the
average annual soil loss must include the cumulative effects of many
moderate-sized storms as well as the effects of the occasional severe
ones. The latter ones are represented by a rainfall erosion index (El)
theoretically presented for "single rainfall events" by the equation:
with
where
Rr = El/100
El = 210 + 89 log
10
(SW-3)
(SW-4)
R = R factor for single storm events [cm/hr]
E = total energy of rain [metric-ton meters/ha/cm of rain]
I- = maximum 30-minutes rainfall intensity [cm/hr]
100 = units conversion factor (from english to metric)
However, for long-term and annual simulations the local value of the
above index generally equals R for the USLE. R-values have been
compiled by the equation developers, and can be obtained for use for
both LEVELO and LEVEL1 simulations from the isoerodent map
[Wischmeier and Smith, 1978, p. 7] presented in figures SW-1 and SW-2.
SW-6
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MOO
A. 197G
-------
190
MAUI
KAUAI
7~V 150 \N
! 300 V
OAh U
MOLOKAI
SW-8
-------
2.2.3 Soil Erodibility Factor (K)
The K factor in the USLE represents the soil loss rate per erosion
index unit for a specified soil as measured on a unit plot, which is
defined as a 21.8 m (72.6 ft) length of uniform 9% slope continuously
in clean-tilled fallow.
The K factor in the USLE is a quantitative value experimentally
determined on a "unit" plot arbitrarily defined. Representative
values of K for various soil types and texture classes can be obtained
from tables prepared by soil scientists using the latest available
research information and data. Table SW-1 and SW-2 are two examples.
For soils containing less than 70% silt and very fine sand, the
following regression relationship has been derived by the USLE
developer:
K = 2.1 x 10~2 M 1-U (10~4) (12-a) + 3.25 (b-2) + 2.5 (c-3) (SW-5)
where:
M = particle size parameter [mm]
a = % of soil organic matter [-]
b = soil structure code used in soil classification
c = profile permeability class
Above equation is presented for practical application and is in figure
SW-3. In tests against measured K values ranging from 0.03 to 0.69,
65% of the nomograph solutions differed from the measured K values by
less than 0.02 and 95% of them by less than 0.04.
SW-9
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L
TAtiLE 1 —( omputed K vo/ues for soils
research sfofions
on eiosion
Sail
Duntirk tilt Ico n
Keene nil loam
Shelby loam
Lodi loam
Foyi'tte nit loc ti
Cec 1 londy nd
Frejhold loam- land
Both flaggy nh loom wnn surface
ilones ^ 2 mihei removed
Albia gravpll) loam
Source of data
Geneva, NY
Zaneiville, Ohio
Bethany, Mo
Diackiburg. Va
LaCrosie. Wn
Watkmsville, Co
Clarinda. Iowa
Cailana, Iowa
Hoyi, Kans
Stain College, PC
Temple, Tex
McCrpdie, Mo
Morcillus. N Y
Cleirton, S C.
Geneva, NY
Watkiniville, Co
Tyler, Tex
Walkmivillc. Go
Guthrie, Okla
Tifton, Go
Marlboro. N J
Arnot. N Y
Beem?rville, N J
Computed K
'069
48
41
39
'38
36
33
33
32
31
29
28
28
26
27
26
25
23
22
10
08
'05
03
1 Evaluated ram continuous fallow All olheri wprr computed
from rowcrop cata
£**fV-,
SW-10
-------
Older
Uh soli
Ousels
Ojutols
tfdtiiolt
Andiiols
Incepliioli
Inccptiiolt
Incept noli
Incfplisols
Incepnioli
/^OURCE
iuborder Greo* group
H'lmulls
Ti rio«
a lex
U lerts
0 thidi
A idepti
A iJi'pli
A tdepli
Atidffpl*
T ercpl.
, El Swo.f/
Tropohumul-i
Toriox
Eulruilox
Chromuilerti
Comborlhidi
Dyitrondepli
Eulrondepls
Eulrondepli
Hydrondppii
Uilropepti
and Dangler (9)
Subgroup
Humojiic Tropohumul ,
Txpi« Torron
Tropcplic Eulruilo*
Typie Chromuslern
Uitollit Camborthids
Hydnc Dyilrondeph
lypic Eulrandcpli
Entic Eutrondepts
lypic Hyclrondeplv
Vcrtit Uilropepti
Clo)i-y, kiolmitic, nohypi-rtliermic
Clayey, kaoliiitic, itohyperthr-rmic
Clo,oy, doolmilic, nohypcrthermic
Vcr, f,ne, monlmorillonitic. nohyperthermic
Mot'ial. itohyponhcrmic
Thi>olrop
-------
to
nT
IT
r
2 hn« fjionutof
Vm«<» or cnorf* qronulor
4-bloeky. ploly, or moiti««
* SOIL STRUCTURE
VL/'X- \
PERMEABILITY
PERCENT^SAND
lTbJO-2 Ommj
1 ^
- vtry tlow
- flow
4- slo« to mod.
- m odir alt
?- mod to r o pid
I - ro pid
Mill ipprnordte dltl. tntpr lult ll Itft Ind pmc»»d to ootntt
lti« ull's 1 »ind (O.IO-7.U •«•), « orjjnlc Mtttr, »«ructure. mil p»r-»«bl I Ity, (n thlt IK]UHK«
lnl»r(wlitf t>»t»Mn plotttd curyei. tht d;>ttt
-------
2.2.A Topographic Factor (LS)
Both the length and the steepness of the land slope affect the
rate of soil erosion by rain. The two effects have been evaluated
separately in research and are presented in the USLE by:
L, the slope length factor, which is the ratio of
soil loss from the field slope length to that
from a-21.8 m (72.6 ft) length under identical
conditions; and
S, the slope-steepness factor, which is the ratio
of soil loss from the field slope gradient to
that from a 9% slope under otherwise identical
conditions.
LS, therefore, is the expected ratio of soil loss per unti area
from a field slope that from a 21.8 m (72.6 ft) length of uniform (9%
slope under otherwise identical conditions. The following equation
was derived [Wischmeier and Smith; 1978].
LS = (0.045 x)m (65.41 sin2G + 4.56 sinQ + 0.065) (SW-6)
where
X = slope length [m]
0 = angle of slope
m = 0.5 for 4.5% < 0 < 4.5%
0.4 for 3.5% < 0
0.3 for % < 0 < 3.5%
0.2 for 0 < 1%
A graphical presentation of equation (SW-6) is presented in
figure SW-4. Those who prefer a table may use table SW-3. For
irregular slopes, the LS values (figure SW-4, table SW-3) have to be
adjusted [Wischmeier and Smith, 1978, p. 16]:
(1) by using table SW-4, and
(2) as shown in table SW-5
SW-13
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s
£
I
*=-
•j.->tl.-«;i)! jo |ua}jad 5 jo
JOI t 0 "» Puo '3«fo|! )0 n|l.un M |.^aj Ul L||6ua|
20.0
puo 'iedo|i iua:>i >d 5 p 0| j £
(S90'0
,,.'9 li \) SI 'SI ''opoj :m|Hoj6odci|)
BO 100 200
SL-HPF I.FNGTH (FEET)
400
600 800 1000
-------
TABLE 4K-Vo/ues of Me fopogroprnc faciir, LS, for spec/fie eombma/ions of s/ope /engf/i
and j/
feic»nt
O1.1
o:
01'
'-•
3
<
.'•
c
f
1C
i:
i.
it.
if.
2(
Slope length (feet)
25
0060
073
086
133
.190
.230
268
336
496
.685
903
1 15
1 42
1 72
204
50
0069
.083
098
163
.233
303
379
476
701
968
1 28
1 62
201
243
288
75
0075
090
107
185
264
357
464
583
859
1 19
1 56
1 99
246
297
353
100
0080
096
113
201
287
400
536
.673
972
1 37
1 80
730
284
343
408
i50
C.086
104
123
*27
'.25
•71
(•$(,
824
1 21
1 68
221
281
348
421
500
200
0072
110
130
248
354
528
758
952
1 41
1 94
255
325
401
386
577
300
0099
119
141
780
400
621
928
1 17
1 72
237
3 13
398
492
595
707
400
0105
126
149
305
437
697
107
1 35
1 98
274
361
459
568
687
8 16
500
0110
13?
156
326
466
762
120
1 50
22?
306
404
5 13
635
768
9 12
600
0114
137
16?
344
492
820
1 31
165
243
336
442
562
695
841
100
800
0121
145
171
376
536
920
1 52
1.90
2.81
387
5 11
649
803
971
11 5
1.000
0 126
152
179
402
573
1 01
1 69
2 13
3 14
433
571
726
898
109
129
'IS = i\ 72 6)m 16541 sin (I J 456 sin (I---0065) where \ slop... length m feel, m 0 2 for
rrocienis < 1 percent. 0 3 for 1 to 3 percent •lopci. 0 4 for 3 5 to 4 5 percent slopes. 0 5 for 5 percent
slopi s one steeper, anil II - angle of slope (Per other combinations of length an.4 gradient, interpolate
CICIM sen oiliacent values or see fig *4f £^.44 I
SW-15
-------
TABLE X- Estimated relative soil losses from successive
'ngl'/i segments of a uniform slope'
, Sequence number
Nun *rr ot S( gnienu
of legmen!
2 1
2
3 1
2
3
4 1
2
3
4
5 1
2
3
4
5
Fraction
m -• 0 i n
035
63
19
35
46
12
23
30
.35
09
.16
21
25
28
of foil
l =.04
0.38
.62
22
35
43
14
24
29
.33
.11
.17
21
24
27
lost
in = 0.3
0.41
.3*
24
.35
.41
17
.24
.28
.31
12
18
21
23
.25
Derived by the formula
m+1 m+1
I - !!•»
Soil Ion fraction —
m+1
N
wlipre | irgmrn1 sequence1 number, m -- slope length exponent
!0 5 ior slopes ^ 5 percent, 0 4 lor 4 percent slopes, and 0 3 for
3 pcicpnt or less;, and N - number of equal-length legmenti into
v. hich the slope was divided
SW-15 v'i
-------
Segment f a T.iMf. J lob/.' -i
1 1C" 0'9
2 274 35
3 512 46
K
027
32
37
5
10
15
107
274
019
35
Proajcl
0055
307
S71
KLS - I 233
IS = 3517
SW-16
-------
2.2.5 Cover and Management Factor (C)
The factor C represents the ratio of soil loss from an area with
specified cover and management to that from an identical area in tilled
continuous fallow.
This factor represents the combined effect of all the interrelated
cover and management variables. Deriving the appropriate C values for
a given locality requires knowledge of how the erosive rainfall in that
locality is likely to be distributed through the 12 months of the year
and how mud erosion protects the growing plants, crop residues and
selected management practices will provide at the time when erosive
rains are most likely to occur.
For an optimal derivation of C values, the reader is referred to
the corresponding chapter of the original research. [Wischmeier and
Smith, 1978, p. 17.] The estimation of the C-factor is the most time
consuming effort when employing the USLE. C-values can be estimated for:
(1) Agricultural areas, (2) Construction areas, (3) Pasture, Range and
Idle Land, and (A) Woodland. Some information is presented below.
Agricultural Areas
Tables SW-6 through SW-11 provide details needed by a trained
agronomist to develop simple handbook tables of C values for conditions
in specific climatic areas. The tables are self-explanatory and within
their broad limits of accuracy these tables can supply the research data
needed to complete the estimation of C. The procedure is not that
straightforward for site specific applications; however, it is well
explained in a "problem-procedure" on page 29 of the original work.
Construction Areas
Applied mulches immediately restore protective cover on denuded
areas and drastically reduce C that has a maximum value C=l. Soil loss
ratios for various percentages of cover are presented in table SW-12.
Pasture, Range, and Idle Land
Factor C values for a specific combination of cover conditions on
these types of land may be obtained from table SW-13.
SW-17
Arthur D Little, Inc
-------
TABtt^—Ratio cf soil /n«s from cropland lo corresponding loss from continuous tallow
en
f
oo
l.i.. Coocr c.io|j Svquuiitv.
Ni, and manacjfmenl1
residue-
Ib
COPN AFTFR C. GS, C OR CO1
IN MtADOWLCSS SfSTFMS
1 Rcll sarg TP
7
J
4
5 RdL. full TP
6
7
0 RdR. iprq fP
10
1 1
12
13 RdR, foil TP
14
1 5
17 WrWff-art pi. Rdt, TP'
18
10
70
. 1 fW-i ofF $r-> rf'iiV «,
?r di»k r.LW
"3
75 No / /' p/onF m crop residue*
?i>
*7
i»
•»
JU
31
Chucl ll allow dill, or
fid cufl as only 'ilfnge
33 On nioderaf slopes
34
36
17
30
3? Do
40
41
42
4500
3.400
2.600
J.COO
HP1
GP
fP
IP
HP
GP
n-
IP
HP
GP
FP
IP
4.300
3,400
2.600
2000
4500
3400
7600
7000
6.030
6000
4 500
3.400
3 400
3 400
7600
7600
6.000
4.500
Cover
uflr-r
. '?•'
Pel
10
1!)
S
95
90
80
70
40
50
JO
30
70
60
50
40
30
70
70
to
SO
40
30
20
r
Pel
31
36
43
5<
44
49
57
65
66
tf
68
69
76
77
78
79
Soil loss ratio' tor cropstoge
period and canopy co.er'
bo
Pel
M
60
«4
68
65
70
74
73
74
75
76
77
82
83
85
BJ
31
36
4)
51
45
52
57
61
2
3
5
S
i:
15
76
3
10
1]
15
18
73
9
12
14
17
21
25
i
Pel
48
52
56
60
53
37
61
65
65
ti
67
68
70
71
72
73
27
32
36
43
38
43
48
51
2
3
5
8
12
15
70
24
8
9
II
13
IS
70
8
10
13
IS
18
27
7
Ptl
38
41
43
45
38
41
43
45
47
47
48
49
49
SO
SI
52
23
30
32
36
34
37
40
42
2
3
S
8
12
14
18
22
7
8
10
11
13
IB
7
9
II
13
IS
19
3 SO
Pel
32
33
32
37
33
35
35
35
29
31
32
33
!2
14
17
21
,C
PC-
24
25
75
24
25
76
27
•n
27
27
11
23
24
24
25
26
8
9
11
13
17
76
Pel
20
20
21
27
20
20
21
72
22
23
22
23
18
18
19
70
20
20
71
22
2
3
S
6
8
9
11
14
7
8
9
10
12
16
7
8
9
10
13
16
.1
Pel
23
30
37
47
Line
No
Cove*. HOP seqvente. Sprniij
and management* residue
er
"• ; -B
tb Pel Pel Pel
CORN AFTER WC OF CYEGDASS
OR WHEAT SEEDED IN
79
80
81
67
r
/or
76 -SI
Pel Pel
6 '' )
9
M
Strip lill one-fourth row space
56
62
69
74
73
30
37
47
23
30
37
47
14
14
15
19
23
27
30
36
17
17
IB
19
20
21
18
IB
19
20
21
27
83
84
85
86
87
88 '
89
90
91
92
93
94
95
96
97
98
99
100
101
icr
103
IOJ
105
106
107
108
109
110
111
112
113
114
Rows U/D slope
Rows on conlour"
TP. cans seedbed
WC sueeufonl blades only
No-till pi m killed WC
Strip till one-fourth row space
CORN IN SOD-BASED SYSTEMS
No till pi m killed sod
3 lo 5 tons hoy yld
1 to 2 Ions hay yld
Strip lill. 3 i Ion M
50 percent cover, tilled strips
20 percent cover, tilled strips
Slnp 1,11. 1-2 Ian M
40 percent cover tilled strips
20 percent cover, tilled strips
Older tillage o/fer sod
CORN AFTER SOYBEANS
Sprp If. conv lilf
Fall IP. conv till
4.000
3.000
2.000
1.500
4,000
3.000
2.000
1.500
4,000
3.000
2,000
1 500
3,000
2.000
1,500
1.000
3.000
2000
1,500
1.000
HP
GP
FP
HP
GP
FP
13
1C
73
78
10
IS
70
25
36 60
43 64
SI 68
61 73
11
IS
20
76
IB
13
73
33
7
7
3
I") (")
40 77
47 78
56 83
47 75
S3 81
62 86
17
17
22
26
10
15
20
24
5?
56
60
64
11
15
21
18
78
33
I
2
3
in,
60
65
70
60
65
70
II
1A
70
24
10
IS
19
23
41
43
45
47
17
20
23
17
21
?5
28
3<
1
2
7
3
("1
48
51
54
48
51
54
!6
19
22
IS
19
22
31
33
J5
?3
21
26
27
25
??
33
79
:
"')
•iO
40
II
13
15
17
10
12
IS
17
24
25
76
77
18
20
21
22
20
21
23
1
7
7
3
("1
30
31
30
31
9 I")
1C
12
14
8 <")
9
12
14
20 (' )
31
27
16 ("i
17
13
19
17 1 )
13
19
20
1 1
2 2
2 4
3 5
!"> I")
75 29
25 37
26 44
25
25
76
s!
CP
-------
4*1
4A
a
43
47
sn
51
52
SJ
51
55
56
57
58
i9
60
61
A2
c 1
«4
e5
',6
• f
bo
Do
Do
On slopes .- 12 percent
3.400
7.600
2.000
60
50
40
30
70
1C
50
40
30
70
10
•10
30
20
10
I MP^ 33 59 t me: factor sf
D'i>nos factor of
Rows on cortour"
Ro^sU'D slope < 7 percent
Sfnp fill one 'aurfji of row tpacinr?
»,=
69
70
71
72
73
7-1
75
76
77
71
Rows on contour"
Ro vs U D S'OPL>
Vo'i-lill
Raws on contour"
4.500
3.400
2.600
2,000
4.500
3400
2.600
2,000
3.400
3,400
2.600
'•60
50
40
30
1 60
50
40
30
40
30
20
u
lo
19
23
79
36
17
21
:s
32
41
23
27
35
46
1 i
1 1
1 f
1
7
9
7
1 0
12
16
22
27
16
20
26
31
13
16
21
II
,3
17
"• 1
A 1
75
37
16
20
29
36
71
25
32
47
> 3
1 1
1 4
7
7
9
85
10
10
14
19
23
13
17
22
26
12
15
19
10
1C
16
19
73
29
19
28
34
20
24
70
38
1 1
1 1
1 2
7
1 0
1 0
1 0
1 0
9
12
17
21
11
14
19
23
II
14
19
15
19
27
32
20
23
23
33
1 0
1 0
1 0
7
1 0
1 0
1 0
1 0
17
70
17
20
14
19
10
1 A
14
17
21
24
13
15
22
25
15
19
77
26
1 0
1 0
1 0
10
1 0
1 0
1 0
11
14
16
12
14
16
13
16
E
7
11
14
16
20
10
12
17
21
12
15
18
22
1 0
1 0
1 0
7
10
1 0
1 0
1 0
8
10
12
13
9
II
12
13
11
12
14
20
;.:
25
26
27
30
jv
30
34
37
37
39
42
47
1 0
1 0
1 0
1 0
1 0
1 0
1 0
23
27
30
36
23
27
30
36
22
26
34
115
Mi
117
118
119
12G
III
122
123
124
125
126
127
12S
.
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
See
FaM 4 spig chise! "i full
No till pi in CfviJ i*-s U*
BEAi-iS /.FTEK CGEN
Sprq IP. Rd(. ronv Ml
Foil IP. Kdl. cnnv till
Chi(»f or flrf c"lr
BEANS AFTER BEANS
GRAIN AFTER C. G. GS, COT1'
In disfced residues
Do
Do
In disted stubble. RdR
Winter G alter foil If, Kdl
GRAIN AFTER SUMMER FALLOW
With groin residues
With row crop residues
POTATOES
Rows wifh slope
Contoured fowl, ridoed when
canopy cover is about
50 percent11
footnotes, p_24 (VtCr-V V,CU
HP
r p
GP
FP
IP
HI-
fP
HP
GP
FP
HP
GP
F?
4,500
3.400
2.600
2.000
HP
GP
FP
IP
290
500
750
1.000
1.500
2,000
300
500
750
1.000
1.500
2.000
2.500
«•
< 30
?s
20
15
10
1 10
JU
20
70
60
50
40
30
2C
40
20
10
30
20
10
10
30
40
SO
60
70
5
15
23
30
45
55
65
33
39
45
45
52
59
i1 )
')
31
36
43
53
-
-
43
43
10
4r
SI
58
67
25
4*
60
64
65
6?
73
77
C i
( i
12
16
22
77
32
38
29
43
5?
38
46
56
79
55
60
64
68
70
43
34
26
20
14
82
62
50
40
31
23
17
64
64
1<
-c
44
51
i?
20
32
52
56
60
57
61
65
1
I
12
14
18
2!
24
30
74
34
I?
30
3'
43
62
43
52
56
60
S5
34
27
21
16
II
65
49
40
31
24
19
U
56
56
27
">?
39
44
48
19
3:
38
41
43
31
41
41
( ,
II
12
U
In
18
; 1
19
24
2'
23
76
30
4.'
31
3J
36
38
43
2:
18
15
12
9
44
35
29
24
18
14
12
36
18
34
?4
36
-7
29
"
f )
7
7
8
5
9
10
9
11
17
II
12
13
17
12
13
14
15
18
13
10
8
7
7
19
17
14
13
10
8
7
26
13
77
27
28
2R
14
23
70
21
22
20
21
22
>'")
4
4
5
5
6
6
6
7
7
;
7
8
II
7
8
9
10
13
10
7
7
5
S
U
13
11
10
8
7
5
19
10
?3
•n
23
73
23
11
13
17
18
17
18
C J
2
2
3
3
3
.1
T
4
4
4
4
S
6
5
S
5
6
11
8
7
6
5
S
12
11
9
8
7
5
4
16
8
79
37
37
44
5<
76
40
("I
("!
;"i
<")
• '<
; )
r i
' 1
i 'I
(rl)
r
in
-------
CO
N>
O
footnotes for table S/
Symbol, B. soybeons. C. corn, conv Ml plow. dll|, ond horrow ,„, ,cpdbert c"on ipMnt' r°"d" ""d """ " th. iurloce ofrer crop Wd,n9 „ .ofiec.ed
m -hn 5o.l leu roi 01 O! rcsiduci mi»d with ihc topioil
'h^ %o.l lo» roi.ot gi.nn o, per.en.og«. olsun,e ihot the md.coled crnp sequence
.nd pror,,co, ore followed con,,,,en,ly One yco, dnv-o.-on, Iron, normol p,oc,.«c, do no.
Co., -ho »P,f, Of 0 p.prnoncn, chongc llncor in.,,po|olion be,ween fc ....... tommended
wh«n luiti-.pd by fiold conditions
C-opfoge per,od, ore o, def.n.d on p 13 Ih, ,h,ee «olumn, |or croD,,oge 3 ore for
KO -50. ond "6 le> 100 ne.cenl conopy cover ot malurily
Colum-, 41 ., »0, 0,| rc,.due, lei. on field Corn stalk, porholly s.ond.ng o, left by
,0-,, .hon.,01 p.«VPr5 II ...ft, ore ,hrcdded ond ,prMd b (eker se|t( r|
o-' 4 volue, ,n Im^s 9 to 12 ore for corn stubbl- (.lover ,emo«d)
' ln.er,ion plowed, na .econdory t.lloge. For ,h,, p,oc..ce. rcs.due, mi*, be left ond
•So-l ,u,fo,, ond chopped r«,du« of mo.urerf preceding CrOp undLtu-bed e.cep. ,n
narrow tlo>s in which seeds a'e plan<-d
'"-Top of old row ridge ,l,ced ofl. throwing residue, ond some »,l ,nla fu,,ow aret<4
Kendgmg o.turned to occur near end of cropstago J
oddTT Ih""" '^ Tr™"" "' li'"d '°r r°W> °n "" """°"- th" 'edu'"°" !« '"
odd,,,on to the .tondard field conlour.ng credit The P volue fo, con-our.n,, „ u,ed w.th
thpsc reduced loss ratios
'- ',e.d-ovcro3e percent cover, probnbly o*,u, ,h,.e-.nu,,h. Of pCrrrn, cove, on „„
nisturbed ifnps
' If .gam seeded to WC crop ,n corn stubble, e.oluotc w.n.er per,,d o, o w.nter
a,o,n seeding ,line, 132 to 148) Otherwise, see toble 5 C
,h.""*del 'n °PPrOPri?le 'ine '°r 'he tr0"- "»•••• "rf P-d0c,,v,,y ,,.., ond mUl,,Ply
the luted soil lou ratio, by sod residual factors from table 5 D
"Sprmg residue may include carryover from prior corn crop
" See table 5 C
' U,e value, from line, 33 to 62 w.th oppropnat, dote, ond Ung.h, of crops.ogc
periods for beans in the locality opsrogc
"Value, .„ line, 109 ,„ ,22 are bM, a.o.lobl, „„„„,.,. bu, jm, „„,„ ond
length, of crops.agc, may differ
"When meadow ., seeded w.th the gro.n. ,., effect .,|| be rc-flr-ctcd through higher
percentages of cover in cropslaget 3 and 4
•" Ratio depends an percent cover. See table 5-C
' See item 12. table 5 B.
$
-------
1AULE i< - -Approximate soil loss ratios for <.olton
EAC'*ctod final t anopy percent cover
Estimated m.lisi percent cuver from oefol nhon -
jtalr.j dowi
Pro. nee
Kun-ber Ti|icige operation, j
COITON AN'.'C VllY
i None
Dclo alien 10 life 31
J T ] o Iru or Mrv lilfnge
CL Pd only
PC* & 2C percent ccver vol veg
Re n 30 percenl cover >nl vey
1 Cfi. t»l >lcw • oon offer cot fiorvesl
Cl lelmn lo Dec 31
Ja< i *o iprg tillage
1 foli di I. orrrr chisel
Oi fovv ItbMar, no prior fil/roe
Cc Rd oily
Rd & 20 percent vol veg
Rd & 30 percent val vog
5 £ed f IP ! lob Mar no prur lillape
Cc Rd onl>
Kr & 20 percent vol vug
Rd & 30 percent vol veg
Split m'gei a plant after hip, 01
Cul & plait offer crinel 'SB
Ce Rd >nly
Re & 20 percenl vel vcg
Rr & 30 percoi t vol veg
Crc>r loge 1
Ci Kd onl)
l!r & 20 percenl vol vcg
Re & 30 percent vol vvg
Croc lage 2
Croi lage 3
i Bed 1/1 ji atl'r 1 prior fiflarje
Ce t Kd only
Ri & 2C percenl veg
Rr & 3C penent veg
Spill ridge* nfter hip 'SB1
Ci> Rd only
Rr. & 20 to 30 percent vrg
Croi .loge 1
Cc Rd inly
R' & 20 to 30 percenl veg
Cro; .lage 2
Croi >ioge )
7 hip o' er 2 prior tillages
C> t Ra nnl>
Kti & 20 30 percent veg
Spk ridge, afier hip ISB
B Hip n/1* r 3 rr nore fil'iiqi'i
Spli* ridgei after hip (SB'
? Carivri Nona/ molrfboorri pljv. und duk
Follow period
Seenaed ajriod
Croi >tafjc 1
' ioi untji :
C.o, .trg. 3
Cro,>sloge 4 ,See practnri s 1 2 and 3
1C I TON AFTEf SOD CROP
For llir fi* ii nr second crop ccter a grmt
ii idow hos 1 >en iuirp'ov/»d mulnplv volurs n
65
30
BO
45
Sen loss
95
60
•-ho'
Fen er"
36
52
32
26
40
56
53
62
50
39
34
100
78
68
61
53
50
57
49
46
45
40
no
94
90
66
61
60
56
47
42
116
ins
67
120
68
42
68
63
49
.14
24
Jl
26
20
31
47
45
54
42
33
2V
84
66
58
54
47
44
50
43
41
39
27
96
82
78
61
55
5e
51
44
3P
108
9:
62
no
6-
3V
^
i?
4A
3:
or qrriss n id
ivcn
in the 1
15
32
20
14
24
40
37
47
35
28
25
70
56
50
47
41
38
43
38
36
34
17
84
72
68
52
4?
49
46
38
19
98
BB
57
10?
J9
36
59
55
41
J.
leg. me
•.' f..i
CC1TON ACUS SOIEE/'KS
Select \oli , fron ov"iv<- and m-i'tip1) o, 1 21
1 A'fcrnofo procedure for eifirnahng fhe I0i/ /Off ratios
The ratios givnn cbovc for cotton ore ba^d on estir-.zjics for ro
diHtiOi & in percent cover tnrough normal wmier lost and by the ftucees-
s»vf> tiling* oprrononi Research is underway in Mniiksipp- to obtain
more atturo'c re&irlue data m relation to tillage practice! This reseortn
should provide more accurate soil loss ratios fnr cotton within a fow
>cori
Where tht> re'luc'ions m percent cover by winter loss und tillage
i-pcrniion& rrc small, *ht> following aro'odure may be used to compute
sail loss rahos for ihc preplan) and seedbed periods Enter figure 6 with
the percentage of the field surface covered ay renduc mulch, move
vertirnll> lo trie uppf-r curve and read the mulch factor on the sco'e
in fho left Multiply 'his factor by a factor selected from the following
•cibul I
Ploilucft ".
Irvi-l
Hir,"-
rWtrfiu-!
No
tillage
066
71
7J
V el i.-c P. -.0.' o , •
Rough
surface
050
54
5?
.l3R't 0' U-,1 1 n 1
Snoothea
surface
056
41
6;
.c i'<• \uliM. copipv'"U cibo i- 'v ntgn su-fo;. •
•Sou/ct '• [
sw-21
-------
—Soi/ loss rorios for conditions not evaluated
in table 5
COTTON
at lot.lt 5-A
CROPSTAGE 4 fO'-i R.1WCROPS
Stalks aroken ond joriiolly liondino.' U»e col 41
'>tolk» Mondmp oil. r lionil picking Col 41 nmci 1 13
Slolki .hiedded v>i lout soil hlloge See toble 5C
(all chi»l Sele:t > alues I'om hnei 33-42, seedbed column
CKOPS1AGE 4 F0« SnAll RRAIN'
->«i lollt 3-C
DOUBLE CROPPING
Derive annual C v lue b, ulecling frcmi fable 5 (he toil lo»s pel
ce-tagei for It t tucceisive cropttage periodi of each crop
ESTABLISHED MEADO'V. FULl-YEAR PERCENTAGES-
Gran end legume n IA, 3 to I I hay 0 4
Do. 2 to 3 t hay .6
Do 1 t hoy 10
Sericeo. after uconil year 1-0
Red cluver 1 5
Alfalfa leipedeio, jnd ircond-year unceo 2.0
Swectciover 2.5
MEADOW SEEDING WITHOUT NURSE CROP-
Delermme apprnpnute lengths of crepttage periods SB, I, and 2 end
apply valuel g ven fur imall groin leedmg
PEANUTS
Companion with 11 ybeani it tuggested
PINEAPPLES.
Direct ilola not avuloble Tentative voluri derived onalylicolly 01
oviiilable from th« SCS in Hawaii cr the Weitcrn Technical Se'
vic'i Center ct Portland. Oreg |Re(erence J)
SORGHUM
be loci voluel giver fcr corn, on the bam of expected crop leiirlur*
anil conop) cc^er
SUSARBEI TS-
Direct dole not ov ilc-ble Probably moil nearly comparable to pr
taioei, without the ridging credit.
SUSARCANE.
~entaii>e value-, a' oilobl.) from leurcei giirn for pineapples
SUMMER FALLOW It LOW-RAINFALL AREAS. USE GRAIN Oft ROW
CROr RESIDUES
The approximate ml laii percentage after each lucceisive tiMar-
operation mot M obtained from the following tabulation by e'.li
mating thr per.ent surface cover of'?' thai tillage and lelecun.j
thi column fa the jpprapriote amount of initial residue Tr-«
given valves o -di' bi-nefitt of the residue mulch, residue' mm-d
wi-h »ii b> nl age, and the crop lyitem reiidual
by n tjlch
91.
8C
•c
of
51
1C
3:
2d
1C
--4 000
4
8
12
16
20
25
29
35
a
3.00C
—
'8
13
17
22
27
33
39
55
2.000
_
'14
•18
24
30
37
44
63
1,500
—
'19
'25
32
39
46
68
For i ran ri'iiaue only
<:OV=R SEIC NG IN ROW CROP STUBBL: Of RESIDUES
9 cropstogi > >iod& acved on the cover seeding date cue1 apply
'clues from h e» 12° to U5
-------
Soi( /oss ra'los 'Percenf^ for cr°Ps'°9e 4
when sl«iils o.c chopped and dislnbutee/ wilhoul toil
tillage
Corn or Soighum
Mulch
20
30
40
JO
60
70
80
90
95
lillrV»«- —
This column applies lor oil systems other Ihon no till
Covrr i.lli> bran harvest muv include an opprec.obl* number of
stalks carried over irsm the prior corn crop
• For gram witS meadow seedinQ. include meadow Orowlh in percent
cover and l.m.t g-o,., period 4 to 2 mo. Thereafter, classify as estab-
lished meadow
t -*
sw-23
-------
TABLE 5 D - Faiiors to credit residua/ efiec/s of turned
sod1
Factor for cropstage period
CIOPJ May y»ld •
SB and 1 2
Firs' yeor iiftci mead
Row crop or yrom
Second yfar after meaJ
Row crop
Spring groin
Winter groin
Tom
3 5
2-3
1-2
35
23
1-2
3 5
23
1.2
35
2-3
1.2
025
30
35
70
75
80
-
040
45
50
80
.85
.90
75
80
.85
60
65
70
045
.50
55
.85
90
95
80
85
90
70
75
85
050
55
60
90
95
1.0
.85
90
95
65
90
95
060
65
70
.95
10
1 0
.95
10
10
95
10
1.0
1 These faciois arc to be multiplied by the appropriate toil less per-
centages selected from table 5 They are directly applicable for lod
forming meadows of 01 least 1 full year duration, plowed net mort
than 1 month before final sr-edbcd preparation
When sad 11 foil plowed for spring planting the listed values far oil
cropitage periods arc increased by adding 002 for each additional
month by which Ihe plowing precedes spring seedbed preparation For
example. September plowing would precede May disking by 8 months
and 002:8 1), or 0 14, would be added to each value in Ihe table Far
noniod forming meadows, lite swpetclovcr or lespcdno, multiply the
factors by 1 2 When Hie computed value is greoier than I 0, uu as I 0
sw-24
-------
TABLE 6.-PWM age of /he overage (-nnual El wfiicr normo,/y occurs facUoen Jonuory ? ono1
Compu/cd for /he geogcaph/c airas s/ own in figured
indicated dafes.
Arm
No
1
3 .
4
c
t
1C
1 1
12 .
Ki
i:
17
18 ..
19
20
21
22
25 . . .
/4
2i .
2i
27
Tr
33 . .
31
32
lor
Jcr f*k Mat Ap
' '- 1 15 1 15 1 15
Of 00 CO 12
0 C 00 11 23
•PC 00 11 : 3
0 ' 1 • 23 47
C 23 46 8 13
0 123*66
0 35 71? u ?0
0 '• 46 9 I'. 17 23
c 24 66 10 '5
0 35 79 il 14
• C : 00 11 23
• 0 '' 01 1 ;> 35
-.-. 0 ! 01 23 46
° 23 46 8 10
0 i 23 45 68
° 24 68 10 13
0 36 9 12 16 21
0 • 35 7 10 13 16
0 •• 6 10 1- 16 l? 23
0 .. 69 13 17 21 27
0 :' 57 10 14 18 23
3-1 69 12 16 20 24
0 35 7 10 13 17
0 ' 46 £ 12 16 20
0 23 57 10 14
3 35 79 12 15
0 23 45 68
0 -1 0 ' 23 45
31 23 45 68
0 ! 24 6 S 11 ;3
•utul nul I,..,.,J ,n the table, In'n.oolol.. brlw..
A-OY
1 15
3 6
6 10
6 13
12 18
21 2=
6 16
13 25
28 r
30 37
21 29
IB 27
5 9
7 12
9 14
11 15
14 18
11 15
19 J6
26 31
19 23
26 29
33 38
27 31
28 33
21 24
25 30
16 22
18 21
11 14
10 14
7 12
10 13
15 18
June
1 '5
11 23
17 29
23 37
27 38
37 46
29 39
40 -•
48 :-6
43 49
38 47
35 41
15 27
19 33
20 28
22 31
25 34
20 28
34 42
37 43
27 34
33 39
44 49
35 39
38 43
27 33
35 41
27 32
25 29
17 22
K 26
17 24
17 22
21 26
July
1 15
36 49
43 5:>
51 f
48 5'.
54 6J
46 53
56 (2
6! 64
54 58
53 57
46 •>]
38 50
48 57
39 52
40 49
45 56
41 54
50 58
50 57
44 54
47 58
55 61
45 53
50 59
40 46
47 56
37 46
36 45
31 42
34 45
33 42
31 42
32 38
Aug
1 15
63 77
67 77
69 76
62 69
65 69
60 67
67 72
68 72
62 66
61 65
57 62
62 74
65 74
63 72
59 69
64 72
65 74
63 68
64 71
63 72
63 75
67 71
60 67
69 75
53 61
67 7i
58 69
56 66
54 65
56 66
55 67
52 60
46 55
Sepl
1 15
90 95
85 91
85 91
7.-. 83
74 81
74 81
76 80
77 81
70 74
70 76
68 73
84 91
82 88
80 87
78 85
79 84
82 87
74 79
77 81
80 65
80 83
75 78
74 80
8C 84
69 78
81 65
80 89
77 83
74 ,3
76 82
76 83
68 75
64 71
«*«-BVO
Oct
98 99
96 98
94 96
90 94
87 92
88 95
85 91
86 89
78 82
83 88
79 84
95 97
93 96
91 94
91 94
89 92
92 94
84 89
85 88
89 91
86 89
81 84
84 86
87 90
^9 92
87 89
93 94
88 91
89 92
86 90
89 92
80 85
77 81
N
100
99
98
97
95
90
97
92
84
91
89
96
98
97
96
95
96
93
91
93
90
86
88
92
94
91
95
93
95
93
94
89
0*
100
100
99
9E
97
99
95
90
94
93
99
99
98
98
97
97
95
93
95
92
90
90
94
95
93
96
95
97
95
96
92
89
;
100
100
99
99
95
IPO
99
96
94
96
96
99
100
99
99
98
98
97
95
96
95
94
93
96
97
95
97
97
98
97
98
96
93
)ec
100
100
100
100
99
100
99
99
97
98
98
100
100
100
100
99
99
99
97
98
97
97
95
9;
96
97
99
99
99
99
98
97
^^r^^t, *>23f -^
;•:•:•:•:•:; yT/V—-i" s^~r' V
T$p |t>j»-'«7» C&$tH$
^-v> <'^V*--' ^.v-ivrXt •._.'.*;
0"j^ Jr'Ttf^
25
"••--P 'or nWt.Or 0. a|,p|,cafc|r Eld,,,,;, „,,
frorr. tat In £,\jt —\ /
-------
TABLE 9 ~-A/b/ch factors ond /engfh l,m,ts for
construction slopes'
Tym. of
mulch
None
Straw or ho;
urd down by
anchoring and
'arking
equipment
Do
CrL'.ncrl itcno
'i I.I 1 . ,„
Do
Wood rlniv.
Do
DC
Fnjni Mr>i r niul
'' '1 *lirn | n t tin.
d."u
'• i-in-iiin .1 ,|,.
ccni. Inrrd ( 1c-;in>
1'. ngih is rraui-cH
Wl,. „ K .-,0.
*nl • en mo.' • .!•. ,
iliui 0 50 siio-ilii In
Mulch
Rate
Land
Slope
Toni per acre Percent
0
1 0
1 0
1.5
1 5
20
20
20
20
20
20
20
135
135
135
135
240
240
240
7
7
12
12
12
25
25
2i
25
Torn (?,'| Devi..'
oil
1 5
6-10
1-5
6-10
1 5
6 10
11 15
1620
21 25
2633
3450
<\t
1620
21 33
3450
<21
21 33
3450
•'16
1620
-'16
1620
21 33
'"16
1620
21 33
3450
Factor Length
C limit9
Feel
1.0
0 20 200
20 100
12 300
12 150
06 400
06 200
07 ISO
n 100
14 75
17 50
20 35
05 200
05 J50
05 100
05 75
02 300
02 200
02 150
08 75
08 50
05 150
05 100
05 75
02 200
02 150
02 100
02 75
oped ny on mi ni agency worr.-
liii'i ol field ftDi'ipnrn onH 1
li'nfjib lor whicl
W'icn ihn lirut
nmch.inicol ihor
or hfi) mulch n
Ji Jli'fp
-------
7A31E 10 —roc/or C for permanent pasture, range, and
idle land'
Vi-gelotivi. (tinopy
Cover that contact!
IXPO nnd Percent
h"01"" cover Typ<;,
No opprecioblp
canopy
Toll weeds or 2J
short brush
with averacie
drop fall hcighl 50
of 20 in
75
Appreciable brush 25
or busho with
iivi rage diO|> fall
height of 6'j fi 50
75
Trees, hul no 25
appreciable low
brush Avrrage
drop fall ncighl 50
of 13 ft
75
G
W
G
W
G
W
G
W
G
W
G
w
G
w
G
W
G
W
G
V
Percent
0
045
45
36
36
26
26
17
17
40
40
34
34
28
28
42
42
39
39
36
36
20
020
24
17
20
13
16
10
12
18
22
.16
19
14
17
19
23
18
21
17
20
40
0.10
15
09
13
07
11
06
09
09
U
00
13
08
12
10
14
09
14
09
13
the soil turfact
ground
60
0042
.091
038
083
035
076
032
.068
040
087
.038
082
036
078
041
089
040
087
039
084
cover
80
0013
.043
.013
041
012
039
Oil
038
013
042
.012
.041
012
040
013
042
013
042
012
04)
95+
0003
Oil
003
Oil
.003
Oil
003
on
003
on
003
Oil
003
on
003
on
003
on
003
on
11
assume thai the vegetation and mulch ore
lo.iilomly f'niiibuiorl ovnr the entire area
Canop) ho.pht „ rmosurrd as the overage fall height of water
il-op. foil..,w|
G CO .r („ ju,loci is grass grasslike plant! decoying ton,
l»i inl -Ijh 01 l-n.-i at I, osl 2 in deep
w cc.or at t,.,fncp ,s mostl, broadleaf herha'eous p'onn los
WCPt'l Ml>l. I.M. I . I . I
~i i 111 it icmral root retwoik ncoi the -.urlocei o-
•jnil 'cj),!) residues o- boih
SW'27
-------
Woodland Areas
Three categories of woodland can be can be considered separately:
(1) undisturbed forest land; (2) woodland that is grazed, burned, or
selectively harvested; and (3) forest lands that have site specific
preparation treatments for re-establishment after harvest.
Factor C values for undisturbed forest land may be obtained from
table SW-14. Factor C-values for mechanically prepared woodland sites
can be obtained from table SW-15.
sw-28
Arthur D Little Inc
-------
^- Factor C for undtstwbed forest /one/'
Per. ent of ore,
covurfd by car of) of
Ireei ond undo-grc. «lh
100-75
70-45
40-20
Percerr of area
covered by duff
ol leas- 2 in deep
100-90
85-75
70-40
Fo-'o- C
0001 001
007 004
003 009
-*•• '• "•" '"a" «u percent or i anopy
cover „ le,, ,h.,n 20 percent. u« .obi. 6 Al.o u,e table 6 w,,cre
woodland! are b. ,nB grojed, harveired, or burned
Th- rangei ,. !,„,„• C voluc, ore cou.ed by the ranges ,n ,h.
.pec,fi,d fore,, I. -er and canopy cover, and by voriolion, ,„ r'fcc
live canop> heigh ,
sw-29
-------
TABUED—
..—Fa -tor C for mechanically prepared
woodland i/tes
^"' Mulih
prc.>,Uirotion cove1
Prninl
Diilcd, roled.
or beadvd* None
10
20
40
60
80
Bui-.ed Non,
10
20
40
60
60
Dium chopped Mono
10
20
40
60
BC
Soil condition
NC
)S2
33
74
17
11
OS
.:s
23
19
14
08
04
16
U
12
09
Oo
03
we
U20
15
12
11
08
04
10
10
10
09
06
04
07
07
06
06
Oi
03
Coed
NC
072
46
34
23
15
07
26
24
19
14
09
05
17
16
12
.09
06
03
we
027
20
17
14
11
.06
10
10
10
09
07
04
07
07
Od
06
05
03
ond w»ed covoi '
Fait
NC"
085
54
40
27
18
.09
31
26
21
15
10
05
20
f
14
10
07
03
we
032
24
20
17
14
08
12
11
11
09
08
04
.08
08
07
06
05
03
Poor
"NC"
C94
60
44
30
20
10
45
36
27
17
11
06
29
23
18
11
07
04
««^»_
we
026
76
r?
19
15
09
17
16
U
n
08
05
11
13
0°
07
Oi
01
,,' """'•" " •"'- <-'•<' * •-*. ,. ...,.„ ...»
,„
- •— - -
NC — No live vcgttolion
wc~" pf ;rr °; 9T" °nd • ...... -9
foil he,9hl of 20 in for ,nlermcdlote pepce9
"""• 'n!erpolote b«'"een «.|Mmnl
on,, by 090 ,or lmoo,h (dpp
More Ihon 8 yoorj uie loblo 7
For firs, 3 yeor, Ui. C .D|UC1 o% ,,1(,d
f«- 3-: -o B yen« oil., .roomen, „,.
Mo,c i|.to 8 yeo,, ollor ,,Polm,.n| U
SW-30
-------
2.2.6 Support Practice Factor (P)
The P factor is the ratio of soil loss within a support practice
like contouring, stripcropping, or terracing to that with straight-row
fanning up and down the slope.
The P factor is related to the C factor and to practices that can
slow the runoff water. The most important of these supporting cropland
practices are contour tillage, stripcropping on the contour and terrace
systems.
Current recommendation for contouring are presented in table SW-16.
Effects of contour stripcropping are shown in table SW-17. Terracing
effects are presented in table SW-18.
sw-31
Arthur D Little, Inc
-------
L"n" ""'>
im-dlmgi will ,
f values ond slope-length lit
contesting
f yo'ue H.B
060
SO
SO
60
70
8C
00
nuts io(
)
J0 p<.reenl
Cu-tf
TABLE W^ P vo/ues maximum strip widths, ond slope-
lenalh limits for contour stripcropping
tnml 4 lope
pirCC'll
1 to 2
3 to 5
9 10 12
13 to 16
17 to 70
11 to 25
, .
P
030
25
25
30
3i
*0
45
,..lu»
e
045
38
38
45
52
60
68
C
060
SO
SO
60
70
80
90
Strip wid.h-
Feet
130
100
100
80
80
60
SO
Mommum IvnglH
800
600
400
240
160
120
100
— ^ —
A ror 4,-or rolnlron of row Cfop small gram with mrodO~
sneHin,. cm! J y-rm of mrodo. A trronri -o» crop e»n r«
„!„„ -no imnll gram ,1 mrodow ,t cttoblnhod .n ,.
H lor 4,.c,r ,«».... of 2 ycor, ro- crop ..«!« 1-u-n -H-
„„ Cl.l0> M • .l""l ""•' ' V- °' "" t"'t""
c. For ol.ernoto Mr.p- "I ""• »°» ond !I"0" 9"""
Ari.ut. ,.np*,dih l.m,. gcn,.,olly do-n~ord I. oc.ommodo.e
-idthi of forrp i-auipmcnl
Computing sediment yield1
Lend slopp
1 to 2
3 to 8
9 to 12
13 to 16
17 to 20
21 to 25
Form
Contour
fiirtor
060
SO
60
70
GO
90
planning
Stripe rop
factor
030
25
30
35
40
45
Croded chonnelt
tod outlrti
012
10
12
14
16
IB
Steep backilope
underground
autleit
005
05
OS
05
06
06
Mope li-nc.ll. n the horizontal ter.oce mlervol TSe luted
err for contoui lurn ,ng No addmnnol contouring (octor .1 uied ,n
the lamputc-iior
Uic l^,c^e value* for eonirol of mlerlerrocr eronon w,,h.n ipeu
fird soil lot', loi roncei
Tht-sc >oljci mcLdc pntropmonl cfficicnc/ ond ore uied «or
control of LC.IT scd-mert w.th.n limit ond for eiiimoling the field t
con'rinjliou 10 wotprshed tcd.menl yield
rf-32
-------
2.2.7 Sediment Delivery Factor (D)
The D factor is the ratio of the watershed sediment yield (SY)
versus the upland erosion potential (A); D - SY/A.
Many factors and processes contribute to its estimation, such as
redeposition of the particulates in the surface water runoff, storage,
trapping of the sediment by vegetation and its residues, local scouring
and redeposition in rills and channels, and possibly other yet uniden-
tified. [Novotny, V., 1980.]
For D, the following formula has been proposed in the literature
[Williams, 1975]:
-bt(d50)1/2
D = e (SW-7)
where:
D = sediment delivery factor
b = decay constant (or routine coefficient)
t = travel time between two sections of a channel
d,-n = mean particle diameter of sediment.
A graphical presentation of sediment delivery ratio as a function
of the watershed size is shown in figure SW-5 [Roehl, 1972]. The
statistical relationships relying on the morphological characteristics
of the watershed have limited applicability for estimating long term
(annual or more) deliveries. Furthermore, their reliability for "event"
deliveries is almost nil as demonstrated by Berkowitz. [Berkowitz,
1979.] Another relation of D to the storm characteristics (El) and the
runoff volume (V) is shown in figure SW-6 [Berkowitz, 1979]. An inter-
esting discussion regarding D is presented by Novotny. [Novotny, 1980.]
sw-33
Arthur D Little, Inc
-------
11-'
100
DRAINAGE AREA .KM2
'. D.livvry ilaii.i Relationship ta the
\V-,tcr«hc(l Sii'e (from Roehl, 1962).
000
^CND Sm— &Jx
7. rU,..:i li ' iJil.:i:..nl l!i.-U . !<•
iucu-K'n-.i A Ih'- I Ill|n '•''' '"' "'
sw-34
-------
2.3 Subroutine SEDIMA
2.3.1 General
Subroutine SEDIMA (Sediment Annual) estimates the annual sediment
washload of the soil compartment due to rain, based upon the USLE-theory
previously outlined. It is "important" to keep in mind that all the
sediment of the compartment will reach an adjacent receiver that has to
be at a distance not exceeding 330 meters (1000 ft), as mandate by the
assumption of the USLE. If the receiver happens to be at a greater
distance, then it might be assumed that only the 330 m area will contri-
bute sediment.
2.3.2 Input/Output Parameters
Input parameters and their associated units (metric system) for
subroutine SEDIMA are:
R [ cm/hr] = R x 10~2; figure SW-1 for R index
m
K [t/ha/EI unit] = 1.292 K; figure SW-3 for K
m
(LS) - LS ; figure SW-4 for LS
m
^ = C ; see section 2.2.5 for C
p
m = P ; see section 2.2.6 for P
Dm = D ; see section 2.2.7 for D.
Output from SEDIMA is:
SYA [tons/ha]
2.3.3 Parameter Units
Metric equivalents were not included in the general procedures and
tables presented in the original USLE documentation [Wischmeier and
Smith, 1978]. Metric untis can then be selected so that each factor
will have a counterpart whose values will be expressed in numbers that
are easy to handle and to combine in computations.
It is recommended, however, by the USLE designers rather to
converting into metric individual empirically derived parameters
(especially R), to converting into metric the USLE as a whole. The
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overall converting formula (1 t/ha = 2.242 tons per acre) for the
metric (m) system is:
SYA,,, = 0.446 SYA (SW-8)
An = t/ha/yr =0.1 kg/m2/yr
A = tons/acre as estimated by the USLE.
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2.4 Numerical Example
Annual soil loss from a particular field area is estimated by
LEVELO and LEVEL1 SESOIL operations by inputing the values of
R, K, LS, C, P and D. These variables describe both the average
climate of the area and the agricultural or field conditions, and can
be obtained from the tables of the previous sections, as demonstrated
by the following numerical example [see also Wischmeier and Smith, p.40].
Assume, for example, a field on Russell silt loam soil in the Topeka
area, Kansas. The dominant slope is assumed 8% with a length of 200 ft.
Fertility and crop management on this field are such that crop yields
are rarely less than 85 bu corn, 40 bu wheat, or 4 t alfalfa-brome hay.
The probability of meadow failure is slight.
The USLE equation factors are obtained as follows:
(1) Factor R is taken from the isoerodent map of figure SW-1.
Topeka, Kansas, in north-east Kansas, lies between iso-
erodents 200 and 250. By linear (graphical) interpolation
R = 205.
(2) Factor K can be obtained: (a) from a table (SW-1, SW-2)
of K values derived either by direct research measure-
ments, or (b) by use of the soil erodibility nomograph
(figure SW-3). For the Russell silt loom soil, K=0.37 (figure SW-3).
(3) Factor LS is obtained from figure SW-4, the slope-effect
chart, where an 8% slope along a 200 ft distance gives
LS = 1.41.
If the field was continuously in clean tilled fallow and the delivery
factor was assumed D = 1, the average annual soil loss from the dominant
slope would equal (equation SW-8):
SYA = 0.446 (205)(0.37)(1.41) = 47.69 t/ha/yr
However, for the present agricultural area we need to account for the
effects of the cropping and management system and support practices
existing in the field, this effect being represented by factors C, P
and D as follows:
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(4) Factor C for the field may be: (a) either derived by
the procedures described in the original USLE theory
[Wischmeier and Smith, p. 28] using data of tables 5
and 6; or (b) obtained from centrally prepared C value
tables available from the SCS (Soil Classification
System). Let us assume for the present example that
C = 0.085 [Wischmeier and Smith, p. 40].
(5) Factor P = 1.0, because rows and tillage are in the
direction of the land slope. However, if farming were
on the contour, the average P value would have been
P = 0.5 (see section 2.2.6).
(6) Finally the sediment delivery factor can be assumed
D = 80% (see section 2.2.7) without having any particular
justification for its value in this illustrative example.
Thus, total annual sediment yield of the field is estimated to
(equation SW-8)*
SYA = 0.446 (205)(0.37)(1.41)(0.085)(1.0)(0.80) = 3.24 t/ha/yr
The USLE may also be used to compute the average soil loss for each
crop in the rotation or for a particular cropstage period, during annual
simulations. For such additional information regarding C, and P values,
the reader is referred to the original work. [Wischmeier and Smith,
p. 41.]
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2.5 Discussion
The USLE is designed to predict longtime-average soil losses for
specified conditions. Best predictions are "averaged-annual" losses
from small watersheds, because the USLE factors are more difficult to
evaluate for large mixed watersheds. Under "small" watersheds it is
meant watersheds with adjacent receivers at a distance not exceeding
330 m (1000 ft), as shown in figure SW-7. For larger watershed simula-
tions it can be assumed that only one portion of the watershed delivers
sediment to the receiver, because upland erosion will be deposited
within the watershed, thus, not contributing to the sediment yield of
the basin. For large watersheds, factor D (delivery factor) becomes of
paramount importance, and USLE predictions should be calibrated or
validated with field data.
The USLE does not consider the basic processes of soil detachment,
transport and deposition separately and does not account for various basin
forms as schematically shown in figure SW-7. Therefore, above equation is
employed only for LEVELO and LEVEL1 (annual simulation) of SESOIL. For
more site specific, accurate and monthly sediment simulations, the user
has to employ LEVEL2 of SESOIL, whose sediment routine is described in
the following section.
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j
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TV
^
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3.0 "MONTHLY" WASHLOAD SIMULATIONS
3.1 OBJECTIVE
The objective of this section is to select and document the most appro-
priate sediment transport routine to meet the following criteria; the
routine should: (1) represent the state-of-the-art, (2) be physically
based and not require calibration, (3) be driven by a limited number of
input parameters, (4) simulate sediment detachment, transport and
deposition, (5) account for various basin shapes, (6) be applicable
to an entire watershed and to discrete portions of the watershed as
well, and (7) account for both long-term (monthly) and short-term (peaks
within a month) simulations.
3.2 BACKGROUND/ACKNOWLEDGMENTS
Numerous factors and processes have been reported in the literature as
providing statistically significant correlations to the attenuation of
sediment and particulate pollutants from nonpoint sources. These factors
include: (1) the effect of rainfall energy, that detaches the soil
particles from small rills and keeps them in movement as long as the
overland flow persists, (3) the effect of vegetation, that slows down
the flow and filters out the particles during shallow flow conditions,
(4) infiltration, which filters out the particles from the overland flow,
(5) small depressions and surface roughnesses in which particles can
settle due to reduction of velocity, and (6) change of slope of the
overland flow. [Novotny, V.; 1980.]
The number of available sediment transport formulas in the literature
is extremely large. Some of these formulas have not received extensive
application, others are too complicated or require knowledge of the
concentration of the suspended load and, therefore, have not been suit-
able for hydrologic simulations. A comprehensive analysis and evaluation
of sediment transport theories have been conducted by Alonso [Alonso, C.V.;
1980] with reference to flume and silt data (Table SW-19).
Theories examined range from simplified formulas to sophisticated
modeling packages accounting for the micromechanics of sediment movement.
Following the testing of the formulas presented in Table SW-19,
Foster, G.R. et_ al [1980] developed a model to estimate sediment yield
from field-size areas. The model summarizes the state-of-the-art in
erosion and sediment yield modeling with appropriate simplifications
required to couple the governing equations.
SESOIL employs the sediment yield model as developed by Foster e± al,
however, adapted to the statistical needs of SESOIL for monthly~yield
and maximum yield of individual rainstorms within a month. Interested
readers are advised to the original work of Foster. [Foster, G.R. ^t al;
1980, Knisel, W.G.; 1980], since the following sections have been mainly
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TABLE SW-19. SUMMARY OF AVAILABLE SEDIMENT TRANSPORT FORMULAS
!yP8
Predicted
load
Author(s) and reference
Date
Detenrn rustic Rpd
Detenr.imsiic Red
Delernnn', stic 8ed
Deterministic Bed
Deterministic Bed
Deterministic B-ed
Determinist ic lied
Deterministic Bed
Ec,piriccl Total
Deterministic Bed
Stochastic Bed
Stochastic Total
Stochastic Bed
Stochastic Total
Deterministic Bed
Deterministic Total
Deterministic Total
Deterministic Total
Deterministic Bed
Deterministic Bed
Empirical Total
Stochastic Total
Stochastic Total
Deterministic Total
Stochast ic Total
Deterministic Total
Deterministic Total
Deterministic Tot al
DeternimsLic Total
Deterministic Total
Deterministic Total
Source: [Alonso, C.V.; 1980]
DuBoys., (11)
Schokhls>i, (26)
Meyer-Peter, (22)
Suaub, (29)
Watet w.i>s Experiment
Station, (_3_1)
Shields, (L'8)
Schoklitsh, (_27)
Kalinske, (_19)
Inglis, (v_13)
Meyer-Peter ana Muller, (_23_)
Einstein, (13)
Einstein, (13)
Einstein and Brown, (_7)
Colby ^nd Hembree, (10)
Bagnold, (2)
Egiazaroff, (12)
Bogardi, (£)
Laursen, (21)
Rottner, (25)
Yalin, (37)
Blench, (S)
Colby, (9)
Bishop, Simons and
Richardson, (4)
Bagnold, (_3)
Wilson, (36)
Chang, Simons and
Richardson, (8_)
Engelund and Hansen, (M)
Graf. (Jj;)
Toffaleti, (_3p)
Ackers and White, (1)
Yang, (39)
1879
1934
19J4
1935
1935
1936
1943
1947
1947
1948
1950
1950
1950
1955
1956
1957
1958
1958
1959
1963
1964
1964
1965
1966
1966
1967
1967
196R
1968
1973
1973
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"abstracted" from his work. The author of this section gratefully acknowl-
edges the assistance received by Professor Foster (Agricultural Engineer-
ing Department, Purdue University, West Lafayette, Indiana 47907) while
working out the adaptation for SESOIL of his sediment yield theory.
3.3 OVERVIEW OF THE MONTHLY WASHLOAD MODEL
Erosion of soil particulates and their transport can be broken down into
four processes [Foster and Meyer; 1972]: (1) detachment by rainfall,
(2) detachment by overland flow, (3) transport by rainfall, and (4)
transport by overland flow. On a given field, either detachment or
sediment transport capacity may limit sediment yield depending on
topography, soil characteristics, cover, and rainfall/runoff rate and
amounts.
Control of sediment yield by detachment or transport can change from
season to season, from storm to storm, and even within a storm. The
relationship for detachment is different from the one for transport
so that they cannot be lumped together into a single equation.
Furthermore, the interrelation between detachment and transport is non-
linear and interactive for each storm, or each storm category, which
prevents using separate equations to linearly accumulate the amount of
detached sediment transport capacity over several storms. Therefore,
to simulate erosion and sediment yield and to satisfy the need for a
continuous simulation model, a rather fundamental approach was selected
by Foster et al [1980] where separate equations are used for soil detach-
ment and sediment transport.
Every model is a representation and a simplification of a real environ-
mental situation. Various techniques, including plains and channels,
square grids, converging sections, and stream cubes have been used to
represent subsections of an area. [Foster jet _al; 1980.] Most erosion/
sediment yield models have adequate degrees of freedom to fit observed
data. Some models, depending on their representation scheme, distort
parameter values more than others do. Distortion of parameter values
greatly reduces the transfer ability of parameter values from one area
to another. An objective, therefore, in Foster's model, was the develop-
ment of a theory representing the field in a way minimizing parameter
distortion. In addition, a minimum number of input parameters have to
be compiled by the user, the simulation being performed with the aid of
theoretically derived equations rather than the employment of massive
input data sets and calibration coefficients to account for the processes
previously described.
Regarding the possible shape of elements and the calling sequence used
to represent field-size areas, Foster e± al distinguish between overland
flow, channel flow, and impoundment (pond) elements as shown in Figure SW-8.
The model user selects the best combination of elements and enters the
appropriate sequence number according to Table SW-20. Computation
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starts in the uppermost element, which is always an overland flow
element and proceeds downslope. Sediment concentration (for each
particle type) is the output from each element which becomes the
input to the next element in the sequence.
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OVEKIAND FLOW
OVERLAND FLO*
ITRCAM
! 0,* )
AVIHACl JLOM
ID OVERLAND FLOW
SEQUENCE AND SLOPE REPRESENTATION
OVEHLAM)
TCftftACC
UdtOEMCMOuNO
OUTLET
(2) OVERLAND FLOW
POND SEQUENCE
CONCCNTftATCO FLOW
(3) OVERLAND FLOW
CHANNEL
OVEHI.AND
FLO*
TERMACL
FLO»
OUTLET
CHANNtl FLOW
U) OVfftLAND FLOW
CHANNEL-CHANNEL SEQUENCE
OvF.*LANO FLO*
I I I i
CMANNtl FLO*
POND AT _
FIELD OUTLET
(3) OVERLAND FLOW
CHANNEL-POND SEQUENCE
Source: [Foster, G.R. et_ al; 1980]
FIGURE SW-8. SCHEMATIC REPRESENTATION OF TYPICAL FIELD SYSTEMS
IN THE FIELD-SCALE EROSION/SEDIMENT YIELD MODEL
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TABLE SW-20. POSSIBLE ELEMENTS AND THEIR CALLING SEQUENCE
USED TO REPRESENT FIELD-SIZED AREA
Sequence number Elements and their sequence
1 Overland
2 Overland-Pond
3 Overland-Channel
4 Overland-Channel-Channel
5 Overland-Channel-Pond
6 Overland-Channel-Channel-Pond
Source: [Foster, G.R. £t al; 1980]
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3.4 MODEL MATHEMATICS
3.4.1 Basic Concepts and Equations
Sediment load is a function of the sediment quantity available: (1) after
detachment by precipitation energy, and (2) by the transport capacity of
overland flow. Quasi-steady state conditions can be assumed, so that a
single rainfall and runoff rate characteristics of each storm (or storm
series) can be used in computational procedures. [Foster and Meier;
1975.] The major sequence of computation is shown in Figure SW-9.
Sediment transport downslope of an area can be described with the steady
state equation of sediment mass continuity [Foster, G.R. et al; 1980]:
dq /dx •= DL + Dp (SW-10)
where:
qs = sediment load per unit width per unit time
x = distance (location)
DL = lateral sediment inflow (mass/unit area/unit time)
Dp «= sediment detachment or deposition by overland flow
(mass/unit area/unit time)
Lateral sediment inflow to a watershed segment may originate from
interill erosion on overland flow elements, or from overland flow (or
a channel, if two channel segments are in a sequence) for the channel
elements. Flow in rills on overland flow areas or in channels, trans-
ports the sediment load downslope. Lateral sediment inflow can be
independently assumed of whether the flow is detaching or depositing.
During simulations of a watershed segment (overland flow element or in
a channel), the initial "potential sediment load" is estimated. This
load equals the sum of the sediment load from the: (1) immediate upslope
segment and (2) the lateral inflow. If:
(1) the initial potential sediment load is less than the
"transport capacity" of the overland flow, detachment
takes place at a rate: "equal or less" the detach-
ment capacity of the flow. When this detachment takes
place, it adds particles having the particle size dis-
tribution for detached sediments. No sorting is assumed
to take place during detachment;
(2) the initial potential sediment load is greater than the
transport capacity of the overland flow, deposition is
assumed to take place.
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COMPUTE fLO*
DETACHMENT
CAPACITY
COMPUTE NE» POTENTIAL
JEDIMENT LOAD AS
lUH Of $COIH(NT FROM
DETACHMENT CAPACITY
AND INITIAL-POTENTIAL
SEDIMENT LOAD
COHPUTC TRANSPOIIT
CAPACITY BA*(D ON
Him POTENTIAL
SEDIMENT LOAC>
SCDIMENT LOAD LEAVING
trOMENT (OUALS
NC« POTENTIAL
SEDIMENT LOAC
i
LIMIT FLO* DETACHMENT
TO THAI OHIC" WILL
JUST FILL TRANSPORT
CAPACITY
00 TO NfHT
UOMN1
SEDIMENT LOAD
LEAVING 'EBMENT
EQUALS TRANSPOPt
CAPACITY
OO TO Nl«T
SEGMENT
Source: Foster, G.R. et al; 1980]
FIGURE SW-9. FLOW CHART FOR DETACHMENT-TRANSPORT-DEPOSITION
COMPUTATIONS WITHIN A SEGMENT OF OVERLAND FLOW
OR CONCENTRATED FLOW ELEMENTS
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Sediment deposition within a segment is described in the simulation by:
D = a(Tc - qs) , and
(SW-11)
0 • evs/qw
where :
D = sediment deposition rate (mass/unit area/unit time)
a = first order reaction coefficient (length"1)
Tc= transport capacity (mass/unit width/unit time)
e = 0.5 for overland flow, and
1.0 for channel flow
Vg= soil particle fall velocity
]+Du(xu/x)1+4'
dTc/dx = constant over segment (SW-13)
Du = a(Tcu - qsu)
^3 • Tc -(D/a)
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in which:
Tc = transport capacity
qs = sediment load at distance x
D = deposition rate
<|> = depositing coefficient
Vs = soil particle fall velocity
qj, = discharge rate
DL - lateral sediment inflow
xu = distance (location)
Du = deposition rate at xu
Tcu= transport capacity at xu
qsu= sediment load at xu
a •» first order reaction coefficient
Case (2) takes place when:
•"•c < ^s within the segment
Tcu > qs , Tc may decrease below qs
within the segment. The point location where qs = Tc is determined
(defined) as xdb (xu in equation SW-13), with Du - 0. Deposition and
sediment load are estimated from equations SW-13.1, SW-13.2 and SW-13 5
(equations group SW-13).
Case (3) takes place when:
Tc > Qs within the segment
Tcu < ^su and (SW-14)
dTc/dx > 0
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At a point (location) xde "deposition" may end. In this case DU = 0,
Tc = qg. Downslope, detachment and "sediment load" take place.
Deposition ends at:
xde = xu 1 - [(!+«(,)/«j,][Du/(dTc/^ - DL)]|1/(1+^ (SW-15)
Sediment load is given by:
Is = (°Fu + DLu + DFL + DLL) Ax/2 + qsu (SW-16)
where:
xde = location where deposition ends
xu = distance
= deposition coefficient
Du = deposition rate at xu ; see equation (SW-13.4)
Tc = transport capacity
DL •= lateral sediment inflow
qs = sediment load
u,L = segment subscripts; u - upper, L = lower
DF = DFu» DFL ' sediment detachment or deposition
°L "" ^u' DLL '• lateral sediment inflow
Ax = length of segment where detachment occurs
Isu = sediment load from upper segment
in which:
Ax is from xde to the lower end of segment
qsu is at xde, which is TC at xde ; ie qsu(xde) - Tc
Case (4) takes place when:
Tc > qg over the entire segment.
Sediment load is estimated with equation SW-16.
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3.4.2 Modeling Issues
Eroded sediment is a mixture of particles having various sizes and
densities. Simulations are performed for each particle type.
Equations describing: (a) sediment characteristics, (b) flow detachment
capacity, (c) rainfall erosivity, (d) effects of overland slope,
(e) sediment transport capacity, and (f) other parameters are presented
[Foster, G.R.; 1980] in the following sections for the:
(1) overland flow element
(2) channel element
(3) impoundment element
The following four sections describe sedimentation characteristic issues,
and issues relating to the modeling of the three elements; overland,
channel and impoundment.
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3.4.3 Sediment Characteristics
Eroded sediment is a mixture of primary particles and aggregates of
various sizes. Size distribution is either an input to the model, or
can be estimated by the model analytically if distribution is not given.
In the latter case the model assumes 5 particle size distributors derived
from surveys of existing data as described in the following paragraph.
Typical sediment characteristics assumed for detached sediment before
disposition, typical for midwestern silt loam soil are presented in
Table SW-21. Equations employed to estimate particle size distributions
are presented in Table SW-22. Particle sizes assumed to derive the
equations for the particle size distributions are presented in Table SW-23.
Primary particle composition of the sediment load is estimated for small
and large aggregates with the equations presented in Table SW-24.
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TABLE SW-21.
SEDIMENT CHARACTERISTICS ASSUMED FOR DETACHED
SEDIMENT BEFORE DEPOSITION; ASSUMED TYPICAL
OF MANY MIDWESTERN SILT LOAM SOILS
Particle Type
Primary clay
Primary silt
Small aggregate
Large aggregate
Primary sand
Diameter
(mm)
0. J2
.010
.030
.500
.200
Specific
Gravity
(g/cm3)
2.60
2.65
1.80
1.60
2.65
Fraction of Total
Amount
(mass basis)
0.05
.08
.50
.31
.06
Source: [Foster, et al.; 1980]
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TABLE SW-22. EQUATIONS EMPLOYED TO DESCRIBE PARTICLE
SIZE DISTRIBUTION
PSA = (1.0 - ORCL)2-49 ORSA
PSI =0.13 ORSI
PCL - 0.2 ORCL (SW-14)
SAG =
2 ORCL ORCL < 0.25
0.28(ORCL - 0.25) + 0.5 0.25 < ORCL £ 0.50
0.57 0.5 0.0: In case LAG <0.0 multiply all other parameters
with a coefficient to make LAG =0.0
Source: [Foster, et al.; 1980]
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TABLE SW-23. ASSUMED TYPICAL DIAMETERS OF PARTICLE SIZES
DPCL = 0.002 mm
DPSI = 0.010 mm
DPSA . 0.20 -
-------
TABLE SW-24. EQUATIONS EMPLOYED FOR PARTICLE COMPOSITION
OF SEDIMENT LOAD*
Small aggregates:
CLSAG = SAG • ORCL/(ORCL + ORSI)
(SW-16)
SISAG = SAG • ORSI/(ORCL + ORSI)
SASAG =0.0
Large aggregates:**
CLLAG = ORCL - PCL - CLSAG
SILAG = ORSI - PSI - STAG (SW-17)
SALAG = ORSA - PSA
where CLSAG, SISAG, and SASAG = gractions of the total for the sediment
of, respectively, primary clay, silt, and sand in the small aggregates
in the sediment load, and CLLAG, SILAG, and SALAG are corresponding
fractions for the large aggregates.
*The text of this table was "quoted" from Foster, G.R, et al. [1980].
**If the clay in the large aggregate expressed as a fraction for that
particle alone is less than 0.5 times ORCL, the distribution of the
particle types is recomputed so that this constraint can be met. A
sum, SUMPRI, is computed whereby:
SUMPRI = PCL + PSI + PSA.
The fractions PSA, PSI, and PCL are not changed. The new SAG is:
SAG = (0.3 + 0.5 SUMPRI)(ORCL + ORSI)/[1 - 0.5 (ORCL + ORSI)].
Above equation is derived given previously determined values for PCL,
PSI, and PSA; the sum of primary clay fractions for the total sedi-
ment equals the clay fraction in the original soil, and the assump-
tion that the fraction of primary clay in LAG equals half of the
primary clay in the original soil.
The model also computes an enrichment ratio using specific surface
areas for organic matter, clay, silt, and sand. Organic matter is
distributed among the particle types based on the proportion of pri-
mary clay in each type. Enrichment ratio is the ratio of the total
specific surface area for the sediment to that for the original soil.
Although these relationships are approximations to the data found in
the literature (Young, R.A.; 1978), they represent the general trends.
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3.4.4 Overland Flow Element
Detachment on interrill and rill areas and transport and deposition by
rill flow are the erosion-transport processes on the overland flow
element. Detachment equations are presented in Table SW-25 (Equation
18.1 and 18.2). Mathematical expressions for the storm erosivity (El)
and slope length exponent (m) of above equations are also presented in
Table SW-25 (Equation 18.3 through 18.4).
Sediment transport capacity is described by the Yalin equation [Yalin, S. ;
1963]; however, it has been modified by Foster and Meyer [1972] to
account for various particle sizes and types. All equations employed
are presented in Table SW-26. Foster, G.R., ££ £^. [1980], presented
six computational steps to redistribute the transport capacity when
excess and deficits of sediment occur.
Regarding the computational procedure the authors [Foster, £££!,•; 1980]
established a sequential simulation starting with the upper end of a
slope and routing sediment downslope, as in most discretized sediment
models. Computations take place for each particle size type. Concen-
tration multiplied by the runoff volume and overland flow area repre-
sented by the overland flow profile gives the sediment yield for the
stone on the overland area of the field.
The overland flow is represented by a typical land profile selected
from possible overland flow paths. Its shape may be uniform, convex,
concave, or a combination of these shapes. Inputs are total slope
length, average steepness, the slope at the upper end of the profile,
the slope at the lower end of the profile and location of end points
of a miduniform section.
Given the above information, the model establishes segments along the
profile. The procedure is illustrated by the convex shape shown in
Figure SW-10. Coordinates of points A, C, and D are given, as are slopes
Sfc and S^ A quadratic curve will pass through point C tangent to the
line CD and through point E tangent to line AB. The location of point
E is the intersection of a line having a slope equal to the average of
Sb and Sm with line AB. If X2 is less than xi, X3 is shifted downslope
so that xi = X£. [Foster, e£ al.; 1980].
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TABLE SW-25. OVERLAND FLOW ELEMENT EQUATIONS
(Equation category SW-18; for
notation see next page)
DLi = 4.57 (El)(s + 0.014) KCP (jpAj (SW-18.1)
DFr = (6.86 x 106)m Vuap1/3 (x/22.1)m-1s2KCP(op//u) (SW-18.2)
where:
El
= 0.103
or
m
= 0.0276 VRI or (SW-18.3)
= e=H.9 + 8.73(logioi) (if hyetograph is available)
= 1.0 + 3.912/ln(x); x>50m (SW-18.4)
= 2 ; x<50m
where :
= interrill detachment rate (g/m2/s)
Dpr = rill detachment capacity rate (g/m2/s)
«
El = £130 = Wischmeier's rainfall erosivity (N/h) expressed
as total rainstorm energy (E) times 30 -minute
(130) intensity*'
m = slope length exponent (-)
s = sine of slope angle
K = USLE soil erodibility factor (gh/Nm2)2/
SW-59
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TABLE SW-25. OVERLAND FLOW ELEMENT EQUATIONS (Continued)
C = soil loss ratio of the USLE cover-management factor
P = USLE contouring factor^/
Op = peak runoff rate expressed as volume/area/time (m/s)
Vu = runoff volume/area (m)
x = distance downslope (m)
Vg = volume of rainfall (mm)^'
1 = maximum 30-minute intensity (mm/h)
e = rainfall energy per unit of rainfall (J/m2/mm of rain)^/
i = rainfall intensity (mm/h)
1/EI[English]*1.702 = EI[metric; N/h]
2/Units of K must be carefully noted. K[English]*131.7 = Kfmetric; gh/Nm2]
•*'Only the contouring part of P is used.
^/Equation SW-18.3a was derived from 2700 data points (r2=0.56)
5/EI=e [Foster, et aj.. ; 1980]
Source: [Foster, G.R. et al; 1980]
July 1981
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TABLE SW-26. DIMENSIONLESS SEDIMENT TRANSPORT
CAPACITY EQUATION OF S. YALIN [1963]
(SESOIL Equation Category SW-19;
For notations, see next page)
Single Particle Equation:
Ps = , Ws = 0.635 6[1 - £ In (1 + a)] = Pf
where:
a = 5A
-- i iwnen i < icr, o = u;
(SW-19)
6 = TT-- 1 (when Y < Ycr, 6
Ycr
A = 2.45(Sg)-0-4(Ycr)l/2
Y =
V2,
(Sg - 1.0) gd
o
= (gRSf)l/2
Modified Multiparticle Supporting Equations:
ns
T = Z 6i
• (Pe)i = Pi6i/T
(Wsi) = (Pe)i (S
where:
Yys(nbov/ncov)°-9
- [qwnbov/sO-5]o.6
SW-61
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TABLE SW-26. DIMENSIONLESS SEDIMENT TRANSPORT
CAPACITY EQUATION OF S. YALIN [1963] (Continued)
where:
Ps = nondimensional transport
Ws = transport capacity (mass/unit time/unit flow width)
Sg = particle specific gravity
g = acceleration due to gravity (g=9.81 in/sec^)
pw = mass density of fluid (water)
Vj. = sheer velocity = (T/PW)^'^
T = sheer stress
0.635 = constant from Shield's diagram
0,A,6 = defined dimensionless expressions
Y = actual lift force given by Yalin
Ycr = critical lift force given by Shield's diagram as a
function of the particle Reynolds number
d = particle diameter
R = hydraulic radius
Sf = slope of energy gradeline
i = sediment particle type
T = total value of S's in the mixture
ns = number of particle types in the mixture
(Ne)i = number of transported particles of type i in a mixture
Ni = number of particles transported in sediment of uniform
type i for a 6i-
(Pe)i = effective P for particle type i in a mixture
(Ps)i = the Ps calculated for uniform material i
(Ws)i = transport capacity of each particle type in a mixture
Tsoil = sheer stress acting on soil
Y = weight density of water
y = flow depth for bare smooth soil
nbov = Manning's coefficient (n) for bare soil; =0.01 for
overland flow; =0.03 for channel flow
ncor = total Manning's (n) for rough surfaces or soil covered
by mulch or vegetation
qw = discharge rate per unit width
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z
o
I
Ul
_l
U)
COORDINATES OF POINTS
A, C, AND 0 AND SLOPES S,
AND S_ GIVEN AS INPUT
IV V \ D
4 '4
DISTANCE
Source: [Foster, et al.; 1980]
FIGURE SW-10. SCHEMATIC REPRESENTATION OF CONVEX SLOPE
PROFILE FOR OVERLAND FLOW
July 1981
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3.4.5 Channel Element
The channel element (Figure SW-8) is used to represent flow in terrace
channels, diversions, major flow concentrations whose topography has
caused overland flow to converge, grass waterways, row middles or graded
rows, etc. This element does not describe gully or large channel erosion
[Foster, G.R.; et_ al; 1980].
The spatially varied flow equation of the channel element is given in
Table SW-27. Equation system (SW-21) is solved for a range of typical
values GI, C2> €3 for subcritical flow, and regression curves are derived
for the components of the normalized friction slope of the channels (SSF).
Curves are fitted to the solutions in order to reduce computation time.
The equation for: (1) the detachment capacity (Dpc) by flow over a
loosely tilled seedbed; (2) the erosion rate in the channel (Ecjj);
(3) the width of the channel (W) at any time after the channel has
eroded to the nonerodible layer; (4) the final width of the channel (Wf);
(5) the hydraulic radius due to soil (Rsoil)» (6) tne shear stress
acting in the soil (Tsoil); and (7) the shear stress acting on the soil
cover (TCOV) are given in Table SW-28 (equationsSW-22 to SW-28).
SW-64
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TABLE SW-27
SPATIALLY VARIED FLOW EQUATION; CHANNEL ELEMENT
- C2
C, = [Z5/2/2(Z2+l)1/2]2/3
[Qe n L/Cy] (SW-21)
C3 = 2 6 Qe2/g z2
where:
y = y/yg
y = flow depth
y = flow depth at the end of the channel
s = channel slope
x = distance along channel
x* = x/Leff
L ff = effective channel length (i.e. , the length
e of the channel if it is extended upslope to
where discharge would be zero with the given
lateral inflow rate
C.. , C_, C, = constants
m = Manning coefficient
z = side slope of channel
Q = discharge at end of channel
B = energy coefficient (app. 1.56)
2
g = 9.81 m/sec ; acceleration of gravity
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TABLE SW-28
OTHER EQUATIONS DESCRIBING SEDIMENT TRANSPORT
Dpc = Kch (l.SST-T^)1'05 (SW-22)
Ech = WacKch (1'35^- V1'05 (SW-23)
(dW/dt). = 2 k , (T - T )1<05/p (SW-24)
i en D cr soil
Wf = [On/Sf1/2]3/8 [{1-2 x cf)/ xcf573] (SW-25)
R ., =
soil
T .« = Y R .. S*
soil soil f
Tcov = Y IV
where:
D = rate of sediment detachment by
flow in channel (mass/area/time; i.e., kg/m /s)
2 1 05 2
K = soil erodibility factor of the USLE (m /N) (kg/m /s)]
en
T = average shear stress (N/m ) of the
flow in the channel.
2
T = critical shear stress (N/m ) below which
erosion is negligible.
E , = rate of soil loss per unit channel length
c (mass/unit/channel length/unit time)
W = width of an eroding channel at equilibrium
ac
W. = width at time t=t.
W = width at time t
(dW/dt). = rate that channel widens at t=ti
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TABLE SW-28 (Continued)
T = shear stress in a channel at a
nonerodible boundary
p ., = man density of soil
soil
Wf = final channel width
3
Q = discharge rate (m /s)
n = Manning friction coefficient
Sf = Friction slope for flow hydraulics
in a channel
x - = Normalized distance around wetted perimeter
where T=T at nonerodible boundary
R .. = hydraulic radius due to soil
T = shear stress at which the cover starts to move
cov
n = total Manning coefficient
n, , = Manning coefficient for a base channel.
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3.A.6 Impoundment (Pond) Element
The impoundment or pond element (Figure SW-8) describes deposition
behind impoundments (including parallel tile outlet terraces) that drain
after each storm. The pond element (receiver) is the last element of an
element series.
The equations for: (1) the sediment fraction (Fpi) deposed in an impound-
ment and (2) the runoff volume (V ) out of an impoundment are presented
in Table SW-29.
3.A.7 Discussion
Discussion regarding use of the model will be presented later.
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TABLE SW-29
SUPPORTING EQUATIONS; IMPOUNDMENT ELEMENT
A1[exp(B1du) - expCB^J/CB Ad) (SW-29)
(SW-39)
where :
A-j^ = 1.136 exp (Zs)
B1 = -0.152 exp (Ys)
Zs - Zs (fa, Cor , Vro, lp)
YS = YS (fa, Cor, Vro, Ip)
Cor = °-15 do2r ' <7'02 * 10'
Zr ' Zr (fa' Cor» Vro' Ip)
in which:
F . = fraction passed for particle i
A., B.. = coefficients
d = equivalent sand diameter of upper end of a
sediment particle class; (mm)
d. = equivalent sand diameter of lower end of a
sediment particle class: (mm)
Ad = width of a particle class; (mm)
3
V = volume of runoff Jischsrged (out of impoundment); (m /storm)
V. = runoff volume into impoundment; (m /storm)
Z = exponent in equation for runoff reduction by
an impoundment; (-)
Z = exponent in equation for deposition in an impoundment; (-)
Y& = exponent in deposition equation of an impoundment; (-)
fa = coefficient in surface area-depth relationship for impoundment
V = runoff/volume (m-Vstorms)
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3.5 Subroutine SEDIMM
3.5.1 General
3.5.2 Input/Output Parameters
3.5.3 Data Files
3.5.4 Discussion
3.6 Sensitivity Analysis of SEDIMM
3-6.1 General
3.6.2 Hydrologic Parameters
3.6.3 Sediment Yield Parameters
3.6.4 Discussion
3.7 Conclusions
Sections 3.5 and 3.6 will be presented in the draft report of this
contract. Section 3.7 will be presented at a later time.
SW-70
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4.0 REFERENCES
Adams, R.T.; Jurisu, P.M. Simulation of pesticide movement on small
agricultural watersheds. Report No. EPA-600/3-76-066. Athens, GA: U.S.
Environmental Protection Agency Research Laboratory; 1976. Available
from: NTIS, Springfield, VA; PB-259933.
Beasley, D.B.; Monke, E.J.; Huggins, L.F. The ANSWERS model: A planning
tool for watershed research. Paper No. 77-2532. St. Joseph, MI:
American Society of Agricultural Engineers; 1977.
Chow, V.T. Open-Channel Hydraulics. New York, NY: McGraw-Hill Book
Company; 1959.
Crawford, N.H.; Donigian, A.S., Jr. Pesticide transport and runoff
model for agricultural lands. Report No. EPA-660/2-74-013. Washington,
DC: U.S. Environmental Protection Agency; 1973.
Daniel, H.A.; Elwell, H.M.; Fox, M.B. Investigation in erosion control
and reclamation of eroded land at the Red Plains Conservation Experiment
Station, Guthrie, Oklahoma, 1930-40. USDA Technical Bulletin No. 837.
Washington, DC: United States Department of Agriculture; 1943.
David, W.P.; Beer, C.E. Simulation of Soil Erosion—Part I. Development
of a mathematical erosion model, Transactions ASAE 18:126-1; 1975.
Daniel, T.C.; McGuire, P.E.; Stoffel, D. ; Miller, B. Sediment and
nutrient yield from residential construction sites. Journal of En-
vironmental Quality 8:304-308; 1979.
Donigian, A.S., Jr., e_t a_l- Agricultural Runoff Management (ARM) model
version II. Report No. EPA-600/3-77-098. Athens, GA: U.S. Environ-
mental Protection Agency Research Laboratory; 1977.
Donigian, A.S., Jr.; Crawford, N.H. Modeling pesticides and nutrients
on agricultural lands. Report No. EPA-600/2-7-76-043. Athens, GA: U.S.
Environmental Protection Agency Research Laboratory; 1976.
Donigian, A.S., Jr.; Crawford, N.H. Modeling nonpoint source pollution
from the land surface. EPA-600/376-083. Washington, DC: United States
Environmental Protection Agency; 1976.
Foster, G.R. Sediment yield from farm fields: The Universal Soil Loss
Equation and Onfarm 208 plan implementation. Chapter 3. Universal Soil
Loss Equation: Past, Present, and Future. Madison, WI: Soil Science
Society of America; 1979.
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Foster, G.R.; Huggins, L.F. Deposition of sediment by overland flow on
concave slopes. Soil Erosion Prediction and Control, Special Publi-
cation No. 21. Ankeny, IA: Soil Conservation Society of America; 1977.
Foster, G.R.; Lane, L.J. Simulation of erosion and sediment yield from
field sized areas. Proceeding of the International Conference on
Watershed Management and Land Development in the Tropics. London: John
Wiley. Forthcoming; 1980.
Foster, G.R.; Lane, L.J.; Nowlin, J.D. A model to estimate sediment
yield from field-sized areas: selection of parameter values. CREAMS—
A Field Scale Model for Chemicals, Runoff, and Erosion from Agricultural
Management Systems, Volume II: User Manual. Washington, DC: United
States Department of Agriculture, Science and Education Administration.
Forthcoming; 1980.
Foster, G.R.; Lane, L.J.; Nowlin, J.D.; Laflen, J.M.; Young, R.A. A model
to estimate sediment yield from field-sized areas: development of
model. Report No. CP-80-10. Laxenburg, Austria: International
Institute for Applied Systems Analysis; 1980. 40 p.
Foster, G.R.; Meyer, L.D. Transport of soil particles by shallow flow.
Transactions of the American Society of Agricultural Engineers 15(1):99-
102; 1972.
Foster, G.R.; Meyer, L.D. Mathematical simulation of upland erosion by
fundamental erosion mechanics. Present and Prospective Technology for
Predicting Sediment Yields and Sources. ARS-S-40. Washington, DC:
United States Department of Agriculture, Science and Education Ad-
ministration; 1975: 190-207.
Foster, G.R.; Meyer, L.D.; Onstad, C.A. A runoff erosivity factor and
variable slope length exponents for soil loss estimates. Transactions
of the American Society of Agricultural Engineers 20(4):683-687; 1977.
Graf, W.H. Hydraulics of Sediment Transport. New York, NY: McGraw-Hill
Book Company; 1971.
Knisel, W.G. A system of models for evaluating nonpoint source
pollution—An overview. CP-78-11, Laxenburg, Austria: International
Institute for Applied Systems Analysis; 1978.
Lane, L.J.; Foster, G.R. Concentrated flow relationships-CREAMS—A
Field Scale Model for Chemicals, Runoff and Erosion from Agricultural
Management Systems, Volume III: Supporting Documentation. Washington,
DC: United States Department of Agriculture, Science and Education
Administration. Forthcoming; 1980.
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Lane, L.J.; Woolhiser, D.A.; Yevjevich, V. Influence of simplification
in watershed geometry in simulation of surface runoff. Hydrology Paper
No. 81. Fort Collins, CO: Colorado State University; 1975.
Langdale, G.W.; Barnett, A.P.; Leonard, R.A.; Fleming, W.G. Reduction
of soil erosion by no-till systems in the southern Piedmont. Trans-
actions of the American Society of Agricultural Engineers 22(0:82-86,
92; 1979.
Lombardi, F. University Soil Loss Equation (USLE), runoff erosivity
factor, slope length exponent, and slope steepness exponent for in-
dividual storms. Ph.D. thesis. West Lafayette, IN: Purdue University;
1979.
Neibling, W.H.; Foster, G.R. Sediment transport capacity of overland
flow. CREAMS—A Field Scale Model for Chemicals, Runoff, and Erosion
from Agricultural Management Systems, Volume III: Supporting Docu-
mentation. Washington, DC: United States Department of Agriculture,
Science and Education Administration. Forthcoming; 1980.
Novotny, V. Delivery of suspended sediment and pollutants from nonpoint
sources during overland flow. Water Resources Bulletin 16(6):1057-
1065; 1980.
Onstad, C.A.; Foster, G.R. Erosion modeling on a watershed. Trans-
actions of the American Society of Agricultural Engineers 18(2):288-292;
1975.
Schwab, G.O.; Frevert, R.K.; Edminster, T.W.; Barnes, K.K. Soil and
Water Conservation Engineering. New York, NY: John Wiley and Sons,
Inc.; 1966.
Shields, A. Anwendung der Ahnlichkeits—mechanik und der Turbu-
lenzforschung anf die Geschiebebewegung, Preuss. Versuchanstalt fur
Wasserbau and Schiffbau. Berlin; 1936.
Springer, D.L.; Breinig, C.G.; Springer, M.E. Predicting soil losses in
Tennessee. Journal of Soil and Water Conservation 18(4):157-158; 1963.
U.S. Department of Agriculture. Sediment sources, yields and delivery
ratios. In: National Engineering Handbook, Section 3, Sedimentation.
U.S. Department of Agriculture, Soil Conservation Service; 1971.
Williams, J.R. Sediment routing for agricultural watersheds. Water
Resources Bulletin 11:965-974; 1975.
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Wischmeier, W.H.; Smith, D.D. Predicting Rainfall Erosion Losses.
Agricultural Handbook Number 537. Washington, DC: United States
Department of Agriculture, Science and Education Administration; 1978.
Wischmeier, W.H.; Johnson, C.B.; Cross, B.V. A soil erodibility
nomograph for farmland and construction sites. Journal of Soil and Water
Conservation 26(5):189-193; 1971.
Wischmeier, W.H.; Mannering, J.V. Relation of soil properties to its
erodibility. Soil Science Society of America Proceedings 33:131-137;
1969.
Woolhiser, D.G. Simulation of unsteady overland flow. In: Unsteady
Flow in Open Channels. Fort Collins, CO: Water Resources Publications,
Volume II, Chapter 12; 1975; 485-508.
Yalin, Y.S. An expression for bedload transportation. Journal of the
Hydraulics Division, Proceedings of the American Society of Civil
Engineers 89(HY3):221-250; 1963.
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SR • soil resuspension
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APPENDIX SR
SOIL RESUSPENSION*
Page
1.0 INTRODUCTION SR-3
2.0 MATHEMATICAL MODELING SR-4
2.1 General SR-4
2.2 Mathematical Approach SR-4
2.3 The SESOIL Subroutine SR-10
2.4 Subroutine Parameters SR-13
3.0 EXAMPLES OF APPLICATIONS SR-15
3.1 Waste Disposal SR-15
3.2 Agricultural Application of Wastes SR-15
4.0 REFERENCES SR-16
TABLE
SR-1 SOIL ERODIBILITY INDEX (I) SR-6
FIGURES
SR-1: THE SOIL RESUSPENSION MODULE STRUCTURE SR-5
SR-2: RELATIONSHIP OF SOIL RIDGE ROUGHNESS FACTOR K,
FROM HEIGHT OF SOIL RIDGES SR-7
SR-3: RELATIONSHIP BETWEEN L, 1, K, C AND E SR-9
SR-4: RELATIONSHIP BETWEEN I, K, C, L, U AND E SR-11
SR-5: SIMPLIFIED FLOWCHART FOR SR SUBROUTINES SR-12
Contribution from Diane Gilbert.
Dec 81
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SR-2
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1.0 INTRODUCTION
The transport by wind of ground surface particles is called soil resus-
pension or wind erosion. In many geographical areas the amount of
material (fugitive dust) involved is significant; therefore sediment
associated pollutant load entrained by the air can also be significant.
"Fugitive dust processes" involve mechanical disturbances on the ground
surface causing atmospheric pollution dishcarges. The physics of soil
resuspension are complex, with several dependent variables.
This appendix is not intended to thoroughly describe the fugitive dust
(soil resusJensionTmechanics; rather it provides i-?""-* ^ST
information on the nature of the process, the assumptions made for the
mathematical modeling developed, and examples of the ^-"^enS^s
routine of SESOIL. Alternative modeling approaches are possible. This
routine i not operational in the 1981 version of SESOIL;.therefore no
special attention is given to the drafting of this —nrf.v. However.
of this routine is a minor task.
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2.0 MATHEMATICAL MODELING
2.1 General
The Soil Resuspension model (SR) estimates the amount of soil lost from
the surface layer due to wind erosion. The amount of pollutant carried
with the resuspended particles is proportional to the soil loss and the
concentration of adsorbed pollutant on soil particles. Depending upon
data availability, or the desired degree of accuracy, the model output
provides estimates of: (1) the monthly soil loss, (2) the average
annual loss, or (3) the annual loss as the sum of monthly losses.
Figure SR-1 shows the overall module structure of SESOIL. The module
accounts internally for a check for average wind speeds below a "criti-
cal velocity" and passes on to the next time step if the critical
condition is not met. A similar check is carried out for frozen or
snow-covered ground conditions; this check is carried out differently
for the annual as opposed to monthly time step analysis.
2.2 Mathematical Approach
Soil resuspension has been described and analyzed by Chepil and Woodruff
(1963), Woodruff and Siddoway (1965) and Evans and Cooper (1980) among
others. This subroutine is based primarily on the work of Chepil,
Woodruff, and Siddoway in the development of an erosion equation and
upon the work of Evans and Cooper in application of the equation to
estimate particulate emissions from various open sources.
The amount of soil eroded by wind, E, as estimated by Chepil and
Woodruff (1963) is:
E = f(I, K, C, L, V) (SR-1)
The variables are:
• I: soil erodibility index (tons/acre/season)
This parameter is based upon the percentage of
soil fractions larger than 0.84 mm (A) as deter-
mined by dry sieving.
The value for I, as used in equation SR-1, however,
is given in tons/acre/month (or year). For flat
sites, values of I are provided in Table SR-1 for
various soil types covering the range of particle
sizes.
• K: soil ridge roughness factor
K is approximated from the soil ridge height
(in inches) using Figure SR-2 or Equation SR-2.
K = ah2 + bh + 1 (SR-2)
SR-4
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Time Step Selection
Annual vs. Monthly
Simulation
i
Data Input
Calculation of Intermediate
Parameters
Calculation of Amount
of Soil Eroded
FIGURE SR-1: THE SOIL RESUSPENSION MODULE STRUCTURE
SR-5
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TABLE SR-1
SOIL ERODIBILITY INDEX (I)
Soil Types
Sand
Loam
Loamy Sand
Sandy Loam
Sandy-clay-loam
Silt Loam
Clay, Silty-clay
Sitly-clay-loam
Clay Loam
Sandy-clay
Silt
Source: Evans and Cooper 1980.
(Tons/Acre/Year) t/A/mo
436 36
207 17
180 15
156 13
129 11
91 7.6
60 5
59 4.9
44 3.7
31 2.6
11 0.92
SR-6
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1.0
0.4
0123*5678
Soil Ridge Height, H (inches)
1C
FIGURE SR-2: RELATIONSHIP OF SOIL RIDGE ROUGHNESS
FACTOR K, FROM HEIGHT OF SOIL RIDGES
SR-7
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where h is the height (in inches of the soil
ridges and must be less than 10. Parameters
"a" and "b" will be determined for the opera-
tional version of SESOIL, which will not
require any user interaction.
climatic factor
The relationship defining C is based upon work
by Thornthwaite (1931) in establishing a P-E
(precipitation-evaporation) index. The general
equation for C is:
0.0026 • 2 • (SR-3)
222
""2
where
z = height of mean wind velocity measurement (ft)
v = mean wind speed at elevation z (ft/sec)
P = mean precipitation (inches)
T = mean temperature (°F)
This relationship was derived from the equation
correcting for wind speeds not measured at 30 ft
elevation (e.g. SR-4), the equation for determining
P-E (e.g. SR-5), and the original relationship for
C (e.g. SR-6).
V = (l.2 _ (SR-4)
30
P-E = 11((P/T)-10)1'111 (SR-5)
.483 \X2P
C = 34.483 \X2PA (SR-6)
(P-E)^
L: field length factor
This parameter is dependent upon the values of I, K,
and C already determined and upon dimensions of the
site. These latter are used to find the equivalent
(or unsheltered) field length, L. Graphs provided
by Woodruff and Siddoway (1965) (Figure SR-3) are
SR-8
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FIGURE SR-3: RELATIONSHIP BETWEEN L, 1, K,
C AND E
SR-9
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used to determine an intermediate value for E as
K, C, L).l
The field length factor is used to account for the
shielding effect of barriers around the site. A
boundary barrier, such as wind break or building can
reduce wind speed in the upwind direction and may even
cause an adjacent dead spot, i.e. vo = 0. Within the
site itself, due to the presence of barriers, effec-
tive length of field exposed to the wind may, there-
fore, be decreased.
t V: vegetative cover factor
The presence of vegetation reduces erosion through
the combined action of three mechanisms: increased
soil moisture held in root zone, physical presence
of the roots, and raising of the mean aerodynamic
surface above the ground surface. The latter pheno-
menon reduces the movement of air (i.e. wind velocity)
at the ground surface.
This parameter is a function of 1, K, C, and L, found
graphically from a family of curves representing
different values of V (Figure SR-4).1
2.3 The SESOIL Subroutine
A simplified flowchart for the SR simulation subroutine is shown on the
next page (Figure SR-5). In order to keep this figure simple, the
details of time step decisions and summation of monthly erosion are
omitted.
The SR subroutine requires input data for parameters which are not used
by other subroutines. These parameters are:
• SOI - the soil erodability index, I; (tons /acre /month)
• WVZ = mean wind velocity at elevation z. (ft/sec)
• WEZ - elevation, z, of wind velocity (WVZ) measurement, (ft)
• SRH - soil ridge height. (inches)
• DFG = days the ground is frozen per month- (days)
• APW = angle of prevailing wind
In the final, fully automated version of SR, this graph will not be
necessary. It is shown here to demonstrate the relationships between
the variables.
SR-10
»
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a: 03 i
~t i « » « 11 io 20 » «o «o 10100 toe
C4. I'K-CY (TONS/ACRE/AMNUMI
FIGURE SR-4: RELATIONSHIP BETWEEN I, K, C, L, U AND E
SR-11
Arthur DUttle,lnc
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Data Input:
1. SR input parameters: SOI, WVZ, WEZ,
SRH, DFG, DTS, BBH, APW
2. Climatic parameters: MPM, TA, NDM
3. User: EAI2, EAF
Check for critical conditions:
1. WVZ1 > 14.7 ft/sec
2. DFG < NDM
CLI = 0.43 (WEZ)"3/2 (WVZ)3
(MPM/TA-10)2'222
i
SRF = a(SRH)2 + b(SRH) + 1
i
EAI1 = SOI x SRF x CLI x DFG/NPM
EFL - DTS - 10 x BBH
Output EFL and EAI1 - User deter-
mines EAI2 as f(EFL, EAI1)
graphically
User determines EAF as f(EAI2)
and inputs EAF
i
EAF = final output
FIGURE SR-5: SIMPLIFIED FLOWCHART FOR SR SUBROUTINES
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• DTS = distance across field to site under analysis (ft)
• BBF = boundary barrier height (ft)
The subroutine requires data for two parameters already incorporated
into SESOIL: MPM, the mean monthly precipitation (MPM) and the mean
monthly temperature (TA). The subroutines which use MPM and TA as
inputs require them in units of cm and °C, respectively, Therefore,
the SR subroutine will read the appropriate values from the data files
and automatically convert MPM from cm to inches and TA from °C to °F as
part of calculating the climatic index C.
The subroutine, as currently assembled, requires user inputs to find
the final eroded amount: EAF. Those inputs are necessary because a
single equation expressing the eroded amount, as a function of all the
variables, has not yet been derived. The relationship between E and V
is of the form E = f(e)v, while that between E and L is of the form
E = f(l - b). The vegetative cover factor (V) is called VCF and the
field length factor (L) is named FLF in the SR subroutine.
The FLF is a function of I, K, and C as well as the physical dimensions
of the site/field relative to the prevailing wind direction. Therefore,
the model outputs an intermediate value for E, defined as EAI1, and a
value for the unsheltered wind distance or equivalent field length
(EFL). These two are applied to Figure SR-3 to determine a second
intermediate value for E, called EAI2.
The final value for E, defined as EAF, is also user determined as the
relation for the VCF is handled graphically based upon EAI2. The,user
must then input EAF so it can be integrated into the pollutant cycle
subroutine. Figure SR-4 is used for this purpose.
The time steps used in the SR subroutine correspond to the four levels
of simulation used by SESOIL: monthly - time-specific, monthly -
general, annual - time-specific, and annual - general.
Note: The final version of the SR subroutine will not require user
input as we will determine the mathematical relationships
involved to allow SR to run unaided.
2.4 Subroutine Parameters
Input Parameters
• Climatic Parameters
MPM = mean precipitation (inches)
TA = mean temperature (°F)
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Soil Erosion Parameters
SOI = soil erodability (I) (tons/acre/month)
WVZ = mean wind velocity at elevation z (ft/sec)
WEZ = elevation z at which WVZ was measured (ft)
SRH = soil ridge height (inches)
DFG = days of frozen or snow-covered ground per month
DTS = perpendicular distance across field to site of analysis (ft)
BBH = boundary barrier height (ft)
APW = angle of prevailing wind (°)
NDM = number of days in the current month
• User Specified Parameters
EAI2 = second intermediate value for eroded amount
EAF = eroded amount — final value
• Program Parameters (not user inputs)
CLI = climatic index, C
SRF = soil ridge height factor
EFL = equivalent field length
EAI1 = first intermediate value for eroded amount
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3.0 EXAMPLES OF APPLICATIONS
3.1 Waste Disposal
For the simple and probably commonly-encountered situation of a waste
disposal site, the following assumptions may be made:
1. Soil types will vary greatly, thus relying upon the
specification of a value for 1 for each site.
2. The site will be flat and have no ridges, thus SRH = 1.
3. C will be determined by the data input for the site.
4. The site will be of sufficient size to eliminate any
reductions in the equivalent field length. Thus
F(L) = 100% or a factor of one.
5. No vegetation will be present at the site of recent
pollutant (waste) application. Thus f (V) = 100% or
a factor of one.
Thus equation SR-1 reduces in this case to
0.43 (z)"3/2 (v )3
Assumption 4 is based upon the fact that EFL = DTS if not the analyti-
cal location is at least 6000 feet from the site's boundary along the
direction of the wind and if I > 30; if I > 130, and the location of
analysis is 2000 feet from the edge, then boundary barrier effects do
not reduce EFL.
3.2 Agricultural Application of Wastes
Whether liquid or sludge wastes have been applied to agricultural lands,
there will likely be a residual pollutant load in the surface soil layer.
While some amount of the residues may be taken up by the crop, the
possibility of erosion exists. In this case, a value for SRH and deter-
mination of the VCF is necessary. The user must specify from Figure SR-2
(or equation SR-2) a value for SRH during data initialization and use
Figure SR-3 during the program. Similarly, if the site does not meet
the size limitations described in application 3.1 above, the procedure
for EAI2 is necessary — also to be input by the user during the program.
Because this function is particularly difficult to utilize with any
degree of accuracy from Figure SR-4, it is recommended that assumption 4
always be made.
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4.0 REFERENCES
Evans, J.S., Cooper, D.W. "An Inventory of Particulate Emissions from
Open Sources" J.A.P.C.A. December 1980, 30(12):1298.
Thornthwaite, C.W. "Climates of North America According to a New
Classification" Geographic Review 21:633, 1931.
Woodruff, N.P., Siddoway, F.H. "A Wind Erosion Equation" Soil Science
Society Proceedings, 1965, p. 602.
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VO • volatilization
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APPENDIX VO
DIFFUSION AND VOLATILIZATION
Page
1.0 INTRODUCTION VO-3
2.0 BACKGROUND VO-4
2.1 General VO-4
2.2 Diffusion/Volatilization VO-4
2.3 Partitioning/Distribution VO-5
2.4 Factors Affecting Volatilization VO-8
3.0 MATHEMATICAL MODELING VO-9
3.1 General VO-9
3.2 Diffusion Coefficients VO-10
3.3 Concentrations of Compound VO-12
3.4 Theoretical Models VO-14
3.5 Experimental Models VO-17
3.6 The SESOIL Diffusion/Volatilization Models VO-19
3.7 Numerical Examples VO-22
4.0 DISCUSSION VO-23
5.0 NOMENCLATURE VO-24
6.0 REFERENCES VO-27
Table VO-1 The Farmer et al Model in SESOIL VO-20
Figure VO-1 Schematic Presentation of Diffusion and
Volatilization VO-6
Figure VO-2 Soil Matrix Partitioning VO-7
Dec. 81 VO-1
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1.0 INTRODUCTION
Diffusion and dispersion (terminology is given in Section 2.0) are two
processes by which molecules of a compound in a region of high
concentration move into a region of lower concentration. Diffusion
occurs most readily in gases, less so in liquids, and least in solids.
Volatilization is a form of diffusion that occurs when a compound moves
from the soil environment into the atmosphere. For many pollutants,
volatilization is an important mechanism for their loss from the soil.
The rate at which a chemical volatilizes from the soil is affected by
many factors, such as soil properties, chemical properties, and en-
vironmental conditions. The magnitude of these factors and the
complexity of their interactions are such that assumptions must be made
in order to develop volatilization mathematical models. Many models are
available in the literature, and some of these models can be applied only
to specific environmental situations and only for the chemicals for
which they were developed. Obviously, all models do not provide the same
numerical results when employed to provide answers to a particular
problem.
This appendix is not intended to thoroughly describe the dispersion,
diffusion and volatilization processes of chemical species in soils;
rather, it provides: background information on the nature of these
processes, a short discussion on the physicochemical parameters af-
fecting volatilization, a short discussion of available volatilization
models and a presentation of the volatilization models employed in
SESOIL. Additional information regarding diffusion and volatilization is
given by Freeze and Cherry (1979) and Thomas (1981).
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2.0 BACKGROUND
2.1 General
In order to select a volatilization model, it is important to understand
the mechanism of movement of chemicals in the soil matrix and from the
soil to the atmosphere. An elucidation of this mechanism will also aid
in enumerating the factors affecting volatilization and the complexity
of their interaction.
It is known that flow regimes of soils have the ability to transport
dissolved substances known as solutes. Solutes are transported by
advection, at an average rate equal to the average linear velocity of the
flow regime. In addition, there is a tendency for the solute to spread
out from its path both longitudinally and transversally. This phenoroenum
is called mechanical dispersion, or dispersion. Diffusion is a
dispersion process of importance only at low flow regime velocities.
Throughout this appendix only the terminology of diffusion will be used.
2.2 Diffusion/Volatilization
Substantial information in this section has been obtained from Freeze
and Cherry (1979).
Diffusion in solution is the process whereby ionic or molecular
constituents move under the influence of their kinetic activity in the
direction of their concentration gradient. Diffusion occurs in the
absence of any bulk hydraulic movement of the solution. If the solution
is flowing, diffusion is a mechanism, along with mechanical dispersion,
that causes mixing of ionic or molecular constituents. Diffusion ceases
only when concentration gradients become nonexistent. The process of
diffusion is often referred to self-diffusion, molecular diffusion, or
ionic diffusion.
The mass of diffusing substance passing through a given cross section per
unit time is proportional to the concentration gradient (Pick's first
law), or
F = -D(dc/dx) (VO-1)
where
F = solute mass flux along x; (ug/cm^-s)
D = diffusion coefficient of pollutant in aqueous solu-
tion; (cm^/s)
c = solute concentration of pollutant; (ug/mL)
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dc/dx= concentration gradient; (-)
x = direction
The diffusion coefficients for electrolytes, for example, in aqueous
solutions are well known. The major ions in saturated soil layer
(groundwater) of NA+, K+, Mg2+, Ca2+, Cl~, HCO_3~ have diffusion
coefficients in the range of 1x10"^ to 2xlO~9 mVs at 25°C. The
coefficients are temperature-dependent and at 5°C, for example, they are
about 50% smaller. In unsaturated soil zones, estimation of the overall
diffusion coefficient (aqueous, vapor phase) is more complicated as will
be discussed in a later section.
In summary, it is important to realize that both diffusion and vol-
atilization refer to the movement of pollutants from a region of high
concentration towards a region of lower concentration (minus sign in
equation VO-1). Thus, in soils, when a "slug" of highly concentrated
pollutant is introduced into a volume of soil (soil, soil moisture, air),
it will "spread" out (diffuse) and will occupy a greater volume and at a
lower concentration. (Figure VO-1.) Within the soil compartment, this
spreading is called diffusion. When the pollutant spreads from the soil
column to the atmosphere, the process is called volatilization. There-
fore, diffusion and volatilization are the two processes contributing to
the continuous movement of a pollutant from its point of release into the
soil compartment to the atmosphere.
2.3 Partitioning/Distribution
A soil environment consists of three media: air, water and soil. (Figure
VO-2.) Therefore, a compound incorporated into a soil matrix will be
partitioned, and the pollutant will be present in all three phases: (1)
mixed in soil air, (2) dissolved in soil moisture, and (3) sorbed on soil
particles. The concentrations of the compound in each medium can be
related to equilibrium partitioning coefficients (frequently constant
parameters or isotherms) as discussed in Appendix AD (Adsorption) and in
Appendix PT (Pollutant Transport).
The three main distribution pathways involved in the diffusion/volatil-
ization process of a compound incorporated in a soil matrix can be
summarized as:
Compound on soil particles
Compound in solution
Compound in vapor phase
compound in solution
compound in vapor phase
(in soil air)
compound into atmosphere
(volatilization)
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'-f-
Sort
FIGURE VO-1
SCHEMATIC PRESENTATION OF DIFFUSION AND VOLATILIZATION
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: -© « Yw A'T
FIGURE VO-2
SOIL MATRIX PARTITIONING
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Diffusion occurs in all three media of the soil environment; however, it
takes place most rapidly in air and least rapidly in solids. Diffusion
in the vapor phase (air) occurs 10^ times faster than in water.
Diffusion in the solid phase is extremely slow compared to other
pollutant transport processes, therefore, it is neglected by most pol-
lutant models.
Volatilization at the soil surface can also occur from all three phases.
However, volatilization from every phase is much faster than diffusion.
Thus, diffusion is the rate-controlling process in the movement of
chemicals from a soil layer, to a soil surface, and then into the
atmosphere.
Due to the interaction of diffusion within a phase with partitioning
among phases, the rate of volatilization depends on both diffusion rates
and partitioning behavior. Therefore, any factor which causes a small
change in the distribution of a compound among the soil, soil-water,
soil-air, and atmosphere can have a large effect on the rate of
volatilization of that compound. For example, when a pollutant is in a
soil to which it is strongly adsorbed, very little pollutant will be in
the soil-air or the soil-water. Since diffusion in solids is slow, only
small amounts of pollutant will be available to volatilize. When this
(same) pollutant is in a slightly less adsorbant soil, soil-air
concentrations can become significant, and the faster air diffusion
process will contribute large amounts of pollutant to the soil surface.
In the latter case, volatilization releases can be quite high.
2.4 Factors Affecting Volatilization
Chemical, soil and general environmental properties affect volatili-
zation. Some of the physicochemical properties of a compound which can
affect volatilization are vapor pressure, solubility in water, ad-
sorption behavior, and diffusion coefficients in air and water. Some
soil properties which influence volatilization behavior include moisture
content, density, porosity, organic carbon content, clay content, and
soil diffusion characteristics. Typical environmental factors impacting
volatilization can be wind speed at the surface, humidity, temperature,
pH, surface cover, and hydrology at the site (e.g., infiltration,
capillarity).
The impact on volatilization rates of many of the above factors is not
quantifiable yet. Therefore, to formulate mathematical models, assump-
tions have been made by researchers by limiting the factors included in
their equations. As of now, no one general model is available to
estimate volatilization rates in all situations, but effective and
promising research is underway. The SESOIL model is designed to employ
existing volatilization models; therefore, as more knowledge and in-
formation become available regarding the process, refined volatilization
models might be implemented by SESOIL.
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3.0 MATHEMATICAL MODELING
3.1 General
Volatilization modeling encompasses the
(1) Selection of a model most applicable to a user's needs
(e.g., problem to be simulated, data availability);
(2) Estimation of the diffusion and other coefficients for
the model selected.
Generally speaking, there exist two types of models for estimating
volatilization rates
(1) Theoretical models based upon Pick's first and second
laws;
(2) Experimental models based upon laboratory or field ex-
perimental data and statistically derived equations.
Pick's first law describes the steady state mass flux of a pollutant due
to diffusion. (See Section 2.2.) Pick's second law is obtained from
Pick's first law and the equation of continuity and describes the
nonsteady state mass flux of a pollutant due to diffusion. Pick's second
law is also known in the literature as the diffusion equation of solutes
in porous media (air, water, soil).
Pick's first law in one direction z is expressed as
F = -D (dc/dz) (VO-2)
Pick's second law is expressed as
dc/dt = D" (d2c/dz2) (VO-3)
where
D* = k • D (VO-4)
in which
F = mass flux across a surface; (ug/cm^-s)
D = aqueous diffusion coefficient of compound; (cm^/s)
c = solute concentration of compound in soil moisture;
(ug/mL)
z = distance (depth) normal to diffusing direction;
(cm)
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t = time; (s)
D* = apparent diffusion coefficient of compound in soil
matrix; (cm^/s)
k = proportionality coefficient, to correct for soil
matrix effects; (-)
Diffusion coefficient (D, D*) definitions and other issues are discussed
in the following section.
No scientist can argue that theoretical models are better or worse than
experimental models since each type has its own strengths. In the first
category are the models of Mayer et al U973), Jury et al (1979), and
Farmer et al (1980). In the second category are the models of Hartley
(1969), Hamaker (1972), and Dow (1979). Each model cannot be applied to
all situations. One model might be appropriate for pollutant applied on
surface, another model might be more appropriate for a chemical
incorporated into an upper soil layer, and a third one the most
appropriate for a buried compound. Some of these models are presented in
subsequent sections.
3.2 Diffusion Coefficients
Pick's law applies to all environmental media—air, water, and soil.
Therefore, for a particular compound, we may have its diffusion
coefficients in air (Da), in water (Dw), in soil (Ds), in soil-air (Dsa),
in soil-moisture (Dsm), and overall apparent coefficients (D*) in all
above media.
In the second Pick's law, the diffusion coefficient of ions is
characterized as an "apparent" diffusion coefficient, D*, which in soil
systems is smaller than that in water bodies, because in porous media the
ions follow longer paths of diffusion caused by the presence of the
particles in the solid matrix and because of adsorption on the solids.
In laboratory studies of diffusion of nonadsorbed ions in porous
materials, k values between 0.5 and 0.01 are commonly observed (Freeze
and Cherry 1979). No specific definition of an apparent coefficient can
be made. Estimation of this apparent diffusion coefficient D* is
equation- and chemical-specific, and such issues are discussed in the
following sections with the work of each individual researcher.
Most of the volatilization equations require as input a chemical-
specific diffusion coefficient, primarily in air or water, in units of
cm/s. It is worth mentioning at this point a few ways of obtaining this
parameter since this information will facilitate readers to better
understand the correct way of applying the various volatilization
equations or models that will be presented in the subsequent sections.
Diffusion coefficients in the air (Da) are available in the literature
for some chemicals (e.g., Weast et al 1978). Diffusion coefficients in
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water (Dw) are also available in the literature or have been estimated by
researchers individually (Bode et al 1973). Nelken (1981) gives some
estimation techniques for both air and water diffusion coefficients.
3.2.1 Molecular Weight Effects
Air diffusion coefficients of two similar compounds 1 and 2 can be
related by the expression
Dai/Da2 = (M2/M1)1/2 (VO-5)
where
Da = vapor phase (air) diffusion coefficient; (cm2/s)
M = molecular weight of compound; (g/mol)
3.2.2 Porosity Effects
Millington and Quirk (1961) have proposed a correcting relationship for
relating the apparent diffusion coefficient of a compound in the soil-
air (Dga) to the diffusion coefficient of the same compound in the air to
^a).
Dsa = Da (na?r3/n2) (VO-6)
where
Dsa = apparent diffusion coefficient of compound in soil-
air; (cm2/s)
Da = diffusion coefficient of compound in vapor (air);
(cm2/s)
nair = soil air-filled porosity; (cm-Vein-*); (mL/mL)
n = soil (total) porosity; (mL/mL)
Frequently, it has been assumed in model applications that D* = Dsa;
where, Dsa, the apparent diffusion coefficient of the compound in the
soil-air and Dsa the "real" coefficient of the compound is the soil-air.
This is done because of the difficulty in defining the meaning of the
"apparent" diffusion coefficient.
The soil air-filled porosity in equation VO-6 can be estimated from
(a) either the (total) soil porosity (n) and the soil
moisture content (6)
nair = n - 6 ('.'0-7)
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(b) or the soil bulk density (p^) and the soil particle
density (p)
n • 1-pb/P (VO-8)
where
Pb = soil bulk density; (g/cm-*)
p - particle density; (g/cm^)
The particle density can be measured, but for most soil minerals,
materials it usually equals 2.65 g/cm-*.
3.2.3 Temperature Effects
Temperature affects values of an air diffusion coefficient according to
(Farner et al 1980)
Da2 " Dal (T2/T!) (VO-9)
where
^a2»Dal = air diffusion coefficients of a compound at T2
and TI; (cm2/s)
T2,Tj = temperatures; (°K)
According to Hanaker (1972), vapor-phase (air) diffusion coefficients of
the same compound and at different temperatures may be related by
Dal/Da2 = P2/P1 (Ti/T2)m (VO-10)
where
p = ambient total pressure; (consistent units)
T = temperature; (°K)
m = experimental coefficient; (-)
3.3 Concentrations of Compound
Volatilization equations have to be employed with care because of
diffusion and the concentration definitions. Some equations, for
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example, account for the total concentration of the pollutant in the soil
c0, other equations account only for the solute concentration c and
others only for the pollutant concentration in the soil-air csa.
The total concentration of a chemical in the soil matrix can be expressed
(Jury et al 1980) as
c0 =(Pb ' s + 6 • c + nair • csa) (VO-10)
where
c0 = overall (total) concentration in soil matrix;
(ug/cm-* soil)
Pb = soil bulk density; (g/crn-*)
s = adsorbed concentration on soil particles (ug/g of
soil)
6 = volumetric soil moisture content; (mL/mL)
c = solute concentration (in liquid phase) of compound;
(ug/mL)
nair = soil-air content or air-filled porosity; (mL/mL)
csa = concentration of compound in the soil-air; (ug/mL)
The solute concentration c of a compound can be related to its soil-air
concentration csa via Henry's law.
csa = c • H/R(T+273) (VO-12)
where
csa = concentration in soil-air; (ug/mL)
c = concentration in soil moisture; (ug/mL)
H = Henry's law constant; (m^-atm/mol)
R = gas constant; (8.2xlO~5 m3-atm/mol-°K)
T = temperature; (°C)
°K = °C+273
The solute concentration c of a compound can be related to its adsorbed
concentration s on soil particles via adsorption isotherms, the latter
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being described in Appendix AD (Adsorption). Two well known isotherms
are Freundlich and Langir.uir.
3.4 Theoretical Models
The following sections present only a general overview of available
mathematical volatilization models. Discussions are tailored to the
needs of this appendix.
3.4.1 Farmer, Yang, Letey
A simple volatilization model to study the steady state rate of
volatilization of hexachlorobenzene (HCB) wastes in soil through _a soil
cover is developed by Farmer et al (1980).
This model is based on a discretized version of Pick's first law
(equation VO-2) over space, and assumes vapor phase diffusion being the
rate controlling processes. The volatilization rate of HCB fron the
landfill, equals
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3.6 The SESOIL Diffusion/Volatilization Models
3.6.1 Diffusion Model
The diffusion equation VO-1 (Pick's first law) is employed by the
volatilization routine of SESOIL to estimate upward mass flow in the soil
column and to the air. Upward diffusion is omitted since it is accounted
explicitly via the volatilization model of the pollutant transport
routine. Downward diffusion is omitted (as a diffusion term) since the
pollutant transport routine accounts for diffusion (partitioning of
phases; see Appendix FT) in the soil matrix explicitly. In that respect,
downward diffusion is also accounted in a different way.
3.6.2 Volatilization Models
The selection of the appropriate volatilization model is entrusted to
the user. Needs of certain simulations performed mandated the employ-
ment of two models, one of which is coded in Subroutines VOLA and VOLM.
(See Appendix FC.) Only minor changes to the code are necessary to add
other volatilization models. The following two sections describe models
the developers of SESOIL have tested.
3.6.2.1 Fanner, Yang, Letey
The Fanner et al (1980) model, applied to HCBs (see Section 3.4.1),
accounts for the Stephan equation which describes pollutant loss via
volatilization of a pollutant that is buried under a layer of clean soil
(cover). According to Farmer et al, this is an appropriate model to
describe pollutant movement through soils where air diffusion is the
rate controlling process of volatilization.
For convenience to SESOIL users, the model (equations)—applied over a
simulation time step t—and its input parameters are summarized in a
table. (Table VO-1.) The chemical-specific parameters (Henry's law and
diffusion constants) are available from handbooks or may be estimated
according to methods presented by Lyman et al (1981). The soil porosity
values are available from the SESOIL documentation (Appendix ID), soil
handbooks (USDA, USGS), or from experimental data. Temperature values
for a site-specific area are obtained from NOAA reports. The compartment
geometry parameters are chosen according to the needs of the investi-
gation. Upward mass flux is accounted in SESOIL only by the existence of
a concentration gradient (Pick's law).
3.6.2.2 Hamaker
The Hamaker (1972) experimental model which estimates time dependent
volatilization fluxes of pollutants mixed in an upper soil layer was
coded in the past in volatilization subroutine VOLATA of SESOIL.
Information of this model is presented in Section 3.6.2. The diffusion
coefficient of the model was obtained from handbooks. Other co-
efficients were estimated on-line by SESOIL. The code accompanying this
version of SESOIL, however, does not contain the Hamaker model for
various reasons.
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TABLE VO-1
THE FARMER et al MODEL IN SESOIL
Governing Equation
P0 = Da[(n-e)10/3/n2][c-H/(R-(273+T)-L)]-At
(VO-14)
Derived by employing
The Stephan equation VO-13, Henry's law equation VO-12, the
Millington and Quick (1961) equation VO-6, and the porosity
convecting equation VO-7 which are given below.
where
n
e
c
H
R
T
L
St.eq :
H.law :
MQ.eq :
Po.eq :
P =
csa
1*.
nair
-Dsa
= c-H/R(T+273)
= D (n10/3/n2)
a air
= n-0
(VO-13)
(VO-12)
(VO-6)
(VO-7)
FORTRAN Variable
'sa
total pollutant flux across soil surface within
time At; (ug/cm2) PVOL
diffusion coefficient of chemical in air; (cm2/s) D
soil (total) porosity; (fraction) N
soil moisture content; (fraction) THA
concentration of compound in the soil moisture; (ug/mL) C
Henry's law constant for compound; (m^-atm/mol) H
gas constant; (8.2xlO"5m3-atm/mol °K) R
temperature; (°C) T
thickness of covering soil layer; (cm) L
apparent diffusion coefficient of chemical in soil-
air; (cm2/s) DA
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TABLE VO-1 (continued)
catm
csa
"air
At
0.0; concentration of compound in the atmosphere;
(ug/mL)
concentration of compound in the soil-air; (ug/mL)
air-filled porosity (fraction)
length of simulation time step; (s)
FORTRAN Variable
CATM
CAIR
NAIR
DT
Assumptions
-air
0.0
Covering layer thickness (L) is equal to the length (depth)
from the center of the SESOIL layer to the soil surface.
Input Parameters to SESOIL Subroutine
Parameters
n
H
T
du,dL
FORTRAN
Description Variable
Diffusion coefficient of the pollutant
in air; (cm^/s) DA
Porosity (total) of the soil; (-) N
Henry's law constant of pollutant;
(m^-atm/mol) H
Temperature; (°C) TA
Soil depths; (cm) DU, DL
Soil depth to groundwater; (m) Z
Schematic of Model Use
for cu ^ CM, CM < CL
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3.7 Numerical Example
Assuming trichloroethylene (TCE) as a chemical compound, in a sandy loam
soil and constant environmental conditions as, for example
Da = 0.072 cm2/s
H = 0.060 m3-atm/mol
R = 8.2xlO~5 m3-atm/mol-°K
n = 0.25
0 = 0.10
T = 14°C
L = 2.0 m = 200 cm
At = 1 month = 2.6xl06s
c = 10 ug/mL
We estimate (equation VO-14) the pollutant mass volatilized within a
month through the soil cover to the atmosphere
P0 = 0.072[(0.25-0.10)10/3/0.252][10-0.060/8.2xlO~5(14+273)-2.6xl06 =
= 685 ug/cm2
VO-22
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4.0 DISCUSSION
As repeated consistently throughout this Appendix, SESOIL users' vol-
atilization equations must be employed with care because of both the
diffusion and the concentration definitions employed by various re-
searchers. Since input data to SESOIL are summarized in Table VO-1
together with the corresponding model employed, special attention has
been given by the SESOIL model developers to facilitate use of this model
and to prevent incorrect input data inserts. Therefore, input data are
kept to a limited number and internal (on-line) model calculations
(e.g., csa versus c partitioning) assist in accomplishing this ob-
jective. Users have to make sure to input the correct number only for an
input parameter. (Table VO-1.)
VO-23
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5.0 NOMENCLATURE
Symbol Description Units
A Function, Equation VO-18
B Function, Equation VO-18
b Soil bulk density g/crn-^
°C Temperature in Celcius °C
c Concentration of compound in soil
moisture (solute concentration) ug/mL
catm
csa
cto
Concentration of compound in
atmosphere ug/mL
Concentration of compound in soil-air ug/mL
Initial (t=0) concentration in soil
moisture ug/mL
Concentration (total) of compound in
soil matrix ug/g soil
d[]/dx Gradient along x
Da Diffusion coefficient of compound
in air
Dw Diffusion coefficient of compound
in water
Ds Diffusion coefficient of compound
in soil
Dsa Diffusion coefficient of compound
in soil-air
Dsm Diffusion coefficient of compound
in soil moisture
D- Apparent diffusion coefficient of
compound in various media
^/
cms
^/
cms
e Coefficient, Equation VO-15 mL/mL
erf[] Error function
VO-24
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Symbol
F
g
H
°K
L
m
M
n
nair
£vp
R
RO
SL
T
t
Description
Solute flux along a direction x,
Equation VO-1
Coefficient, Equation VO-15
Henry's law constant
Adsorption coefficient based on organic
carbon content
Proportionality coefficient to correct
for soil matrix effects
Temperature (in Kelvin)
Depth of soil cover
Exponent, Equation VO-10
Molecular weight of compound
Soil porosity (total)
Soil-air filled porosity
Pollutant flux (volatilized) across
soil cover
Volatilized (total) chemical mass
after time t
Volatilized mass after Dow
Vapor pressure of compound
Gas constant = 8.2xlO~5
Isotherm coefficient, Equation VO-16
Solubility of compound
Temperature
Time
Direction
Units
ug/cm2•s
ug/cm3
nr-atm/mol
(ug/g)/(ug/mL)
°K
cm
g/mol
fraction
fraction
ug/cm2-s
ug/cm2
ug/cm2
mm Hg
m3-atm/mol-°K
ug/mL
°C
VO-25
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Symbol Description
z Vertical distance/direction
6 Soil moisture content
p Soil particle density
Pb Soil bulk density
TT 3.14
Units
cm
fraction
g/cm3
VO-26
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6.0 REFERENCES
Bode, L.E.; C.L. Day; M.R. Gebhardt and C.E. Goering (1973); Prediction
of Trifluralin Diffusion Coefficients, Weed Science, 21(5): 485-489.
English, C.J.; J.R. Miner and J.K. Koelliker (1980); Volatile Ammonia
Losses from Surface-Applied Sludge, Journal WPCF, 52(9): 2340-2349.
Technical Paper 5100, Oregon Agricultural Experiment Station, Corvallis,
Oregon, Projects 116 and 324.
Farmer, W.J. ; K. Igue and W.F. Spencer (1973); Effects of Bulk Density on
the Diffusion and Volatilization of Dieldrin from Soil, J. Environ.
Qual, 2, 107-09.
Farmer, W.J.; M.S. Yang; J. Letey and W.F. Spencer (1979); Hexachloro-
benzene: Its Vapor Pressure and Vapor Phase Diffusion in Soil, un-
published, undated manuscript received as personal communication from
W.J. Farmer, 4 December 1979.
Farmer, W.J.; M.S. Yang; J. Letey and W.F. Spencer (1980); Land Disposal
of Hexachlorobenzene Wastes: Controlling Vapor Movement in Soil, EPA-
600/2-80-119, Office of Research and Development, U.S. Environmental
Protection Agency, Cincinnati, Ohio.
Freeze, F.A. and J.A. Cherry (1979); Groundwater, Prentice-Hall, Inc.,
Englewood Cliffs, New Jersey.
Hamaker, J.W. (1972); Diffusion and Volatilization, Chapter 5 in Organic
Chemicals in the Soil Environment, Vol. 3, C.A.I. Goring and J.W. Hamaker
(eds.), Marcel Dekker, New York.
Jury, W.A.; R. Grover; W.F. Spencer and W.J. Farmer (1980); Modeling
Vapor Losses of Soil-Incorporated Triallate, Soil Sci. Soc. Am. J., 44,
445-50.
Letey, J. and W.J. Farmer (1974); Movement of Pesticides in Soil, Chapter
4 in Pesticides in Soil and Water, W.D. Guenzi (ed.), Soil Science
Society of America, Madison, Wisconsin.
Lyman, W., et al (1981) Research and Development Methods for Estimating
Physicochemical Properties of Organic Compounds of Environmental Con-
cern. Prepared by Arthur D. Little, Inc., Phase II Final Report for U.S.
Army Medical Bioengineering Research and Development Laboratory, Fort
Detrick, Maryland; McGraw-Hill Book Company, New York.
Mayer, R. ; J. Letey and W.J. Farmer (1974); Models for Predicting
Volatilization of Soil-Incorporated Pesticides, Soil Sci. Soc. Am.
Proc., 38, 563-68.
Thomas, R. (1981), in Lyman, W. (1981); Chapter 16.
Weast, R.C. and M.J. Astle (eds.) (1978); CRC Handbook of Chemistry and
Physics, 59th ed., CRC Press, Inc., West Palm Beach, Florida.
VO-27
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AD • adsorption
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APPENDIX AD
ADSORPTION AND DESORPTION
Page
1.0 INTRODUCTION AD-3
2.0 BACKGROUND AD-4
3.0 MATHEMATICAL MODELING AD-6
3.1 General AD-6
3.2 The Freundlich Model AD-7
3.3 The Langmuir Model AD-9
3.4 The SESOIL Model AD-11
4.0 DISCUSSION AD-13
5.0 NOTATIONS AD-14
6.0 REFERENCES AD-15
TABLE
AD-1: REGRESSION EQUATIONS FOR THE ESTIMATION OF Koc AD-10
Dec. 81 AD-J
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AD-2
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1.0 INTRODUCTION
Adsorption is the adhesion of pollutant ions or molecules to the surface
or soil solids, causing an increase in the pollutant concentration on the
soil surface over the concentration present in the soil moisture.
Adsorption occurs as a result of a variety of processes with a variety of
mechanisms and some processes may cause an increase of pollutant
concentration within the soil solids—not merely on the soil surface.
Processes which can contribute to increased soil concentrations include
ion exchange, physical sorption, specific adsorption, partitioning,
fixation, and chemisorption. The general term sorption is often used to
describe these phenomena, particularly when the adsorption mechanisms
are not known. Most sorption processes are reversible; the reverse
processes result in desorption.
Adsorption and desorption can drastically retard the migration of
pollutants in soils, therefore, knowledge of this process is of impor-
tance when dealing with contaminant transport in soil moisture to
groundwater. Sorption is usually considered to occur rapidly, relative
to the rate of pollutant migration in the soil matrix due to the movement
of soil moisture or groundwater flow. In addition, adsorption and
desorption are usually considered to be in equilibrium—in mathematical
modeling studies—and are modeled as one reversible process. This
assumption facilitates modeling without substantially impacting overall
long-term model estimates. Nonetheless, discrete adsorption and de-
sorption modeling is always feasible.
Various scientists have carried out numerous experiments aimed at
understanding the adsorption and desorption process, for example, Rifai,
et al (1956), Day and Forsythe (1958), Biggow and Nielsen (1962), Kay and
Elrick (1967) and Chiou, et al (1979). Their studies, however, do not
always address questions of the nature of the chemical interactions
occurring; they focus, rather, on the movement of pollutants in a soil
column, from which estimates of the magnitude of pollutant involved in
the sorption process.
This appendix is not intended to thoroughly describe the sorption
process of pollutants in soil; rather, it provides background informa-
tion on the nature of the adsorption, mathematical modeling issues and
the way adsorption is modeled in SESOIL.
AD-3
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2.0 BACKGROUND
Background information contained in this section was obtained from the
Encyclopedia of Soil Science, Part 1 (Fairbridge and Finke, 1979), and
its chapter on adsorption phenomena authored by D.R. Kenney. Additional
information is presented in the literature by Lyman (1981) and Dragun
(1980).
In general terms, the sorption of pollutant refers to processes that
result in a higher concentration of a particular component at the surface
or within a solid phase than is present in bulk solution of soils and
sediments. The general term sorption is frequently used instead of
adsorption because the actual sorption mechanisms are not often known.
Sorption is the major general retention mechanism for many organic
compounds and metals, and the sorption and desorption phenomena play an
important role in controling the availability of several plant nu-
trients, the rate of leaching to groundwater, volatilization from soil
surface, or degradation of organic compounds such as pesticides. The
sorption and desorption phenomena also protect water supplies by
retaining numerous potential pollutants including nutrients, heavy
metals, pesticides, and pathogens. Compounds or ions adsorbed on a soil
particle surface are in equilibrium with the soil solution and are
capable of desorption.
In the past the sorption of inorganic ions by soils was often thought to
be due largely to precipitation reactions, i.e., the formation of a
sparingly soluble solid phase. However, careful studies have shown that
the solubility product principle will not account for the extremely low
concentrations of phosphorus and many of the metals in the bulk solution
of an aerated soil (Lindsay 1972). These studies have brought about the
realization that precipitation generally dominates only at relatively
high concentrations of the reactants.
Cation exchange, the interchange between a cation in solution and
another cation on the surface of any surface-active material, is one
important adsorption mechanism for cationic plant nutrients (potassium,
calcium and magnesium) in soils. A similar type of anion exchange may be
involved in the retention of nitrate and chloride in acid highly
weathered soils carrying a net positive charge.
Physical sorption involves the attachment of the sorbent and sorbate
through weak atomic and molecular interaction forces (van der Waal
forces) that operate when the electron clouds of the atoms do not overlap
sufficiently to cause strong attractive forces. The activation energy
for this type of attraction is characteristically low, much lower than is
normally observed for ions (e.g., orthophosphate) which are bound more
strongly.
AD-4
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Most anions, as well as several heavy metals, exhibit a property termed
specific adsorption. This property involves the exchange of the ion with
surface ligands to form partly covalent bonds with lattice ions. The net
result is that the amount of ion adsorbed is far greater than would be
expected for nonspecifically adsorbed species that are adsorbed accord-
ing to their relative abundance (Mott 1970).
Organic compounds, including materials such as proteins, enzymes,
viruses, pesticides, and bacteria can be sorbed to soil particles
(McLaren and Peterson 1965, Marshall 1971, Green 1974, Weed and Weber
1974). As with inorganic species, the mechanisms are extremely complex
and are even more difficult to categorize because of differing chemical
and physical characteristics of natural and synthesized organic ma-
terials .
In summary, sorption is the equilibrium association of pollutants by
soil particles. If adsorption is the dominant process for pollutant
behavior in soils, then pollutant migration to groundwater can be
substantially "retarded." When no sorption occurs the pollutant can—
theoretically—follow the soil moisture or the groundwater flow veloc-
ity. In general terms sorption processes mediate pollutant mass par-
titioning between the solute and adsorbed phase of a compound. This
partitioning forms the concept of mathematical modeling presented in the
following section.
AD-5
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3.0 MATHEMATICAL MODELING
3.1 General
Sorption models have been developed by various researchers by assuming
the existence of a relationship between adsorbed and dissolved concen-
tration of a compound in the soil matrix.
s = s(c) (AD-1)
where
s = adsorbed concentration of pollutant on soil par-
ticles; (ug/g soil)
c = dissolved concentration of pollutant in soil mois-
ture; (ug/mL)
By differentiating the above equation with respect to time, we have
8s/3t = (ds/dc)-(dc/dt) (AD-2)
in which ds/dc represents the partitioning of the contaminant between
the solution and the solids. The temporal adsorbed concentration change
of a pollutant may be estimated in two ways: from (1) tabulated values
of ds/dc versus c, and (2) algebraic empirical formulas giving
s as a function of c, known as adsorption isotherms. The latter approach
is the most common in mathematical modeling and has been also employed in
SESOIL.
Tabulated values of ds/dc versus c and algebraic formulas are derived
from laboratory experiments. From these experiments, the partitioning
of solutes between liquid and solid phases in a porous medium is ex-
pressed in two-ordinate graphical form, where the mass adsorbed per unit
mass of dry solids is plotted against the concentration of the
constituent in solution. These graphical relations of s versus c and
their equivalent mathematical expressions are known as isotherms because
they are derived from experiments conducted at constant (isothermic)
temperature. (Freeze and Cherry 1979.)
Laboratory results of adsorption experiments are commonly plotted on
double logarithmic paper. For solute species at low or moderate con-
centrations, straightline graphical relations are commonly obtained over
large range of concentrations, a fact that can be expressed by
log s = b-log c + log K (AD-3)
or by
s = K-cb (AD-4)
AD-6
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For b=l, we have the linear solution
ds/dc = K (AD-5)
where
s = adsorbed concentration of pollutant; (ug/g soil)
c = dissolved concentration of pollutant; (ug/mL)
K = adsorption (partitioning) coefficient; (ug/g
soil)/(ug/mL)
b = coefficient; (-)
K is a valid presentation of the partitioning between liquid and solids
only if the reactions that cause the partitioning are fast and reversible
and only if the isotherm is linear. Many contaminants meet this
requirement.
Several mathematical descriptions of adsorption isotherms have been
presented in the literature. The Freundlich and the Langmuir relations
are widely used, and the literature provides numerous examples of
experimental data to agree with these isotherms.
3.2 The Freundlich Model
The Freundlich sorptive model is expressed by
s = x/m = K-c1/0 (AD-6)
where:
s = adsorbed concentration of contaminant on soil par-
ticles; (ug/g soil)
x = adsorbed pollutant mass on soil; (ug)
m = mass of soil; (g)
K = adsorption (partitioning) coefficient; (ug/g)/
(ug/mL)
c = dissolved concentration of pollutant in soil mois-
ture; (ug/mL)
n = Freundlich equation parameter; (-)
The Freundlich equation is frequently written as x/m=K-cn; therefore,
care should be taken to determine the form of equation used before any
value of n obtained from the literature is used. Values of 1/n in
AD-7
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equation AD-6 are generally found to range from 0.7 to 1.1, although
values as low as 0.3 and as high as 1.7 have been reported. (Hassett et
al in press.) No methods are available for estimating n; therefore, in
the absence of data, it is frequently assumed n=1.0. (Lyman et al 1981.)
The value of the adsorption coefficient K can be measured directly for
many inorganic pollutants. For most organic pollutants, sorption
(partitioning) occurs mainly on the organic portion of the soil par-
ticles. For these organic chemicals, a partitioning coefficient Koc can
be determined, which is the ratio of the amount of pollutant associated
with the organic carbon of the soil to the pollutant remaining in
solution. The adsorption coeffient K is related to Koc by
K = Koc-Uoc)/100 (AD-7)
where
K = adsorption coefficient of compound; (ug/g)/(ug/mL)
Koc = adsorption coefficient of compound on organic car-
bon (oc) contained in soil; (ug/g oc)/(ug/mL)
(%oc)= percentage of organic carbon contained in the soil
or sediment; (-)
A discussion related to Koc is presented by Miller (1980). Some in-
vestigators have related Koc to the K of the soil on organic matter (Kom)
rather than on soil-organic carbon.
KOC = k ' Kom (AD-8)
where the value of k has been found in many studies to be approximately
equal to 1.724. (Lyman et al 1981.)
Values of Koc may range from
-------
of soil and water, water salinity, particle size distribution and
surface area. Regression equations for the estimation of Koc are given
in Table AD-1. The uncertainty in values of Koc , K and x/m=s estimated
from the equations presented, is related to a number of factors including
estimation method errors, uncertainty in input data, variability in
environmental factors, errors from extrapolating the linear isotherm
equations and errors associated with the assumption of desorption. (Rao
and Davidson 1980. )
3.3 The Langmuir Model
The Langmuir isotherm model was developed for single layer adsorption;
however, it has been found to closely describe soil adsorption phen-
omena. (Novotny et al 1978.) It is based on the assumption that maximum
adsorption corresponds to a saturated monolayer of solute molecules on
the adsorbent surface, that the energy of adsorption is constant, and
that there is no transmigration of adsorbate on the surface phase. The
Langmuir model (Weber 1972) is described by
ds/dt = Ksw-(se-s)
(AD-9)
se =
where
ds/dt= temporal variation of adsorbed concentration of
compound on soil particles; (ug/(g soil)-s)
s = adsorbed concentration of compound on soil par-
ticles; (ug/g soil)
KSV7 = Langmuir equilibrium soil-water adsorption kinetic
coefficient; (s~^)
se = maximum soil adsorption capacity; (ug/g soil)
Q° = number of moles (or mass) of solute adsorbed per
unit weight of adsorbent (soil) during maximum
saturation of soil; (ug/g soil)
b = adsorption partition coefficient; (ug/mL)
t = time; (s)
c = concentration of pollutant in soil moisture;
(ug/mL)
Laboratory studies can provide the values of Q° and b; however, for most
modeling and pollutant transport studies, these variables can be
estimated only roughly from a few routinely measured soil parameters.
(Krenkel and Novotny 1980.) Several authors have correlated phosphate,
AD-9
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TABLE AD-1
REGRESSION EQUATIONS FOR T1IE ESTIMATION OF
i
i—*
o
Eq. No.
45
46
4-7d
48
49
4 10
4 11
4-12
4-13"
4 14'1-'
4.15
4 16
Equation3
log Koe •= -0 55 log S + 3 64 (S in mg/LI
log Koe = -0 54 log S + 0 44
(S in mole fraction)
log Koe = -0 557 loq S ' 4 277
(Sinjj molpt/LI
log Koc = 0 544 log Kovv + 1.377
log KQC = 0 937 loq KQW - 0 OOG
loqK = 100 Ion K -021
oc nw
Ion Ko(. - 0 94 loq Knw « 0 02
loq KO(. = 1 029 loq Kow - 0 18
log Kne - 0 5?4 loq KOM • 0 855
loq Knc = 00007 (P - 45N) «• 0 237
loq Knc = OG81 Ion RCF(I) i- 1 963
log K c = Of.81 loq BCfltl • 1 S8G
No.b
106
to
15
45
19
10
n
13
30
79
13
72
'2
071
094
099
074
095
1 00
r
091
084
Ob9
076
083
Chemical Clasiei Represented
Wide variety, mostly pesticides
Mostly aromatic or poly nuclear aromatic!, two chlorinated
Chlorinated hydrocarbons
Wide variety, mostly ppsticidcs
Aromatics. polynuclcar aromaiics. triazincs and dmitro
anihnp herbicides
Mostly aromatic or polynuclrar aromaiics. two rhlormalpd
s Triarmcs and dinitroaniliiir hprbicidps
Van' ty ol insecticides, lierlncidi-s and lumiicidcs
Substituted phciiylurcas and alkyl N-phpnylcaih.imatcs
Aromatic compounils ureas. 1.3,5 tria/ini-s. caihamatps.
and uiacils
Wide vaniMv. mostly iirslicides
Wide variety . mostly (KSticidcs
a K - soil (or si-ilimnnt) adsoriilion cordicinnl S - watrr snlulnlity KOW - octanol walci partition rnrlficicnt BCF(I) - liioronrrcitialion t.ictui
Ironi llowinq walrr tests OCTdl - Inuconcfiitrjlion l.icloi linen mocli'l ecosystems. P » pjiachor. N - numhPi ol sites in molruilr wlm h cjn p.ir
ticipatc in the lofmation ol .1 hvdroi|i(n boiui
b No • number of chemicals iisi-d to olil am rpgrcssmn cmiation
c i" = correlation cocllicirnt Inr rr-qinssion cniiation
d Equation onrimally given in trims ol Kom Thr ruLilioinhip Knm * K^/1 724 w.is osi-rl toiewntc the cmiation in tcrmsol Knc
e Not available
t Sprcilic chomirals used to nlilain ipqirssion nnualioii not S|iccilifd
Source: Lyman eL a] (1981).
n
-------
phosphorus and organic chemical sorpitivity to various soil parameters,
including Novotny et al (1978), Chesters (1967), and Sanks et al (1976).
For example, Novotny et al (1978) proposed
Q° = a^ej-lO-pH+cjUclay/lOO+diUoc/lOO) (AD-10)
b = a2+e2-10-PH+C2(%clay/100)+d2Uoc/100) (AD-11)
where
a, e, c, d = coefficients; (-)
Uclay) - percent of soil clay content; (%)
(%oc) = percent of organic carbon content; (%)
3.4 The SESOIL Model Equation
The Langmuir isotherm is often preferred in simulation models because of
the equation linearity, as contrasted to the Freundlich equation that is
nonlinear and may require numerical trial and error solution algorithms.
However, it has been determined that adsorption of most chemicals — and
especially of organic chemicals — more nearly approximates the Freundlich
isotherm. Because of this fact, more laboratory and other data are
available for the Freundlich equation in the literature; therefore, the
Freundlich equation is employed and coded in the version of SESOIL
accompanying this documentation. Coding of the Langmuir equation into
SESOIL is a minor task.
Table AD-2 presents a summary of the Freundlich model and the input par-
ameters required for SESOIL.
AD-H
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TABLE AD-2
THE FREUNDLICH ADSORPTION MODEL IN SESOIL
Equation
P(t) = c(t)-K1/n-p-di (AD-6)
where
K = K (overall adsorption)
or
K = Koc-« oc)/100 (AD-7)
in which
FORTRAN Variable
P(t) adsorbed pollutant mass at time t; ug PADSU, PADSL
c(t) dissolved pollutant concentration at CUS, CUM, etc.
time t; ug/uL
* K overall adsorption coefficient; (ug/g)/(ug/mL) KU, KM, KL
* Koc adsorption coefficient on organic
carbon (oc); (ug/g oc)/(ug/mL) KOC
* % oc organic carbon content
of soil; (%) OC
* n Freundlich parameter; (-) FRN
* di soil layer depth i (i=l,N); (cm) DU, DM, DL
* p soil specific weight; (g/cm-*) RS
Note: The user has to input to the data file of the model, either
K £r the set (Koc,%oc), since these sets are mutually
exclusive.
*v
= input variables to this adsorption model.
AD-12
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4.0 DISCUSSION
Equation AD-6 implies that desorption processes between two sequential
time steps t and t+1 are also explicitly accounted by SESOIL because, as
long as c(t+l) is greater than c(t), adsorbed transformation will take
place in the soil matrix; otherwise, [when c(t+l) less than c(t)]
desorption will take place.
Adsorption and desorption processes can be also studied by writing two
separate equations for each phase, namely
SA = KA • c1/1^ for c(T+l)>c(t); adsorption (AD-12)
and
SD = KD • c1/00 for c(T+l)
-------
5.0 NOTATIONS
a, coefficients; (-)
b adsorption partition coefficient, equation AD-4; (ug/mL)
b coefficient; (-)
c dissolved concentration of pollutant in soil moisture; (ug/mL)
d coefficient; (-)
e coefficient; (-)
K overall sorption (partitioning) coefficient; (ug/g)/(ug/mL)
KA adsorption coefficient, equation AD-12; (ug/g)/(ug/mL)
Kg desorption coefficient, equation AD-13; (ug/g)/(ug/mL)
Koc adsorption coefficient of compound on organic carbon; (ug/g
oc)/(ug/mL)
Kom adsorption coefficient of compound on organic matter; (ug/g
oir)/(ug/mL)
Ksw Langmuir equilibrium soil-water adsorption kinetic coeffi-
cient; (s"1)
m mass of soil; (g)
n Freundlich equation parameter; (-)
s, SA adsorbed concentration of pollutant on soil particles; (ug/mL)
SD desorbed concentration of pollutant on soil particles
se maximum soil adsorption capacity; (ug/g soil)
t time; (s~l)
Q° number of moles of solute adsorbed per unit of weight of
adsorbent (soil) during maximum saturation of soil; (ug/g
soil)
x adsorbed pollutant mass on soil; (ug)
% clay percent of soil clay; (%)
% oc percentage of organic carbon contained in the soil or
sediment; (%)
AD-14
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6.0 REFERENCES
Chesters, G. (1967). Terminal Report on Phase I of Insecticide Ad-
sorption by Lake Sediments as a Factor Controlling Insecticide Accumu-
lation in Lakes. Office of Water Resour. Res. Grant No. B-008-Wis.,
University of Wisconsin, Madison.
Chiou, C.T.; L.J. Peters; V.H. Freed (1979). A Physical Concept of Soil-
Water Equilibria for Nonionic Organic Compounds. Science 206(16)
831-832.
Dragun, J. (1980). Sediment and Soil Adsorption Isotherm. Draft Report
to U.S. Environmental Protection Agency, Office of Pesticides and Toxic
Substances, Washington, D.C.
Ellis, E.G. and B.D. Knezek (1972). Adsorption Reactions of Micro-
nutrients in Soils, in J.J. Mortvedt, P.M. Giordano, and W.L. Lindsay
(eds.). Micronutrients in Agriculture. Madison: Soil Science Society
of America, 59-78.
Fairbridge, R.W. and C.W. Finkl, Jr., eds. (1979). The Encyclopedia of
Soil Science, Part 1. Stroudsburg, PA: Dowden, Hutchinson & Ross, Inc.
646 pp.
Freeze, R.A. and J.A. Cherry (1979). Groundwater. Englewood Cliffs, NJ:
Prentice-Hall, Inc. 604 pp.
Hassett, J.J.; J.C. Means; W.L. Banwart; S.G. Wood; S. Ali and A. Khan
(in press). Sorption of Dibenzothiophene by Soils and Sediments. J.
Environ. Qual.
Keeney, D.R. and R.E. Wildung (1977). Chemical Properties in Soils, in
F.J. Stevenson and L.F. Elliot (eds.). Soils for Management of Organic
Wastes and Waste Waters. Madison: American Society of Agronomy, 379-
402.
Krenkel, P.A. and V. Novotny (1980). Water Quality Management. New York,
NY: Academic Press, Inc. 672 pp.
Lyman, W., et al (1981) Research and Development Methods for Estimating
Physicochemical Properties of Organic Compounds of Environmental Con-
cern. Prepared by Arthur D. Little, Inc., Phase II Final Report for U.S.
Army Medical Bioengineering Research and Development Laboratory, Fort
Detrick, Maryland; McGraw-Hill Book Company, New York.
Miller, S. (1980). Adsorption on Carbon: Theoretical Considerations.
Environmental Science and Technology, 14(8), 910-914.
AD-15
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Novotny, V.; M.A. Chin; and H. Iran (1978). Description and Calibration
of a Pollutant Loading Model—LANDRUN. Draft Final Report Volume A.
Chesters, G. and Diamantis, J., eds. International Joint Commission,
Menomonee River, Pilot Watershed Study. Grant No. R005142. Madison, WI:
University of Wisconsin-Madison.
Novotny, V.; H. Iran; G.V. Simsitnan; and G. Chesters (1978). Mathe-
matical Modeling of Land Runoff Contaminated by Phosphorus. J. Water
Pollut. Control Fed. 50(1), 101-112.
Rao, P.S.C. and J.M. Davidson (in press, 1979/1980). Estimation of
Pesticide Retention and Transformation Parameters Required in Non-Point
Source Pollution Models, in Environmental Impact of Non-Point Source
Pollution, Ann Arbor Science Publishers, Inc., Ann Arbor, Michigan.
Sanks, R.L.; J.M. LaPlante; and E.F. Gloyna (1976). Survey—Suitability
of Clay Beds for Storage. Technical Report EHE-76-040CRWR-128, Center
for Research in Water Resources, University of Texas, Austin.
Weber, W.J. (1972). Physicochemical Processes for Water Quality Con-
trol. Wiley (Interscience), New York.
AD-16
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• degradation
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APPENDIX DE*
DEGRADATION AND DECAY
Page
1.0 INTRODUCTION DE_3
2.0 BACKGROUND DE_4
3.0 MATHEMATICAL ANALYSIS DE_5
4.0 REFERENCES DE-7
*
Contribution by K. Scow
Dec 81 DE-1
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DE-2
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1.0 INTRODUCTION
Biodegradation is an important environmental process causing the break-
down of organic compounds. It is a significant loss mechanism in soil
and aquatic systems contributing the mineralization process of organic
compounds, that is their conversion to inorganic substances.
Biodegradation or decay (designated in the following paragraphs as
degradation) of pollutants in the soil is a complex phenomenon involv-
ing a variety of mechanics. The quantification of these mechanics and
the effects of environmental factors on the degradation rates of pollu-
tants is an active research area.
This appendix is not intended to review and describe the biodegradation
or decay process of chemical compounds in soil systems; rather it pro-
vides an overall background information on the nature of biodegradation
and the way this chemical process is modeled. Alternative modeling
approaches are also possible by SESOIL.
Detailed information regarding the biodegradation process, constant
estimates and data availability has been presented in the literature
by K. Scow (1981).
DE-3
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2.0 BACKGROUND
Several definitions of biodegradation have been proposed in the litera-
ture such as primary, ultimate and acceptable biodegradation. In this
chapter biodegradation is defined as the primary degradation of organic
compounds, namely any structural transformation in the parent compound
that changes its identity.
Microorganisms are the most significant group of organisms involved in
biodegradation. Although higher organisms, both plant and animal, are
capable of metabolizing numerous compounds, microorganisms may convert
to inorganic substances (H20, C02, mineral salts) many organic mole-
cules that higher organisms are unable to metabolize.
The most important natural habitats for microorganisms in relation to
environmental biodegradation are soil and water. In both environments,
microorganisms are essentially aquatic organisms, and certain character-
istics are shared by all species (Stotzky 1979).
Soil environments have a diverse microbial population, because they
offer a large variety of food sources and habitats (Hamaker 1972).
The mobility of microorganisms, is decreased in soil, however, because
of physical barriers (such as clay aggregates) and particularly distri-
bution of supportive microhabitats (Scow 1981).
The parameters that influence the rate of biodegradation can be grouped
into two general categories:
(1) those that determine the availability and concentration
of the compound to be degraded or that affect the
microbial population size and activity (eg. population
interactions) and
(2) those that directly control the reaction rate itself
(eg. population size, temperature).
Both direct and indirect variables can be classified as substrate-
related, organism-related or environmental-related. Because of consi-
derable variation in species, habitat, and chemical environment, not
all variables will influence all situations in the same way. For example,
low pH is likely to decrease metabolic activity in most bacteria but it
favors activity in fungi (Scow 1981).
Important environmental and other parameters affecting biodegradation
can be pH, temperature, moisture content in soil, adsorption, oxygen
pressure (aerobic, anaerobic reactions), salinity, solute concentration
of the substance in soil etc.; however, all these parameters are lumped
in one quantified constant describing total loss over time. This is the
biodegradation rate constant discussed in the following section.
DE-4
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3.0 MATHEMATICAL ANALYSIS
The process of biological degradation of pollutants is limited to
microbial metabolism of the compound under aerobic conditions.
Degradation is defined as any structural alteration in the parent
compound at which point it disappears from the soil. Metabolic
products as new chemicals would re-enter a new model run as biotic
input to soil.
The equation describing biodegradation requires input of a first-order
rate constant determined for the particular pollutant being modelled.
It should be measured in a soil culture test under conditions similar
to the site being simulated and complying with state-of-the-art
technology.
Pollutant losses in soil moisture due to biological degradation is
estimated by:
dc/dt = - KD£.cn (DE-1)
c = dissolved concentration of pollutant in
soil moisture (ug/mL)
K-.., = rate of degradation; (day )
n = order of the reaction; (n=l; first order)
Although soil moisture content, temperature and other environmental
parameters strongly influence biological activity, the present SESOIL
routine does not describe their influence on the rate of degradation.
Expansion of the equation to account for these factors is possible
assuming that enough general or chemical-specific data are available
to define the limits they set on degradation rates.
Equation (DE-1) has a general application in all soil zones of the
soil compartment (see Appendix FT), and is employed as a first order
reaction, n=l to express loss/transformation of pollutants from the
moisture content of the unsaturated soil zone.
The total pollutant mass decayed over a short period At in a soil
compartment (layer i) can be finally expressed by
PDE = KDE'9-c-di-At
where
p 2
DE = decayed chemical mass within At; (ug/cm )
= biodegradation rate; (day"*)
DE-5
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0 = soil moisture content; (fraction)
c = solute concentration of pollutant in
soil moisture; (ug/mL)
di = soil layer depth; (cm)
At = time step; (day)
DE-6
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4.0 REFERENCES
Hamaker, J.W. (1972); Decomposition: Quantitative Aspects. In: Organic
Chemicals in the Soil Environment, Vol. 1, C.A.I. Goring and J.W. Hamaker
(eds.), Marcel Dekker, New York.
Lyman, W., et al (1981); Research and Development Methods for Estimating
Physicochemical Properties of Organic Compounds of Environmental Concern.
Prepared by Arthur D. Little, Inc., Phase II. Final Report for U.S. Army
Medical Bioengineering Research and Development Laboratory, Fort Detrick,
Maryland; McGraw-Hill Book Company, New York.
Scow, K. (1981); see Chapter 9, in W. Lyman (1981).
Stotzky, G. (1974); Activity, Ecology, and Population Dynamics of Micro-
organisms in Soil. In: Microbial Ecology, A.I. Laskin and H. Lechevalier
(eds.), CRC Press, Cleveland, Ohio.
DE-7
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APPENDIX HD*
HYDROLYSIS OF ORGANIC COMPOUNDS
Page
1.0 INTRODUCTION HU-3
2.0 BACKGROUND HD-4
3.0 MATHEMATICAL MODELING HD-8
3.1 Governing Equations HD-8
3.2 Numerical Example HD-10
3.3 Input Parameters HD-11
4.0 DISCUSSION HD-13
5.0 REFERENCES HD-14
Table HD-1 Input Parameters to the Hydrolysis Routine HD-12
Figure HD-1 Typical Seasonal Variation of Soil Temperature
Profile HD-7
"Contribution by W. Lyman, Ph.D.
Dec. 1981
HD-1
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HD-2
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1.0 INTRODUCTION
Organic chemicals may undergo a variety of reactions with water. One
family of reactions that leads to an ultimate transformation of the
organic molecule is called hydrolysis. Some chemical classes (e.g.,
hydrocarbons) are known to be generally resistant to hydrolysis while
others (e.g., alkyl halides, carbamates) are potentially susceptible.
The relative importance of the hydrolysis degradation pathway is
enhanced in the soil/groundwater compartment—especially at depths of
approximately one meter below ground surface—since other degradation
and loss pathways (e.g., photolysis, biodegradation, and volatilization)
are eliminated or minimized. Other reactions involving organic mole-
cules and water do occur, but these processes are not included in this
chapter. These other reactions include reversible reactions (e.g.,
acid-base reactions and hydration) and additional reactions which
require reaction conditions that are unlikely to occur in the environ-
ment.
The hydrolysis subroutine of SESOIL allows the user to simulate neutral,
base-catalyzed and/or acid- or base-catalyzed hydrolysis reactions. The
current hydrolysis subroutine is based upon the assumption that both
dissolved and adsorbed organics are equally susceptible to hydrolysis.
Existing experimental data regarding this assumption is contradictory,
although some data show that rates of hydrolysis are not significantly
affected by the presence of moderate amounts of suspended solids in
aqueous systems.
The following sections provide additional background on hydrolysis
reactions, the mathematical equations involved and the limitations the
user should be aware of. For additional information, model users are
referred to the work of Harris (1981), since much of the information
presented in this appendix is a summary of a more detailed investigation
presented by this author.
This appendix is not intended to thoroughly describe the hydrolysis
process of organic compounds in soils; rather it provides background
information on the nature of hydrolysis and the way this chemical process
is modeled. Alternative modeling approaches are also possible by
SESOIL.
HD-3
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2.0 BACKGROUND
Hydrolysis is a chemical transformation process in which an organic
molecule, RX, reacts with water, forming a new molecule. By the normal
definition of hydrolysis this involves the formation of a new carbon-
oxygen bond and the cleaving of the carbon-X bond in the original
molecule:
R-X
H20
R-OH
(HD-1)
Other reactions involving water may result in the elimination of a
hydrogen (H) and a leaving group (X) from neighboring carbons. This
mechanism is apparently favored, for example, in the hydrolysis of
Nemagon®:
Br Br Ci
I I I
CH2- CH - Ch2
(H20)
Major
Product
Minor
•
Product
Br C£
I I
CH2- C - CH2 + HBr
Br Br
-------
CH3P(OCH3)2
j +CH3OH
phosphonic acid
diester
OH
phosphonic alcohol
acid
monoester
(HD-3)
CH3OCNHC6HS
car hamate
CH3OH + C02 +NH,C6HS
alcohol amine
(HD-4)
V —"HOCHjCHjOH
epoxide glycol
(HD-5)
CHjCOOH
NH
nitrile
carboxylic
acid
(HD-6)
CH3CH2CH2CHCH3-I!ilcH3CH2CH2CH-CH3 +Br-
Br OH
alkylhalide alcoho,
anion
(HD-7)
H,0
"^X • "
arboxyUc acid
ester
~ ^
carboxylic
acid
+ CH3OH
alcohol
(HD-8)
Source: Lyman et al (1981).
HD-5
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Rates of hydrolysis are usually measured under controlled laboratory
conditions that include constant temperature and may include the use of
buffered solutions and solvating agents. Extrapolation of such data to
environmental conditions involves considerable uncertainty, partic-
ularly with regard to the influence of temperature, solution ionic
strength, adsorption on soils, and the possibility of catalytic action
by either dissolved material (e.g., heavy metal cations) or solid
surfaces. If uncorrected laboratory data are used in SESOIL—and this
may often be the only choice—then model predicted pollutant concen-
trations should be considered as rough approximations only. Harris
(1981) provides instructions for estimating hydrolysis rate constants
for certain classes of chemicals.
It may be possible for a user to employ rate constants (k) that have been
corrected for the difference between the temperature used for the
measured (or estimated) value, and the temperature of the soil system.
For example, if the activation energy (E^) for the reaction is known,
then extrapolation from a reported value of k.. , at temperature Tj, to an
adjusted value of \<-2 at temperature T2 is given by:
k, = k. exp - ££ (_!-_!)] (HD-9)
z L R T2 TI
where:
k2 =extrapolated hydrolosis rate constant of the
compound at T2; (sec"*)
kj = given hydrolysis rate constant of compound at Ti;
(sec-1)
E£ = activation energy of reaction; (cal/mol)
R = gas constant of compound; (=1.987 cal/mol-K)
Tj,T2 = temperature; (°Kelvin)
If a measured value of EA is not available, a value of 17,500 cal/mole may
be assumed (Harris 1981).
Soil temperature is generally a complex function of various parameters,
such as geographic location, soil nature (including water content), soil
depth, air temperature, and heat flow from below. For SESOIL, the
diurnal variations in soil temperature (important for approximate the
top meter of soil) can be ignored because of the longer time scales used
by the model. Seasonal and depth variations, however, may be important
and the user should seek to correct the estimated hydrolysis rate
constants to the appropriate temperature. A typical soil-temperature
profile as it might vary from season to season in a frost-free region is
shown in Figure HD-1.
HD-6
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H
C-i
10
TEMPERATURE (°C)
15 20
25
winter
30
Source: Hillel 1980.
FIGURE HD-1
TYPICAL SEASONAL VARIATION OF SOIL TEMPERATURE PROFILE
HD-7
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3.0 MATHEMATICAL MODELING
3.1 Governing Equations
It is generally observed that hydrolysis of organic chemicals in water
follows a first-order kinetic law, that is, the rate of its disappearance
is proportional to the concentration of the compound:
-d[RX]/dt = kT[RX]
(HD-10)
or by approximating the differential to a difference, by:
-A[RX]/At = kT[RX]
where :
[ ] =
d[] a AM =
kj =
At =
concentration of organic compound RX; (mol/mL)
differential
hydrolysis rate constant;
time, step in units compatible with k ; (days)
The rate constant in equation (HD-10) is an oversimplification for most
organic hydrolysis reactions. It is often appropriate to consider k_ as
having contributions from neutral, acid-catalyzed and base-catalyzed
reactions :
kT = k0 + kH[H+] + kOH [OH']
(HD-12)
where:
[H+]
[OH~]
rate constant for neutral hydrolysis; (days~^)
rate constant for base-catalyzed hydrolysis; (days"*
mol'i-L)
rate constant for acid-catalyzed hydrolysis; (days"*
mol'i-L)
hydrogen ion concentration = 10~PH; (mol/L)
hydroxyl ion concentration = 10P^~^; (mol/L)
HD-8
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The neutral rate constant (k0) has units of (time"1), while RQH and 1
-------
At = simulation time step; (days)
0(t) = soil moisture at time t; (fraction)
dj_ = depth of soil layer i; (cm)
p = soil density; (g/cm3)
VH-Q = volume of water in the compartment; (cm3)
Vsoii = volume of soil in the compartment; (cm-*)
AR - surface area of soil compartment; (cm2)
3.2 Numerical Example
Calculate the mass of ethyl acetate hydrolyzed after one month in contact
with a wet soil given: (1) an initial concentration of 100 ug/ml; (2) a
soil temperature of 10°C; (3) hydrolysis rate constants at 25°C of
1.1 x 10~4 L/mol-s for kH, 1.5 x 10~10 s"1 for k0 and 1.1 x 10'4 L/mol-s
for koH> (4) a soil moisture pH of 8.0; (4) no pollutant adsorbed on soil;
(5) a soil moisture volume of 10 mL.
(1) To correct the rate constants from 25°C (298 K) to 10°C (283 K), use
equation (HD-13) with an assumed value of 17,500 cal/mol for E^.
k2/k, = exp [- 17.500 (_L_ - _L)] = 0.209
L L 1.987 283 298
Thus, kH (10°C) = 0.209 • 1.1 x 10~4 = 2.3 x 10~5 L/mol-s
k0 (10°C) = 0.209 • 1.5 x 10-10= 3.1 x 10'11 s"1
kOH (10°C)= 0.209 • 1.1 x 10'1 = 2.3 x 10~2 L/mol-s
These corrected values (as well as pH) would be the user's input
into SESOIL which would then carry out the following calculations.
(2) From equation (HD-12):
kT - 3.1 x 10"11 + 2.3 x 10~5 • 10'8 + 2.3 x 10~2 • 10-(8-14) =
= 2.3 x 10~8 s'1 = 1.99 x 10~3 day"1
(3) From equation (HD-14) with At = 30 days:
MH-Q = Mass hydrolyzed=1.99xlO~3day~1-100ug/mL-30days-10mL=59.7ug
HD-10
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3.3 Input Parameters
The input parameters to the hydrolysis routine are presented in
Table HD-1. The chemical specific parameters (k, k^, ^OH^ can be obtained
from handbooks (e.g., Lyman 1981). Site specific parameters must
satisfy the needs of a site specific simulation and study.
HD-11
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TABLE HD-1
INPUT PARAMETERS TO THE HYDROLYSIS ROUTINE
Parameter Units FORTRAN Variable
k-. Neutral hydrolysis rate constant day"^ KNH
kjj Acid catalyzed rate constant day"!-mol"^-L KAH
ROH Base catalyzed rate day~l-mol~l-L KBH
p Soil density g/cm-* RS
dj Compartment depths cm DU, DM, Z
A Compartment area cm^ AR
pH pH of soil - PH
HD-12
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4.0 DISCUSSION
It is worth emphasizing again the assumptions made for the development of
the hydrolysis subroutine in SESOIL.
• First, the calculations assume that dissolved and ad-
sorbed organic species are equally susceptible to hy-
drolysis. If subsequent experiments show this to be a
serious error, then the computer code would have to be
modified to account only for an "available" fraction of
pollutant.
• Second, the calculations consider only simple hydrolysis
reactions (neutral, acid-catalyzed and base-catalyzed)
and do not follow for general catalysis by other diverse
acids, bases, cations or solids. The model does not
consider effects of ionic strength or the presence of
other dissolved organics, nor the variation of pH in
the soil compartment, or temperature along the soil column.
. Third, the model assumes that the hydrolysis rate con-
stants that are entered have been previously corrected to
the correct soil temperature for the simulation.
The above assumptions imply that the model user should not "blindly" use
just any laboratory-measured (or estimated) rate constants, but should
give some considerations to the soil system modeled and the corrections
that might have to be undertaken for the input data.
HD-13
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5.0 REFERENCES
Harris, J. (1981), in Lyman, W. (1981); Chapter 7.
Hillel (1980) Fundamentals of Soil Physics, Academic Press, Ann Arbor,
Michigan.
Lyman, W. , et al (1981) Research and Development Methods for Estimating
Physicochemical Properties of Organic Compounds of Environmental Con-
cern. Prepared by Arthur D. Little, Inc., Phase II Final Report for U.S.
Army Medical Bioengineering Research and Development Laboratory, Fort
Detrick, Maryland; McGraw-Hill Book Company, New York.
HD-14
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CI - cation exchange
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APPENDIX CE*
CATION EXCHANGE
Page
1.0 INTRODUCTION CE-3
2.0 BACKGROUND CE-4
3.0 MATHEMATICAL MODELING CE-6
3.1 Governing Equations CE-6
3.2 Input Parameters CE-6
4.0 DISCUSSION CE-8
5.0 REFERENCES CE-9
Table CE-1 Input Parameters to Cation Exchange Routine CE-7
•'Contribution by W. Lyman, Ph.D.
Dec. 81 CE-1
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CE-2
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1.0 INTRODUCTION
Cation exchange is a mechanism by which cations in solution may be ad-
sorbed on soil and thus removed from the mobile aqueous phase; charged
species (cations) may exchange with various minerals and/or other soil
constituents. The process of cation exchange is complex; for several
ions—particularly metal cations—and under certain conditions, the ca-
tion exchange capacity of the soil is strongly correlated with the ad-
sorption of the ion, as discussed in the next section.
The cation exchange subroutine of SESOIL is designed as an optional way
of considering adsorption. Therefore, if this routine is used, the
adsorption equation in SESOIL should not be used unless the user has
selected the model inputs (cation exchange capacity and adsorption para-
meters) in a way to avoid any "double counting" for adsorption.
It is incumbent upon the user to insure that cation exchange is the
predominant adsorption mechanism at the site being modeled. This may
require considerations of the leachate characteristics (pH, ionic
strength, concentration of major cations), metal speciation and soil
characteristics.
This appendix is not intended to thoroughly describe the cation exchange
chemistry of species in soils; rather it provides background information
on the nature of cation exchange and the way this chemical process is
modeled. Alternative modeling approaches are also possible by SESOIL.
CE-3
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2.0 BACKGROUND
The cation exchange capacity (CEC) of a soil is usually defined as the
number of milliequivalents (m.e.) of the ion that can be exchanged (ad-
sorbed) per 100 g (dry weight) of soil. The process is viewed as an
exchange with some other cation that initially occupies the adsorption
site on the solid. With clays, the exchanged ion is often calcium:
M++ + [Clay] • Ca ^=£" Ca++ + [Clay] • M (CE-1)
Among soils, clays tend to have the highest CEC values, although ma-
terials other than clay may contribute. Brady (1974) lists, for example,
the following typical CEC values (m.e./lOO g) for various materials:
humus, 200; monomorillonite, 100; vermiculite, 150; hydrous mica and
chlorites, 30; kaolimite, 8; and hydrous oxides, 4. He also provides
data showing a range of CEC values in soils of 2-60 m.e./lOOg. This range
is somewhat larger than the 2-37 m.e./lOO g range associated with 11
soils studied by Fuller (1978), which in turn is larger than the 0-4.2
m.e./lOO g range given by Wang et al (1975) for 30 soils in Rhode Island.
The cation exchange capacity of a soil is not an invariable property of
the soil; in most soils the exchange capacity increases with pH (Brady
1974).
The actual cation exchange reation—equation (CM-1)—is probably fast
and is also reversible. One cation with a high affinity for an exchange
site may displace the cation previously at the site if the latter has a
lower affinity. This is called the "mass action" effect. The relative
strengths of soil-cation interactions are seldom available from the
literature; therefore, they are not modeled in SESOIL. Furthermore,
very high concentrations of certain cations (e.g., the common Ca++, Na+,
Fe++, and K4) may so overwhelm the exchange capacity of a soil that low
concentrations of other cations—including those with higher affin-
ities—will not be significantly adsorbed. Landfill leachates and
aqueous industrial wastes often have very high concentrations of total
dissolved solids (including Na+, Ca++, etc.) and one would expect the
major cations in these wastes to effectively block the adsorption (by
cation exchange) of other trace cations for some significant time and
distance in the migration through the soil/groundwater system.
Without some laboratory data, it is difficult to predict when cation
exchange will be important and for what cations. This is not to say that
some situations have not been modeled. They have, but the models usually
require the use of equilibrium constants, the consideration of the "mass
action" and pH effects, and also require detailed knowledge about the
nature of the soil and the constitutents (e.g., other major cations and
anions) of the leachate. This information will seldom be easy to
assemble. Griffin and Shimp (1978) give examples of cases in which
cation exchange is likely to be important for Pb, Cu, Zn, Cd, Na, K, Mg,
and NH^. For the heavy metals, cation exchange is unlikely to play a
significant role if the leachate pH is above 7; above this pH,
precipitation may be the controlling factor in mobility.
CE-4
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It should be mentioned that the present version of SESOIL does not spec-
ifically consider the process of fixation for pollutants in the lea-
chate. Fixation is a process whereby the pollutant (e.g., a metal
cation) diffuses into the small pores or interstitial layers of the soil
matrix and, following some form of chemisorption or bonding, becomes
permanently bound (fixed) to the soil. Fixation can be a very important
removal process for heavy metals in some situations. The fixation
process might be simulated for SESOIL, however, by appropriate use of the
adsorption or cation exchange routines that are available.
CE-5
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3.0 MATHEMATICAL MODELING
3.1 Governing Equations
The SESOIL subroutine for cation exchange is optional and when used will
presumably obviate the need for any other adsorption subroutine. For
modeling purposes, the process is considered to be "irreversible." The
calculation of the pollutant mass immobilized by cation exchange is
given by:
MECM = a • CEC • MWT/VAL (CE-2)
where:
MECM = maximum pollutant mass immobilized (cation ex-
changed) by the soil; (ug/g soil)
a = 10.0; units coefficient; (-)
CEC = cation exchange capacity of soil; (m.e./lOOg of dry
wt. soil)
MWT = pollutant molecular (or atomic) weight; (g/mol)
VAL = valence of cation; (-)
Example:
Pollutant: Pb++ (MWT = 207, VAL=2)
Soil with: CEC = 3 m.e./lOO g (of dry soil)
MCEC = 10.3.207/2 = 3100 ug/g soil
Once the maximum capacity of the soil has been reached in a given soil
element, SESOIL will assume that no further adsorption takes place un-
less another adsorption subroutine has also been employed (e.g., for
fixation modeling). Cation exchange is assumed to be instantaneous;
therefore, it is modeled as proceeding to completion before the start of
all other processes. These assumptions must be made in order to model a
cation exchange process that is general to many situations. When more
specific data are available, modifications to this routine can be made.
3.2 Input Parameters
The input parameters to the cation exchange routine are presented in
Table CE-1. Data are available from soil and chemical handbooks.
CE-6
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TABLE CE-1
INPUT PARAMETERS TO CATION EXCHANGE ROUTINE
Parameter Units FORTRAN Variable
Cation exchange capacity of the soil (ug/100 g dry soil) CEC
Molecular or atomic weight of pollutant (g/mol) MWT
Valance of pollutant (-) VAL
CE-7
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4.0 DISCUSSION
It is incumbent upon the user to determine when it will be appropriate to
use the cation exchange subroutine. This may require, as mentioned
above, a consideration of the "speciation" of the pollutant, the soil pH,
the presence of other cations, and the nature of the soil. For most
metals the speciation can be predicted with models such as REDEQL (Ingle
et al 1980). In general, no other adsorption routine should be used when
the cation exchange routine is employed. The calculations in SESOIL
assume a fast, irreversible removal of the cations from solution, no
competition with other ions, and a higher priority than any other process
in competition for the cation in solution.
CE-8
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5.0 REFERENCES
Brady, N.C., (1974), The Nature and Properties of Soil, 8th ed. ,
Macmillan Publishing Co., Inc., New York.
Fuller, W.H., (1978), "Investigation of Landfill Leachate Pollutant
Attenuation by Soils," Report No. EPA-600/2-78-158, U.S. Environmental
Protection Agency, Cincinnati, Ohio. (NTIS Report No. PB-286 995.)
Griffin, R.A. and N. F. Shimp, (1978), "Attenuation of Pollutants in
Municipal Landfill Leachate by Clay Minerals," Report No. EPA-600/2-78-
157, U.S. Environmental Protection Agency, Cincinnati, Ohio.
Ingle, S.E.; J.A. Keniston; D.W. Schultz (1980); "REDEQL.EPAK: Aqueous
Chemical Equilibrium Computer Program", Report No. EPA-600/S-80-049,
U.S. Environmental Protection Agency, Corvallis Environmental Research
Laboratory, Corvallis, Oregon.
Wang, M.C. and V.A. Nacci, (1975), "Movement of Trace Metals with
Percolating Water," Report on Project No. A-052-RI to the Office of Water
Research and Technology (U.S. Department of the Interior), Washington,
D.C. (NTIS Report No. PB-246-104.)
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CM - complexation
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ft
APPENDIX CM
COMPLEXATION OF METALS IN SOLUTION
BY ORGANIC LIGANDS
Page
1.0 INTRODUCTION CM-3
2.0 BACKGROUND CM-4
3.0 MATHEMATICAL MODELING CH-7
3.1 Mathematical Expressions CM-7
3.2 Input Parameters CH-9
4.0 DISCUSSION CM-13
5.0 REFERENCES CM-14
TABLES
CM-1 Equation Describing the Complexation Concept
in SESOIL CM-10
CM-2 Input Parameters for Complexation Algorithms CM-12
Contribution from W. Lyman, Ph.D.
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CM-2
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1.0 INTRODUCTION
Complexacion (or chelation) is the process by which metal ions and
organic or other nonmetallic molecules (called ligands) can combine to
form stable metal-ligand complexes.
It is well known that a number of organic materials, of both natural and
anthropogenic origin, are capable of complexing with several heavy
metals including (but not limited to) Cu, Pb, Fe, Zn, Cd and Ag. The
complex that is formed will generally prevent the metal from undergoing
other reactions or interactions that the free metal cation would.
The current level of understanding of this process is not very advanced
(less so for interactions in groundwater and leachates than in surface
waters) and the available information has not been shown to be
particularly useful to quantitative chemical modeling (Jenne 1979;
McCrady and Chapman 1979). However, complexation can have a significant
effect on the behavior of metals and soils; therefore, a simplified
representation of the complexation process is incorporated in SESOIL.
As the process (and factors that affect it) becomes better understood and
quantifiable, this routine can be improved to reflect the new knowledge.
The current complexation subroutine of SESOIL allows the user to
consider only a process in which a metal ion in solution is complexed by
an organic ligand resulting in the formation of a soluble complex. It is
incumbent upon the model user to determine if such a process is likely in
the situation being modeled and to supply the appropriate stability
constant, ligand concentration and mole ratio of metal to ligand in the
complex.
This appendix is not intended to fully describe the complexation process
of metals in solution by organic ligands; rather, it provides background
information on the nature of complexation and one way this chemical
process is modeled. Alternative modeling approaches in SESOIL are
possible.
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2.0 BACKGROUND
It is believed that metals bind to humic and fulvic acids through three
possible types of bonds as shown in equations (CM-1), (CM-2) and (CM-3).
(Giesy and Alberts 1981.)
R - C - 0~ + M2+ + H20
0
R - C - 0 - M - OH + HH
(CM-1)
C-C-0~+C-C-0~+ M2+
C-C-0-M-0-C-C + H+
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1978; Giesy et al 1978) and in soils this material would likely be
associated with the solid matrix of the soil. Low concentrations of
these materials will be in solution although complexation with metals
may cause some precipitation (Saar and Weber 1980) and adsorption of a
soluble complex by soil is certainly possible. The complexation
subroutine in SESOIL is only intended to model the situation where a
soluble ligand reacts with a metal ion to form a soluble, nonadsorbable
complex. Complexation by materials in the solid phase of the soil may be
modeled (in some cases) by the cation exchange subroutine.
Considerably more information appears to be available on metal com-
plexation in surface waters than in ground waters. Reports covering
complexation in soils, sediments, groundwaters and/or leachates that may
be useful to the reader include the works of Saar and Weber (1980), Kuo
and Baker (1980), Davis and Leckie (1978), Knox and Jones (1979), Nriagu
and Coker (1980), Oakley et al (1980), Oakley et al (1981), Pagenkopf
(1978), Griffin and Shirap (1978), and Khalid et al (1977); papers by
Fuller et al (1980) and O'Donnell et al (1980) report, in part, on the
inverse correlation between metal mobility in soils and the total
organic carbon content of the carrier fluid (leachate). The organic
material in the leachate presumably contains low molecular weight
carboxylic acids and higher molecular weight acids, including humic and
fulvic acids, which complex the metals to form a complex that is less
mobile than the free metal due to increased adsorption of the complex
and/or to hindered movement of large molecules in the small pores of the
soil. More general infomration on complexation may be found in the works
of Geisy and Alberts (1981), Brinkman and Bellama (1978), and Sposito
(1981).
In sediments, and presumably in soils, some studies (Pagenkopf 1978;
Griffin and Shimp 1978) have shown that metals may be solubilized
(desorbed) by the presence of complexing agents. However, just which
metals can be solubilized, to what degree, and under what conditions is
not predictable. If the user of SESOIL selects both the cation exchange
and complexation subroutines, the model will assume that cation exchange
takes precedence (i.e., happens first) and that ions involved in cation
exchange are unavailable for complexation. (See Appendix CE). Other
adsorption processes (e.g., via Langmuir or Freudlich equations) are
modeled as being competitive with complexation. There is no clear
justification for this order of operations and revisions of the
subroutine are desirable as new data and better understanding are
obtained.
In summary, agents or ligands can "pull" metals off the soil in certain
cases, but when and how this occurs is unknown. Hence, in modeling
cation exchange (see Appendix CE), we do not allow solubilization. The
other sorption processes are modeled as being fully reversible, and thus
complexation and adsorption will be competitive for available pollutant.
However, complexation is not modeled as having an active role in the
desorption of pollutant.
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As with cation exchange, competition from other metal ions is an
important consideration in complexation. A variety of metal cations may
be complexed and a particular metal ion that is complexed may be
displaced by a cation (present in equal concentrations) of higher
affinity or by a cation of lower affinity if the latter is present in
greater concentrations. In landfill leachate, competition with iron for
complexation sites may be the most important consideration (Knox and
Jones 1979). The present complexation subroutine in SESOIL does not
consider such competition.
The complexation reaction is relatively fast compared to the simulation
time steps of SESOIL although equilibrium partitioning in some cases may
not be achieved for a few days (Oakley et al 1980). Values of the
stability constant appear to range from about 10^ to 10^ for the
complexation of some common heavy metals (Cn, Cd, Zn, Fe, Co, Ni, Pb, Hg)
with humic and fulvic acids (Fagenkopf 1978). Significantly higher
values (10^ to 10^1) are associated with some of the manmade chelating
agents such as NTA, EDTA, HEDTA and CDTA (Drake et al 1976). As mentioned
previously, the values of K are a function of pH and ionic strength. In
general, K increases with increasing pH, and decreases with increasing
ionic strength (Khalid et al 1977).
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3.0 MATHEMATICAL MODELING
The mathematical expressions employed to model the complexation process
and their corresponding input parameters are discussed in the following
sections.
3.1 Mathematical Expressions
The mathematical modeling of complexation in SESOIL is based upon
equation (CM-5) and the constraint of conservation of mass. Thus for
either of the uncomplexed species, the concentration of the free species
is equal to the total input (T) of that species minus the amount com-
plexed (c):
[MX+] = [MT] - [M]c (CM-6)
[Ly~] = [LT] - [L]c (CM-7)
The equilibrium constant (equation CM-5) has been written so that the
each mole of complex includes one mole of meta] and b moles of ligand.
[M]c = [ML] (CM- 8)
[L]c = b[ML] (CM-9)
By combining equations (CM-5) through (CM-9) and omitting the designa-
tion of charges we have:
[ML] = K ([MT] - [ML]) ([L]T - b[ML])b
where:
= total concentration of metal in solution; (mol/mL)
[ML] = complexed concentration of metal (with organic
ligand) in solution; (mol/mL)
K = stability (or dissociation) constant of the
complex; (-)
[L ] = total concentration of organic ligand in
T solution; (mol/mL)
b = number of moles of organic ligand reacting with
one mole of metal cation (M) ; (-)
This equation is a non-linear equation (b does not necessarily = 1)
and must be solved numerically. This numerically solution is performed
for the monthly routines in subroutine COMP which used the same itera-
tive procedure as used to the pollutant cycle (see appendix FT).
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For the annual routines, which require an analytic solution, the ligand
input concentration is assumed to be large compared to the amount of
ligand complexed:
[L]T> [L]c therefore
[Ly] = [LT] - [LJ* [LT].
In this case equation CM- 10 reduces to
[ML] = K[L]b[MT]
1 + K[LT]b
The masses of free and complexed species can be obtained from the
concentrations by multiplying the concentration of the complex by
the volume of the subcompartment:
PML = a ' [ML] • VR20 (CM-8)
where:
P,_ = pollutant mass complexed during time step of
simulation (mol)
a = 1 conversion units factor (mL/cm3)
[ML] = complexed concentration of metal in solution;
(mol/ml)
VH20 = 6 • d-A; volume of water (moisture) in soil
subcompartment; (cm^)
6 = volumetric moisture content of soil subcompartment;
(fraction)
d = depth of soil layer; (cm)
A = cross sectional area of soil compartment; (ci&2 )
In SESOIL, pollutant (i.e., metal) masses are expressed in units of
micrograms (ug), in contrast to the previous expressions which are
expressed in moles (mol). To convert from moles to micrograms, the
molecular weight of the compound can be used as follows:
ole) (QI~9)
P (in Ug) =
r vj.il us/ nw i • r
where :
P = pollutant mass
MWT = molecular weight of pollutant; (g/mol)
f = units conversion factor; (10^ ug/g)
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The expressions used in SESOIL for obtaining the mass of pollutant com-
plexed are shown in Table CM-1. Note that the engineering designations
of concentration ([M]) have been changed, so that the pollutant concen-
tration at the step t is not designated as c(t).
3.2 Input Parameters
Input parameters to the complexation routine are presented in Table
CM-2.
Compartment depths and input masses are chosen according to the needs of
the simulation. Chemical/ligand specific constants are available from
handbooks and laboratory studies.
Laboratory data sometime imply non-integer values for b. These non-
integer values are accepted and used by SESOIL. For example, studies of
the complexation of cadmium in landfill leachate by Knox and Jones (1979)
indicated b values were in the range of 0.7 to 1.5 with an average of
about 1.1.
For further information about input parameters and formats, see the
user's manual section.
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TABLE CM-1
EQUATION DESCRIBING THE COMPLEXATION CONCEPT IN SESOIL
Annual Routines (LEVEL 0, 1):
[L] = LIGi/(0-di)
P[ML]
K([L]/MWTL-106)
•MWT- e(t)-d£-106
(CM-10)
Monthly Routines:
[L] = LIGi/(0-di)
[ML] = K-
- [ML]) ([L]T - b[ML])
P[ML] = [>CL]-0(t)-MWT-10-di
[L]p = [ML]-0(t)-b-MWTL-106-di
(solved iteratively)
Parameter
P[ML]
K
[L]
c(t)
MWTj,j
_ Parameter Description _
pollutant mass complexed during time
step of simulation
stability constant of the complex
concentration of organic ligand in
solution
molecular weight of L
concentration of pollutant
in solution
molecular weight of pollutant
Units
FORTRAN Code
(ug/cm2) PCOM
(-) SK
(ug/mL) LIGCU, LIGCL
(g/mol) MWTLIG
(ug/mL) CUM, CMM, CLM
(g/mol) MWT
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TABLE CM-1 (Continued)
EQUATION DESCRIBING THE COMPLEXATION CONCEPT IN SESOIL
9(t)
LIG
number of moles of organic ligand
reacting with one mole of the metal
cation (_)
volumetric soil moisture content of
soil (_)
time of simulation
depth of soil layer i (cm)
f
input mass of ligand ug/cn/
free ligand concentration ug/mL
B
THA, THM
DT
DN, DM, DR
LIGU, LIGL
LIGUF, LIGLF
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TABLE CM-2
INPUT PARAMETERS FOR COMPLEXATION ALGORITHMS
Parameter
FORTRAN Variable
Name
Soil Compartment
Depths
Complexation Stability
Constant
Designation
K
Input Mass of Ligand LIGi
Input Mass of Pollutant -
Ratio: Moles Ligand/
Mole of Complex b
Molecular Weight of
Metal MWT
Molecular Weight of
Ligand MWTT
Units
cm; m
g/mol
g/mol
DL (upper), DM (middle)
DL (lower)
SK
LIGIN
POLIN
B
MWT
MWTLIG
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4.0 DISCUSSION
As discussed in the previous sections, the subroutine calculations for
complexation in SESOIL:
(1) are primarily for heavy metal cations in solution;
(2) do not consider competition with other ions or the effect
of pH and ionic strength;
(3) assume equilibrium exists at all times;
(4) assume that complexation is fully reversible and competes
with all other processes (except cation exchange); and
(5) assume that the complex formed is soluble, does not
adsorb on the soil, and does not migrate from zone to
zone.
(6) assume (for annual routines only) that the total ligand
mass input is large compared to the ligand mass involved
in complexation. This assumption is not made in the
monthly routines.
It is incumbent upon the user to use this routine in the appropriate
manner for environmental conditions where complexation is known to be
a dominant factor in the mobility of the metal ions.
CM-13
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5.0 REFERENCES
Brinkman, F.E. and J.M. Be llama (eds.) (1978); Organometals and Organo-
metalloids, Occurrence and Fate in the Environment, ACS Symposium Series
82, American Chemical Society, Washington, D.C.
Davis, J.A. and J.O. Leckie (1978); Effect of Adsorbed Complexing
Ligands on Trace Metal Uptake by Hydrous Oxides, Environ. Sci. Technol.
12:1309-15.
Drake, E.; D. Shooter; W. Lyman and L. Davidson (1976); A Feasibility
Study of Response Techniques for Discharges of Hazardous Chemicals that
Disperse Through the Water Column, Report No. CG-D-16-77, U.S. Coast
Guard, Office of Research and Development, Washington, D.C.
Fuller, W.H.; A. Amoozegar-Ford; E. Niebla and M. Boyle (1981); Behavior
of Cd, Ni and Zn in Single and Mixed Combinations in Landfill Leachates,
page 18-28 in Land Disposal: Hazardous Waste, Report No. EPA-600/9-81-
0026, U.S. Environmental Protection Agency, Cincinnati, Ohio.
Gachter, R. ; J.S. Davis and A. Mares (1978); Regulation of Copper
Availability to Phytoplankton by Macromolecules in Lake Water, Environ.
Sci. Technol. Vol. 12, pp. 1416-21.
Giesy, J.P., Jr.; L.A. Briese and G.J. Leversee (1978); Metal Binding
Capacity of Selected Marine Surface Waters, Environ. Geol., Vol 2, pp.
257-68.
Giesy, J.P., Jr. and J.J. Alberts (1981); Trace Metal Speciation: The
Interaction of Metals with Organic Constituents of Surface Waters,
Chemtech (in press).
Griffin, R.A. and Shimp, N.F. (1978); Attenuation of Pollutants in
Municipal Landfill Leachate by Clay Minerals, Report No. EPA-600/2-78-
157, U.S. Environmental Protection Agency, Cincinniti, Ohio.
Jenne, E.A. (1979); Chemical Modeling—Goals, Problems, Approaches, and
Priorities, in Chemical Modeling in Aqueous Systems, E.A. Jenne (ed.),
ACS Symposium Series 93, American Chemical Society, Washington, D.C.
Khalid, R.A.; R.P. Gambrell; M.G. Verloo and W.H. Patrick, Jr. (1977);
Transformations of Heavy Metals and Plant Nutrients in Dredged Sediments
as Affected by Oxidation Reduction Potential and pH. Volume I:
Literature Review, Contract Report D-77-4, Dredged Material Research
Program, U.S. Army Engineer Waterways Experiment Station, Vicksburg,
Mississippi.
Knox, K. and P.H. Jones (1979); Complexation Characteristics of Sanitary
Landfill Leachates, Water Res., Vol. 13, pp. 839-46.
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Kuo, S. and A.S. Baker (1980); Sorption of Copper, Zinc, and Cadmium by
Some Acid Soils, Soil Sci. Soc. Am. J., Vol. 44, pp. 969-74.
McCrady, J.K. and G.A. Chapman (1979); Determination of Copper Com-
plexing Capacity of Natural River Water, Well Water and Artificially
Reconstituted Water, Water Res., Vol 13, pp. 143-50.
Nriagu, J.O. and R.K. Coker (1980); Trace Metals in Humic and Fulvic
Acids from Lake Ontario Sediments, Environ. Sci. Technol. , Vol. 14, pp.
443-46.
Oakley, S.M.; C.E. Delphey, K.J. Williamson and P.O Nelson (1980);
Kinetics of Trace Metal Partitioning in Model Anoxic Marine Sediments,
Water Res., Vol. 14, pp. 1067-72.
Oakley, S.M.; P.O. Nelson and K.J. Williamson (1981); Model of Trace-
Metal Partitioning in Marine Sediments, Environ. Sci. Technol., Vol. 15,
pp. 474-80.
O'Donnell, D.F.; P.A. Alesii; J. Artiola-Fortany and W.H. Fuller (1981);
Predicting Cadmium Movement Through Soil as Influenced by Leachate
Characteristics, U.S. Environmental Protection Agency report (in press).
Pagenkopf, G.K. (1978); Metal-Ion Transport Mediated by Humic and Fulvic
Acids, in Organometals and Organometalloids—Occurrence and Fate in the
Environment, F.E. Brinkman and J.M. Bellama (eds.), ACS Symposium Series
82, American Chemical Society, Washington, D.C.
Saar, R.A. and J.H. Weber (1980); Lead (II)-Fulvic Acid Complexes,
Conditional Stability Constants, Solubility, and Implications for Lead
(II) Mobility, Environ. Sci. Technol., Vol. 14, pp. 877-80.
Sposito, G. (1981); Trace Metals in Contaminated Waters, Environ. Sci.
Technol., Vol. 15, pp. 396-403.
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APPENDIX PH
PHOTOLYSIS
Photolysis of pollutant on soil surface layers might be another mechanism
of pollutant loss. This process — important for certain compounds — will
be incorporated in another SESOIL version.
Dec. 81 PH-1
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FX - fixation
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APPENDIX FX
FIXATION
Fixation is an important transformation process for certain compounds.
It has been suggested by many scientists who are interested in SESOIL's
modeling to incorporate into the model this process in the near future.
Dec. 81 FX-1
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iS - biologic activity
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APPENDIX BI
BIOLOGIC ACTIVITIES
SESOIL is structured in a way that may allow the modeling of processes
dealing with biologic activities in the soil. Although no definite
plans are made by the developers regarding these issues, they believe
that a SESOIL expansion in this area would lead to quite a useful tool
for studying biologic soil activity due to manmade actions, as for
example, POTW disposal actions on land.
Dec. 81 BI-1
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nutrient cycle
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*
APPENDIX NU
NUTRIENT CYCLE**
1.0 INTRODUCTION NU-2
1.1 General NU-2
1.2 Literature Review NU-3
2.0 BACKGROUND NU-6
2.1 Physical, Chemical and Biological Processes NU-6
2.2 The Nitrogen Cycle NU-7
2.2.1 Forms of Soil Nitrogen NU-9
2.2.2 Nitrogen Transformations in the Soil Column NU-9
2.3 The Phosphorus Cycle NU-13
2.3.1 Forms of Soil Phosphorus NU-13
2.3.2 Phosphorus Transformations in the Soil Column NU-15
2.4 Summary of Background of Nutrient Cycles NU-16
3.0 MATHEMATICAL FORMULATIONS NU-18
3.1 General NU-18
3.2 Nutrient Transformations NU-18
3.3 Rate Constants NU-21
3.4 System of Equations NU-21
3.5 Input/Output Parameters NU-26
3.6 Numerical Solution Techniques of Equation Systems NU-26
4.0 CONCLUSIONS NU-30
5.0 REFERENCES NU-31
This subroutine is not operational; therefore, no great emphasis has
been placed in its accurate documentation.
** r
Contribution from Joo Hooi Ong.
Aug. 81 NU-1
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1.0 INTRODUCTION
1.1 General
Certain elements are essential for the growth of plants. These elements
are called nutrients and are obtained from air and from water in the soil.
Carbon, oxygen, and sometimes nitrogen (e.g. legumes can use gaseous
nitrogen) are obtained from air. Of the nutrients required from soil,
nitrogen, phosphorus, potassium, calcium, magnesium and sulfur are needed
in relatively large quantities. Essential elements used in small
amounts, i.e. trace elements include iron, manganese, boron, molybdenum,
copper, zinc, chlorine, and cobalt. Nitrogen and phosphorus will be
considered in the model because they are the principal nutrient pol-
lutants.
In agricultural applications, nitrogen and phosphorus are usually supplied
to the soil in the form of manure and commercial fertilizers. Nitrogen
is commonly applied in the form of ammonium and nitrate salts and as urea.
Other major ways by which nitrogen becomes available to plants are through
fixation of gaseous nitrogen by bacteria, and through nitrogen dissolved
in precipitation. These latter ways are especially important in natural
ecosystems. Phosphorus is mostly applied as phosphates.
Nutrients in the soil are subject to various fate processes. They are
absorbed by plant roots, transformed from one chemical form to another,
adsorbed onto organic matter and clays, transported from the soil sur-
face in runoff, or leached into the groundwater zone. Environmental
quality is related to nutrient fate, for example, when nitrogen or
phosphorus is transported from land into waterways and lakes, eutrophi-
cation and fish kills may result. If nitrates migrate into the ground-
water zone and into drinking water supplies, health effects may result
from ingestion of these supplies. A form of anemia called methaemogloban-
aemia which predominantly affects children is caused by ingestion of
nitrates. The use of fertilizers to increase productivity in agricultural
areas must therefore by managed to minimize adverse environmental effects.
A tool to predict nutrient concentrations in runoff, in the soil column,
and in groundwater would be an important part of this management process.
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The nutrient cycle module of SESOIL simulates the transport, transforma-
tion, and storages of nitrogen and phosphorus in the soil column. The
nitrogen and phosphorus cycles in the environment and the nature of the
microbial and chemical reactions involved in these cycles are described
in the following sections. Following this background information, the
mathematical formulation of these processes and the solution technique
are explained.
1.2 Literature Review
A pioneering work in modeling nutrient cycling in soils is presented in
the Agricultural Runoff Management (ARM) model (Donigian, £t _al., 1977).
The same subroutines, together with some extensions have later been
incorporated into the Hydrological Simulation Program - Fortran (HSPF)
model (Johanson, et_ al. , 1979). Both the ARM and the HSPF models simu-
late nitrogen and phosphorus transport and transformations in the soil
column, and nutrient content in sediments and runoff from small agri-
cultural watersheds. The soil column is divided into four zones in the
ARM and HSPF models: (1) surface zone, (2) upper zone, (3) lower zone,
and (A) groundwater zone. The transformations of the nutrient species
are described by first order kinetics with a temperature correction
using the Arrhenius equation. ARM uses regression equations for estimating
soil temperatures, from air temperatures. The ARM model simulates plant
uptake of nitrate and phosphate by using monthly rate constants. HSPF
includes uptake of ammonium by plants. It varies plant uptake on a monthly
basis and distributes the uptake rate of nitrogen between nitrate-N and
ammonium-N by factors, the sum of which is 1.0. The effect of moisture
content on nutrient transformations is taken into account by discontinuing
all transformations at very low moisture values. On the surface zone,
transformations do not occur except during storm events since ARM assumes
that the surface zone is dry except when runoff is occurring.
Another model which simulates nutrient transport and transformation is the
CREAMS model (Knisel, 1980). This model is to be applied to field size
areas and gives as output, the average concentrations of soluble nitrogen
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and phosphorus in runoff, the amount of nitrate leached and its average
concentration, and the amounts of nitrogen and phosphorus associated
with sediments. Phosphorus compounds are not simulated in the soil
column, i.e. , no phosphorus is assumed to leach into the soil. The
soluble nitrogen compounds leached into the soil are assumed to be
nitrate or compounds that are quickly converted to nitrate and are added
to the nitrate pool in the soil. The soil column in CREAMS is divided
into the surface layer and the root zone. On the surface, nutrients
(soluble nitrogen and phosphorus) are removed with runoff and with the
sediments. In the root zone, mineralization and denitrification are
simulated using first order kinetics. Plant uptake and percolation of
nitrate also occur at the root zone. Two options are available for
calculating plant uptake: (1) plant growth as a function of plant water
use and nitrogen uptake as a function of plant nitrogen content, and (2)
by assuming that nitrogen uptake follows a normal probability curve. The
denitrification rate is modified by the moisture content of the soil by
assuming that the rate constant is only positive when the moisture con-
tent exceeds field capacity.
The nutrient cycle module in SESOIL simulates nitrogen and phosphorus
transport and transformations in the soil column, and the concentrations
in sediments and in runoff. SESOIL is not limited by the size of the
watershed modeled and it does not need to be calibrated.
Many of the principles in the ARM model are used in the nutrient cycle
module in SESOIL. The differences between the two models are:
(1) SESOIL uses monthly temperature inputs for each soil zone
while ARM uses regression equations for estimating soil
temperatures. The advantage of having user-input temper-
atures is that the model does not have to be calibrated
to each site.
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(2) SESOIL includes plant uptake of ammonium-N whereas ARM only
has an uptake rate for nitrate-N. HSPF does however include
plant uptake of ammonium-N. Since uptake of ammonium-N is a
major nitrogen uptake path in most applications, it would
be more accurate to include it.
CREAMS is useful in applications when nitrate leaching, availability of
nitrogen to plants, and nutrient concentrations in runoff and sediments
are the primary interests. Since it does not simulate storages of any
other species except nitrate in the soil column, it cannot be used to
predict nutrient concentrations in soils. The nutrient cycle module
in SESOIL would, therefore, have a wider application than the CREAMS
since the soil column is modeled in SESOIL.
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2.0 BACKGROUND
Both the nitrogen and phosphorus cycles consist of many physical, chemical
and biological processes, and very often combinations of these processes.
Because of the difficulty involved in defining precisely which mechanism
is involved in each phenomenon, this section provides only background
information about the nitrogen and phosphorus cycles. Detailed descrip-
tions are not given here of the process mechanisms and dependencies on
environmental factors, such as temperature, organic carbon content,
oxygen content, soil moisture content, and pH. Quantitative knowledge
of these relationships are generally lacking. A comprehensive qualita-
tive source for understanding the nitrogen cycle in soils is Bartholomew
(1965). Similarly, Larsen (1967) provides a review of the phosphorus
cycle. Other sources used in writing the following sections are Brady
(1974) and Odum (1971).
2.1 Physical, Chemical and Biological Processes
Physical, chemical and biological processes all play a role in the nitro-
gen and phosphorus environmental cycles. A physical process is one that
does not alter the nature of the chemical species involved. Chemical
processes generally involve reactions in which there is a transformation
of chemical species without the aid of any organisms. Biological pro-
cesses are biochemical transformations of chemical species by microbial
metabolism. In the natural environment it is very difficult to define
in a clear-cut fashion whether a phenomenon is due to an individual, or
more likely, a combination of physical, chemical, or biochemical pro-
cesses. For example, adsorption is usually considered a physical
process but chemisorption contributes to the concentration of the ad-
sorbed species.
The factors which affect the growth of bacteria are important in deter-
mining the rates of transformation of the nutrient species. Some processes
(e.g. mineralization) involve primarily bacteria requiring oxygen gas,
or aerobic bacteria. Other processes (e.g. denitrification) involve
anaerobic bacteria using mostly combined oxygen. Bacteria which can
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use either of the two oxygen forms are called facultative bacteria.
Soil moisture affects bacterial growth in two ways: water is needed by
bacterial metabolic activities, and the moisture content in soil affects
the diffusion rate of oxygen through the soil. The temperature range
at which most bacterial activity is optimal is between 20°C and 40°C,
with the optimum temperature at around 35°C. Under ordinary soil temp-
erature extremes (e.g. in winter) however, bacterial activity seldom
halts. Organic matter is used as the energy source for the majority of
bacteria. The amount and nature of the soil organic matter determines to
a certain degree the types of bacteria present in the soil and their
growth rates. Under conditions of high calcium, the pH of the soil
column is usually between 6 and 8 which is generally best for most
bacteria, although certain bacteria species are adapted for low pH
and others at high pH. The calcium content and the pH values play a
role in determining the specific bacteria present.
2.2 The Nitrogen Cycle
Figure NU-1 shows the nitrogen cycle in nature with some typical magni-
tudes of the transformations. In arable soils, nitrogen is acquired by
soil primarily in three ways: through nitrogen fixation, additions
through precipitation, and application of nitrogen in fertilizers and
manures. Atmospheric nitrogen is fixed by bacteria in symbiosis with
legumes. Depending on the soil conditions and the crop, the amount of
nitrogen fixed can range from 50-250 Ibs/acre-year (Brady, 1974). Soil
conditions required are good aeration, drainage, moisture, optimal pH,
and a certain amount of active calcium. The nitrogen added in this way
is used by the host plant and also passed into the soil itself. Certain
organisms in symbiosis with non-legumes, mostly angiosperms can also fix
atmospheric nitrogen under conditions of low soil nitrogen. Free-living
organisms that are not directly associated with higher plants, for example,
several groups of bacteria, blue-green algae and fungi, are also capable
of nonsymbiotic or free fixation of atmospheric nitrogen. The rate of
fixation is assumed to be low. Direct addition of nitrogen through rain
and snow is variable with season and location. In a humid temperate
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1.5 Ib N03-N
b.5 Ib NH^N/acre-yr
PRECIPITATION
50-2501 Ib/acre-yr
N-TIXATION
FERTILIZATION
ANIMALS
GASEOUS LOSS
c
GO
VOLATILIZATION
LEACHING
3-
-i
D
ET
RESIDUES
MANURE
WASTES
N2 (10-15% of
N20 annual add!
NO
FIXATION (greater:
where clay con-
tent is high)
LOSSES
Oil
ORGAN ISriS
I*
h. k w
SOIL ORGANIC (not available for plant
MATTER uptake, leaching or
\ volati1izat ion)
2-3% of total-N/yr in
wel1-drained, aerated
soil1
FIGURE NU-1: MAIN PORTIONS OF THE NITROGEN CYCLE
Source: Brady (1971*)
obtained from Brady (19*0.
-------
climate, it is estimated that additions to soil average around 4.5 Ibs
of NH^-N and 1.5 Ibs of NO,-N for every acre per year (Brady, 1974).
In agricultural lands, the nitrogen additions in fertilizer is probably
the largest component of the three contributions. The forms added are
nitrate, ammonia and urea. The amount of nitrogen added depends on the
kind of crop to be grown, the chemical condition of the soil, and the
physical state of the soil. Application rates range from less then 100
Ibs of nitrogen per acre to 300 Ibs of nitrogen per acre.
Nitrogen is depleted from the soil in crop removal, drainage, erosion,
and volatilization of the gaseous form. In an arable situation, crop
removal is the most significant way by which nitrogen is removed.
Gaseous losses are usually small but can become significant under
anaerobic conditions, such as in water-logged soils.
2.2.1 Forms of Soil Nitrogen
There are basically three forms of soil nitrogen: (1) organic nitrogen
associated with the soil humus, (2) ammonium fixed by certain clay
minerals, and (3) soluble inorganic ammonium and nitrate compounds.
Most of the nitrogen is associated with organic matter. A very small
percentage (2-3%) of this organic-N is converted to inorganic forms
a year (Brady, 1974). Mineral surface soils contain from 0.4 to 10%
of organic matter (Brady, 1974). Typical soils contain around 4% of
organic matter. Subsoils generally contain much less organic matter.
Up to 8% of the total-N is fixed by clay (Brady, 1974). The soluble
ammonium and nitrate compounds in soils seldom form more than 1-2% of
the total-N present (Brady, 1974).
2.2.2 Nitrogen Transformations in the Soil Column
Mineralization
Mineralization is a biological process whereby organic nitrogen forms
are converted to inorganic forms, usually to ammonium. Soil organisms
attack the organic nitrogen compounds by enzymic digestion converting
the more complex proteins to ammonium. Using the example of an amino
combination, the reaction is as follows:
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R-NH, + HOH .—»• R-OH + NH. + energv >»
2 hydrolysis 3 B-
2 }
2NH3 + H2C03 »• (NHA) 2 CO.J ^ » 2NHA+ + CO.J I
In general the overall reactions are described by:
organic-N »• ammonium-N (NU-2)
This transformation proceeds best in well-drained aerated soils but will
take place to some extent under almost any conditions because of the
diverse species capable of this process. Annually, only 2-3% of organic-
N may be expected to be mineralized (Brady, 1974). Mineralization is a
very slow process relative to the other soil reactions.
Immobilization
This phenomenon is the conversion of inorganic species to organic forms
and may be regarded as the reverse of the mineralization process. Soil
microbes or plants take up soluble nutrient species for growth, converting
these to organic compounds which are released to the soil upon death and
cell decay. Immobilization may be represented as:
NH -N]
^org-N (NU-3)
N03-N j
The rate constants for these transformations are dependent on those factors
affecting mineralization. Suboptimum temperature and soil mositure slow down
the rate of immobilization. Anaerobic conditions may also have an important
effect on slowing down the rate; however, there is a possibility of
adaptation of different microbial species across a range of oxygen concen-
tration. The sensitivity of different microbes to ranges in pH could
also affect the rate constants for these reactions. Immobilization is a
fast process relative to mineralization.
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Nitrification
Nitrification is a process of enzymic oxidation of ammonium. It takes
place in two steps due to the activity of two separate groups of bacteria.
The first step is the production of nitrous acid and the second step is
the oxidation of the nitrite form to nitrate. The group of bacteria
primarily responsible for the first step is the Nitrosomonas bacteria
and for the second, Nitrobacter bacteria.
ivm • on enzvmic oxidation «.,_ - . .,, _ .„+ ,.
2NH. + 30, — ;— : - ». 2N00 + 2H00 + 4H+ + energv
4 *• Nitrosomonas ^ ^
> (NU-4)
iMr. ~ . n enzymic oxidation _.... -
2N00 + 00 J _ ». 2NO_ + energy
* l Nitrobacter J
Other bacterial species are also able to oxidize and produce nitrate pro-
ducts but it is uncertain whether they are significant contributors of
nitrate to soil. Soil conditions affecting nitrification are soil
oxygen content, temperature, moisture, pH, fertilizer salts, and the nitro
gen-carbon ratio. The temperature range under which nitrification occurs
is between 0°C and 52°C. The most favorable temperatures are between
27-32°C (Brady, 1974). Nitrification is slow at very low or very high
moisture content although it is known to proceed appreciably under very
dry conditions. The most favorable soil moisture content is similar to
that for growth of higher plants. Nitrification is low at low pH values
but acidity itself is not significant when adequate exchangeable bases
are present. Under ideal temperature, soil and moisture conditions,
nitrification is a very fast process. Daily rates from 6 to 22 Ibs of
nitrogen per 2 million Ibs of soil when 100 Ibs of ammonium-N was added
have been observed (Brady, 1974).
Denitrification
Denitrif ication is a reduction of nitrate-N to gaseous compounds. Facul-
tative anaerobic baceria which prefer free oxygen use the combined
oxygen in nitrate-N. The exact mechanisms are not known and may be
chemical as well as biochemical. One way to describe it is as in
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reaction (b), which is basically respiration using nitrate instead of
free oxygen as an oxygen source. The reactions could be adequately
described in several ways:
-2[0]
(a) 2NH03
nitrates
(b) C6H1206
-2[0]
'*• 2NH02 —
nitrates
4NO,
-[0]
-H20
— lN2u
nitrous
oxiae
6CO, +
^ No
elemental
nitrogen
6H90 + 2N, ^
biochemical
> reduction
'(NU-5)
(c) 2HN02 + CO(NH2)
nitrite
urea
CO.
3H20
+ 2N,
chemical
reduction
In general, the process may be described as:
NO.
-»- NO,
The rate of disappearance of HQyH is dependent on soil oxygen content,
and the presence of reducing agents and organic matter. The pH, temper-
ature and moisture content are important factors as well. The rate of
denitrification is slow under acidic conditions and high under alkaline
conditions. Higher soil moisture content also increases the rate of
denitrification possibly by indirectly affecting oxygen diffusion in
the soil column (Bartholomew, 1965). Denitrification is most likely
to occur in poorly drained soils and in acidic soils containing nitrates.
Poor aeration enhances denitrification. Under conditions of poor drain-
age and aeration, loss of nitrogen through denitrification can be sub-
stantial.
Plant Uptake
Nitrogen is taken up by plants mostly in the forms of ammonium or nitrate.
The form that is taken up depends on the conditions of the soil, the kind
of plant and the stage of plant growth. Factors which influence plant
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uptake of nitrogen are biomass or root surface area of plants, temperature,
soil moisture, soil oxygen content, season of the year, among others.
When the plants are harvested, a large fraction of nitrogen is removed
from the immediate location.
Adsorption-Desorption
Ammonium-N is adsorbed by clay minerals. Colloidal clay particles
ordinarily carry negative charges. Positively charged ions are
attracted to the colloidal crystal and are held in a non-exchangeable
form. This non-exchangeable or fixed ammonium is released slowly.
»» NH4+ (NU-6)
(soil "* (exchangeable) "* - (fixed)
solution)
Ammonium fixation by clay minerals is greater in subsoils than in top-
soil because of the higher clay content in subsoils. Organic matter
or humus in soil also behaves like clay colloid particles in that
ammonium-N can be fixed by these particles as well. The exact mech-
anism is unknown but it could be a chemical reaction by which compounds
are formed between the soil organic matter and ammonium. This latter
fixation is most favorable in the presence of oxygen and at high pH.
2.3 The Phosphorus Cycle
Figure NU-2 shows the phosphorus cycle in nature. Phosphorus is added
to soils mostly in the form of fertilizers, especially in agricultural
applications. Phosphorus is depleted from the soil in crop removal,
drainage, and erosion.
2.3.1 Forms of Soil Phosphorus
In most soils, more than 50 percent of the total soil phosphorus is
organic, present either as specific organic phosphorus compounds or as
organic compounds linked with inorganic phosphorus groups (Larsen, 1967).
Inorganic phosphorus forms present in soils depend on the pH of the soil.
2_
Under alkaline conditions, the HPO, ion is dominant. At low pH values,
the H_PO,~ ion is prevalent. Both these ions prevail at intermediate pH
values.
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WEATHERING
OF PHOSPHATE
ROCKS
a
c
PHOSPHATE
FERTILIZER
SOURCE
REMOVED FROM CYCLE
HARVESTING
DECOMPOSITION
AND EXCRETA
BLEACHING
>
"n
r-t
3-
FIGURE NU-2: MAIN PORTIONS OF THE PHOSPHORUS CYCLE
Source: Donigian, Beyerlein, Davis, and Crawford, 1977
n
-------
2.3.2 Phosphorus Transformations in the Soil Column
Mineralization
Organic forms of phosphorus are converted to inorganic forms by bacteria
in a process called mineralization similar to that of the mineralization
of organic-N.
organic-P - »> phosphate-P (NU-7)
The same conditions which affect nitrogen mineralization regulate phos-
phorus mineralization.
Immobilization
Inorganic phosphorus is transformed to organic phosphorus through the
process of immobilization. Soil organisms and plants take up soluble
inorganic phosphorus for growth, converting these to organic forms which
are released to the soil upon death.
phosphate-P - »• organic-P (NU-8)
Plant Uptake
2_
Both the phosphate forms, HP04 and ^PO^' are adsorbed by higher plants.
The forms available depend on the pH of the soil. Organic phosphorus
cannot be used to any extent directly by higher plants but only after
mineralization. Plant uptake of phosphorus is influenced by biomass or
root surface area, temperature, soil moisture, soil oxygen content,
season of the year, among others.
Adsorpt ion-Desorpt ion
The mechanism by which inorganic phosphorus ions are fixed by soil
particles is not a simple adsorption mechanism. In acid soils, phos-
phates are precipitated by iron, aluminium, and manganese ions, and
fixed by hydrous oxides and by silicate clays. At high pH values,
phosphates are precipitated by calcium compounds. Therefore, it is
more accurate to assume the process as a combination of precipitation
and adsorption-desorption.
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2.A Summary of Background of Nutrient Cycles
Table NU-1 shows typical dominant pathways in a soil column and trans-
formations that may be expected in each soil zone. It must be emphasized
that the relative rates vary with climate, soil type, vegetation, among
other factors.
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TABLE NU-1: DOMINANT NUTRIENT PA1IIWAYS IN EACH SOIL ZONE
Surfnee
Upper
Unsaturated
Antmon ium-N
In Solution
Runoff
Leaching
Volatilization
Plant Uptake
Adsorpt ion-Desorpt ion
Immobilization
Mineralization
Nitrification
leaching
Plant Uptake
Adsorption-
Mesorption
Immobilization
Mineralization
Nitrification
Anunon ium-N
Adsorbed
Loss in Sediments
Adsorption-
Desorption
Adsorption-
Dcsorption
Nltratc-N
in Solution
Runoff
Leach Ing
Plant Uptake
Immobi] Lzat Ion
Nitrification
Leaching
Plant Uptake
Immobilization
Nitrification
Den itrl f (cation
Organ Ic-N
in Solution
Runoff
Leaching
Immobilization
Mineralization
1 .caching
Immobilization
Mineralization
Tnorganlc-P
Adsorbed
Runoff
Leaching
Plant Uptake
Adsorpt Ion-
Desorpt Ion
Immobilization
Mineralization
Leaching
Plant Uptake
Adsorpt ion-
Desorption
Immobilization
Mineralization
Adsorbed
Loss in Sediments
AdsorpLion-
Desorpl Ion
AdsorpLion-
Dcsorpt ion
Organic-!1
In Solution
Runoff
Leaching
Immobilization
Mineral izalion
Leaching
Inimobil ination
Minerali7alion
Lower
Unsaturated
leaching
Pi ant Uptake
Adsorptlon-Desorptlon
Immobilization
Adsorption-
Desorpt Ion
Leaching
Plant Uptake
Immobllization
DcntrIf(cation
(.caching
Immobilization
Leaching
Plant Uptake
Adsorptlon-
Desorptlon
Tmmobl lizat Ion
Adsortpion-
Desorpt inn
(•caching
Lmmobil l7.nL Inn
NU-17
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3.0 MATHEMATICAL FORMULATION
3.1 General
The important nutrient species included in this modeling effort are:
organic nitrogen in soil solution (org-N), ammonium in soil solution
(NH^-N(s)), ammonium adsorbed on soil particles (NH^-N(a)), nitrate in
soil solution (N03~N), organic phosphorus in soil solution (org-P),
orthophosphate in soil solution (P04-P(s)), and orthophosphate adsorbed
on soil particles (PO^-P(a)). These are the dominant species in a soil
column. Each of the organic nutrient species is considered as a group
because they are insufficiently characterized and because data are
usually available for the organic nitrogen and organic phosphorus as
individual groups. Nitrite (N02-N) is not considered as a separate
species by itself since it is unstable and usually exists at concen-
trations that are orders of magnitude less than nitrate-N. The fluxes
in and out of the N02~N pool are expected to be high; the storage
capacity is very small.
Schematic diagrams of the nitrogen and phosphorus cycles modeled by the
nutrient module of SESOIL are shown in Figures NU-3 and NU-4 respectively.
These models are simplified representations of the cycles in nature.
Table NU-1 gives the processes in the soil column that affect transport
and transformation of nutrient species in each soil zone. The physical
processes of losses in runoff, sediments, leaching, and volatilization
are modeled by the pollutant transport routine in SESOIL and will not be
repeated here. The pollutant transport routine is called by the execu-
tive program of the model.
3.2 Nutrient Transformations
Each of the nutrient transformations is modeled as a first order reaction.
Assuming that the soil being modeled is microbially active, at the low
nutrient concentrations normally present in soils, first order kinetics
best estimates what happens in the soil column. Since the Freundlich,
the Langmuir and an overall adsorption equation are modeled by the
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2!
C
c
plant
uptake
vo1 a t i 1
NH
N2, N20
i mmobi1i z a t i on
KIN
desorption
KD
adsorption
KA
LEGEND:
tion KDN
Leaching
"I storages
fl transformation
pathway
gaseous loss
FIGURE NU-3:
SCHEMATIC DIAGRAM OF NITROGEN CYCLE MODELED
soi 1
~ surface
-------
INPUT
a
f
ho
o
LEGEND:
plant
uptake
KPP
mineralization KMP \J
soi 1
surface
immobilization KIP
adsorption
KAP
desorption
KDP
storages
transformation
pathway
FIGURE NU-*»: SCHEMATIC DIAGRAM OF PHOSPHORUS CYCLE MODELED
-------
adsorption-desorption routine of SESOIL, a choice is given to the user
depending on the data availability and other factors.
3.3 Rate Constants
Table NU-2 shows the rate constants used in the model to describe the
transformations in the soil column. These are first order rate constants
to be specified by the user for each reaction and for each soil zone
being modeled. The dependency of the rate constant on temperature is
described by the Arrhenius equation.
(T-35)
*T " K35°C Y
where:
1^ = rate constant at T°C (day )
K35°C = °Ptlmuin K at 35"c (day'1)
Y = temperature coefficient (constant)
T = temperature (°C)
The temperature coefficients for the nutrient transformations are shown
in Table NU-2. The user has to input the values of rate constants at
35°C and the temperature coefficient for each of the rate constants.
Some typical values of rate constants and temperature coefficients are
given in Table NU-3.
3.4 System of Equations
The system of equations governing the nitrogen and phosphorus transfor-
mations in soil is given in Table NU-4. The transformations are based
on nutrient mass per mass of soil or soil water in each zone, i.e., mass-
based concentrations. The ammonium desorption rate KD, the nitrogen
mineralization rate KM, the phosphate desorption rate KDP, and the phos-
phorus mineralization rate KMP are based on per soil mass. All the
other rates are based on per soil water mass in each zone.
To calculate soil and water masses in each zone, soil bulk densities have
to be specified for each zone, and soil moisture content has to be
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TABLE NU-2: RATE CONSTANTS AND TEMPERATURE COEFFICIENTS
10
10
Rate Temperature
Constant Coefficient
(day'1)
Nitrogen
KA
KD
KN
KDN
KIN
KIA
KM
KPA
KPN
Phosphorus
KAP
KDP
KIP
KMP
KPP
TKA
TKD
TKN
TKDN
TKIN
TKIA
TKM
TKPA
TKPN
TRAP
TKDP
TRIP
TKMP
TKPP
Transformation Process in Soil Column
Adsorption of ammonium from solution to adsorbed phase
Desorption of ammonium from adsorbed phase to solution
Nitrification of ammonium in solution to nitrate
Denitrification of nitrate to gaseous nitrogen
Immobilization of nitrate to organic nitrogen
Immobilization of ammonium in solution to organic nitrogen
Mineralization of organic nitrogen to ammoniun in solution
Plant uptake of ammonium in solution
Plant uptake of nitrate
Adsorption of phosphate from solution to adsorbed phase
Desorption of phosphate from adsorbed phase to solution
Immobilization of phosphate in solution to organic phosphorus
Mineralization of organic phosphorus to phosphate in solution
Plant uptake of phosphate in solution
D
CT
n
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TABLE NU-3: TYPICAL RATE CONSTANTS AND TEMPERATURE
COEFFICIENT VALUES
PROCESS
Nitrogen;
Mineralization
org-N—fr-NH^-N
Immobilization
NH4-N
N03-N »-org-N
Nitrification
N02-N
Den i t r i f i c at i on
NO,-N »-(N, + I
j 2.
Adsorption
RATE CONSTANT
(day"1)
0.001 - 0.0078
(11 soils with wide
range of properties)
0.151 (Ontario loam)
0.15 (Ontario loam)
0.22'
,1
(Salinas clay)
9.01
0.1431 (Milville loam)
9.01
0.0033 - 1.11
(Milville loam)
1
(various loams)
0.004 - 0.1921 (various loams)
i.oooo
TEMPERATURE
COEFFICIENT
1.07
1.07
1.072
1.07
1.072
1.07^
1.07
1.07
1.050
Desorption
NH4-N(a)
Plant Uptake
N03-N—*-Plant-N
NH^-N—
l.OOOO
0-0.0975"
0-0.0975'
1.050
1.070-
1.070:
Phosphorus:
Mineralization
org-P-
-POA-P(s)
0.002 - 0.02'
1.070'
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TABLE NU-3: (Continued)
RATE CONSTANT TEMPERATURE
PROCESS (day"1) COEFFICIENT
Immobilization
P04-P(s)—p-org-P O3 1.0703
Adsorption
P04-P(s) »-P04-P(a) l.OOOO3 1.0503
Desorption
P04-P(a) -P04-P(s) 0.0015 - 0.01503 1.0503
A
Plant Uptake
P04-P(s)—»-Plant-P 0 - 0.05253 1.0703
1. Adapted from Knisel, Davidson, et_ a_l. , 1978. Laboratory values under
various conditions.
2. Brady, 1974 gives a typical doubling of a rate constant for every
10°C increase in temperature, which would indicate a temperature
coefficient of 1.07 for biochemical reactions.
3. Donigian, et^ al., 1977. P-2 Watershed, Uatkinsville, PA.
A. Range due to seasonal dependence.
5. Obtained by assuming equal uptake of NH.-P and NO,-N.
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TABLE NU-4: DIFFERENTIAL EQUATIONS DESCRIBING NITROGEN AND
PHOSPHORUS TRANSFORMATIONS
Organic Nitrogen
^ (org-NJ = KIA JNH4-N(s)j + KIN | N03~N | - KM (org-N J
Ammonium in Solution
^•JNH4-N(s)) = KM | org-N } + KD | NH4-N(a)| - (KPA+KIA+KA+KN) JNH4-N(s)|
Adsorbed Ammonium
^ (NH4-N(a)j = KA JNH^-NCs)) - KD [NH4-N(a)J
Nitrate
|jT JN03-NJ = KN [NH4-N(s)| - (KIN+KDN+KPN) { NOg-
Organic Phosphorus
^ {org-PJ = KIP [P04-P(s)j - KMP {org-PJ
Phosphate in Solution
^ [P04-P(s)} = KMP {org-p} + KDP Jp04-P(a)j - (KIP+KAP+KPP) [p04-P(s)
Adsorbed Phosphate
|f [P04-P(a)| = KAP {p04-P(s)J - KDP [p04-P(a)j
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obtained from the hydrologic cycle routine of SESOIL. Soil mass in
each zone is the product of the bulk density and volume of the zone.
Knowing soil mass and soil water mass, the nutrient concentrations may
be calculated appropriately to be used in the transformation equations.
NH4~N(a), PO^-P(a), org-N and org-P are therefore in the units of mass
per soil mass and the other nutrient species are in the units per soil
water mass.
3.5 Input/Output Parameter's
The input and output parameters used in the nutrient cycle module of
SESOIL are summarized in Table NU-5.
3.6 Numerical Solution Techniques of Equation Systems
Table NU-A gives the nitrogen and phosphorus equations modeled by the
nutrient subroutine of SESOIL. An analytical solution of first order
differential equation systems might be possible (theoretically), but for
practical reasons SESOIL employs numerical algorithms.
Various solution algorithms are available in the literature, such as the
simple Euler integration technique employed by the Agricultural Runoff
Management (ARM) model [Donigian, et al., 1977] and the Runge-Kutta
techniques [Abramowitz and Segun , 1968]. SESOIL employs a second
order and fourth order Runge-Kutta solution method for the annual and
the monthly simulations respectively.
For a given system of two first order differential equations as an
illustration:
y'=f(x,y,z)
, , , (NU-9)
z =g(x,y,z)
The "second order" Runge-Kutta discretized solution is obtained from:
1(ki+k2)+0(h3)
(NU-10)
)
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TABLE NU-5: INPUT/OUTPUT PARAMETERS
PARAMETER
INPUT
1. Loadings of:
NH.-N
4
UNITS
kg/m!
org-N
2. Times of applications of:
NH -N
4
historical dates
-1
-1
org-N
P04-P
3. Method of incorporation of loadings
4. Monthly rate constants (35°C) for nitrogen and day
phosphorus uptake by plants for each soil zone.
KPA; KPN; KPP
5. Rate constants (35°C) for each transformation day
other than plant uptake for each soil zone.
KA; KD; KN; KDN; KIN; KIA; KM; KAP; KDP;
KIP, KMP
6. Temperature coefficients for each rate (-
constant.
TKA; TKD; TKN; TKDN; TKIN; TKIA; TKM; TKPA;
TKPN; TRAP; TKDP; TRIP; TKMP; TKPP
7. Monthly temperatures in each soil zone.
8. Volume of soil in each soil zone. ID
9. Bulk density of each soil zone. g/cm
10. Soil moisture content (from hydrologic simulations). (-)
11. Time step of simulations. month
°C
3
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TABLE NU-5: INPUT/OUTPUT PARAMETERS
(Continued)
PARAMETER
UNITS
OUTPUT
1. Monthly concentrations of nutrient species
in each soil zone.
(A) NH4-N(a)
org-N
P04-P(a)
org-P
(B) NH4-N(s)
P04-P(s)
mg
kg of soil
mg
' kg of soil water
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where :
ki=h-f(xn,yn,zn)
k2=h-f(xn+h,yn+k1,zn+k1)
The "fourth order" Runge-Kutta discretized solution is obtained from:
yn-f- 1 =yn+i(k i+2k2+2 k 3+ku )+0 (h 5) ,
where:
k2=hf xn+h ,
k 3=h f hcn+ih iy n+-2k 2 , zn+2l 2J
k4=hf(xn+h,yn+k3,zn+l3)
ll=hg(xn,yn»zn)
i K A ^kl J
1 2=hg (xn+f» yn+2~» zn+2
h k2 12\
+j-, yn+^- , zn+— •)
t=hg (xn+h , yn+k 3 , zn+l 3 )
The FORTRAN code of the Runge-Kutta solution techniques is presented in
subroutine HUNGER, Appendix FC.
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4.0 CONCLUSIONS
The nutrient cycle of SESOIL simulates the transport, transformations
and storages of nutrient species in soil and gives as an output the
storages of each species in each zone of the soil column.
The accuracy of the nutrient cycle output depends on the accuracies
of the hydrologic and pollutant transport simulations because it uses
both these routines in its simulations. This module can be used in
the management of agricultural runoff, nutrient residues in the soil
column, and the contamination of groundwater by nutrients via leaching.
NU-30
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5.0 REFERENCES
Abramowitz, Milton and Irene A. Segun, eds. Handbook of Mathematical
Functions, Dover Publications, Inc., New York; 1968.
Bartholomew, W.V. and F.E. Clark, eds. Soil Nitrogen. Agronomy Monograph
No. 10, American Society of Agronomy, Madison, Wisconsin; 1965.
Brady, Nyle C. The Nature and Properties of Soils, 8th edition, MacMillan
Publishing Company, Inc., New York; 1974.
Davidson, James M., D.A. Graetz, P.S.C. Rao, and H.M. Selira. Simulation
of Nitrogen Movement, Transformation, an'd uptake in Plant Root Zone.
Ecological Research Series, Environmental Research Laboratory, Athens,
GA; 1978. EPA-600/3-78-029.
Donigian, A.A., Jr., D.C. Beyerlein, H.H. Davis, Jr., and N.H. Crawford.
Agricultural Runoff Management (ARM) Model Version II Refinement and
Testing, Environmental Research Laboratory, Athens, GA, U.S. EPA,
Washington, D.C.; 1977. PB-273 105.
Johanson, Robert C., J.C. Imhoff, H.H. Davis, Jr., User's Manual for the
Hydrological Simulation Program - Fortran. Hydrocomp, Inc., Preliminary
Draft; September 1979.
Knisel, Walter G., ed. CREAMS; A Field Scale Model for Chemicals, Run-
off, and Erosion from Agricultural Management Systems. U.S. Department
of Agriculture, Conservation Research Report No. 26; 1980.
Larsen, S. "Soil Phosphorus," in A.G. Norman, ed., Advances in Agronomy.
American Society of Agronomy, Vol. 19, Academic Press, New York; 1967,
p. 151-210.
Odum, Eugene P. Fundamentals of Ecology, 3rd edition, W.B. Saunders
Company, Philadelphia, PA; 1974.
NU-31
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APPENDIX PT
POLLUTANT CYCLE
Page
1.0 INTRODUCTION PT_3
2.0 MODELING BACKGROUND pT_4
2.1 Literature Review PT-4
2.2 The SESOIL Pollutant Transport Routine Concept PT-5
2.3 Chemical Partitioning PX-7
2.4 Pollutant Mass Balance PT-9
2.5 Compartments PT-12
3.0 POLLUTANT CYCLE ROUTINES PT_15
3.1 General PT-15
3.2 Annual Pollutant Cycle Routine (LEVELO, LEVEL1) PT-15
3.2.1 General PT-15
3.2.2 Governing Equations PT-16
3.2.3 Solution Procedure PT-L6
3.3 Monthly Pollutant Cycle Routine (LEVEL2, LEVEL3) PT-28
3.3.1 General PT-28
3.3.2 Governing Equations LEVEL2, LEVEL3 PT-28
3.3.3 Numerical Solution Procedures PT-40
3.3.3.1 General PT-40
3.3.3.2 Constraint Criteria PT-55
3.3.3.3 Simulation Time Step PT-55
3.3.4 Moisture Molecule Penetration Constraint PT-57
3.4 Storm-by-Storm Pollutant Cycle (LEVELN) PT-59
4.0 DISCUSSION PT-59
5.0 REFERENCES PT-60
Dec. 81 PT-1
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FIGURES
PT-1: CONCEPTUAL PRESENTATION OF THE SOIL-LAYER ACTING
AS A "POLLUTANT MASS CARRIER" OVER TIME PT-6
PT-2: SCHEMATIC OF PHASES DESCRIBING THE SOIL MATRIX,
AND INTERRELATION OF SOIL LAYERS PT-8
PT-3: PARTITIONING AND OTHER TIME OR NON-TIME DEPENDENT
PROCESSES WITHIN At. PT-11
PT-4: SCHEMATIC OF MATHEMATICAL CONVERGENCE CRITERIA
OF EQUATION SYSTEMS PT-56
TABLES
PT-1: SUMMARY OF LEVEL FEATURES PT-14
PT-2: ANNUAL POLLUTANT CYCLE EQUATIONS — LEVELS 0, 1 PT-17
PT-3: SOLUTION TO POLLUTANT CYCLE EQUATIONS — LEVELS 0, 1 PT-26
PT-4: MONTHLY POLLUTANT CYCLE EQUATIONS — LEVEL2 PT-29
PT-5: MONTHLY POLLUTANT CYCLE EQUATIONS — LEVELS PT-41
PT-2
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1.0 INTRODUCTION
The ultimate fate or distribution of a pollutant in the SESOIL compart-
ment is governed by the hydrologic cycle processes, the sediment cycle
processes and the interaction of the various chemical fate processes
related to the pollutant involved. The actual quantity or mass of a
pollutant in any one process will depend at a particular time on the
"competition" among all the processes for the available pollutant mass.
This competition constitutes the basic philosophy of the pollutant-
transport routine of SESOIL that will be described in the following
sections.
The hydrologic cycle processes have been described in appendix HY. The
sediment cycle processes have been outlined in appendices SW and SR.
The individual chemical fate processes (diffusion, volatilization,
sorption, etc) have been described separately in previous appendices.
In SESOIL all these processes are considered interrelated and are
combined under different equation systems — depending on the level of
SESOIL operation. The solutions of these systems determine the spatial
and temporal distribution of a pollutant in the various subcompartments
(soil-air, soil-moisture, soil, etc) of the SESOIL "environment." The
mathematical routine/equation that combines all the previously described
processes (from appendix HY to appendix NU) is designated as the "pollu-
tant cycle" routine of SESOIL.
The processes of sedimentation, soil resuspension, photolysis, fixation,
biologic activity and nutrient transportation are not modeled in this
version (1981) of SESOIL. Such a modeling effort is anticipated by the
model developers in the near future (maybe 1982) in connection with the
watershed features of SESOIL.
This appendix presents the pollutant cycle routine of the model
including: (a) a short literature review of previous modeling efforts;
(b) the rationale governing the pollutant cycle equation structure and
the actual equations employed; and (c) the numerical techniques devel-
oped for each level of SESOIL operation. Information regarding input
data requirements to the pollutant cycle routine is presented in
section 3.0, User's Manual, of this report. One of the model objec-
tives has been to provide the literature with a "user friendly" package;
therefore input parameters to this routine have been kept to a minimum
by using many values that are estimated on-line by the model. Thus,
although SESUIL models a complex system of many processes and interac-
tions, it is intended to be relatively easy to use.
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2.0 MODELING BACKGROUND
2.1 Literature Review
The watershed modeling features of SESOIL are not presented in this
documentation; therefore the following literature review focuses only
in the unsaturated soil zone modeling aspects of the soil environment.
Previous sophisticated pollutant transport modeling efforts have mainly
employed the one- or two-dimensional time dependent diffusive, convec-
tive mass transport differential equation in homogeneous isotropic
soils, which in a one-dimensional domain is written
where 0 = soil moisture content, c = dissolved pollutant concentration
in soil moisture, Kp = apparent diffusion coefficient of compound in
soil-air, V = Darcy velocity of soil moisture, p = soil density, s =
adsorbed concentration of compound on soil particles IP = sum of
sources or sinks of the pollutant within the soil volume and z = depth.
The above equation has been solved principally: (a) numerically over a
temporal and spatial discretized domain, via finite difference or finite
element mathematical techniques (eg. Bonazountas et al 1979); and
(b) analytically, by seeking exact solutions for simplified environ-
mental conditions (eg. Enfield et al 1980). It must be pointed out that
the theoretical derivation of the mass transport equation PT-1 is based
upon a mass balance consideration of the pollutant in a representative
soil element of volume dV=dxdydz.
The principal scientific deficiencies when modeling pollutant transport
via equation PT-1 are: (1) only diffusion, convection, adsorption and
possibly decay can be modeled, whereas other processes such as fixation
or cation-exchange have to be neglected; (2) this equation is applicable
mainly to pollutant transport of organics, whereas transport of metals
which can be strongly affected by other processes cannot be directly
modeled; (3) this equation can predict volatilization only implicitly
via boundary diffusion constraints, however, experimental studies have
frequently demonstrated an overestimation or underestimation of the
theoretical volatilization rate; (4) no experimental or well accepted
equation for a process (eg. volatilization) can be incorporated in
PT-1, since the model has its own predictive mechanism; (5) pollutant
concentrations are estimated only in the soil-moisture and on soil-
particles, whereas pollutant concentrations in the soil-air are omitted;
(6) the discretized version of the equation has a pre-set temporal and
spatial discretization grid that results in high operational costs
(professional time, computer time) of the model, since input data have
PT-4
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to be entered into each node of the grid; and (7) it is difficult and
costly to run above models for typical canonical environmental scenarios
(soils, climates, pollutants) for reasons discussed in section 3.16
canonical environments, of the User's Manual.
In order to bypass the above and other deficiencies of the traditional
mathematical modeling, the SESOIL model developers have designed —
based on their experience with the traditional modeling (Bonazountas
et al 1979) — a new pollutant transport routine, which is presented
conceptually in the following section.
2.2 The SESOIL Pollutant Transport Routine Concept
In SESOIL, any soil subcompartment of irregular cross area Ai and of
depth di is considered a "pollutant mass carrier," that can receive
pollutant mass from other subcompartments, store pollutant mass and
export pollutant mass to other subcompartments. Assuming, for example,
that a compartment (Figure PT-1) contains originally a pollutant mass
Morig — of a particular pollutant — and receives during an infini-
tesimal time step At=(t)-(t-l) an impulse of pollutant mass Minput,
then for this subcompartment we can write the equation
M . (t) + M. (t) = M (t) + M (t)+ M« _(t) (PT-2)
ongv ' input ' transv ' renr ' outv v '
where
M . (t) = initially available pollutant mass
ori& in the soil compartment, at time t
M. (t) = input pollutant mass to the soil
compartment in fct)
MQut(t) = time dependent exported pollutant
mass by the pollutant carrier
M (t) = time dependent pollutant transformation
(or loss) within the compartment
Mrem(t) = remained pollutant mass in the compart-
ment due to various reasons.
Some of the processes of individual terms of equation PT-2 are time
dependent over the infinitesimal time step At (eg. volatilization),
others are assumed time independent (eg. adsorption). These issues
are discussed in later sections.
The mass balance concept (above) has been applied in SESOIL to a soil
matrix consisting of three phases: (a) solids (soil); (b) liquid (soil-
moisture); and (c) gas (soil-air). Phases anc3 subcompartments in SESOIL
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INPUT (t)
OUT (I)
input(t) = Pollutant mass introduced in a soil layer or
in its subcompartments of soil-air, soil-moisture,
at time (t).
orig(t-l) = Pollutant mass available in subcompartments of
soil-air, soil-moisture, soil-solids at (t-1).
trans(t) = Pollutant mass transformation within the soil layer
during the time step At«(t)-(t-1).
out(t) = Pollutant mass exported by soil compartment at the
end of time (t).
rem(t) = Remaining pollutant mass in the compartment at time (t)
FIGURE PT-1: CONCEPTUAL PRESENTATION OF THE SOIL-LAYER ACTING
AS A "POLLUTANT MASS CARRIER" OVER TIME
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are interrelated (Figure PT-2). It is the pollutant cycle that simulates
these interrelations by modeling both the chemical partitioning among
the three phases, and transport between subcompartments i.
2.3 Chemical Partitioning
The soil environment consists in SESOIL of three media: (1) soil-air
(gaseous phase); (2) soil-moisture (liquid phase); and (3) soil (solid
phase). The fate (transport/transformation) of pollutants in the soil
column — and consequently their ultimate fate — depends on the pollu-
tant partitioning among these three phases. This partitioning is a
function of various parameters such as the chemical-specific partition
coefficients (eg. air/soil moisture) and rate constants.
In SESOIL, the three phases are assumed to be in equilibrium at all
times. Thus once the concentration in one phase is known, the concen-
trations in the other phases can be calculated. In SESOIL, the pollu-
tant cycle is based on the pollutant concentration in the soil-moisture.
The concentration in the soil-air is then calculated by Henry's law,
and the concentration in the soil is calculated from the adsorption,
cation exchange, and other sorption processes included in the model.
Henry's law and the sorption processes are briefly described below.
The solute (dissolved) concentration of a compound is related to its
soil-air concentration via Henry's law (see equation VO-12).
c = c-H/R(T+273) (PT-3)
S3
where
c = pollutant concentration in soil-air; (ug/mL)
sa
c = dissolved pollutant concentration; (ug/mL)
H = Henry's law constant; (m^-atm/mol)
R = gas constant; (8.2xlO~5 m3-atm/mol-°K)
T = temperature; (°C)
°K = 8C + 273
In SESOIL, the pollutant concentration on the soil is determined from the
sum of the concentrations of the pollutant adsorbed, cation-exchanged,
and/or otherwise associated with the soil particles, eg. via adsorption
isotherms as discussed in appendix AD (adsorption) and in appendix CE
(cation exchange). One commonly used adsorption isotherm equation is
the Freundich equation
s = K- c1/n (PT-4)
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i? Lauev • u.
*=a\t kai\Kfe) . C,M
v_, X J )
lpue\r Soit ICUAW ; L
FIGURE PT-2: SCHEMATIC OF PHASES DESCRIBING THE SOIL MATRIX,
AND INTERRELATION OF SOIL LAYERS
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where
s = absorbed concentration of compound; (ug/g soil)
K = partitioning coefficient; (ug/g soil)/(ug/mL)
c = dissolved concentration of compound; (ug/mL)
n = Freundich constant; (-)
All these sorption processes are — and are expressed in SES01L as — a
function of the dissolved concentration of the pollutant in the soil
moisture.
The total concentration of a chemical in a soil matrix can be calculated
from the concentration of the pollutant in each phase and the related
volume of each phase (see also appendix VO) by
c0 = (n-0)csa + (0)c + (pb)s (PT-5)
where
C0 = overall (total) concentration of pollutant
in soil matrix; (ug/cm3 soil)
n = soil (total) porosity; (mL/mL)
0 = soil moisture content; (mL/mL)
n-0 = n . ; soil-air content or soil-air filled
aj.r
porosity; (mL/mL)
csa = P°llutant concentration in soil-air; (ug/mL)
c = pollutant concentration (dissolved) in soil-moisture; (ug/mL)
Pb = soil bulk density; (g/cm3)
s = pollutant concentration on soil particles; (ug/g soil)
2.4 Pollutant Mass Balance
The pollutant concentration in the SESOIL compartment changes with both
time and space due to the change of pollutant mass within the subcompart-
ment of the soil column. According to the law of mass conservation for
a representative element, the change of pollutant mass and over a small
time step At in that element will equal
AM = M. - M ^ - M_ (PT-6)
in out trans \ L D'
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where: AM = change in pollutant mass in the element; Min = mass entered
the element; M0ut = mass left the element; and Mt = mass transformed
(le. degraded) within the element.
Assuming that pollutant mass entered rapidly (instantaneously) at the
beginning of the time step, and by discretizing equation PT-6 over the
finite time step from, for example, t=0 to t=t (ie. At=t), we have
= M - M = M. - M - M (PT-7)
t o in,o out,t trans,t ^ '
where: Mt = pollutant mass in the element at time t; MQ = original
pollutant mass in the element; Min>o = input pollutant mass at t=0;
Mout,t = pollutant mass lost in time t; and Mtran«5 t = pollutant mass
transformed in time t. trans,t
When the original (initial) mass in the element, and the input to the
element are known, the fate of the pollutant at time t can then be deter-
mined by rearranging the terms of equation PT-7 and by expressing the
right hand side of the equation as a function of unknown variables such
as the dissolved, the adsorbed, and the vapor concentration of the
pollutant, or
Min n + Mn = Mf-(c»s»Coa»t) + M_ (C,S,C ,t)+ (PT-8)
iii) o o t S3 trsns t S3. \*-*w^
The above equation, which forms the basic philosophy of SESOIL, is
consistent with a discretized version of equation PT-1 for a constant
soil moisture content 0-;
0(ct " ct-l)/AC = f(c,s,D*,V,t) (PT-9)
however, in PT-8 pollutant mass balance (and not transport) is performed
for all three pollutant phases (vapor, liquid, solid) as contrasted to
PT-9 whose pollutant transport is studied only in the liquid and solid
phase. Pollutant transport will result from the mass balance equation
(PT-8) where the soil matrix is considered as a "pollutant carrier" as
previously described and discussed below.
In addition, each of the terms of PT-8 is expressed in SESOIL as the
weighted sum of the contributions (see equation PT-5) of various indivi-
dual processes that cannot be accounted for by PT-9. For example, the term
Mtrans.t, the mass transformed during an infinitesimal time period At,
is equal to the sum of the masses involved in hydrolysis from water (soil
moisture), hydrolysis from soil solids and other degradation processes.
This is a feature that cannot be studied via equation PT-9.
Finally, the SESOIL pollutant cycle equation is formulated for individual
processes and for an infinitesimal time step At (Figure PT-3), and not
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OR\&(Vl)
OUT
t>cnf -
(tj
FIGURE PT-3: PARTITIONING AND OTHER TIME OR NON-TIME
DEPENDENT PROCESSES WITHIN At.
PT-11
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for a differential time step .At=(t)-(t-l). This formulation allows
SESOIL to easily prioritize strength of individual processes when
necessary (eg. cation exchange takes precedence over all other processes,
only that mass not able to be exchanged is available for other sorption
processes) a modeling approach not followed before. This infinitesimal
approach for interrelated soil subcompartment on soil layers, in each of
which all pollutant phases are further interrelated, allows model
developers to be able to employ more than one well accepted equation
of the literature for one and the same process; for example, volatiliza-
tion via Hamaker (1979), Farmer et al (1980), others — see appendix VO.
The individual components of the SESOIL basic equation PT-8 are different
depending on the number of soil layers considered/modeled, the nature
of the process (eg. time-, non-time dependent), and the temporal resolu-
tion of the simulation. This results in the employment of different
numerical procedures for solving the equation systems and in other
scientific issues discussed in the following sections. Model users,
however, need not be concerned with these issues which are handled
internally (on-line) by the model.
2.5 Compartments
The mass balance equation PT-8 presented in the previous section was
formulated for any representative soil element that was assumed to be
homogenous and isotropic. The model calculated pollutant concentration
for this element reflects an average over the entire compartment, which
means that spatial variation within the selected compartment is ignored.
However, the user can select a fine cross-sectional (areal) resolution
of his compartment in order to increase areal-accuracy of his predictions
as discussed at the end of this section.
To increase the depth dependent spatial resolution of the model, without
incurring the numerical and computational difficulties of formulating
and solving discretized partial differential equations, the SESOIL com-
partment has been treated as a series of interconnected layers. Each
layer then has its own mass balance equation, and can both receive and
release pollutant to and from other layers (above or below).
Presently, SESOIL can handle simulations with two or three soil zones
(Figure PT-2). A top layer exposed to the atmosphere, a middle layer and
a lower layer are of user specified depth. There is no optimal advice
for the physical boundaries of these
soil layers. In many cases, these layers can be used to simulate a
shallow root zone of 5-25 cm; in other cases a wider depth may be used.
However, the minimum depth is 1 cm, for mathematical reasons only.
Multiple soil layers (eg. N instead of 3) can be simulated even with this
version of SESOIL; however, potential users should contact model developers
(Bonazountas, Wagner) for this issue.
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In SESOIL, a soil column can be specified to cover any area from 1 cm^
(finite approach) to several km2 (watershed approach). To simplify the
mathematics and to avoid computer round-off errors, the hydrologic cycle,
the sediment cycle and the pollutant cycle equations of SESOIL are
normalized to an area of 1 cm2. Pollutant fluxes across and within an
element boundary have been simulated via equation PT-8 which has been
formulated as
where
+P
P+
t
+p
transf,t
(PT-10)
in,o
'out,t
trans,t
- normalized (per cm ) pollutant input flux; (ug/cm2)
= normalized original pollutant mass in compartment;
(ug/cm*)
= normalized pollutant mass in compartment at time t;
(ug/cm2)
= normalized pollutant output flux; (ug/cm2)
= normalized pollutant mass transformed within time t;
(ug/cm2)
Equation PT-10 has been expanded to include various processes (hydrologic
cycle, chemistry) taking place in the soil compartment. Time has become
part of each individual processes within the time step of each simulation
or level of operation. (Table PT-1).
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TABLE PT-1
SUMMARY OF LEVEL FEATURES
LEVEL (//)
TIME
Resolution
SPATIAL
3)
Resolution
OTHER
Annual
2 soil layers Hydrocycle is user input
Annual
2 soil layers Hydrocycle is estimated
2)
2
3
Monthly
Monthly
1)
1)
2 soil layers Hydrocycle is estimated
3 soil layers Hydrocycle is estimated
2)
2)
1)
2)
3)
Provides annual averages of monthly estimates.
Hydrocycle estimate infiltration and groundwater
recharge participation for mass balance purposes.
User should employ n+1 layers, where n is the user's
needs. The +1 layer (next to groundwater) is for mass
balance purposes.
PT-1 A
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3.0 POLLUTANT CYCLE ROUTINES
3.1 General
Currently SESOIL can be operated at four different levels — LEVELO,
to LEVELS (Table PT-1) — each level serving a different purpose and
providing a different temporal and spatial resolution of processes
simulated (eg. soil quality, pollutant mass to groundwater). LEVELO
and LEVEL1 are associated with annual simulations and two soil layers,
whereas LEVEL2 and LEVEL3 are associated with monthly simulations and
either two soil layers (LEVEL2) or three soil layers (LEVELS).
The SESOIL theory is structured around the temporal resolution of a
simulation. The spatial resolution is separately studied within each
temporal subset (sections 3.2 and 3.3 below). For information as to
the appropriate level of model operation for a particular application,
consult section 3.0, user's manual, of this document.
3.2 Annual Pollutant Cycle Routine (LEVELO, LEVEL1)
3.2.1 General
Rough annual pollutant cycle simulations can be performed via LEVELO and
LEVEL1 of SESOIL. These two levels differ only in the hydrologic cycle.
In LEVELO, the hydrologic cycle components (soil moisture, infiltration,
groundwater, runoff, etc) are user input to the model. In LEVEL1, these
components are estimated by the model via its annual hydrologic cycle
routine (HYDROA) and the site specific climatological (ie. NOAA) and
soil data. The hydrologic cycle drives the pollutant cycle.
The same pollutant cycle routine (TRANSA) is used for both levels,
LEVELO and LEVEL1. The routine design is based upon:
(1) a discretization of the soil compartment into two
zones, upper unsaturated zone (watershed) exposed
to the atmosphere and lower unsaturated zone which
extends to the groundwater table; and
(2) the formulation of annual mass-balance equations
PT-10 for each of the two soil layers.
The principal assumptions made for the formulation of the annual pollu-
tant cycle equations are:
(1) the total pollution entering the subcompartment
over the year is a "one-hit-event" which takes
place at the start of the simulation;
(2) the total pollutant mass entering the subcompart-
ment is instantaneously distributed throughout the
subcompartment;
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(3) the soil column is uncontaminated at the start of
the simulation;
(4) the simulation is to be performed for only one year;
(5) the soil moisture content is represented by its
long-term annual average value and does not vary
with time within the year or spatially along the
soil column.
LEVELO and LEVEL1 have specialized applications, for example: screening
of a large number of chemicals that have to be compared for their envi-
ronmental effects when released into a soil compartment. These levels
should be employed with care (see also section 1.4 in the user's manual);
therefore, if any of the previously given assumptions are not relevant
to a particular application, the user has to select a higher level for
his simulations, such as LEVEL2 or LEVELS.
3.2.2 Governing Equations
Each of the two soil layers is considered a pollutant carrier with its
own individual processes. The pollutant cycle equation system is solved
analytically for reasons described in the following section and is coded
in FORTRAN in subroutine TRANSA and in its related programmed functions —
eg. VOLA, ADSA. The equation system, formulated for an upper soil layer
and a lower soil layer, is presented in Table PT-2.
3.2.3 Solution Procedure
The annual pollutant routine is designed for approximate studies,
where the emphasis in both LEVELO and LEVEL1 is placed on the differences
among predicted concentrations — for various environments and chemicals —
and not on "accurate" values of the concentrations. Therefore, all pro-
cesses in the annual routines are modeled as being of first-order, thus
allowing a simple analytical solution of the systems to be obtained. A
moisture penetration constraint is incorporated in both LEVELO and LEVEL1
simulations. This is discussed in detail in section 3.3.4 for all levels
of SESOIL operations.
Because all of the individual fate processes/terms of the mass balance
equation are linear functions of the pollutant concentration in the soil-
moisture of each zone, the equations have been rearranged to give the
pollutant concentrations in the soil-moisture directly as a function of
the input parameters to the model (Table PT-3). The pollutant concentra-
tions in the media of soil-air and soil-solids are calculated from the
dissolved pollutant concentration, either via the partitioning equations
presented in Section 2.3, or by dividing the pollutant masses previously
calculated as being in each phase by the volume of that phase.
PT-16
Arthur D Little. Inc
-------
TAB. • t»T-2
ANNUAL POLLUTANT CYCLE EQUATIONS - LEVELS 0,1
2
{_, A1J terms in paragraphs 1, 2, and 3 below are in units of |ig/cm .
e
M
V-
K "• General Mass Balance Equation I'JN>J + PQ>i = PREM>± + POUT>I +
00
10
2. Individual Processes - Upper Zone
PIN,U = PINP,U + PINF,U
Mass available at beginning of year: P = 0.0 (assumption 3, section 3.2.1)
Mass remaining at end of year: P^^ = P^ + P + P + P +
Mass out in year: POUT)U = PRg -I-
H
H Mass transformed within year: PTRANS>U = PHYD_H20>U + PHYD_S)U + PDEG>U
3. Individual Processes - Lower Zone
PIN,L ' PINP,L + PINF,L
Mass available at beginning of year: P = 0.0 (assumption 3, section 3.2.1)
U j LJ
Mass remaining at end of year: P^^ = P^^ + PADS>L + P^^ + PCQM>L +
Mass out in year: PQUTjL = PRG
Mass transformed within year: P = P HYD_^0>L + P ,,YD_S>L + P
o
-------
TABLE t-T-2 (Continued)
ANNUAL POLLUTANT CYCLE EQUATIONS - LEVELS 0,1
Where:
i subscript for soil layer i
U subscript for the upper soil layer
L subscript for the lower soil layer
P = pollutant mass input to soil compartment (total)
P = pollutant mass originally in soil compartment
Pnr.». = pollutant mass remaining in soil compartment
REM
P = pollutant mass output from soil compartment
i
oo p = pollutant mass directly input to soil compartment
P-rnr. = pollutant mass infiltrating to a zone
INr
P = pollutant mass dissolved in soil moisture
= pollutant mass adsorbed on soil particles
P = final pollutant mass cation exchanged
CEC~F
= pollutant mass complexed
? = pollutant mass in vapor phase (soil air)
VAIr
c
r^
«-»
(L
R
-------
c
-i
D
ET
TABf T-2 (Continued)
ANNUAL POLLUTANT CYCLE EQUATIONS - LEVELS 0,1
PRS - pollutant mass in surface runoff
PVOl. = P°llutant mass volatilized
PTRANS = P°llutant mass transformed in the soil compartment
PI1YD-H 0 = P°llutant mass hydrolyzed from soil moisture
PHYD-S = P°llutant mass hydrolyzed from soil solids
PDEG = P°llutanc mass degraded (other than by hydrolysis)
PRo = pollutant mass in groundwater recharge
-------
VO
™
TAliLL i*T-2 (Continued)
ANNUAL POLLUTANT CYCLE EQUATIONS - LEVELS 0,1
A. Individual Fate Process Equations
INP,i
INF,U
1NF,L
MOI,i
VAP
ADS,i
CEC i
'
Kb
VOL,U
POLIN
' SL
CU(A) ' ZA,dU
Ci(A) ' ° '
/
\
(c±(A)/(MUT . 106)) .
6b
. 10))
. . - , . .
/ MWT 1U 0 d
,6 .
,i = ci(A) * (H/(R ' (Ta+ 273))) • (n - 8) . d±
Ci(A) ' Ki ' P ' di
Calculated by comparing the total Ion exchange capacity of the soil with the input mass
TCFC i = (CECi ' MWT/VAL) . 10 . p . d±
Case 1: All available pollutant is exchanged P___ . = PTlil .
CEC,i IN,i
Case 2: Exchange capacity of soil is exceeded P___ , = !
c (A) .. R . i
U * S , A RS , A
[Cu(A) '
* (V 273)
[Da •(
-------
oo
N)
TABL. 'T-2 (Continued)
ANNUAL POLLUTANT CYCLE AQUATIONS - LEVELS 0,1
P = c (A) . Km . . 6 . d. . 365
HYD-H20,1 iv ' T,i i
P = fc.(A) . K. . K_ . . p . d, . 365J+ (P^^ , . KT , . 365)
•HYD-S.i = IC1W ' "i • *T.i ' V • "i ' "" •' V CEC.I "T.I
- Ci(A> ' Vi ' 9 ' 'i ' 3"
PRG = CL(A) '
5. Supporting Equations
I* A - Rr A + ( *
A,d G,A v A O,A
= MWT + b . MWTL1G
. (% oc±)/100
(for organics)
OCL
Arthur D Little Inc
CECL = CECU ' 3CEC
pHL = P11U ' 3pH
PCEC-P,1 = PCEC,1 ~ PCEC,i ' KT,i
KDE,L = ^E.U "a KDE
-------
TABLE l'T-2 (Continued)
ANNUAL POLLUTANT CYCLE EQUATIONS - LEVELS 0,1
DEPTH
00
to
£
IxJ
Where:
U
L
i
POLIN.
SL
LA,d
U
subscript for upper soil layer
subscript for lower soil layer
subscript for any soil layer
2
annual direct pollutant input; (gg/cm )
annual rainfall infiltration; (cm)
concentration of pollutant in the rainfall infiltration
as fraction of solubility; (-)
pollutant aqueous solubility; (pg/mL)
annual concentration of pollutant in soil moisture
(layer i) ; (|jg/cm2)
annual infiltration at depth d ; (cm)
• u
depth of soil layer; (cm)
average annun.I soil moisture content; (fractional)
Fortran Variables
POLINU.POLINL
IA
ASL
SL
IADU
DU.DL
THA
-------
N>
o
cr
t-r
r-»
(L
R
P
MWT
MWT
LIG
MWT
MI,
eq
H
R
T
a
n =
K
T =
CEC.l
CEC.i =
VAL
TAB7 "T-2 (Continued)
ANNUAL POLLUTANT CYCLE EQUATIONS - LEVELS 0,1
soil bulk density; (g/cm )
molecular weiglit of pollutant; (g/mol)
molecular weight of ligand; (g/mol)
molecular weight of pollutant-ligand complex; (g/mol)
stability constant of pollutant-ligand complex; (-)
concentration of ligand in soil moisture; (pg/mL)
number of moles of ligand per mole of pollutant
coraplexed; (-)
Henry's Law constant; (m . atm/mol)
gas constant; (8.2 x 10 m . atm/mol - °K)
temperature; (°C)
soil effective porosity; (fractional)
adsorption coefficient on soil; [(pg/g)/(pg/mL)]
o
total compartment (i) cation exchange capacity; (pg/cm )
soil layer i cation exchange capacity; (mill! equivalents/lOOg soil)
pollutant valence; (-)
Fortran Variables
RSA
MWT
MWTLIG
MWTML
SK
LIGCU.LICCL
B
1!
R
TA
N
K
TCECU.TCECL
CECU.CECL
VAL
-------
TABLL i'T-2 (Continued)
ANNUAL POLLUTANT CYCLE EQUATIONS - LEVELS 0,1
vo
oo
TJ
10
S,A
RS.A
D.
K..
R
G,A
K
C
oc
oc
a
oc
3CEC
s
•s.
KOH
annual surface runoff; (cm)
Index (=0,1) of surface runoff participation in
pollutant distribution; (-)
2
diffusion coefficient of pollutant In air; (cm /S)
total hydrolysis rate constant; (day )
degradation rate constant;
annual groundwater recharge (cm)
depth to groundwater; (cm - data input in m)
adsorption coefficient on organic carbon;
[(ug/g OC)/(ug/mL)]
soil organic carbon content; (%)
ratio soil organic carbon content lower: upper; (-)
ratio soil cation exchange capacity lower: upper; (-)
neutral hydrolysis rate constant; (day )
acid-catalyzed hydrolysis rate constant;
(day-1 . mol-i/L"1)
base catalyzed hydrolysis rate constant;
(day'1 . mol-i/L'1)
Fortran Variables
RSA
IRSA
I)
KTN
KDE
RCA
Z
KOC
OC
AOC
AC EC
KN
KAH
KBII
-------
TABLE 2 (Continued)
ANNUAL POLLUTANT CYCLE EQUATIONS - LEVELS 0,1
CEC-F,1
DEPTH
LIG.
pll in layer i; (-)
ratio soil pll lower: upper; (-)
ratio degradation rate constant lower: upper;.(-)
2
final pollutant mass remaining cation exchanged; (pg/cm )
depth rain penetration since start of simulation; (cm)
ligand input mass
Fortran Variables
PH
API!
AKDE
PCECU,PCECL
DEPTH
LIGU.LIGL
10
-------
vO
00
N>
TAULE l'T-3
SOLUTION TO 1'OLLUTANT CYCLE EQUATIONS FOR LEVELS 0,1
t_
M Upper Zone:
VA) • [PINP,U + PCEC,UJ/I° ' dU + kU ' P * dU + H ' ' V R ' L)/ (P - dL)
CSA,L(A) - CL(A) ' H/ R •
-------
1-3
ISi
-1
o
cr
TABLE FT-3
SOLUTION TO POLLUTANT CYCLE EQUATIONS FOR LEVELS 0,1
Where:
C.(A) = pollutant concentration in moisture of zone i
= pollutant concentration on soil of zone i
CSA i^ = P°llutant concentration in soil-air of zone i
For other symbols and supporting equations, see table PT-2
-------
Because such a direct solution can be obtained only when all equation
terms are linear with respect to the dissolved pollutant concentration,
only the linear Freundlich adsorption isotherm (n=l) has been incorpor-
ated into these levels. In addition, the equations of the time dependent
chemical processes are solved with an annual time step, which in fact
causes numerical computational inaccuracies in the predicted pollutant
concentrations. This is one of the reasons why these levels of operation
should not be employed for site specific simulations.
3.3 Monthly Pollutant Cycle Routine (LEVEL2, LEVEL3)
3.3.1 General
Both LEVEL2 and LEVELS routines simulate monthly cycles. They differ
only by the number of user specified layers that form the soil column.
In LEVEL2, the soil column has been divided into two soil zones; the
upper unsaturated soil zone and the lower unsaturated soil zone. LEVELS
has three soil zones; the upper, the middle and the lower unsaturated
zones. A monthly pollutant cycle subroutine has been formulated for
each of the above layers.
The principal assumptions made for the formulation of the pollutant
transport equations are:
(1) the total pollutant mass enters a subcompartment sequentially
(at a user specified rate) during the simulation period;
(2) all physical phases of the subcompartment (soil, air,
soil-moisture, soil-particles) are in equilibrium
within a time step;
(3) the soil-moisture content is represented by its monthly
long-term averaged value and does not vary over the
course of the month or along the vertical of the soil
column (an improved version of SESOIL is underway).
It is believed that these levels of SESOIL will cover a wide range of
applications with predictive accuracies within expected limits and
simultaneously offer great savings in user input data effort and
computer time. For situations where the above assumptions are not con-
sidered satisfactory development (and use) of a fully discretized (over
time and space) numerical version of SESOIL is necessary. Model devel-
opers (Bonazountas & Wagner) have planned for this level of operation —
LEVELN.
3.3.2 Governing Equations LEVEL2 , LEVELS
For each level, the individual pollutant carrying layers account for
different sets of individual processes. Table PT-4 presents the deriva-
tion of the pollutant cycle equations for LEVEL2, Table PT-5 presents
PT-28
Arthur D Little Inc
-------
TAB ^T-4
MONTHLY POLLUTANT CYCLE EQUATIONS - LEVEL 2
2
t.4 All terms in paragraphs 1, 2, and 3 below are In units of "ug/cm .
(-•
<
£ I- General Mass Balance Equation ^IN.i + P(t)0,i = P(t)REM,i + P(t)OUT,J + P(t)TRAN,i
CO
ro
2. Individual Processes - Upper Zone
•
Input mass: PIM.U " P(t)INP,U + P(t)INF,U
Mass available at beginning of time step: P(t)Q y = P(t-l)MO]. y + p(t-]L)SOIL v + '^^COM U + P(t~1)VAP U
Mass remaining at end of time step: PREM>u - PCO^^ + P(t)ADSp|I + P(t)CEC_F>u
Mass out in time step: POUT,U = P(t)RS + P(t)INF,L + P(t)VOL,U + P(t)SINK,U
I
Mass transformed within time step: l'(t)n,nAKi .. = P(t)..,, + P(t) +P(t) +P(t) + P(M
'TRAN.U v 'HYD-H2OfU V MIYD-S.U VC;DEG,U ^^TRANS.U FUJHYD-C,U
3. Individual Processes - Lower Zone
Input mass: P(t>IN,L = P(t)INP,L + P(t)INF,L
Mass available at beginning of time step: P(t)0>1 = P(t-l)MOI>L + P(t-l>SOIL>L + P(t-DCOM>L + pVAPfL
Mass remaining at end of time step: V^\m,TRAN>L - ^^HYD-H^.L + P(t>HYD-S,L + ^'(^DEC.L + P(t)TRANR,L + P
-------
Where:
i
t
t-1
U
L
PIN
REM
OUT
IRAN
INP
INF
MOI
SOIL
TABLE FT-4 (Continued)
MONTHLY POLLUTANT CYCLE EQUATIONS - LEVEL 2
subscript for soil layer i
indicates the current time step
indicates the previous time step
subscript for the upper soil layer
subscript for the lower soil layer
= pollutant mass input to soil compartment (total)
= pollutant mass originally in soil compartment
= pollutant mass remaining in soil compartment
= pollutant mass output from soil compartment
= pollutant mass transformed in the soil compartment
= pollutant mass directly input to soil compartment
= pollutant mass infiltrating to a zone
m— pollutant mass dissolved in soil moisture
= pollutant mass associated (adsorbed, exchanged) with soil
COM
pollutant mass complexed
-------
TABLl -ft (Continued)
MONTHLY POLLUTANT CYCLE EQUATIONS - LEVEL 2
VO
00
to
VAP
ADS
CEC-F
RS
VOL
SINK
HYD-HZO
HYD-S
HYD-C
DEC
TRANS
RG
= pollutant mass In vapor pliase (soil air)
= pollutant mass adsorbed on soil particles
final pollutant mass cation exchanged
= pollutant mass In surface runoff
= pollutant mass volatilized
= pollutant mass In other sinks (e.g., sediment transport)
pollutant mass hydrolyzed from soil moisture
= pollutant mass hydrolyzed from adsorbed pollutant
= pollutant mass hydrolyzed from exchanged pollutant
= pollutant mass degraded (other than by hydrolysis)
= pollutant mass in other transformations (e.g., fixation)
= pollutant mass in groundwater recharge
-------
VO
oo
H
U)
ro
TABLE PT-4 (Continued)
MONTHLY POLLUTANT CYCLE EQUATIONS - LEVEL 2
Individual Fate Process Equations
P(t)
'iNP.i = POLIN /NI
1
P(t)
'INF.U = I • a01 • SL/NI
M SL
P(t)INF,L = cU(t)
P(t)MOI,i
P
ADS.i = c ^c; • K • p •
P(t)
CEC.i = Calculated by comparing the total ion exchange capacity of the soil with the input mass
rCEC,i = (CECi ' MWT/VAL) • 10 - p - d±
Case 1: All available pollutant is exchanged P(t) = P(t)
e yCEC,i v 'lN,
Case 2: Exchange capacity of soil is exceeded P(t) = T
'CEC.l CEC.i
P(t>RS
ST P(t)VOL,U - h(t) • H" • (Ta+ 273> '
-------
TABLE T (Continued)
MONTHLY POLLUTANT CYCLE EQUATIONS - LEVEL 2
<_
P
vo
00
ro
f = Calculated according to concentration gradient
'
Case 1: c,,(t) < c (L) (Gradient is upward.)
U Ij
P(t)
VOL,L '
Case 2:
P(t
>_ CL
,L
(Gradient is downward or zero.)
NT. /
CO
3
6
{L
R
P(t)
SINK,
P(t)
" PSINK,i/NI
P(t)
P(t)
HYD-ll20.i
HYD-S,i
DEG,i
• .
ci(t) •
P(C)TKANS,i = PTRANS,i/NI
P(t)
RG
cL(t) ' RG,M/NT
P(t)
HYD-C,i '
. . . p . d± . (30/NI))
COM,i
[ML]i ' MWT ' 1() ' 0(t) ' di SK
C±(t)
,MWT .10
Solved numerically in subroutine COMP
[L]
MWT. _ . 10
6- ~b^Lh
-------
CO
TABLE I'T-4 (Continued)
MONTHLY POLLUTANT CYCLE EQUATIONS - LEVEL 2
5. Supporting Equations
— • • " - * -
du
U LJ
MWTMf = rWT + b . MWTTT_
ML LIG
K± = KQC . (% OC±)/100
(for organics)
oc. = oc .a
L u oc
K = K + K 10 + K
KT,i K K ' 10 A + K '
N M ' OH
'SlE.L = KDE,U ' <1KDE
P(t)CEC-F,i ." P(t)CEC,i - P(t)CEC,i ' KT,i ' (30/NI)
Si(t) ' (P^ + ^-)' (P '
DEPTH(t) = (I + R KI)/(2 . 0 . n . NI)
n IP , rl
-------
u>
Ln
o
cr
TABL V-4 (Continued)
MONTHLY POLLUTANT CYCLE EQUATIONS - LEVEL 2
[L]
± = LiG±/(e . d±)
CSA,i(c) * ^O • " / (X • tt, + 273))
-------
TABLE PT-4 (Continued)
MONTHLY POLLUTANT CYCLE EQUATIONS - LEVEL 2
Where:
OJ
I
a
cr
r-*
r-»
(L
o
t
t-1
U
L
i
POLINj
NI
aSL
M,d
U
indicates current time step
Indicates previous time step
subscript for upper soil layer
subscript for upper soil layer
subscript for any soil layer
2
monthly direct pollutant input; (gg/cm )
number of numerical iterations per month; (-1)
monthly rainfall infiltration; (cm)
concentration of pollutant in the infiltration
as fraction of solubility; (-)
pollutant aqueous solubility; (ug/mL)
concentration of pollutant Jn soil moisture
(layer i) ;
= monthly infiltration at depth d..; (cm)
= depth of soil layer; (cm)
= average soil moisture content; (fractional)
= concentration of pollutant on soil solids
(layer i); (pg/g soil)
Fortran Variables
POLINU.POLINL
NI
IM
ASL
SL
CUM.CLM
IMOU
DU.DL
THA
SUM.SLM
-------
00
N>
TJ
V
U)
p
MWT
MWT
MWT.
F
k
eq
-i
o
tr
n
R
Ta
n
K
FRN
TCEC,i
CEC.i
VAL
TABF 'T-4 (ConLinued)
MONTHLY POLLUTANT CYCLE EQUATIONS - LEVEL 2
= soil bulk density; (g/cm )
= molecular weight of pollutant; (g/mol)
= molecular weight of llgand; (g/mol)
= molecular weight of pollutant-ligand complex; (g/mol)
= stability constant of pollutant-ligand complex; (-)
= concentration of ligand in soil moisture; (ug/mL)
= number of moles of ligand per mole of pollutant
complexed; (-)
2
= Henry's Law constant; (m . atm/mol)
= gas constant; (8.2 x 10~ m • atm/mol - °K)
= temperature; (°C)
= soil effective porosity; (fractional)
= adsorption coefficient on soil; [(ug/g)/(gg/mL)]
= Freundich exponant; (-)
2
= total compartment cation exchange capacity; (|jg/cm )
Fortran Variables
RS
MWT
MWTLIG
MWTML
SK
LIGCU.LIGCL
B
U
R
T
N
K
FRN
TCECU, I'CECI.
soil cation exchange capacity; (milli equivalents/lOOg soil) CECU.CECL
pollutant valence; (-) VAL
-------
7
OJ
03
R
S,M
1RS,M
DA
POUT,i
KT,i
^E
PTRANS,N
Rc
Z
Koc
OC
aoc
aCEC
c
•n
0
TABLE PT-4 (Continued)
MONTHLY POLLUTANT CYCLE EQUATIONS - LEVEL 2
= monthly surface runoff; (cm)
= index (=0,1) of surface runoff participation in
pollutant distribution; (-)
2
= diffusion coefficient of pollutant in air; (cm /S)
2
= other pollutant sinks per month; (ug/cm )
= total hydrolysis rate constant; (day )
= total degradation rate constant; (day )
= other pollutant transformations per month; (»g/cm )
= monthly groundwater recharge
= depth to groundwater; (cm)
= adsorption coefficient on organic carbon;
[(Ug/g OC)/(ug/mL)]
= soil organic carbon content; (o/o)
= ratio soil organic carbon content lower: upper; (-)
= ratio soil cation exchange capacity lower: upper; (-)
= neutral hydrolysis rate constant; (day )
Fortran Variables
RSM
IRSM
D
POUTU.POUTL
KTN
KDE
PTRANU.PTRANL
RCM
KOC
OC
AOC
ACEC
KN
-------
\o
co
NJ
CO
VO
•Si
OH
KDE
P(t)
k(l)
CEC-F,i
DEPTH
C
LIG.
IL]
i.FREE
TABLE -ft (Continued)
MONTHLY POLLUTANT CYCLc. EQUATIONS - LEVEL 2
acid-catalyzed hydrolysis rate constant;
(day . mol /L ')
base catalyzed hydrolysis rate constant;
(day . mol
soil pll; (-)
(day . mol /L )
[ML]
= ratio .soil pH lower: upper; (-)
= ratio degradation rate constant lower: upper; (-)
2
= final pollutant mass remaining cation exchanged; (ug/cm )
2
= average Intrinsic soil permeability; (cm )
2
= intrinsic permeability of soil zone i; (cm )
= depth rain penetration since start of simulation; (cm)
= pore disconnectedness index; (-)
= saturated hydraulic conductivity; (cm/day)
2
= ligand input mass; (jjg/cm )
= free ligand concentration; (pg/mL)
3
= pollutant concentration in soil air; (ug/cm )
= concentration of ligand-pollutant complex (mol/mL)
Fortran Variables
KAH
KBH
PH
APH
AKDE
PCECU.PCECL
Kl
K1U.K1L
DEPTH
C
BK1
LIGU.LIGL
LIGCUF.LIGCLF
CUSA.CLSA
MLC
-------
the derivation of these equations for LEVELS. The LEVEL2 equations are
coded in FORTRAN in subroutine TRANSM, those of LEVELS are coded in
subroutine TRANS3. Both subroutines call several functions containing
individual fate equations (see appendix FC, FORTRAN code).
3.S.3 Numerical Solution Procedures
3.3.3.1 General
All of the individual fate processes which compose the SESOIL mass
balance equation are — and are expressed as — functions of
(1) a variety of rate, partitioning and other constants;
and
(2) the pollutant concentration in the moisture of each
zone.
Some of the concentration terms are non-linear; therefore, these equations
can not be solved directly as in the case of the annual cycle routines.
An iterative solution procedure has been developed to solve this system
efficiently.
The solution procedure involves the following steps for each layer —
starting at the surface of the soil column:
(1) an initial value c (t) = 0.0 is assumed;
(2) the mass balance equation PT-10 is solved iteratively
P = P +P - P — P p
i in.i o,i a,i out.i transf.i
by incrementally increasing the value of c(t) by
AC (AC is large at the beginning) until P^ meets
one of the five constraint criteria described in
the next section;
(3) the incremental interval Ac is decreased to a new
value Aci
-------
TABL T-5
MONTHLY POLLUTANT CYCLE EQUATIONS - LEVEL 3
All terms In paragraphs 1-4 below are In units of
§1. CgneraJLMasB Balance Equation *MW,± + PREM,i = P(t>A,i + ^OUT.I + P(t)THAMfl
2. Individual Processes - Upper Zone
Input mass: P(t)IN,U = P(t)INP,U + P(t)INF,U
Mass available at beginning of time step: P(t)Q u - P^-^MQI.U + P(t~1)SOIL,U + P^t~1^COM,U + P^t~1)VAP,U
Mass remaining at end of time step: pU + P(t)CEC_F>u + PCOM>u + P(t)VAp>u
Mass out in time step: P(t)OUT,U = P(t)RS + P(t)INF,M + P(t)VOL,U * P(t)SINK,U
V Mass transformed within time step: p(t)TRAN,U = P(t)HYD-H20,U+P(t)HYD-S,U + P(t)DEG,U+P(t)TRANS,U+P(t)HYD-C,U
3. Individual Processes - Middle Zone
Input mass: P(t)IN,M = P(t)INP,M + P(t)INF,M
Mass available at beginning of time step: P(t)Q)M = P(t-l>MOI>M + p Mass out in time step: P(t)OUT,M = P(t)INF,l. + P(t)VOL,M + P(t)SINK,M
5 Mass transformed within time step: P(t)TRAN,M = P(t)HYD-H20,M + P(t)HYD-S,M + P(t)DEG,M + P(t)TRANS,M+P(t)HYD-C,
r
-------
TABLE PT-5 (Continued)
MONTHLY POLLUTANT CYCI.R EQUATIONS - LEVEL 3
4. Individual Processes - Lower Zone
Input mass: Pft) = Pft) 4-
1 ;IN,L IC; +
Mass available at beginning of time step: P(t) = P(t-l)M_T + P(t-l)_rtTI , -»- P(t-l)ortM , +
wilj rlUljli oUlL,L COM,L
Mass remaining at end of time step: *™m.L = P(t)MOI.L + P(t)ADS,L + P(t)CEC,L + P(t>COM,L + P(t)VAP,L
Mass out in time step: "'^OUT.L = P(t>RG + P^>VOL,L + P(t)SINK,U
Mass transformed within time step: P(t).
-^
a
-------
TABLE S 45 (Continued)
MONTHLY POLLUTANT CYCLt EQUATIONS - LEVEL 3
Where:
«~
OJ
I
o
i
t
t-1
U
M
L
PIN
P0
PREM
p
OUT
PTRAN
PINP
PINF
PMOI
PSOIL
PCOM
subscript for soil layer i
indicates the current time step
Indicates the previous time step
subscript for the upper soil layer
subscript for the middle soil layer
subscript for the lower soil layer
«• pollutant mass input to soil compartment (total)
= pollutant mass originally in soil compartment
= pollutant mass remaining in soil compartment
= pollutant mass output from soil compartment
= pollutant mass transformed in the soil compartment
= pollutant mass directly input to soil compartment
= pollutant mass infiltrating to a zone
= pollutant mass dissolved in soil moisture
= pollutant mass associated (adsorbed, exchanged) with soil
=> pollutant mass complexed
-------
TABLE PT-5 (Continued)
MONTHLY POLLUTANT CYCLE EQUATIONS - LEVEL 3
c
£ *\IAT> ** pollutant mass in vapor phase (soil air)
. VAf
H
iS PAno = pollutant mass adsorbed on soil particles
1^ AlJo
PCEC-F = fjLnal pollutant mass cation exchanged
PD_ = pollutant mass in surface runoff
no
= pollutant mass volatilized
PSINK = P°llutant mass Jn other sinks (e.g., sediment transport)
^ PHYD-1I 0 *" P°Hutant mass hydrolyzed from soil moisture
4S
PHYD-S = pollut3"1- mass hydrolyzed from adsorbed pollutant
PIIYD-C = P°Hutant mass hydrolyzed from exchanged pollutant
PDEG = P°Hutant mass degraded (other than by hydrolysis)
PTRANS = P°H-utant mass in othi'r transformations (e.g., fixation)
PRG = pollutant mass in groundwater recharge
-------
tn
TA13LF -5 (Continued)
MONTHLY POLLUTANT CYCLE EQUATIONS - LEVEL 3
., 5. Individual Fate Process Equations
_i
1 v(t}
1 'iNP.l = POLIN./NI
-i l
P(t)
v 'INF.U = IM . a0¥ . SL/NI
n oL
P(t)
;1NF,M = Cu(t) . IM)du/NI
P(t)INF,L
P(t)MOI.,i * Ci * 8<'> '
-.~,1 = S.(t) • p
TJ i
H
P(t)Cf)M ± = [ML]1 . MvJT . 10° . 6(t) . d± SK = [HL11/
fi
MWT . 106
P(t)VAP,i = Ci(t) ' (H/(R ' • 10 • p • dt
Case 1: All available pollutant is exchanged PU)™,, . = p(t)TM
" » j 1 I. Dl 9 1.
Case 2: Exchange capacity of soil is exceeded P(t),,_,, . = T___ .
LliC. , 1
P(t)RS = CU(t) * RS,M ' ^S.
*
Solved numerically in subroutine COMI'
-------
TABLE PT-5 (Continued)
MONTHLY POLLUTANT CYCLE EQUATIONS - LEVEL 3
(-•
V!
M
VO
00
M P(t)
VOL.M = Calculated according to concentration gradient
cr
r-t
r^
Case 1: Cy(t) < CM(t) (Gradient is upwards.)
. (T 4-
a
~2
Case 2: ^(t) J> CM(t) (Gradient is downward or zero.)
P(t)VOL,M - °-°
li3 P(t)
JL. VOL.L = Calculated according to concentration gradient
Case 1: Cy(t) and CM(t) < Cy(t) (Gradient is upward.)
Case 2: Cy(t) or CM(t) _> Cj(t) (Gradient is downward or zero.)
P(t),
'VOL.L "-w
'SINK, 1 = PSINK,i/NI
| P(t)l.YD-..20,i = Ci(t) ' KT,i ' 8<'> ' di ' <30/NI>
-------
{&_
8
TABLE PT-5 (Continued)
MONTHLY POLLUTANT CYCLE EQUATIONS - LEVEL 3
P(t)HYD-S,i = (c^) ' Kj • KT,i ' P * dl ' <30/NI»
P(t)DEG,i = ci(t) * KDE,i'0(t) ' di '
P(t)TRANS,i = PTRANS,i/NI
P(t)RG = CL(t) * RG,M/NI
P(l:)HYD-C,i = *(t>CBC,t ' KT,i ' (30/NI)
6- Supporting Equations
/
= (RG,M +
= (RG,M+ ^M-VM^
k(1)U k(1)M k(J)L
MWT
ML = MWT + b . MWTTTr,
Lid
Ki = Koc • (% OCi)/100
(for organics)
°CM ' OCU ' a2
OC
k
z
-------
w KDE,L
TABLE PT-5 (Continued)
MONTHLY POLLUTANT CYCLE EQUATIONS - LEVEL 3
°CL ' °CU ' 3OC
CEC = CEC.. . a2__r
M U CEC
CECL = CECu . aCE(,
• a2 „
pH
PHL = pHu .
KDE,M ~ SE.U ' a2KDE
P(t)CEC-F,i ' ^CEC.l - P(t)CEC,i • KT,i '
Si(t) ' p(t> + P(t)-/ (P
DEPTH(C) = (IM + RG M)/(2 . °8 . n . NI)
-------
VO
00
TABLE r " (Continued) J
MONTHLY POLLUTANT CYCLE EQUATIONS - LEVEL 3
u
£ ««I
1L11,FREE = (IL11 ' dl * 6 - B ' PCOM ' (^SF-)) /( di ' 0)
CSA,i(t) " (ci(t) ' " ' R ' (Ta + 273»
Vk(1)U
,
VO
-------
Where:
7
Ln
O
o
cr
t
t-1
u
M
L
1
NI
SL
'.d,
TABLE l'T-5 (Continued)
MONTHLY POLLUTANT CYCLE EQUATIONS - LEVEL 3
indicates current time step
•
indicates previous time step
subscript for upper soil layer
subscript for middle soil layer
subscript for lower soil layer
subscript: for any soil layer
2
monthly direct pollutant input; (ug/cm )
number of numerical iterations per month; (-1)
monthly rainfall infiltration; ('cm)
concentration of pollutant in the Infiltration
as fraction of solubility; (-)
pollutant aqueous solubility; (ug/mL)
concentration of pollutant in soil moisture
(layer i) ;
monthly infiltration at depth d ; (cm)
depth of soil layer; (cm)
average soil moisture content; (fractional)
concentration of pollutant on soil solids
(layer 1); ()ig/g r '*)
Fortran Variables
POLINU.POLINL
NI
IM
ASL
SL
CUM.CLM
IMOU
DU,DL
THA
SUK M
-------
VO
00
to
Ui
a
cr
r*
r^
(L
R
P
MWT
MWT,
L1G
ML
eq
[LL
H
R
Ta
n
K
FRN
TCEC,i
CEC.i
VAL
T/ ' PT-5 (Continued)
MONTHLY POLLUTANT CYCLE EQUATIONS - LEVEL 3
3
= soil bulk density; (g/cm )
= molecular weight of pollutant; (g/mol)
= molecular weight of llgand; (g/mol)
= molecular weight of pollutant-ligand complex; (g/mol)
= stability constant of pollutant-ligand complex; (-)
= concentration of ligand in soil moisture; (ug/mL)
= number of moles of ligand per mole of pollutant
complexed; (-)
•j
= Henry's Law constant; (m . atm/mol)
—5 3
= gas constant; (8.2 x 10 m • atm/mol - °K)
• temperature; (°C)
= soil effective porosity; (fractional)
= adsorption coefficient on soil; [ (|ig/g)/()Jg/mL)]
= Freundlch exponent; (-)
2
total compartment cation exchange capacity; (ug/cm )
Fortrr
RS
MWT
MWTLIC
MWTML
SK
LtGCU.LIGCL
B
II
R
T
N
K
FRN
TCECU.TCECL
•iables
soil cation exchange rapacity; (mill! equlvalents/lOOg soil) CECU,CECL
pollutant valence; (-) VAL
-------
TABLE l'T-5 (Continued)
MONTHLY POLLUTANT CYCLE EQUATIONS - LEVEL 3
Ul
S,M
RS.M
OUT,i
K
T.i
TRANS,N
K
OC
OC
'OC
CEC
= monthly surface runoff; (cm)
= index (=0,1) of surface runoff participation in
pollutant distribution; (-)
2
= diffusion coefficient of pollutant in air; (cm /S)
2
= other pollutant sinks per month; (pg/cm )
/., -1%
= total hydrolysis rate constant; (day )
,_, -1\
= total degradation rate constant; (day ;
= other pollutant transformations per month; (ug/cm )
= monthly groundwater recharge
= depth to groundwater; '(cm)
= adsorption coefficient on organic carbon;
[(ug/g OC)/(ug/mL)]
= soil organic carbon content; (o/o)
I
= ratio soil organic carbon content lower: upper; (-)
ratio soil cation excljange capacity lower: upper; (-)
neutral hydrolysis rate constant; (day )
Fortran Variables
RSM
IRSM
D
POUTU.FUUi'L
KTN
KDC
PTBANU.PTRANL
ROM
Z
KOC
OC
AOC
ACEC
KN
-------
vo
00
10
Ut
CO
I
a
tr
•Si
K
OH
°KDE
P(t)
k(l).
CEC
DEPTH
C
LIG
TABL ^-5 (Continued)
MONTHLY POLLUTANT CYCLE EQUATIONS - LEVEL 3
« acid-catalyzed hydrolysis rate constant;
(day . raol /L )
= base catalyzed hydrolysis rate constant;
(day . raol /L )
= soil pll; (-)
= ratio soil pll lower: upper; (-)
= ratio degradation rate constant lower: upper; (-)
2
= pollutant mass remaining cation exchanged; (ug/cm )
o
= average intrinsic soil permeability; (cm )
2
= intrinsic permeability of soil zone i;(cm )
= depth rain penetration since start of simulation; (cm)
= pore disconnectedness index; (-)
= saturated hydraulic conductivity; (cm/day)
2
= ligand input mass; (ug/cm )
= free ligand concentration; (ug/mL)
= pollutant concentration in soil air; (tig/cm )
Fortran Variables
KAH
KBH
PH
APH
AKDE
PCECU.PCECL
Kl
K1U.K1L
DEPTH
C
BK1
LIGU,LIGL
LICCUF,L1GCLF
CUSA.CLSA
-------
2
a2
a2
a2
a 2
OC
CEC
pll
KDE
[ML]
TABLE PT-5 (Continued)
MONTHLY POLLUTANT CYCLE EQUATIONS - LEVEL 3
= average permeability of upper and middle zone; (cm )
ratio soil organic carbon content middle: upper; (-)
ratio soil cation exchange capacity middle: upper; (-)
ratio soil pli middle: upper; (-)
ratio soil degradation rate middle: upper; (-)
concentration of ligand-pollutant complex; (mol/mL)
Fortran Variables
K2
A20C
A2CEC
A2PH
A2KDE
MLC
-------
3.3.3.2 Constraint Criteria
Five convergence/constraint criteria have been designed to assure a
solution within limits (e). These are described below and are graph-
ically presented in Figure PT-4.
(1) abs(Pi[c1t+l)]) < abs(Pi[c(t+l)]) (PT
This criterion assures movement of the initial
?i value towards the zero-axis.
(2) abs(Pi)< e = 0.01 (PT-12)
This criterion implies convergence to a zero
value has occurred.
(3) ^[ct+DJ) • (Pi[c(t+l)]) < 0 (PT-13)
This criterion assures the convergence to zero,
without overpassing the zero value. In the latter
case the value would jump the zero-axis (from the
one or the other direction) and would continue
indefinitely.
(A) abs(P1[c(t+l)]) = 0 (PT-14)
This constraint reflects the case where no pollution
is in the column any more.
(5) c(t+l) has been calculated to 6 significant digits.
For extreme concentrations (either very small/very
large pollutant load), the equations may not balance
to within 1% (criterion 2) due to accumulation of
round-off error. In such a case, this criteria
forces convergence.
3.3.3.3 Simulation Time Step
For LEVEL2 and LEVEL3 the pollutant cycle equations are formulated on a
monthly basis, and the results are reported for each month simulated.
However, since all terms that are time dependent are written with an
explicit time step (At), the model has to be run for smaller time steps
(eg. week, day) in order to account for the non-linear processes (eg.
volatilization). In this case the obtained monthly reports (output)
represent the iterations and summations of results of many smaller
iterations.
The number of iterations per month (NI) is preset in the FORTRAN code.
The actual simulation time step (in days) is equal to 30 (davs/month)
divided by the number of iterations per month NI, or At=30/NI. A large
PT-55
Arthur D Little. Inc
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1)
M
2)
TV*
Diverging iteration corresponding
to the physico-chemical situation
where the soil layer becomes "clean"
before the end of the month.
concentrations in layer =0.0
• solution of equation system
balanced within + 1%
• solution obtained
• equation system solution has
crossed origin
• iteration procedure repeated
with a higher resolution
5>
H
• clean soil layer criterion
• concentrations are set to 0.0
successive approximation to
solution via variable resolution
for computational efficiency
follow criterion 2 above
FIGURE PT-4:
SCHEMATIC OF MATHEMATICAL CONVERGENCE
CRITERIA OF EQUATION SYSTEMS
PI-5 6
Arthur D Little, Inc
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number of iterations per month will increase the accuracy of the model
output, and will also result in increased computational time. Presently,
the model performs four iterations per month (30/4=7.5 days per simula-
tion). It is felt that this number of iterations is a reasonable com-
promise between accuracy and computational cost. However, any number of
iterations per month can be reprogrammed when necessary.
3.3.4 Moisture Molecule Penetration Constraint
A pollutant originating from any unsaturated soil zone layer will theo-
retically reach an underlying soil layer (or the groundwater) as soon
as a moisture drop originating from the first layer reaches the latter
layer (or the groundwater). In practice, however, a "retardation" of
the pollutant front will take place with respect to the bulk mass of
moisture movement. This retardation is mathematically described by
Freeze and Cherry (1979 p. 404) via a retardation factor related to the
adsorption capability of the pollutant on the soil particles. If no
adsorption is assumed, the pollutant front will follow the seepage soil
moisture velocity.
It is not necessary to separately account for such a pollutant in SESOIL,
since the pollutant transport routine of the model will retard pollutant
mass traveling vertically via the adsorption and other processes modeled.
However, it is important to know whether a polluted soil moisture mole-
cule (carrying a dissolved pollutant) originating in an upper layer has
penetrated — even at a negligible concentration — through the entire
layer to the underlying soil layer or has reached the groundwater. If
so, the pollutant transport routine of the underlying layer has to be
activated; otherwise, no pollutant mass input to the underlying layer
will take place. The moisture molecule penetration constraint is
incorporated in all levels of SESOIL operations.
Two methods o[ approximating estimation of the penetration depth of a
soil moisture molecule into the underlying soil compartment are relevant
to the SESOIL analysis: (1) via Darcy's law, (2) via soil dynamics, and
these are combined below into one equation for any soil layer.
The average linear soil flow velocity in a saturated soil is given by
Freeze & Cherry (1979, p.71).
v = Q/n-A =Q/n (PT-15)
where
v = average linear velocity
Q = volumetric flux (or specific discharge, or Darcy's
velocity)
PT-57
Arthur D Little. Inc
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n = soil porosity
A = cross section of soil matrix (assumed 1)
The average linear soil moisture velocity — known also as interstitial
pore water velocity (Enfield et al 1980) — is given by
v(0) = v/0 = Q/n-0 (PT-16)
where _
v(0) = average linear soil moisture velocity
0 = soil moisture content
SES01L employs the theoretical hydrologic routine of Eagleson (1978) as
adapted for time dependent moisture storage and transfer in the course
of the months. Therefore, Eagleson1s principal equations have been also
employed here to describe volumetric fluxes in a soil layer.
The monthly average linear volumetric flux or specific discharge in a
month for a soil layer is given in SESOIL (eg. HY-28.1) by
Q = (I(M)+(Rg(M))/2 (PT-17)
Therefore, by combining above equations, we have the average moisture
molecule penetration depth after t months
d = f(I(M)+Rg(M))/(20n) (PT-18)
where
d = average soil moisture penetration depth (cm)
t = 1,2,3, ... months elapsed; (integer ??)
I(M) = monthly infiltration^depth} to soil layer (cm)
Rg(M) = monthly percolation^depth)from soil laver (cm)
0 = soil moisture content (fraction)
n = soil porosity (fraction)
Numerical example (data from Eagleson 1977):
- Assume: t=12 (ie. months), 0=SQ-n-(0.67) • (0.35)=0.235, I(M)=63.6/12=5.3 cm
(ie. 5.3 cm/month and for the 12 months), Rg(M)=19.8/12=1.65 cm, n=0.35
- then d = 12(5.3+1.65)7(2*0.235*0.35) = 507 cm (ie. cm/yr)
PT-58
Arthur D Little, Inc
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3.4 Storm-by-Storm Po.lutant Cycle (LEVELN)
The LEVELN of SES01L has not been developed; however, designers have
conceptualized the development of this model feature. For additional
information call 617/8d4-5770.
4.0 DISCUSSION
SESOIL is a "user frierdly" model and as such the pollutant cycle sub-
routines are designed to be easily expandable. Processes not currently
included in the simulation can be incorporated simply by adding another
term to one of the mass balance terms. For example, an expression for
the degradation of polJutant by soil bacteria could be added to the
model by including the bacterial degradation term with the other pollu-
tant transformation equations.
The pollutant mass added to the groundwater is estimated by all levels
of operation of the model. The behavior of pollutant within the ground-
water is not currently described by SESOIL, although the simulation of
a groundwater "layer" can be developed and model developers have some
long-term plans. However, SESOIL is also adaptable to provide informa-
tion for (and/or to be interfaced with) other groundwater models of the
literature.
PT-59
Arthur D Little, Inc
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5.0 REFERENCES
Bonazountas, M.; W. Hawes; W. Tucker (1979). Heuristic Unsaturated
Flow/Quality Soil Zone Model. AGU, Spring Meeting, Washington, DC.
Eagleson, P.S. (1978). Climate, Soil, and Vegetation (1-7). Water
Resources Research, Vol. 14, No. 5, pp. 705-776.
Enfield, C.G.; R.F. Carsel; S.Z. Cohen, T. Phan & D.M. Walters (1980).
Method of Approximating Transport of Organic Pollutants to Groundwater
EPA - Internal draft. EPA - Robert S. Kerr, Environmental Research
Laboratory, Ada, Oklahoma.
Farmer, W.J.; M.S. Yang; J. Letey; W.F. Spencer (1980). Land Disposal
of Hexachlorobenzene Wastes: Controlling Vapor Movement in Soil, EPA-
600/2-80-119, Office of Research and Development, U.S. Environmental
Protection Agency, Cincinnati, Ohio.
Fiksel, J.; M. Bonazountas; H. Ojha; K. Scow (1981). An Integrated
Geographic Approach to Developing Toxic Substance Control Strategies.
Arthur D. Little Report to U.S. EPA, Office of Policy and Resource
Management, Washington, DC. EPA Contract No. 68-01-6160.
Freeze, F.A.; J.A. Cherry (1979). Groundwater. Englewood Cliffs, NJ:
Prentice-Hall, Inc.
Hamaker, J.W. (1972. Diffusion and Volatilization, Chapter 5 in Organic
Chemicals in the Soil Environment, Vol. 3, G.A.I. Goring and J.W. Hamaker
(eds.), Marcel Dekker, NY.
PT-60
Arthur D Little. Inc
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ID • input data
-------
TABLE OF CONTENTS
LIST OF TABLES
LIST OF FIGURES
1.0 INTRODUCTION
2.0 CLIMATOLOGICAL INPUT DATA
I
2.1 General
2.2 Manual Estimations of Climatologic Data
2.2.1 Monthly Time-Specific Simulations
2.2.2 Monthly Long-Term Simulations
2.2.3 Annual Time-Specific Simulations
2.2.4 Annual Long-Term Simulations
2.3 Automated Estimation of Input Parameters
2.3.1 Monthly Time-Specific Simulations
2.3.2 Monthly Long-Term Simulations
2.3.3 Annual Time-Specific Simulations
2.3.4 Annual Long-Term Simulations
2.3.5 Program Motes
3.0 SOIL INPUT DATA
Summary of Default Values
Soil Intrinsic Permeability — k(l)
Definitions
Hydrologic Characteristics of Soil Types
Soil Hydraulic Conductivity — X(l)
Factors Affecting K(l)
Guides to Estimating K(l)
Mean Soil Particle Size Estimation
K(l) vs Particle Size
Section of Working Values/Curves
K(l) "vs k(l)
3.2.10 k(l) SESOIL Default Values
Soil Effective Porosity — n
3.3.1 Definitions
3.3.2 Soil Hydraulic Properties
3.3.3 n SESOIL Default Values
Soil Disconnectedness Index — c
3.4.1 Definition
3.4.2 The c Index Sensitivity
Soil Parameter Calibration
3.5.1 General
3 5.2 Calibration of k(l), c via SQ
Calibration of s via k(l), ng, c
Automated Calibration
3.1
3.2
Summa:
Soil :
3.2.1
3.2.2
3.2.3
3.2.4
3.2.5
3.2.6
3.2.7
3.2.8
3.2.9
3.3
3.4
3.5
ID-4
ID-6
ID-6
ID-6
ID-7
ID-12
ID-16
ID-16
ID-19
ID-19
ID-19
ID-23
ID-23
ID-23
ID-23
ID-27
ID-27
ID-29
ID-29
ID-31
ID-33
ID-35
ID-37
ID-37
ID-37
ID-4 2
ID-44
ID-44
ID-46
ID-46
ID-49
ID-51
ID-51
ID-51
ID-54
ID-59
ID-59
ID-59
ID-6 2
ID-6 2
ID-1
Arthur D Little
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TABLE OF CONTENTS (continued)
Page
4.0 CHEMISTRY INPUT DATA ID~63
5.0 CANONICAL CLIMATIC-SOIL COMPARTMENTS ID-63
6.0 REFERENCES ID~64
ID-2
Arthur D Little
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LIST OF TABLES
Table
No.
Page
ID-1 SESOIL Default Soil Input Parameters
ID-2 Range of Values of Intrinsic Permeability
and Hydraulic Conductivity; Unit Conversion Factors
ID-3 Hydraulic Conductivity Classes According to the
* USDA-SCS
ID-4 General Relationship Between Soil Texture and
Saturated Hydraulic Conductivicv
ID-5 Soil Texture, Representative Particle Size
Contents, and Mean Diameters
ID-6 Soil Texture,us Particle Diameter , Soil
Conductivity and Intrinsic Permeability
ID-7 '<(!) Default Values for SESOIL
ID-8 Range of Values of Porosity
ID-9 Representative and SESOIL nfi-Default Values
ID-10 Default c Values for SESOIL
ID-30
ID-32
ID-34
ID-40
10-41
ID-45
ID-4 7
ID-48
ID-52
ID-58
ID-3
Arthur D Little
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LIST OF FIGURES
Figure
No. ZiSi
ID-1 Survey of TD-1440 For: Montana ID-8
ID-2 Sample NOAA Monthly Data Sheet ID-9
ID-3 Sample NOAA Annual Summary Data Sheet ID-10
ID-4 Sample Data Matrix of Input Parameters for a
Two-Year Monthly Simulation ID-13
ID-5 First Sample Data Block from Monthly NOAA
Data Sheets ID-'1"
ID-0 Middle Sample Data Slock from Monthly NOAA
Data Sheets ID~L5
ID-7 Sample Hourly Precipitation Data Block from
Monthly NOAA Data Sheets ID-L7
ID-o1 iacipie of Annual NOAA DaCa ID-Id
ID-9 User Incut Data File t'l? DATA) ojr.plii Values
r r\ "»n
and Formats LJ-^J
ID-LO Sample Program Output
Monthly Parameter Values for the Water Years
1945-1950 ID-21
ID-U Sample Program Output
Monthly Parameter Averages from 1945-1950 ID-24
ID-12 Sample Program Output
Annual Parameter Averages by Year from 1945-1950 ID-25
ID-13 Sample Program Output
Parameter Average for All Observations., from
1945-1950 ID~26
ID-14 Generalized Correlation of Independent Soil
Parameters; k(l), ng, c ID-28
ID-15 Guide for USDA-SCS Soil Textural Classification
Showing Points for Which Mean Particle Diameters
Have Been Calculated ID-38
ID-16 Comparison of Various Soil Particle Si= ;Ranges
Used by Various Agencies iD-39
ID-4
Arthur D Little
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LIST OF FIGURES (continued)
Figure
No.
ID-17 Soil Texture Permeability Curves ID-43
ID-18 Relationships Between Porosities and Soil Grain Size ID-50
ID-19 Hydraulic Conductivity vs Soil Moisture ID-53
ID-20 ' Functional Relationship, c-f(S ); Saturated Intrinsic
Permeability ID~56
ID-21 Saturated Permeability vs Pore Size Distribution
Index (from Eagleson, Personal Communication) ID-47
ID-22 Water Balance Solutions Using Soil Properties from
Equation ID-21 ID~61
ID-5
Arthur D Little'
-------
1.0 INTRODUCTION
Four major input data categories are required by SESOIL
(1) Climatological Data
(2) Soil/Vegetational Data
(3) Chemical Data
(4) Application Specific Data
Data for these categories are handled and input to the model in differ-
ent ways, depending upon the simulation level. Currently four levels
of operation are available, varying from general "Exposure Assessment"
simulations (annual, monthly) to "site-specific" simulations. The four
levels of operation are
(1) LEVELO Annual General Exposure Assessment Simulations
(2 soil layers)
(2) LEVEL1 Annual Site-Specific Exposure Assessment
Simulations (2 soil layers)
(3) LEVEL2 Monthly Site-Specific and Exposure Assessment
Simulations (2 soil layers)
(4) LEVEL3 Monthly Site-Specific and Exposure Assessment
Simulations (3 soil layers)
This appendix will provide in the future a thorough background to
effectively compile all input data for all above categories, in order
to prove to potential users how easy it is to run SESOIL contrasted to
other sophisticated models of the literature. The following sections,
however, give detailed description only for the climatologic data com-
pilation, since time and budget constraints prevented the developers
(Bonazountas, Wagner 1981) to invest more time in this aspect of the
model use.
Data for all data categories are stored in permanent SESOIL data files
for easy retrieval at any time.
2.0 CLIMATOLOGICAL INPUT DATA
2.1 General
Site-specific simulations require monthly or annual and time and site-
specific climatological input data. Non-site-specific (hypothetical)
simulations require long averaged (monthly or annual) climatological
input data. Data compilation for these for types of simulations can
be performed
ID-3
Arthur D Little, Inc
-------
(1) Manually from the National Oceanographic and Atmospheric
Administration (NOAA) climatological data records (sheets);
and
(2) Computerized via a subroutine that compiles on-line data
from NOAA climatological data tapes.
The LEVELO simulation does not require climatologic input data because
the hydrologic cycle components are input to the model by the user (see
Section 3.0, User's Manual). However, this level of operation requires
soil/vegetational, chemical and application specific data, which can be
compiled and stored permanently in the SESOIL data files as described in
Section 3.0 through 5.0 of this appendix.
The climatological input data for levels 1, 2 and 3 can be obtained from
NOAA records in the form of data sheets or data tapes. Information can
be requested — by indicating the weather station number and location
(Figure ID-1) — from the
U.S. Department of Commerce, NOAA
National Climatic Center, Federal Building
Asheville, North Carolina 28801
704/258-2850 (ext. 208, Digitized Data Dept.)
The following paragraphs describe the two methods of analyzing NOAA
climatological data for input to SESOIL: (1) hand calculation based on
the NOAA Monthly Data Sheets, and (2) a computer subroutine (IPDATA)
which uses NOAA data tapes. The hand calculation method will be des-
cribed first to provide some background on the ten parameters and how
they are delivered.
2.2 Manual Estimations of Climatologic Data
NOAA reports provide daily, monthly (Figure ID-2) and annual (Figure
ID-3) summaries of climatologic data for designated sites throughout
the United States.
The ten SESOIL climatologic input parameters are
L latitude; (N°)
TA temperature; (°C)
NN fractional cloud cover -- 24 hrs average; (-)
S humidity (fractional)
A albedo; (-)
REP rate of evapotranspiration; (cm/day)
MPA mean (annual or monthly) precipitation; (cm/yr or
cm/month)
ID-4
Arthur D Little. Inc
-------
FIGURE ID-1
SURVEY OF TD-1440
FOR: MONTANA
STATION
NO.
24033
24132
24135
24040
24137
24138
24139
24034
94008
94010
24143
24112
24035
94012
24144
24146
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24150
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24153
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24161
SERVICE
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Druranond
Glasgow/ WBO
Glasgow/Int.
Glasgow
Great Falls/Int.
Great Falls /Mai Strom
Havre /WBO
Havre/City-Cnty.
Helena
Kalispell/Glacier Prk.
Lewistown/Mun .
Livingston/Mission
Miles City/Mun.
Missoula/ Johnson-Bell Fid.
Superior
Whitehall
PERIOD
01/48-
01/48-12/54
01/48-12/60
01/48-05/50
01/48-
01/48-06/73
01/48-12/54
* 01/48-10/55
* 10/55-
10/58-06/68
01/48-
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* 01/48-12/48;
* 05/50-05/61
* 02/61-
01/48-
* * 01/48-
01/48-
01/48-12/54
01/48-
01/48-
01/48-11/53
01/48-12/54
ID-5
Arthur D Little Inc
-------
FIGURE ID-2
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ID-6
Arthur D Little. Inc
-------
FIGURE ID-3
SAMPLE NOAA ANNUAL SUMMARY DATA SHEET
Local Climatologies! Data
Annujl Sjninury With Comparaiuc D3tj
O 1979
TOPEKA, KANSAS
Narrative C!n»atolocical Summary
Page 1
of form
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Page 2
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ID-7
Arthur D Little. Inc
-------
FIGURE ID-3 (Continued)
HMIhi| Dtcrcl Dan
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ID-8
Page
Arthur D Little Inc
-------
MTR mean (annual or monthly) storm duration; (days)
MN mean number of storm events during (annual or
monthly) simulation period; (-)
MT mean length of rain period (in a year or in a month);
(days)
Aside from L all other data for the above parameters are handled in four
different ways when compiling SESOIL input, depending upon the simulation
level; namely depending upon the time interval (months or years) and the
time period (specific or general/long-term) analyzed.
2.2.1 Monthly Time-Specific Simulations
Values for all ten parameters must be provided for each month of year(s)
under study in a 10 x 12 matrix, as shown in Figure ID-4. Matrix ele-
ments for each month are obtained or calculated from the NOAA climato-
logical forms/sheets as follows
• L - The latitude is given as two digits, minutes only,
and is found in the top left corner of the NOAA
forms (Figure ID-5). Latitude can be also expressed
(input) in decimal degrees; eg. 39° 04' = 39+(4/60) =
39.067°.
• TA - The average temperature for the month is given in °F
at the bottom of Column 4 (Figure ID-5) and must be
converted to °C via C° = 5(F°-32)/9.
• NN - Cloud cover is taken as the average monthly sky cover
(in tenths) from column 22 (Figure ID-5) and is divided
by 10 to convert to fractional cloud cover.
• S - The average monthly humidity is estimated by averaging
the relative humidity given for the 8 observations during
the day in the data block shown in Figure ID-6, and is
divided by 100 to convert to fractional humidity.
• A - Albedo is taken from the corresponding table of Appendix HY
(Table HY-1).
• REP - Because evapotranspiration is estimated by SESOIL from
the five climatic parameters previously described, this
data entry can be input as 0.0. In case site-specific
values are available (e.g. Table HY-1), users may input
REP and disregard compilation of the previous five
parameters.
• MPM - The mean monthly precipitation is given at the bottom
of column 10 (Figure ID-5), in inches and must be con-
verted to centimeters (1 inch = 2.54 cm).
ID-9
Arthur D Little, Inc
-------
FIGURE ID-4
SAMPLE DATA MATRIX OF INPUT PARAMETERS FOR A TWO-YEAR MONTHLY SIMULATION
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FIGURE ID-5
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28 SO
28 31
38 31
38 36
38 33
28 28
28 36
28 40
28 50
28 40
38 40
28 33
28 31
38 OS
30.81
38 17
38 46
28 SS
38 41
28 48
28 32
>• nOul
NINO
•
0
I
s
11
33
25
18
38
IS
3S
33
33
01
ID
32
33
09
02
36
35
34
34
IS
18
34
33
33
31
35
OS
OS
ir
21
5 0
*
I-'
_* a
Ii
14
II 8
. 1
. 1
4
.6
.*
2 3
1 3
8
3
B
.8
1 4
. 4
0
1 0
8
.7
4
3
I .7
1 3
.8
4
1 3
lift
3 B
0 0011
o
r
|
a
IS
13.
B
S
e
4
4.
IO
3O
10
6
8
6
B.
IB
4
4
II
e
3.
7.
7.
14
IS.
8.
8
7
H0«t
I • »
s
•icl'imno" I Mn in mint
111 1S-16 I 2.3
[LOITOi 2 ClOVD' 2O
IS-IO ..
• •VIV
• III
s*
5-
16
33
17
IO
13
1 1
1 1
27
31
IS
10
8
IS
II
24
12
30
1 1
a
17
14
33
27
14
IS
8
18
33l
S
S
O
17
riu
w
su
sw
NM
su
N
N
ft
N
e
N
c
HC
HC
N
N
SU
N
nu
MM
NU
N
NU
N
OlOIIST
ICI 'III
su«v>m
5
c
ia
S68
S68
S'O
137
IDS
345
0
575
227
262
0
288
387
38
384
586
0
3OS
SO 7
0
sa
448
»73
545
603
165
17
•O'«l
8408
10 ins
H'lii 0<
IS 811
«
IM O
S*
r %
19
100
100
100
34
18
60
O
100
38
45
0
SO
66
7
88
100
0
S3
85
0
10
75
85
80
88
37
3
<
rol
4'
OOU
cc m
so- coin
ri«i»i
5 S
32
70
0
0
0
10
10
10
10
0
10
10
10
10
10
e
10
8
0
10
7
1
10
10
7
0
1
1
10
10
SUB
314
flvC
ft B
NO 0*
o nail
o
A A
i i
c •
71
0
O
7
8
7
10
1
8
a
10
a
B
s
10
a
i
a
7
10
4
10
ID
6
O
3
1
a
a
Sun
1U3
a«i.
JU
l-IOii
2 1 21.
5
a
It
10
II
12
13
14
15
IA
1 7
19
7O
21
22
23
24
25
26
27
38
28
30
= NN
= MPM
-~t
a
-------
FIGURE ID-6
MIDDLE SAMPLE DATA BLOCK FROM MONTHLY NOAA DATA SHEETS
SimnRRT BY HOURS
*«
00
03
06
09
19
IB
5
S|
6
6
6
7
7
7
6
e
•
If.
20.33
99.32
29.32
M.3S
99 35
99!3D
29 32
« f • • 5 I 1
ICK'EMI
a
1ft
13
13
IS
2!
2*
22
10
il
13
12
13
19
22
19
17
ugr
8
i
i
i
1C
li
i:
» j
it
™
79
78
74
61
et
«
a
\i
10
7 B
^_fl
KUIIMI
i
w
5
34
34
33
34
33
33
36
•2ft.
o
•i
3
3.
4
4.
3.
4.
3.
_»!»
(humidity.)
1.
/100.
ID-12
Arthur D Little, Inc
-------
• MTR - Mean storm duration is obtained from the Hourly Precipi-
tation chart shown in Figure ID-7. Three conventions
are followed in demarcating storm events
(1) Hours showing the symbol "T" for "trace" precipitation
are not included in storm duration if they appear at
the beginning or the end of an event, or if they occur
alone.
(2) "Trace" hours are counted in the middle of a rain
event.
(3) Rain events that continue into the next month are included
in the month which had the most hours of that event.
The mean storm duration (MTR) is obtained by: counting
the number of distinct storm eve ts (MN); counting the total
number of hours with quantifiable amounts of precipitation
and those hours with trace amounts according to convention
(2) above; and dividing the total hours by the number of
events. This result must be divided by 24 (hours) to
convert the units into days.
• MN - The mean number of storms is reported as counted above
for determing the MTR.
• MT - Presently the model does not distinguish between months
with 30 or 31 days, therefore, for a month full of rain
the length of the monthly time interval MT is input as
30.5 (365-i-12). In the near future, the simulation will
handle the exact number of rainy days during a month
(as if they were the rainy season of a year). MT in
this case will be obtained by bracketing the rainy days
as shown in Figure ID-7.
2.2.2 Monthly Long-Term Simulations
If the simulation is to provide a monthly analysis of an unspecified
time period, data for at least 5 specific years can be averaged to
"damp out" annual variations. The parameters which do not require
averaging are: L, A, REP and MT. The remaining parameters are first
handled as described above for each month of the 5 years, (with the
exceptions of TA and MPM because the mean temperature (TA) and the mean
rainfall (MPM) for the period of record are provided by NOAA with the
annual summary, as shown in Figure ID-8) and then averaged.
2.2.3 Annual Time-Specific Simulations
To perform an analysis which covers a user specified period of time in
annual time-steps (LEVEL 1), data analysis is carried out by averaging
ID-13
Arthur DLittklnc
-------
FIGURE ID-7
SAMPLE HOURLY PRECIPITATION DATA BLOCK FROM MONTHLY NOAA DATA SHEETS
HOURLY PRtCI"irariUN IMHIEK tUUlVflLENT IN INCHES)
10
II
12
14
18
18
30
31
23
24
at
31
at
M
30
1
T
T
T
3)
.01
T
T
-*-
.01
T
.01
. rot"
.01
Wine
l_k_
T
T
L-L-
T
T
-LL
T
ty
©
T
-"-
T
T
T
MBIM
Lu
r"~
T
T
T
_i_
T
T
T
T
T
T
3
T
^
=L
m£L
T
T
T
-1—
T
-s-~
T
1
r-S—
T
ia_
T
T
-u-
9
T
T
(
T
Ji_
T
a
T
T
6)
t
EH
LS.
i
2
4
»
6
T
8
9
10
12
13
t
TF
IT
in
ig
20
22
24
2*
?h
»
•J—
MT
Notes: 1. This figure shows 6 rain events according to SESOIL conventions. The
sixth may carry over into the next month and requires verification
prior to assigning it to either. For demonstration purposes, however,
it is assumed to be one complete event. Thus MN=6.
2. There are 14 hours of rainfall contained within the events bracketed
above. Thus MTR=0.43.
3. The value of MT is given as 30.5 even though the rainy period covers
25 days of the month.
ID-14
Arthur D Little Inc
-------
FIGURE ID-8
SAMPLE OF ANNUAL NOAA DATA
Average Temperature
Precipitation
o
-i
o
ET
Year | Jan | Feb
I'ji-
1191
II.O
1*4 1
11. |l 17.1
11.9 II.I
II.I II.I
ll.l' II.I
II.O 11.4
Mar
• M.i
i.i
r i K.I ii.i' i.i
11. II.I' 11.4 l.t
lit
• it.
ii.
114
1110
1191
1191
mi
in.
|19t
1197
1191
119*
1160
1161
1161
H6I
4|I64
|1*9
11.. I'.l
1
11.4 .1.7
II..! 17.4
11. • II.I
ll.l
ll..
It.i
17.1
Apr
[ May | June
ll.l! 11.6 74.1
14. 1 70.6 Tl.l
91. H tl.tj 79.1
91.4, 70. J 14.1
10. 1 6I.X 7».»
ll.l' tl.l! 7».T
90.1! tl.l1 77.0)
91.4
91.1
91.0
10.!
.... ,..!,
6l.o! 76.*
60.4 11. 6-
61.61 11.9
II..' I0.fr 41. 1! 91.1, 67.41 Tl.l.
It.» !..*> 11.1 10. 1 69.6. Tl.l
I*. el 1..1 ll.l' 10. ll |..7| 67.1
M.» II. • !«.«; 91. 0< t..6< ll.l
ll.l' ll.l .9.0 .1.7 61. l| |l.7
17.6 ....
.I.C
ii.i: ii. ij .i.e
11. 7J II. l] 41.1
II.I 16. l! 41.0
10. 1. 16. 1
It.i
I..O, 11.7' ...7
II. ll !..«, 17. 1
II. • 11.6, .1.1
II.I II. 1, 10.1
11.0 11.9' .7.1
I..I 14.1 10.0
• 1.0, in.,
it. o! 11.1
1161 11.1 19..
lltl Ift.t II. t
lit*
1170
1171
1111
1171
19.1 11.*
"''I "•'
II.O
.7.0
4t.4
41.1
tut
!!:!
ll.l
91.0
94.1
I',:',
li.:
60.0 77. L
...r ,..^
64.1 76. •
II. ll Tl.l,
tl.l! 71.
41 1 74.
tl.l, 11.1
3«.l ll.l
71.7 II.
tl.l1 77.
61.*, 11.
97. l' 11.4' 11.11
1 1 1
90.11 61. ll ll.l!
91..
99.9
11. ll ll.l
•1.1 91.1
29. 6J, ll.l 4t.l
17.3 U.ll 47.1
1176 I7.ll .1.1
11.4
1*71 11.1 17... 41.4
to.i, 11.1;
9*. II 74.11
49.11 44. J
tl.t 71.9
14. 7| tl.t, 74.11
91.1 61.11 14. »
11. Ol 60. •' 71.71
tO. II 70.11 71. l|
H-l
July
Ang
jS.pl
Oct | Nov | Doc jAnnual Year | Jan | Feb | Mar
II. fl II.*1 71. « 61.1 44. d It.
• I.I, 11. d 71.0) tl.l 44. » 11.
11. ij 74. «] 10. ll tl.I| 40. 11 II.
ll.l1 71.6' 71. J 11, l! 41.7 11.
11.1 ii.i' 17.9" 91. i; tt.i io.
11.41 II.I
71. ol 11. e
ii. e
ii.i
ii.i
71.1
10.!
!lt.4> 41.1 10.
10.1 41.4 II.
i7*.6j tl.* 37. w 46.1 13.
77. lj 61.1' 17. t! 44.4 17,
14.1
77.'
71. 1
70.1
61.4, |l, 6 |4,
14.1 49.4' II.
71. II 71. « 01. 4j II. 6j 41.6 13.
11.9 71.11 66. lj tl.tj |9.4. ]4.
11.1 17.1 04. j 96. l! ll.ti 11.
10. ll 71. Ol 70.6. 11,01 41. 6! 11.
ll.l1 11.9; 71.1 4|, l| 41.3 |4.
• *• 3
10.'
14.11 ll.l
10. ol 11.1
10.91 ll.l
ll.l
74.1
71.1
1 ""
70.1
61.0
61.!
31.1, 47. 1' 14.
91. ll !«.» 10.
tl.l 41.1 14.
31.4 41.4 |7.
31.41 46.9 II.
74.41 10.1 67. l' II. 6 |6.1 17.
71.0 11.11 70. Ij 11.41 44,| ||.
76.7) 74. «| 69.0! 37.o' 41. 0 19.
71.1 74.1) 61.il 60.0' 44.0 II.
10. 1! 71.1 71. It 47.6 41.41 11.
• I.II 74.9' tl.l! 14, t 46,2 II.
17.0
ll.l
79. C
71.4
71.4
77. •
1...
11..
71. OJ
7*. 4
,..» ...*
74. 11 61.1
71.1
71.!
69.1
06.6
7I.9> 61.0
10.61 69.1
79. » 7|. <
14.7! tl.l
71. l| tl.t
It.i
16.4
•'
61.0
71.6
'•
17.1. ll.l 11.
11. J 44.| 10.
14,71 41.7 11.
97,11 10. 0 II.
ll.l1 41.3 11.
91. ll 41.1 II.
01. tl ll.J |l.
94.61 11.4. 11.
40.41 44.1 II.
' ii.i mi
' ii.. mi
1 94.4 11,0
11.0 ll.l
11.1 1*41
11.
91.
14.
11.
It.
II.
ll!
91.
11.
31.
91.
91.
91.
91.
91.
11.
II.
II.
11.
II.
14.
91.
11,
II.
91.
34.
91.
14,
30. ll II.41 II.I JI.7
16.7 4l<7| |0. 1 II. 4
= TA monthly averages; for no =
specific time.
= TA monthly. for a specific
/
year.
= TA
annua.
general
1141
1144
• 11.6
1147
1141
1190
1191
1192
1191
119*
1139
1196
1191
1191
119*
1160
lltl
1161
1161
1164
mi
int
nti
1141
lit*
1110
mi
mi
mi
1 Apr | May
June| July
Aug | Sept
1.14 6.13 7.10 I.OL1 11.16 1. 91 1.1* I.ll
0.10 1.92 1.2', 1.73 1.11 9.61 l.lq 1.94
i.ia i.oa i.ii. 1.30; 4.011 1.7* o.oe, 6..q
1 1 1 1 1 1 • 1
.7* O.lj 1.41 1.19 71 I.ll .ft 1.7*1
.1L1 1.19. 1.0l| 4.IH .!• ..11 .92 7.72
.19 0.6* 0.6* 1..0, .11 11.46 .19 I. in
.14. 0.9V ..in 1.61 .II1 1.41 .41 6.*1
... i.K. 4.iij o.ioj .6> l.jlj .1, O.M!
.11 0.11 I.I* J.H l.jJ 6.1. .61 6. Id
.1
1 0.4*, 1.7<
» I.ia «.z
•• ft. Oil 2.6B
.III 1.70 1.11 9.41 9.16
.I*. 0.6^ 0.61 t.o] 6.11
.oq i.ii i.iij 1.31 ..ii
.li 0.40J 1.76 1.14 1.70
.10 1.17 1.10 1.11 4.31
.0
.1
.7
.1
.1
1 I.OA 0.6
1 • ( is • IB
i '-'i •••] '•'} -i
1 o.id o.ta I.M i.ii
1 O.It 1.14J 9.011 ..II
! I.ll I.I'
1.71 1.21
0.71; o.»j i.ia i.7t 4.7d
,.,, ,.,,, ...a .... ,.„
0.01 1.91 4. Ill l.tl 1.1*
1.** I.I* 1.41 1.21 4.11
O.ll, O.Ik I. Ill 0.611 4.11
o.i.) o.i« i.iij t.ia i.o*
1.60 l.llj I.J6 l.llj 1.41
O.ltj O.K. 0.10 I.**! O.»l
I.Ol
0 11
O.K
O.ll
I.Ifl
0.41
I.tl
lilt 0.4V
1117 O.ll
0.21 1.11
0.1
0.3,! I.ll
O.ltj I.Ol
J
1*111 2.0*
Tira
1.4* 7.1.
1 J
•.o,! ..,*!
1
*= MPM, monthly-
= MPM, monthly
TA
annual specific
1.3* .91
!3.11
J.7L
t.l* i.in 7. oil
l.llj II. oi 9.11
10. 3*1 11.11 9.01
0.1* 0.1^ 4. 21
I.Ol 4.11 I.ll
1.1* 9.21
9.04 I.ll
9.11 4.4<
i.ia s.ii
7.11 1.91
• .3a
;;
l.TI
i.ii i.ia i.t:
1.41 |.ld 1.7(
1.4| 1.21 1.11
lllll lill l!lC
1.10 I.ll 1.24
13.19 1.0'
>.!< 10. HI
1.91
l.tJ
1.14
7. in
1.4. |.i^ 0.17
l.llj |.1« 0.1^
l.io i.ol o.d
•'1
.01
• IV
711
.61
!io
'"
. AV
• »n
.01
•'1
1.19
Ocl | Nov
0.11 |.1
O.ll |.4
i.oij i.i
10. ej 0.
2.7* l.
I.I* 4.11! 1.211 4 11
!.» 10. Ill I.ll ll.'lf
l.t*; I.Ol
10. *U 1.11
]
for no
oJ
11.10}
1
4.oJ
I.IS
l.lJ
1 Dee
O.I
0.7
1.1
2.0
.11 0- * 1.7
..a o. tj 1.1
..J 1.0]' t.l
.0% 1.11
Annual
1 1*.OI
I 11. ll
11.47
44.41
14.10
10.11
ll.fll
.27. o.tll l.t
.1* o.l«| o.o
.0* 1 ij O.t
• o«j i.i* i.i
.1* i.n 1.1
.10 T
.71 0.11
.>a i!*i
.111 1-2
.0*' O.ll
.01 0-1!
.«• 2.3(
!lll o'l<
.III 6.11
.ia o.ii
.•li O.K
.on o.'i
.1* i.ia
.11 O.ld
..*; i.i
.111 1.0
.1.71
II. *1
41.40
111.11
X4.ll
O.ll II. .1
1
0.101 11.19
i.ie ii.i4
I.ii
I..I
1.0
o..
0.1
o.it;
11.10
11.44
.1.11
II. It
11.07
11.91
I.**) 17.91
0.71 11.10
.III 10.64
.11 40.11
.1
.t
.11
II.. I
II. tl
11.11
.iv i.i* .14 11.11
.9' I. Ill ..10 60. 11
l.Oll 0.0.
..II I.I
J
Mf itill. -
O.lf 10.19
0.11 41.11
1.'
specific time.
; for a specific
year.
II. jj
— MPM
annual
general
MPM annual
specific
-------
the twelve monthly averages for the year for the following five parameters:
TA, NN, S, MTR and MN.
Parameters L, A, and MT do not change with time. The value for total
annual mean precipitation (MPA) is found either by adding the average
monthly precipitation (MPM) for all twelve months or from the totals
provided in an annual summary table (Figure ID-8) and converting from
centimeters to inches (if not previously converted). While MT varies
seasonally, the variation is considered only for annual simulations.
2.2.4 Annual Long-Term Simulations
The data for a general annual simulation (i.e., an unspecified time
period) are averaged over annual data for five or more specific consecu-
tive years. The specific years' data are determined as described above,
excepting the values for MPM and TA, which may be taken directly from
NOAA data, by referring to the 40 year mean for the period of record.
2.3 Automated Estimation of Input Parameters
The ten parameters described in Section 2.2 above are determined auto-
matically by the IPDATA subprogram, using tapes for data input. Two
of the parameters (latitude and albedo) require user input to the sub-
program.
The subprogram reads the data taken at a weather station from two NOAA
tapes (TD-1440 and TD-9924), obtainable from the National Climatic
Center by calling their Asheville offices. This Office also supplies
an index of station numbers for the U.S. and the world where observations
have been made called "SURVEY of TD-1440, DATA FORMAT," and user manuals
for the tapes.
The data stored on TD-1440 tapes are used to calculate the monthly values
for the following six parameters: TA, NN, S, MPM, MTR and MN. In
addition, the IPDATA subprogram stores the total number of hours pre-
cipitation (TPPT) counted in each month. The value for REP is supplied
as 0.0 by the subprogram, while MT is supplied as the number of days
in the current month. The user may override the value for REP if
desired by editing the input parameters (see Section 3.0, User's Manual).
This would occur only in the case where certain of the input parameters
were lacking or poorly supplied with data. The user might determine
this either before or after scanning the data on the tapes. The second
tape, TD-9924 is required to obtain values for mean monthly precipitation.
2.3.1 Monthly Time-Specific Simulations
To run the IPDATA subprograms for a simulation which will produce 10x12
matrices (10 parameters, 12 months) for all the years within a specific
time period, the user first edits the FILE IP DATA. This file, along
with the appropriate formats are shown in Figure ID-9. All entries
but the value for REP must be changed for each site. Typical Annual
Output is shown in Figure ID-10.
ID-16
Arthur DLittleJnc
-------
FIGURE ID-9
USER INPUT DATA FILE (IP DATA) SAMPLE VALUES AND FORMATS
STATlJ-j •>.*.'= (STAf^A,1') GUANTANA'lCt cAY
•* rr-Y-ra p — c i Y =rr i rs z C-CT; r-n-7r^—(-TTTZT 5-5 5-3
OUTPUT FlL=. * ( NFILE) .CIVI SIUM.NDIV) 9Q 59
-L3rDjii_-,TITjJZ(_iT)t-i:.P i . ^ 3J.O C.O
Line
Number Format
1 40X-, 10A4
2 40X, 12, 5X, 12
3 40X, 12, 5X, 12
4 38X, 3(F7.2)
ID-17
Arthu rD Little. I nc
-------
**i A* *************
• 0 *
•* C
*******<*< t*-?*S*5*,*MPC *Pn«**T ***** *r.*.
H A,« •) f,._ I t H VALUES rG>< T HL "lATc
L
TA
NN
S
A
5EP
MPM
MTfx
VN
y T
TPPT
TO 194O
*V*«
7
oo
I A
HtP
NTH
TPPT
ucr
>c.o
2o . o
J. T
1.0
0.0
0. 0
0.2
1 d . 0
» 1 . 0
. 2 to * °
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17.0
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43.0
«$4«c«££
H VALUE
NOV
30. 0
25.2
<3 9 '? ^ . 0
0.8
1.0
0.0
2.5
0.1
11.0
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DEC
JO.J
2 J. J
9V99.0 9
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1 .0
0.0
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3 1 .0
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5 FUI5 The
DEC
30.0
S9V';Io J
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1.0
0.0
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Oil
6.0
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JAN
JO.O
;><•. 2
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7.5
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4.0
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23.4
9 J99.0
0.8
1 .0
0.0
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28.0
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MAR
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9999lo
0.7
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0.0
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0.0
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Jl .0
15.3
£$£&<::•:$$<:.•}
46 TO 1947
MA*
JO.O
999 i.O
J • t?
1 .0
0.0
12.7
0. I
4.0
31 .0
10.0
AP3
30.0
20.0
9V99.0
0.7
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0.0
15.2
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1 4.0
30.0
90.0
$$$<::}.•>
APR
JO.O
26.0
999V. 0
0.7
1.0
0.0
15.2
0.0
5.0
JO.O
6.0
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26.1
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17.8
0.1
15.0
31 .0
3^.0
$#£# 44$$ £
IL *AY
30.0
26.4
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0.8
1 .0
0.0
17. a
0. 1
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31 .0
16.0
JUNE.
3C. 0
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0.-3
1.0
0.0
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5 .0
30.0
5.0
££t&ft& £:£:&£
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30. 0
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30.0
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I
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a
sr
FIGURE ID-10
SAMPLE PROGRAM OUTPUT
MONTHLY PARAMETER VALUES FOR THE WATER YEARS 1945-1950
o
-------
A JleTLH VALUES F'J,< THE aAFEU YfcA« 1 9 4 7 TU
o
M
vO
L
TA
NN
S
A
KEP
VPM
M,N
TPP r
«$?•
L
TA
NN
A
SEP
MPM
MTR
MN
MI
TPPT
***•>>
L
TA
NN
S
A
KEP
NTH
MI
TPP r
jcr
.JO.O
L' 7.4
0.4
j • U
1 .0
J. 3
0.0
U. 1
I J.O
.11.0
12.0
J!!V*Ife
OCT
« « • * •-•*•-•
JO. 3
27.2
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J . 8
1.0
0.0
0.0
0. 1
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J 1 . 0
J 1.0
$« $.>$«**
P A '-i A Mtl T E
JCT
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'» •> .0
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30 0
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0 1
4 0
30 0
6 0
R VALUE
.MO V
a M*S~S «= *-a
JO.O
26 .5
0.3
0 . Q
1 .0
0.0
2.5
0. 1
1J.O
30. 0
17. 0
H VALUE
NOV
30. 0
2b . J
0.5
0.8
1 .0
0.0
2.G
0. 1
13.0
JO .0
1^.0
DEC
JO.O
2 5 . !J
0 .2
3 . (1
1 .0
0.0
-J.I
0. 1
b.'J
J 1 .0
y.o
S KJH THL
DEC
5 ~a — -= ~~~vs -as-g-j
30.0
I: 4 . •;
0.2
O.d
1 .0
0. J
5.1
0.0
2.0
3 1 .0
2.0
1>0$$ >C*'>0*>!
S FJU THE
DEC
30. U
c!4 .0
0.4
0.3
1 .0
C.O
5.1
0.1
1 2 .0
31 .0
1 5.0
JAN
JO.'J
..' 4 . 7
Jv9 J . 0
u. ^
l.O
0. J
7. (5
0. J
J. J
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J.o
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• S IE SS w~5-S
30.0
21. «
0.2
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7. S
J. J
4. 0
31.0
2 J. J
•< A r.: i
JAN
JO. J
23.3
0.2
0.8
1 . 3
0.0
7.6
0.0
J. J
Jl .0
J.O
Full
JO.O
2 rJ . 1
9? 99.0
0.7
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10.2
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i:3 .0
12.0
*«->$*«i>*4
Y E A K' 1 9 4 >i
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0. 1
0.7
1 .0
0.0
10.2
0.0
2.0
2J .0
2 .0
«««««$«««
YE Al< 1 V4 V
FLK
JO.O
il 3 . 0
0.3
0.8
1 .0
0.0
10.2
0.0
A .0
23.0
y.o
MAW
30.0
20.0
<* 9 y j . j
0.7
1 .0
0.0
12.7
9 •, 1 ') . 0
0.0
31 .0
0.0
«4K:«4:<:«
T (J 194
MA?
JO.O
24.2
0.2
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0.0
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0.0
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6 .0
«*«$«$«
TO 195
•4 AH
JO.O
24.1
3.2
0.8
1 .0
0.0
12.7
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31 .0
2.0
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30.0
26.3
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0.7
1 .0
0.0
lii.2
0. 1
1 1 .0
30.0
1 V.O
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9
APW
30.0
2o. 7
0.3
0.8
1.0
0.0
15.2
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30.0
7.0
««««««»
0
APi?
30.0
24.3
0.4
0.7
1.0
0.0
15.2
0.1
5.0
30.0
9.0
IL v-AY
30.0
27.5
^999.0
C.8
1 .0
0.0
17.8
0. 1
24.0
31.0
73.0
**,**«««**
IL VAY
30.0
25."*
0.6
c.e
1.0
0.0
1 7.8
C. 1
23.0
31 .0
55.0
<.•*$**,«*•*,
JULY
JO.O
27.5
0.5
0.7
1 .0
0.0
?t . 9
O.C
2.0
31 .U
2.0
********
JULY
JO.O
27.3
C.4
0.7
1 .0
C.O
22.7
0. 1
v.o
31.0
1 4.0
AUG
30.0
29. 1
9 J «, 9 . C
0.7
1 .0
0.0
25.4
0.0
7.0
31 .0
7.0
o«««c««
AUG
30.0
27.6
0.5
0.3
1 .0
0.0
25.4
0. 1
12. C
31.0
24 .0
«««««««
AUG
30.0
27.5
0.15
0.8
1 .0
0.0
20.4
0. 1
20. C
21 .0
35.0
SEPT
JC.O
2P.O
Q99S.O
0. 8
1 .0
C.O
27.9
C.2
14.0
3C.C
7ft. 0
••*..*•«
SEPT
30.0
27.3
0.5
0. 8
1.0
0. 0
27.9
0. 1
11.0
30.0
25.0
«**«•«•«
SEPT
3C.O
26.8
0.6
C. 8
1.0
C.C
27.9
C. 1
20.0
30.0
4«;.0
(L
R
FIGURE ID-10 (Continued)
-------
The necessary tapes for the station under study must be loaded and
labeled according to the protocols of the user's computation center.
Presently the subprogram requires labels for ITAPE1 and ITAPE2, defined
in the execution file for IPDATA. This latter file also determines
the location to which the output is sent, i.e., disc storage, line
printer, or terminal.
Output is printed as matrices (Figure ID-10), one matrix for each year
in the range between the input values for IYR1 and IYR2.
2.3.2 Monthly Long-Term Simulations
The subroutine will automatically derive average values for each para-
meter, by month, if more than five year's data are analyzed. The results
are presented as a table labeled "Average Monthly Parameter Values over
the Period 19— through 19—" where the last digits of the period are
IYR1 and IYR2. Typical output shown in Figure ID-11.
2.3.3 Annual Time-Specific Simulations
Average values for each parameter over the space of a year, for each
year within the specified period are also output by IPDATA. These
data are output in a table titled "Annual Parameter Averages for
All Months, By Year from 19— to 19—", where the last digits of
the period are IYR1 and IYR2. Typical output is displayed in Figure
ID-12. Note that MT=365 and >!PA is the sum of the monthly MPM values.
2.3.4 Annual Long-Term Simulations
The averages stored in the ANAV matrix described above, may again by
averaged to obtain an array consisting of one average value for each
parameter over, say, a 20-year period. IPDATA automatically calculates
these values for any period of record specified as greater than 1 year.
Typical output is shown in Figure ID-13.
2.3.5 Program Notes
The IPDATA subprogram was written to retrieve data stored by NOAA on
tape. Some of the quirks used in this form of data storage necessitated
the approaches used in the subprogram. This includes, checking each
entry for missing, invalid or mistyped (i.e., out of range) data entries.
When these circumstances are encountered, the data will be skipped. If
an entire month's data were missing or invalid, as might occur in the
case of monitoring equipment malfunction, the appropriate output value
will be 9999. This holds true for monthly, annual and period-of-
analysis averages as well. In such cases, the user will have to use
best judgment as to how to proceed.
It is foreseen that averages will eventually be taken for many stations
within a region and thus all IPDATA output are designed to be stored
for this purpose.
The formats for all IPDATA output correspond to SESOIL-81's read format.
The annual matrices must be transferred to the GE file for use as
SESOIL input.
ID-20
Arthur D Little Inc
-------
: v. 0 « « 4 $ £ $ 4
.i. MONTHLY PA^AVdTEM VALUiIS GVE* THfc
19«»S-1950
MN
G
A
HEP
NPM
MTM
MN
f'T
TPPT
Q^T
30.0
,!o. ,»
0.5
0. J
1 .0
J.O
0.0
0 . 1
1 7.4
J 0 . '3
J o .O
!JOV
30.0
2j .U
0 .4
o.n
I .0
0.0
2.5
0. 1
11 .6
JO. 5
21 . a
-»-J__l_-»_-4--»-j-_».
DLC
30.0
2'i.<*
0.2
D.d
1 .0
0. J
5.1
0.1
7.0
3 0 . fj
11.4
JAN
30.0
.. J
U.2
0.-3
1 .'J
0. J
7.6
J. 1
J.i
3J.5
7.3
Ftlb
30.0
cjj.e"
0.2
0. 7
1 .0
0.0
10.2
0. 1
7.2
JG.'j
13.2
4Att
30.0
J-* .7
0.2
0. 7
1 .0
y .G
12 . 7
0.0
4.4
10.5
0. 6
AP^IL
30.0
20.5
0.3
0.7
1.0
0.0
15.2
0. 1
8.0
30.5
26.2
MAY
30.0
20.3
0.5
O.U
1.0
0.0
17.3
0. 1
15.6
30.5
39.2
JUNF.
3C.O
27.2
0 .0
C.9
1 .0
C .0
20.3
(J. 1
10.6
30.5
25.6
JULY
30.0
27. J
0.4
C. 7
1 .0
0.0
22. v
0. 1
0.2
20.5
4.3
AUG
30.0
29. 1
0.5
0. 7
1 .0
0.0
25.4
0.1
10.6
JO. 5
18.2
StPT
30.0
27.4
C .6
0.8
1 • C
0.0
27.3
0. 1
15*0
JO. 5
41.6
0
NJ
>
FIGURE ID-11
SAMPLE PROGRAM OUTPUT
MONTHLY PARAMETER AVERAGES FROM 1945-1950
-------
M
7
M
L .
Y C A N
L •
YCA-.J
L t
MPA i
YtA'i
L t
Y£A-«
L t
MPA .
AN
1 t
TA
? t
T A
•"ITU
3.
TA
4 t
TA
M T,i
5 .
A
MT1-?
UUAL PAHAMETEfi AVLK4GEI* FiJ^Z ALL MOM
. NN
1 MN
1 940
: $N
1947
. NiJ
t MN
1 94*
• NiN
. MN
1 94?
. MN
• S
> MT
• S
t .VT
. 5
t MT
! MT
• S ~ '
. MT
t A . ,*F.P
t TPPT
. A . WLP
• TPPT
• A • PE.O
. T P P f
• A ( H C P
i TPPT
i A -;~?7EP •-
t T t- P T
Ju .
1C) 7.
JO.
107.
JO .
1 07.
3C .
157.
-30-.-
VSS- 7^C-?O«9999<:
THS. UY YCAHi
6
C
C
0
o
0
6
c-
o
oT i
20. 1
0. 1
ol i
25. •>
0. 1
25'. T
0. 1
0 .
V.
0.
10.
0.
V.
9'.
- - o;
10.
i««
FW
7
0
C>
3
3
3
3
3
OM 1
0
365
0
365
0
J6CJ
u
360
300
945
To
.8
.0
. 3
.0
. H
.0
. 5
.0
TO
1
1
20
1
1
16
1
19'JC
.0
.7
.0
.S
.0
.7
.0
.4
.0
.5
C.C
C .0
0.0
O.C
o.c
C
FIGURE ID-12
PROGRAM OUTPUT
ANNUAL PARAMETER AVERAGES BY YEAR FROM 1945-1950
o
-------
ArfE.JAi.Er. PUR ALL
IONS ovc* THC PL-MOO i
AVERAGE VALUL
- i
30. JO
0. 76
o . o e
9.75
N>
U)
T
T
****************
21.42
FIGURE ID-13
SAMPLE PROGRAM OUTPUT
PARAMETER AVERAGE FOR ALL OBSERVATIONS FROM 1945-1950
-------
3.0 SOIL INPUT DATA
3.1 General
3.2 Soil Intrinsic Permeability (k)
3.3 Soil Porosity (n)
3.4 Soil Pore Disconnectedness Index (c)
The soil pore disconnectedness index c in SESOIL, is the exponent
relating the "wetting" and "drying" intrinsic permeability k(s) of
the soil to its saturated intrinsic permeability k(l), and is given
by Eagleson (WRR p. 723 e.g. 7). This relation is given in the
literature by Brook and Corey (1966) and its validity for both a
cohesive and a cohesionless soil is graphically presented by Eagleson
(WRR p. 724 Figure 3).
To obtain the c parameter for various soils a user has to follow
the work of Talma (1974) and Moore (1939). Eagleson (1978) has
presented in this work typical c parameters (Table ID-1), however,
these values have to be employed with caution. The authors (Bona-
zountas and Wagner) of SESOIL intend to author a section for this
model providing: (a) c values for the various soils of the USDA -
soil classification triangle, and (b) a discussion for estimating
the effective "real (of the field)" hydrologic/soil properties of
soils from observations of vegetation density via the model itself.
This task has not been performed yet for budget reasons only.
However, it has to be emphasized that any unsaturated soil zone of
the literature (e.g. Bonazountas et al 1979) requires as a user
input instead of a curve relating "permeability~k vs. capillarity
head ijj." This curve is obtained from experimental data. It is
almost impossible to obtain this curve off-the-shelf for any type
of soil, but it also is extremely difficult to obtain this curve
in the laboratory. Therefore, the "one-variable" approach of
Eagleson (1978) employed in SESOIL greatly simplifies data gathering.
Authors of this report advise the user to employ values of Table
ID-1, and to interpolate for different types of soils using also
the work of Freese and Cheery (1979 p. 29).
4.0 CHEMISTRY INPUT DATA
Chemical parameters, coefficients, etc. might be compiled from the
handbook "Research and Development Methods for Estimating Physico-
chemical Properties of Organic Compoundsof Environmental Concern"
(Lyman £t al. 1981), or any other handbook.
ID-24
Arthur D Little Inc
-------
KJ
Ln
4)
Properties
(SESOIL Variable)
TABLE ID-1
INDEPENDENT SOIL PROPERTIES/PARAMETERS1^
SOIL TYPE
Clay
1 x ID"10
0.45
12
Clay-Loam
2.8 x 10~10
0.35
10
Silty-Loam
1.2 x 10~9
0.35
53)
Silty-Loam
2.5 x 10~9
0.25
A
Sand2)
1 x 10~7
0.25
3.5
1) See Table HY-3
2) Compiled from various sources
3) Personal conversation with Eagleson
4) A single relationship between k(l), n and c does not exist.
Main Source: Eagleson (1978)
-i
D
sr
-------
5.0 REFERENCES
Bonazountas, M., W. Hawes and W. Tucker (1979) "Heutistic Unsaturated
Flow/Quality Soil Zone Model," American Geophysical Union, Spring Meeting,
Washington, D.C.
Brooks, R.H., and A.T. Corey (1966) "Properties of Porous Media Affecting
Fluid Flow," J. Irrig. Drain. Div. Amer. Soc. Civil Eng., IR2, 61-88.
Eagelson, P.S. (1978) "Climate, Soil, and Vegetation," Water Resources
Res., 14.
Lyman, W. et_ al^ (1981) "Research and Development Methods for Estimating
Physicochemcial Properties of Organic Compounds of Environmental Con-
cern." Prepared by Arthur D. Little, Inc., Phase II Final Report for
U.S. Army Medical Bioengineering Research and Development Laboratory,
Fort Detrick, Maryland; McGraw-Hill Book Company, New York.
Moore, R.E. (1939) "Water Conduction from Sahllow Water Tables "
Hilgardia 12(6), 383-426.
Talsma, T. (1974) "The Effect of Initial Moisture Content and Infil-
tration Quantity on Redistribution of Soil Water," Aust. J. Soil Res.
12, 15-26. '
ID-26
Arthur D Little Inc
-------
n
e
c
3.0 SOIL INPUT DATA
3.1 Summary of Default Values
The hydrologic routine of SESOIL employs the one-dimensional water
balance model of Eagleson [1978a-g] which has been written in terms of
five surface vegetation and soil parameters: the vegetation canopy M,
the species-dependent plant water use coefficient kv> the soil effective
porosity n , the saturated intrinsic permeability k(l), and the soil
pore disconnectedness index c. A state variable of the problem has
been the average long-term soil moisture concentration SQ The analytic
structure of this model is summarized in appendix HY, however, tailored
to the needs of SESOIL, roughly for bare soils and monthly simulations.
The bare soil requirement reduces the five surface parameters to the
following three independent soil input parameters:
= saturated soil intrinsic permeability; (cm2)
= effective soil porosity; (fractional)
- A[ln(k)]/A[ln(s )]; soil pore disconnectedness index; (-)
There is no unique association of the particular c and n regional values
of a soil type with the value of a k(l). Therefore, model users should
be very careful when employing the default independent soil property
values presented at the end of this section. The soil properties are
critical to the moisture fluxes and vary tremendously spatially. Use of
point measured soil properties can yield results of only local (and
hence not areally averaged) character. It would be also appropriate to
use some observed water balance element such as average basin yield
(surface runoff and groundwater runoff) to evaluate the effective soil
properties, as discussed in section 3.5; soil parameter calibration.
A schematic variation of soil hydraulic properties with textural class
is presented in figure ID-14. Of course, soils evolve having a continu-
ous spectrum of textures from clay through silt to sand and gravel, and
the critical hydraulic properties of soils vary widely even within the
same textural class, but over the variety of classes their range is
enormous. Figure ID-14 is only a gross generalization of the overall
soil characteristics [Eagleson 1982, p.326]. More detailed information
is provided in the subsequent sections.
In a natural ecological system, Eagleson suggested [Eagleson & Tellers
1982, p.341] that there may be ecological pressures for change in
natural soil-vegetation systems, which drive a synergistic development
toward a water- or energy-limited equilibrium state in a given climate.
Identification of the conditions for this equilibrium should allow an a
priori specification of one or more of the physical parameters of the
soil and vegetation, a fact that may lead to elimination of k(l) from
the water balance equation in terms of the long-term average soil
moisture concentration in the root zone s , a state variable of the
ID-27
Arthur D Little In
-------
ce
0 I
log CMII1
(a)
OS
o
tt
o
a
TOTAL
'POROSITY, n
CLAY su.r SAND GRAVEL
PERMEABILITY
(b)
Variation of soil hydraulic properties with texlural class.
.(•i) After Chiliimiir 11'*-4|
-------
budget theory. In a bare-soil system, however, all three input vari-
ables — k(l), n , and c — have to be known and input to the model.
e
Ideally, one should test input values by having direct observations of
k(l), n and c — in addition to the various climate parameters — from
an array of spatially homogeneous natural systems covering a wide range
of the dimensionless climate-soil parameter E (see appendix HY, equation
HY-23). In practice, however, at least the soil parameters of natural
systems are highly variable spatially [Nielsen et al 1973; Libardi et al
1982], so even if dense observations of them were available (which is
rare), the problem of how to average them areally would arise [Eagleson
1982, p.342]. Because of the large spatial variability of the proper-
ties of natural soils, and because of the high degree of non linearity
of the fluxes, spatial averaging over the large area elements of either
climate or water resource models become a non-trivial problem [Eagleson
1982, p.325]. Therefore, given an initial set of input parameters k(l),
n , c, it is recommended to calibrate the input data set of the model by
vlrying the intrinsic permeability k, the pore disconnectedness index c,
and the effective porosity n of the soil, towards obtained field
records of soil moisture content or basic yield (see section 3.5; Soil
Parameter Calibration).
In case of total absence of site specific input data and when
non-site specific long term pollutant fate modeling efforts have to be
performed for canonical climatic environments, SESOIL users may employ
the information compiled in Table ID-1, namely the:
* USDA (U.S. Department of Agriculture) soil textural classifi-
cation system as a guide for soil type selection; and
* Default values of k(l), n , c compiled for the various USDA
soil-types of the soil triangle.
The figure and the table of table ID-1 are self-explanatory for easy use
and for canonical environments only. The rationale behind the default
values generated and the uncertainty when deriving them are outlined in
the following sections for each individual soil parameter. Only
fundamental concepts are discussed as they relate to the SESOIL use,
therefore, model users are advised to consult original publications of
this appendix.
3.2 Soil Intrinsic Permeability — k(l)
3.2.1 Definitions
When various fluids of density p and dynamic viscosity y are run through
a porous medium consisting of uniform glass beads of diameter d, and
under a constant hydraulic gradient dh/dl, the following proportionality
relationships are observed [Freeze & Cherry 1979, p.27]:
v = v(d2), v = v(p.g), v = v(l/vO (ID-1)
ID-2-3
Arthur D Little. In
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Table ID-1
SESOIL Default Soil Input Parameters
'JSJA-SCS Soil TfcTCural CU»«if ic*ciot>
Soli Sc«tatie S«l«crioa
5
(*)
(8)
5
10
.1
Silty clay
Sllcy clay la
Clav Ion
Silt lo*!—1
Sill
Sumy cla«
Sanav clay lo^
v1*] Sjoav
t-J
0.20
0.20
0.22
0.23
0.27
0.30
0.30
0.33
0.27
0.24
0.26
0.25
0.21
0.30
'.-; \->
i: 3. "2
12 O.oS
12 0.64
12 0.39
ID 0.59
7.5 0.58
S.3 0.52
3.3 0.54
12 0.49
o 0.4*
4 0.45
6.33 0..4
3.9 0.33
J.7 0.35
ami
3.032S
0.050
0.0785
0.0236
0.0362
0.103
0.124
0.0726
0.0240
0.157
0.176
0.167
0.230
0.283
1 i«e '.'SJA «oil claiilflcatioti crlanfi« ot -'l«ur« ID-13 iplctur
- Sell ci»«i ia ' , corr««ooM» := an ov«raU sro)>o»«d toll ictaano rtlata
" itti; • intrinsic soil 3«rMaoliity; ••• cael* l>-7
"a, • -lO
6 n • >oll ;oro«icv; IM caMa IS--1 mo !l|ura ID-18
' d • foil sattvela xdua iloacit: i«« caola ID-«
9 taa ;«ol« ::-5
' for toll built danair.- aa ovarall coutanc valua of 1.35 ?/ea ~* aaataaa:
|«< ?iic«=an i 3taoy [19691. Lailaaoc 11970, :.237|. Holcon
•° K • toil cooduccini; •«• caala ::
11
Vh.lao (1967
' ooly for aemica specific
*v«ra|«d valut of caala 12
' ivarai* value* of »oii* ;'l
lins «:£ort«
7.3x10
2.5xlO~3
6.0xlO"3
5.0x10"
a.5xlO~'
6.3x!0"3
S.OxlO"3
3.3X10"1
3.0x10"'
1.5xlO~J
2.5x10"'
:.oxio"2
•.Oxio"1
_i
1.0x10
ig
13
25
6
10
33
.0
J2
5
52
58
55
S3
?!
13
19
23
47
55
33
.0
65
90
6
15
:s
10
3
77
3j
;o
«7
IS
34
:o
u
9
42
:;
10
;
^
Source: Bonazountas & Wagner [1981].
ID-30
Arthur D Little, li
-------
Together with Darcy's original observation that v=v(-dh/dl), the above
three relationships lead to a new formulation of Darcy's law
v = -(C d2p.g/p)(dh/dl) (ID-2)
The parameter C is a constant of proportionality affected by the soil
grain size, sphericity and other factors. Comparison of ID-2 with the
Darcy equation
v = -K dh/dl (ID-3)
leads to K - Cd2p.g/v (ID-4)
In this equation, p and u are functions of the fluid alone and Cd2 is a
function of the medium. If we define
k = Cd2 ; (cm2) (ID-5)
then K = kpg/u ; (cm/sec) (ID-6)
The parameter k is known as the specific or intrinsic permeability (or
permeability) and K. is known as hydraulic conductivity (or sometimes the
coefficient of permeability). Table ID-2 provides values of k and K for
a variety of geological materials, and values of unit conversion
factors.
Beyond the above definition, Eagleson [Eagleson 1978, p. 23] defined the
effective intrinsic permeability (cm2) of a soil as
k(s) = (U/YW) K(s) (ID-7)
where y the specific weight of pore water in dynes per cm3 and based on
the wortc of Brooks and Corey [1966] he indicated for his water balance
that:
k(s) = k(l) sc
For saturated conditions — i.e. s=l (see app. HY) — k(l)=k and K(1)=K as
indicated in expressions ID-5 and ID-6. For unsaturated soil conditions
we have the definition k(0) and K(0) , or k(s) and K(s) to be consistent
with Eagleson.
3.2.2 Hydrologic Characteristics of Soil Types
Over 4000 soils of the United States have been classified into four
hydrologic groups [Chow 1964]; designated as A, B, C and D by the Soil
Conservation Service (SCS) . The majority of the assignments are based
on the judgment of soil scientists and correlators [Chiang 1971]. A
short description [Novotny 1976] of the four soil types follows:
ID-31
Arthur D Little, Ir
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TABLE ID-2
Range of Values of Intrinsic Permeability and
Hydraulic Conductivity; Unit Conversion Factors
Range of Values of Hydraulic Conductivity
and Permeability
_. urcc-sc.'ao'ea * <
*"•* jecos's ^ ido-c>) :-r2' 'CT/SI^/S' iga /aay/f! )
. ^\5 ,p- ! i -*2 «
[10 r 'C r ^ '
1 rlO5
io- '-•?•* -ic j-io-
1 • 1
j
u
11 1
n a O
ID X *n
*s \ §
B«*l. *
5 6 °S |
-1C3 -!C'S -I -!0'2
i
-!C2 r-C'6 -10" -'.C'5
|
-io -iO"7 -ic'2 no"*
i
-, -lO'8 -I0's r!C's
wo" •" 1 '
a. « « : .
?a-c
T3 O C
C) £ 01 «
5 o c - a,
£ — 3 = c
S = 7 5 2
- " = £ i?
1 «< g
= riO" riO - riO'a no'"
i/>
0)
o
^
iT
T3 9
I S52
£ UO
I B «)
^°i =i
™
966 IO-»
1
305 • 10-'
47: io-T
ft/s
i r. io'
2 W 10"
3 17 10-'
32S
1
1 74 • 10-"
gal/dav/tl:
1 !i5
1 71
1 8:
: 12
574
10"
10i:
10>
10°
IO1
1
•To obtain Jt in ft', multiply k in cm* by 1.08 x I0~'
Source: Freeze & Cherry [1979, p. 29]
ID-3 2
Arthur D 'uttle. Ir
-------
* Group A: Soils of low total runoff potential have high
infiltration rates even when thoroughly wetted; these consist
chiefly of deep, well to excessively-drained sand or gravel
and therefore possess a high rate of water transmission.
* Group B: Soils of low-moderate total runoff potential have
moderate infiltration rates when thoroughly wetted, and range
from moderately-deep, moderately-well to well-drained soils
having moderately-fine to moderately-coarse texture. Conse-
quently, these soils have a moderate rate of water trans-
mission.
* Group C: Soils of high-moderate total runoff potential have
slow infiltration rates when thoroughly wetted and consist
chiefly of soils with a layer that impedes downward movement
of water, or soils with moderately-fine to fine texture.
These soils have a resultant slow rate of water transmission.
* Group D: Soils of high total runoff potential have very slow
infiltration rates when thoroughly wetted, and consist chiefly
of clay soils with a high swelling potential, soils with a
permanently high water table, soils with a clay pan or clay
layer at or near the surface, and shallow soils over nearly
impervious material. These have the expected very slow rate
of water transmission.
Potential storage of soil moisture can be partitioned into two moisture
classes: 1) gravitational water, i.e. that held between saturation and
0.33 bar tension, and 2) plant-available water, i.e. that held between
0.33 and 15 bar tension. Moisture content at 0.33 bars is assumed to
represent field moisture capacity or the lower limit of gravitational
water, and 15 bars the permanent wetting percentage in medium textures
soils. Gravitational water, G, is derived by subtracting 0.33 bar
volume percentages from total porosity. Available water capacity (AWC)
is the difference between the moisture contents (volumes) at 0.33 and
15 bar tensions. [Novotny 1976.]
3.2.3 Soil Hydraulic Conductivity -- K(l)
Hydraulic conductivity of saturated soils, vary greatly and natural
soils and soil materials, therefore, behave quite differently. Based on
these differences in performance, soils can be classified according to
their K(l) rate. For example, for earth dams the U.S. Bureau of
Reclamation generally classifies soils with_K-values above 10 4 cm/sec
as pervious and soils with K-values below 10~5 as impervious.
In tile drainage, K-rates may be used in selecting depth and spacing of
tile drains. Using relative permeabilities, guides for average depth
and spacing for tile drains have been established by various agencies or
investigators such as that given in table ID-3.
ID-33
Arthur D Little, lii
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TABLE TD-3
Hydraulic Conductivity Classes According to the USDA-SCS
CO
-c-
K Class
Very slow
Slow
Moderately slow
Moderate
Moderately rapid
Rapid
Very rapid
K Values
inch/hr
Less than 0.5
0.05 to 0.20
0.20 to 0.80
0.80 Lo 2.50
2.50 LO 5.00
5.00 to 10.00
More than 10.00
cm/sec
-3
Less than 0.035 x 10
0.035 x 10~3 to 0.14 x 10~3
0.14 x 10~3 to 0.56 x 10~3
0.56 x 10~3 to 1.75 x 10~3
1.75 x 10~3 to 3.5 x 10~3
3.5 x 10~3 to 7.0 x 10~3
More than 7.0 x 10
-3
m/day
Less than 0.3
0.3 to 0.12
0.12 to 0.48
0.48 toi.52
1.52 to 3.0
3.0 to 6.0
More than 6.0
c
-i
O
ET
Source: Horn 11971]
-------
3.2.4 Factors Affecting K(l)
A summary of the work of Horn [1971] is presented in this paragraph.
Particle size, gradation (particle size distribution analysis), arrange-
ment of soil particles (fabric, structure, micromorphology), organic
matter content, iron oxide content, clay mineral composition, exchange-
able sodium percentage, and total concentration of salts are among the
more important basic factors affecting pore size distribution and
continuity, and hence, K.
Particle size and shape (it is assumed for purposes of particle size
analysis that soil particles are roughly spherical in shape although
many particles are platy or lath-shaped) determines the size of normal
packing voids. If a soil is well graded, i.e. has a good distribution
of particles throughout all size ranges, the smaller particles fit into
the interstices associated with the larger particles and reduce the
total porosity. Smaller clay particles may also be washed into the
subsoil and deposited as films that isolate or block off larger voids
that conduct water is low. Slowly permeable soils of this type are
often referred to as claypan soils. Other special cases of particle
arrangement occurring in natural soils are the fragipan horizons of
silty soils, which also have severely restricted K.
Organic matter tends to increase the K of clayey soils by promoting
aggregation. However, this is only significant when calcium ions are
dominant on the soil exchange and in the soil solution. When this
condition exists calcium humate compounds are formed that link clay
particles into large water stable aggregates.
Iron oxides also cement finer particles together, or form coatings on
aggregates that prevent their dispersion. The high K of many red,
tropical soils is a result of high iron oxide contents. However, under
certain conditions, iron compounds may be translocated downward in the
soil and reprecipitated to eventually form dense ironpans which are very
slowly permeable or sometimes impervious to water movement.
Similarly other compounds, notably those of calcium, may be precipitated
in the subsoils of arid or subarid regions. Once formed, these caliche
pans may drastically inhibit movement of water. Where such pans are
near the soil surface waterlogging may develop under irrigation.
The kind and amount of clay in soils is extremely important in determin-
ing rate of water flow through soils. Considering the size of clay
particles alone it is clear that the theoretical K rate of soil masses
composed of particles with equivalent spherical diameters of less than
0.002 mm is extremely low. If it were not for the aggregation of clays
into larger units (peds) most clayey soils would be virtually impervi-
ous. Some clays (those of the 2:1 layer montmorin group) swell tremen-
dously when they are wetted and reduce permeability greatly. Others
such as kaolinite do not swell. Thus, kaolinitic soils are generally
ID-35
Arthur D Little In
-------
quite permeable while montmorillonitic soils have very low permeability
or are impervious.
Exchangeable sodium (Na) content if in excess of 10% to 15% of the soil
cation exchange complex will cause dispersion of the soil particles. A
highly dispersed soil is very massive and dense and lacks the high
proportion of void spaces associated with strongly structured, floccu-
lated and aggregated soils. The K may be reduced by as much as 90% due
to Na-induced dispersion in some soils (Bonazountas et al 1981). Such
soils include the alkali soils and have pH values of the order of 8.5 to
10.0, although NA dispersion may also be associated with soils of acid
pH. Conversely, soils with a high percentage of exchangeable calcium
(Ca) are usually well aggregated soils and generally have moderate to
rapid permeability.
Soils containing montmorillonite, even in amounts as low as 5% to 10%,
are particularly sensitive to changes in the status of the exchangeable
cations and the soil solution. A well aggregated Ca-dominated soil
containing montmorillonite may be affected very quickly and adversely by
the addition of sodium-rich alkaline water. Therefore, the quality of
irrigation water should be carefully scrutinized before applied to these
soils.
Compaction of soils, by the passage of cattle, or heavy equipment (which
produce traffic pans) over a field surface often causes unwanted reduc-
tion in soil infiltration and permeability rates by reducing the size
and continuity of pores. Intentional compaction of canal bottoms and
sideslopes causes desirable reduction in seepage losses. Frequently,
however, soils will rebound significantly from initial compaction
particularly where water levels fluctuate markedly.
Cultivation of soils, particularly clay soils of low organic matter
content, when saturated or nearly saturated often causes destruction of
natural soil structure which may then result in substantial reduction of
permeability. Wet cultivation (puddling) may be done intentionally as
in paddy rice cultivation to cause destruction of the large natural soil
aggregates (peds) which favor rapid permeability. Puddled soils pro-
duced in this manner lose less water to deep percolation when irrigated
because of the destruction of their continuous macropore system.
For most crops, however, a compacted or puddled soil is deleterious
because it inhibits air, water, and root penetration. After puddling,
it may take several months for the soil to fully recover its natural
structure through alternate wetting and drying (thawing and freezing, or
swelling and shrinking), and the influence of root activity and organ-
isms in the soil.
Temporarily increased K-rates can be achieved by mechanical action such
as subsoiling. Other features affecting permeability, but not consi-
dered inherent soil properties, include relatively short-lived macro-
pores such as wormholes and various other animal burrows, root channels,
ID-36
Arthur D Little In
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etc. Biotic features such as these are most common to noncultivated
soils and less so in cultivated soils.
3.2.5 Guides to Estimating K(l)
Most guides developed as aids in making estimates of soil K-values are
based on the relationship between soil texture and various ranges in
rates or K classes. The USDA has schematically presented soil textural
classification with a triangle (figure ID-15). In addition the USDA-SCS
rates soils into seven relative K classes as shown in table ID-3.
Examples of the empirical relationships that have been established by
various researchers are given in table ID-4.
The chief weaknesses of these guides are first, the inconsistency that
arises in the definition and identification of various soil textural
classes, and secondly, the fact that the differences in permeability
due to factors other than texture (as described previously) are not
accounted for [Horn 1971]. To avoid the difficulty associated with
using textural class names, i.e. sandy loam, clay loam, etc., a more
quantitative approach has been undertaken using mean particle size, as
described subsequently.
3.2.6 Mean Soil Particle Size Estimation
This value may be calculated from particle size distribution analyses
(mechanical analyses) which are often made routinely in laboratories as
a part of project investigations and with much more ease than permeabil-
ity determinations. This calculation is based on selecting a mean
particle size (equivalent spherical diameter) of 0.3 mm for the sand
fraction, 0.01 mm for the silt fraction, and 0.002 mm for the clay
fraction. Values for sand and silt represent the midpoint in the size
range representing each of these two fractions from a log scale (figure
ID-16). For the clay fraction, its upper limit was selected. The
particle size limits utilized are those of the USDA but can be equated
quite readily to size limits used by other agencies by means of the
scale in figure ID-16.
Using the textural triangle (figure ID-15) central points or values of
sand, silt, and clay percentages representing each of the soil textural
classes were selected. The clay textural class was subdivided [Horn
1971] into very fine clay (more than 60% clay) and fine clay. These
values and the mean particle diameters (weighted averages) calculated
from them are summarized in table ID-5 and in table ID-1 (Summary,
section 3.1).
3.2.7 K(l) vs Particle Size
The mean particle diameters in millimeters as given in table ID-5 for
each textural class are plotted on the ordinate axis of a log-log graph
ID-37
Arthur D Little li
-------
V Vdtrl V V // I \ / { V i .' \
J\T\ / \7\/y/ x/LjcAM yy\. AA AA A
7\/\/\/\/\/\AV\AAA/\AA/\/c\/
80
10 ,
z
s2
.90
s/
:S'«T>.
(si).
100
100 90 80 70 60 50 40
Percent sand
30
10
FIGURE ID-15
GUIDE FOR USDA-SCS SOIL TEXTURAL CLASSIFICATION SHOWING POINTS
FOR WHICH MEAN PA-RTICLE DIAMETERS HAVE BEEN CALCULATED
ID-38
Arthur D Little Ir
-------
IS
ȣ1
M
f
runt
I IILT on a«< i
IMO cewsi UNO
FM UNO COUSC JMO
COARSE SAND
rs us
1 i
8n
N
o o
A O O
«WfW» DVMtlHdlM
FIGURE ID-16
COMPARISON OF VARIOUS SOIL PARTICLE SIZE RANGES
USED BY VARIOUS AGENCIES
ID-3 9
Arthur D Little In<
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TABLE ID-4
GENERAL RELATIONSHIP BETWEEN SOIL TEXTURE
AND SATURATED HYDRAULIC CONDUCTIVITY
Soil Type
Hydraulic Conductivity K(1)
** Jonnan et al. [1947]
Coarse sand
Sand
Fine sand
Very fine sand
Loamy sand
Sandy loam
Very fine sandy loam
Loam
Silt loam
Silty clay loam
Silty clay
Clay
** Israelsen and Hansen
Sandy
Sandy loam
Loam
Clay loam
Silty clay
Clay
m /day
120
12
4.8
2.4'
1.2
0.24
0.12
0.048
0.024
0.012
0.0024
0.0012
[1967]
2 (1 - 10)
1 (0.5 - 3)
0.5 (0.3 - 0.8)
0.3 (0.1 - 0.6)
0.1 (0.1 - 0.2)
0.2 (0.05 - 0.4)
inch/hr
196.8
19.7
7.9
3.9
2.0
0.4
0.2
0.08
0.04
0.02
0.004
0.002
1.4 x 10"°
0.7 x 10"3
0.35 x 10"3
0.21 x 10"3
0.07 x 10~3
0.14 x 10"3
cm/ sec
140.0 x 10~3
14.0 x 10~3
5.5 x 10"3
2.8 x 10"3
1.4 x 10"3
0.28 x 10~3
0.14 x 10~3
0.05 x 10~3
0.028 x 10~3
0.014 x 10~3
0.0028 x 10~3
0.0014 x 10~3
1.2
0.6
0.3
0.18
0.06
0.12
Source: Horn [1971]
ID-40
Arthur D Little Ir
-------
TABLE ID-5
SOIL TEXTURE, REPRESENTATIVE PARTICLE SIZE CONTENTS,
AND MEAN DIAMETERS
Textural Class
(USDA)
(1)
Sand, as a
percentage
(2)
Silt, as a
percentage
(3)
Clay, as a
percentage
(4)
Mean diameter,
in millimeters
(5)
1. Sand
2. Loamy sand
3. Sandy clay loam
4. Sandy loam
5. Sandy clay
6. Loam
7. Clay loam
8. Clay (fine)
9. Silt loam
10. Silty clay loam
Clay(very fine)
12. Silt
13. Silty clay
95
83
58
55
52
40
33
(a)40
(b)25
(c)10
(a) 34
(b)22
(c) 7
10
(a) 22
(b)10
(c) 1
5
6
3
10
15
25
6
40
33
10
25
40
53
65
80
55
1
13
22
90
47
2
7
27
10
42
20
34
50
50
50
13
13
13
35
77
77
77
5
47
0.285
0.250
0.176
0.167
0.157
0.124
0.103
0.122
0.0785
0.035
0.107
0.0726
0.029
0.0362
0.067
0.0328
0.007
0.0240
0.0236
Source : Horn [1971]
Note: (b) describes central point; (a) and (c) describe the range
(see Fig. 2).
ID-41
Arthur D Little, b
-------
against K-rate on the abscissa (figure ID-17). It should be noted that
these mean diameters represent only one of many possible values within
each given textural range [Horn 1971].
The theoretical K's relative to various particle sizes, as calculated by
Zunkar [1930], represent a straight line relationship (Figure ID-17).
These K's are calculated for spherical particles of the same diameter
with each occurring as a discrete particle. In natural soils, of
course, particles are only roughly spherical or often platy, and rarely,
if ever, possess uniformity of diameter. Also, cementation of particles
into aggregates commonly occurs. Thus, natural soils would be expected
to differ in K-rate from the theoretical. Nevertheless, the theoretical
K serves as a good base from which K-curves for natural soils may be
anticipated. With coarse, clean, well sorted sands the actual and the
theoretical values approach each other but such sandy soils are quite
uncommon.
3.2.8 Selection of Working Values/Curves
For a particular application and a particular soil region, a working
curve representing the soil texture-k relationship can be selected using
best judgment of how existing local conditions and soil properties tend
to affect soil conductivity. If some K measurements are available for
known particle distributions these can be used in selecting a working
curve for extrapolation to other soils. Ideally, a large number of
reasonably accurate K measurements of soils along with corresponding
particle size distribution data would be on hand for the locality in
order to improve the accuracy of extrapolated values; however, this is
rarely the case.
Without actual correlations, the working curve must be based on judg-
ment. Best judgments are made if a thorough understanding is had of
fundamental physical, mineralogical, and chemical properties of soils.
Field observations, and soils data that may be available will further
guide judgment. For small local areas it can often be safely assumed
that nonparticle size related factors affecting soil permeability rate
such as organic matter content, biotic activity, climatic conditions,
clay mineralogy, and chemistry of the soil solution are more or less the
same throughout. Realistic values and valid comparisons of soil K for
the local area en then be obtained from a single working curve.
Hydraulic conductivities of the very sandy soils and, at the other
extreme the very clayey soils, are not affected by nonparticle size
related factors as much as the in-between soils. The latter comprise
the majority of natural soils and vary considerably in response to these
factors.
Some very general groupings of soils according to their K are separated
in figure ID-17 by the horizontal and vertical dashed lines. For
example, soils with mean particle diameters greater than 0.2 mm have K
rates usually in excess of about 10~3 cm/sec and soils with diameters
ID-42
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FIGURE ID-17
SOIL TEXTURE PERMEABILITY CURVES
ID-A:
Arthur D Little ln«
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less than 0.015 mm have rates of 10 ** cm/sec and are essentially
impervious. Soils between these ranges are greatly affected by the
nonparticle size factors controlling K; these factors vary considerably
from place to place and, in addition, are subject to in situ changes in
relatively short periods of time. As a consequence the intermediate
soils can range from impervious to permeable [Horn 1971].
Rigorous application of the K curves in figure ID-17 presupposes the
availability of data from particle size distribution analyses for all
major horizons of the soils in question. Depending on intended applica-
tion, K in a vertical direction of an entire soil section may be rated
according to the least permeable layer, recognizing that for some soils,
the presence of very thin continuous clay laminae or other abruptly
contrasting layers may exert a profound influence on the permeability
behavior of the soil. Lateral K of soil sections may be rated according
to the layer with greatest K. Alternatively, average K rates may be
taken for the entire section.
The methods for obtaining mechanical analysis data are much easier and
the results more dependable than those associated with measuring
K-rates. Of course, collection of representative soil samples and
laboratory facilities capable of conducting particle distribution
measurements are necessary in order to quantify the soil texture vari-
able in the estimation of K-rates.In cases where both mechanical anal-
yses and soil K determinations are to be made, it is recommended that
soil samples are taken from the same location for laboratory analyses.
This not only results in reducing sampling costs and field time but also
provides valuable data for correlating permeability rates with the
particle size data and other measured soil properties.
When only field estimations of soil texture are available, the K esti-
mate is less quantitative. Nevertheless, using the limits indicated in
figure ID-17, a guided judgment method is provided from which tenable
soil K values can be obtained for a variety of field applications.
3.2.9 K(l) vs k(l)
The hydraulic conductivity (K) is related to the intrinsic permeability
(k) via equation ID-6. Since only fluid (ie. water, soil moisture) is
assumed to flow in a soil system, the conversion factor from K-to-k is a
constant number, to be obtained from table ID-2. By employing: the
values of table ID-2; the soil classification system of table ID-15; and
the soil texture graph of figure ID-17; the intrinsic permeabilities (k)
for the USDA soil texture triangle of figure ID-15 have been derived
(table ID-6).
3.2.10 k(l) SESOIL Default Values
As discussed in section 3.2.6, the theoretical k rates derived would be
expected to differ from the field k rates of natural soils. The last
column in table ID-6 (Eagleson's estimates) indicates a consistent
ID-44
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TABLE ID-6
SOIL TEXTURE VS. PARTICLE DIAMETER SOIL CONDUCTIVITY^
AND INTRINSIC PERMEABILITY 00
Textural Soil
Class (USDA)
Jl_ Designation -
1 Clay (very fine)
(2)2 Clay (medium fine)
3 Clay (fine)
4 Silty clay
5 Silty clay loam
(6) Clay loam
7 Loam
(8) Silt loam
9 Silt
10 Sandy clay
11 Sandy clay loam
(12) Sandy loam
13 Loamy sand
14 Sand
0.785
K
(mm) (cm/sec)
(cm2)
0.0328
0.050
0.0785
0.0236
0.0362
0.103
0.124
0.0726
0.0240
0.157
0.176
0.167
0.250
7.5 x Hf!
2.5 x 10'^
6.0 x 10'^
5.0 x 10~J
8.5 x 10,
6.5 x 10",
8.0 x 10",
3.5 x 10~7
5.0 x 10,
1.5 x 10,
2.5 x 10,
2.0 x 10"^
5.0 x 10lT
7.5 x 10~*
2.5 x 10 3
6.0 x IO'Q
5.0 x IO'Q
8.5 x ID"*
6.5 x 10 3
8.0 x 10 ~I
3.5 x 10 Q
5.0 x 10,
1.5 x 10",
_7
2.5 x 10 ,
_7
2.0 x 10 '
5.0 x 10~J
Eagelson
[1978.1982]
1 x 10
-10
10
-10
-11
-10
10
2.5 x 10
-9
1.0 x 10
1.0 x 10
See Figure ID-15.
Class in ( ) corresponds to an overall proposed soil scenario related
to the USDA soil triangle (Figure ID-15 and Table ID-1).
ID-45
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natural k-rate decrease of 10 1 to 10 2 contrasted to the theoretically
derived values. Since Eagleson's theory deals with the entire seasonal
water budget of the soil compartment, it is more or less expected that
his field k(l) values obtained via model calibration [Eagleson & Tellers
1982, p.353] will be lower because of the number of water budget
processes accounted (eg. infiltration, exfiltration). It may be appro-
priate, therefore, to reduce the k values derived and presented in table
ID-6 to two orders of magnitude (i.e. 10 2) in order to obtain some
consistency with the calibrated k(l) values of Eagleson. There exist no
theoretical justification for doing so (aside from engineering judg-
ment), however, for scenarios and canonical environmental simulations or
modeling efforts, the proposed action is not anticipated to drastically
alter SESOIL output results. No sensitivity model analysis is performed
at this stage to justify above action.
The finally derived saturated intrinsic permeabilities to be input as
default values to SESOIL when dealing with fictitious or canonical
environments are given in table ID-7, and in table ID-1 (summary;
section 3.1).
3.3 Soil Effective Porosity — n
3.3.1 Definitions
If the total unit volume V of a soil or rock is divided into the volume
of the solid portion V and the volume of the voids V , the volumetric
total porosity (or porosity) n is defined as
n = Vv/VT (ID-9)
and is usually reported as a decimal fraction or a percent. Table ID-8
[Freeze & Cherry 1979, p.37] lists representative porosity ranges for
various geologic materials. In general rocks have lower porosities than
soils; gravels, sands, and silts, which are made up of angular and
rounded particles, have lower porosities than soils rich in platy clay
minerals; and poorly sorted deposits have lower porosities than well
sorted deposits [Freeze & Cherry 1979].
The porosity n is an important controlling influence on hydraulic
conductivity K. In sampling programs carried out within deposits of
well sorted sand or in fractured rock formations, samples with higher n
have in general also higher K, but the relationship does not hold on a
regional basis across the spectrum of possible rock and soil types.
Clay rich soils, for example, usually have higher porosities than sandy
or gravelly soils but lower hydraulic conductivities. In practice, it
is difficult to saturate a soil sample and then dry it and measure its
porosity. It is usual, however, to estimate the total porosity (or
porosity) from the relationship [Eagleson 1970, p.286]
n = 1 - (Pb/Ps) (ID-10)
ID-46
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Table ID-7
k(l) Default Values for SESOIL
Textural Soil
Class (USDA)
1
(2)2
3
4
5
(6)
7
(8)
a
10
11
(12)
13
Designation
1
Clay (very fine)
Clay (medium fine)
Clay (fine)
Silty clay
Silty clay loam
Clay loam
Loam
Silt loam
Silt
Sandy clay
Sandy clay loam
Sandy loam
Loamy sand
Sand
7.5xlOU
2.5xl012
6.0xlO~10
S.OxlO"11
8.5xlO~U
6.5X10'10
S.OxlO"10
3.5xlO-10
5.0xlO~U
l.SxlO"9
2.5xlO~9
_9
2.0x10
5.0xlO~8
(cm2)
0.75xlO"10
= 2.5X10-10
e.oxio"10
= o.sxio-10
0.85xlO~10
= 6.5xlO-10
8.0xlO~10
= 3.5xlO-10
= 0.5xlO-10
= 15xlO-10
= 25X10'10
— 1 0
= 20x10
SOOxlO"10
1.0x10
8
100x10
-10
1 See figure ID-15.
Class in () corresponds to an overall
proposed soil scenario related to the
USDA soil triangle (figure ID-15, table ID-1).
ID-47
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Table ID-8
Range of Values of Porosity
Material Porosity n
Unconsolidated deposits
Gravel 25-50
Sand 35-50
Clay 40-70
Rocks
Fractured basalt 5-50
Karst limestone 5-50
Sandstone 5-30
Limestone, dolomite 0-20
Shale 0-10
Fractured crystalline rock 0-10
Dense crystalline rock 0-5
Source: Freeze & Cherry [1979, p.37]
ID-AS
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where p, is the bulk mass density of the sample, and p is the particle
mass density. The bulk density is the oven-dried mass of the sample
divided by its field volume. The particle density is the oven-dried
mass divided by the volume of the solid particles, as determined by a
water displacement test. [Freeze & Cherry 1979, p.337.] In case no
great accuracy is required, it can be assumed for most mineral soils
p =2.65 g/cm3.
s
One should be careful with the use of porosity values, when employing an
unsaturated soil zone model such as SESOIL. The problem is similar to
the specific yield and the porosity issue of a phreatic aquifer [Bear
1979, p.88]. As water is being drained from the interstices of the
soil, the drainage is never a complete one. A certain amount of water
is retained in the soil against gravity by capillary forces. After
drainage has stopped, the volume of water retained is an aquifer per
unit (horizontal) area and unit drop of the water table is called
"specific retention" S , and is related to the specific aquifer yield S
via r y
n - S + S (ID-11)
y r
For this reason S (less than n) is also called "effective porosity" n .
The correlation between porosity n, effective porosity n and median
soil particle (grain) size is schematically presented in rigure ID-18
[Davis & DeWiest 1966]. SESOIL requires the effective porosity n as an
input parameters.
3.3.2 Soil Hydraulic Properties
An ecological and soil genesis pedologic discussion is presented by
Eagleson [1982a, p.326], according to whom the overall soil properties
behavior may be generalized as presented in figures ID-14 a,b (section
3.1). As discussed by Eagleson, soils evolve having a continuous
spectrum of textures from clay through silt to sand and gravel, and the
critical hydraulic properties of them vary widely even within the same
textural class, but over the variety of classes their range is enormous.
Brooks and Corey [1966] show that k(l) is related to both the shape
(i.e. tortuosity) of the pores and to their total size (i.e. porosity)
of a soil. Davis [1969] proposed the overall relationship [Eagleson
1982a, p.327]:
k(l) = AeBn (ID-12)
where the coefficients A and B vary with textural class as sketched in
figure ID-14 (section 3.1).
As discussed by Eagleson, for the fine-particled clayey soils the total
particle surface area is enormous. The total pore volume which can be
occupied by water that is bound to these surfaces through molecular
forces is correspondingly large and the inactive porosity n dominates.
With increasing sand content this volume decreases and the effective
ID-49
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Well-sorted material — — — —
Averace material
60~
50".
40"
?n~
:rr
10 -
Silt
10 ] 10' 10'
Sand Gravel
Cobbles
Median erain size (mm)
Source: Bear [1979, p.88].
Figure ID-18 Relationships Between Porosities
and Soil Grain Size
ID-50
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porosity rises. As the sandy soil becomes gravelly, the falling total
porosity takes over from the decreasing surface area and the effective
porosity becomes smaller. This is sketched in figure ID-lAb. We see
from this diagram that over the clay to sand textural range encompassing
most soil, permeability and effective porosity are directly related.
3.3.3 n SESOIL Default Values
The range of values of the porosity n or the effective porosity n is
known to be quite small in field studies — from about 0.25 to alout
0.45 — and does not have a large effect [Tellers & Eagleson 1980, Chan
& Eagleson 1980] on solutions of the water balance equation HY-32
(appendix HY) as other parameters may have. The effective porosity
affects directly the sigma function (equation HY-34) and consequently
the gamma function of the model and the down-the-road remaining calcula-
tions, but the sensitivity of sigma vs n is not large.
Eagleson reports in 1978 [WRR, p.769, table 2] effective porosity n
(i.e. n ) values for various soils corresponding to the "porosity" curve
of figure ID-14b. In his latest publication in 1982, however, his n
values are slightly decreased [WRR, 1982, p.329, table 1]. The newly
introduced 1982 porosity vs. permeability graph [WRR 1982, p.326, figure
1] indicates potential need for employing the "effective porosity" curve
of figure ID-14b (instead of the n-curve). We will follow the latter
logic in the following pages when developing default values for SESOIL.
Table ID-9 lists representative porosity n values (columns (1) & (2)).
They are obtained from various sources and are reported for the soil
classification scheme presented on table ID-7 (derived from the USDA
soil triangle). The average or the best (using best judgment) value of
the various sources is designed with n. This value has been "adjusted"
to an n value (column (5)) with the aid of figure ID-18, and the latter
has been reported on table ID-1 (section 3.1) as a SESOIL default value.
Adjustment has been performed by correlating the n, n and keeping the
R estimates for clay (#2), clay loam (#6), silt loam (#8) and sandy
loam (#12) to their fixed values of 0.2, 0.30, 0.30 and 0.25 correspond-
ingly .
3.4 Soil Disconnectedness Index — c
3.4.1 Definition
In Eagleson's model, the soil pore disconnectedness index c is defined
as [Eagleson 1982, p.328]:
c - A[ln(k)]/A[ln(s )] (ID-13)
o
where k [cm2] the intrinsic soil permeability and s the long-term
average soil moisture concentration in the root-zone. In other words, c
represents the slope of a k-s , or K-s curve as graphically shown in
figure ID-19. °
ID-51
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lahle 1D-9
Ui
to
(2)
3
4
5
(6)
7
(8)
9
10
11
(12)
13
8)
Texturol Soil Class
USDA
Designation
Clay (very fine)
Clay (medium fine)
Clay (fine)
Sllty clay
Silly clny loam
Clay Joam
Loam
Silt loam
Silt
Sandy clay
Sandy clny loom
Sandy loam
laaay sand
Sand
Representative and SESOIL
Porosity (n)
(fractional)
Terrier & Freeze &
Clbson|198lll Cherry |19791
(I) (2)
0.680 0.4-0.7
0.592
0.588
0.582
0.521
0.535
0.35-0.50
0.442
0.453
0.442
0.330
0.389 0.2.'i-0.40
nc-l)e fault Va
- 7)
n
estimate
(3)
0.70
0.68
0.64
0.59
0.59
0.58
0.52
0.54
0.49
0.44
0.45
0.44
0.33
0.35
Effective I'oroalty (n0)
(4)
0.45
0.35.1\0.302)
0.350-0.458
0.251'
0.379-0422
estimate
(5)
0.20
0.20
0.22
0.25
0.27
0.30
0.30
0.35
0.27
0.24
0.26
0.25
0.20
0.30
5)
-1
0
L~
Kaijlesu.i |MIIK, 1978, p. 7691
El-llemry 6 EagLeann | 1980)
Averageil value from cLay-to-saml (Chan & Eaglcson 19HO]
Kagleson (1970, p.287|
Free estimate liancd on Dear |19RO|
lnter|
-------
u
LJ
(O
CJ
10
-5
0
-6
10
-7
10
-8
10
-9
= ICJ5CM SEC"*1
c= 8.54
YOLO LIGHT CLAY
(MOORE )
= 3.3 x IO"3CM SEC"1
= 4.22
BUNGENDORE
FINE SAND
( TALSMA)
Source: Eagleson [1979].
10
-2
U
UJ
u
'5
10
-2
Figure ID-19 Hydraulic Conductivity vs Soil Moisture
ID-53
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Brooks and Corey [1966] show that during wetting or drying soil cycles
the functional relationship
k(s) = k(l).sc (ID-14)
allows integration of the simplified Burdine [1958] equations governing
the relationship between effective permeability and capillary pressure
in irregular pore structures to obtain the relationship
c • (2+3m)/m (ID-15)
employed in Eagleson's work [Eagleson 1978, p.723]. In that respect the
pore disconnectedness index c in SESOIL can also be defined as the
exponent relating the "wetting" or "drying time dependent intrinsic
permeability k(s) of the soil to its saturated intrinsic permeability
k(l). Relation to ID-14 has been defined by Eagleson. Theoretically k
is a soil property, therefore, it should be independent from the water
or moisture soil content (see equation ID-5). In practice, however,
because of the effective porosity issue discussed in section 3.3.2
(figure ID-14b), k becomes moisture dependent, a fact that may have
resulted to the definition of equation ID-14 via the c exponent.
At this point it is worth emphasizing that any unsaturated soil zone of
the literature [eg. Bonazountas et al 1979] requires as a user input
instead of a curve relating "conductivity k vs. capillarity head ty."
This curve is obtained from experimental data. It is almost impossible
to obtain this curve off-the-shelf for any type of soil, but it is also
extremely difficult to obtain this curve in the laboratory. Therefore,
the "one-variable" approach of Eagleson [1978] employed in SESOIL
greatly simplifies data gathering and data input to a model.
3.4.2 The c Index Sensitivity
A hydrologic balance sensitivity based on the two independent soil
properties k(l) and c is presented in figure HY-38, section HY-3.5.
Roughly speaking, the compartment surface runoff is insensitive to c but
very sensitive to k(l).
In relation to the various soil types, and when dealing with vegetated
areas, Eagleson & Tellers [1982, p.347] proves that the range of climax
values of c (that is values of c at maximum vegetation canopy, given a
specified soil moisture content and an ecological optimality) has been
only
4.74 < c < 5.50 ; c > 3.0 (ID-16)
for six catchments studied. In addition the lower limit of c is re-
ported [Brooks & Corey 1966] to be 3.0. Typical values of c lie around
ID-54
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£ to 5 and the reason for this small range has been recently analyzed
by Eagleson & Tellers [1982, p.348].
The correlation of c and s is evaluated via the f(s) function [Eagleson
& Tellers 1982, p.349]. °
(c-3).gi(c,so) = f(sQ) (ID-17)
which by its expected value results to the very useful empirical
relationship
(c-3).gi(c,so) = 0.75 (ID-18)
that is presented for 6 catchments in the lower half part of figure
ID-20. This relationship allows elimination of c from the water balance
equation HY-32 in terms of the state variable s and when dealing with
ecologically balanced systems. However, because variation of c is
within certain limits, we may employ the equations derived by Eagleson &
Tellers [1982, p.349] from ID-18, i.e.
s [k(l)]1/(c+5) = f(c) (ID-19)
o
and ,
k(l) = (0.058/s )c (ID-20)
o
to make some rough estimates for c values based on k(l) values as
following: for a set of soils (sand, sandy loam, silty loam, loam and
clay) Tellers & Eagleson [1980] report from their experience with
equations ID-19, ID-20, the expression
k(l) = (m/512.7)2'75 (ID-21)
where m = 2/(c-3) as given by parameter set in HY-29 (app. HY) and
graphically reported in figure ID-21. Therefore:
* In general (regression line; figure ID-21):
c = k(l)1/2'75 (512.7/2)+3 (ID-22)
* For sandy soils (m=3, figure ID-21):
c = 3.7 (ID-23)
* For sandy loam soils (m=0.5, figure ID-21), and
c = 6.33 (ID-24)
Table ID-10 summarizes obtained and compiled c values for the USDA soil
texture classification triangle. Values of the last column are reported
in table ID-1 also. Based on information obtained from the literature
ID-55
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EFFECTIVE POBOSIT
0 CLINTON, HA
C. 0.2 0.! 0« C.S
EFFECTIVE POROSITY. n,
D SANTA PAULA. CA
_ £[((«,)]-0.75
\
' g--
Sensitivity of flux properties of climax soils to porosity
(kv =1).
10.9
0.8
0.7
O CATCHMENTS OF TABLE 6
-0.73
0.6
o
l.O
.I I 5t-
-i2.0
(a)
- 7 51
-.1
1
- 9 «(-
1 1 1
NASHUA RIVER -
AND
CLINTON, MA.
\ COORDINATES FOR
SENSITIVITY STUDY
3456 89
SOIL PORE DISCONNECTEDNESS INDEX , C
. Climatic climax soil-vegetation systems.
0.07
006
flc)
0.05
0.04 -
<-—°- J
O CATCHMENTS Or TABLE 6
0.031
4.5
5.0
C
Climatic climax soil properties, (a) Soil pore disconnect-
edness index, (b) Saturated intrinsic permeability.
(c)
Mo = vegetation canopy density
ky " plant coefficient
(b)
Source: Eagleson [1982], Eagleson & Tellers [1982].
Figure ID-20 Functional Relationship, c-f(So);
Saturated Intrinsic Permeability
ID-5 6
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a
c.
-I
D
10
m
o
T
r2=O.32
LEGEND
• SAND
A SANDY LOAM
O SILTY LOAM
D LOAM
O CLAY
JQ-IO
Source:
|Q-9
Tellers & Eagleson [1980].
10
-7
k(l), cm2
10
-6
10'
Figure ID-21 Saturated Permeability vs Pore Size Distribution Index
(from Eagleson, Personal Communication)
-------
Table ID-10
Default c Values for SESOIL
Textural Soil Class
USD A
Designation
c-Soil Properties
SESOIL Default
(cm^)
C2
2)
1 Clay (very fine)
(2) ^Clay (medium fine)
3 Clay (fine)
4 Silty clay
5 Silty clay loam
(6) Clay loam
7 loam
(8) Silt loam
9 Silt
10 Sandy loam
11 Sandy clay loam
(12) Sandy loam
13 Loamy sand
14 Sand
7.5x10
2.5x10
6.0x10
5.0x10
8.5x10
6.5x10
8.0x10
3.5x10
5.0x10
1.5x10
2.5x10
2.0x10
5.0x10
1.0x10
,-10
-10
I
r11
r11
r10
r10
-10
-11
-9
-9
-9
-8
-8
25
16
16
23
10.6
13
11.0
16.0
23.0
6.33
8.70
8.70
5.00
3.7
12
12
8.544)
3.84>
10,5.05
8.54'
6,4.95
4
12.0
12.0
12
12
10
7.5
6.5
5.5
12
6
4.0
4.0
3.9
3.7
approximate values by employing equation ID-22 and the k(l)
values of table ID-7
Eagleson [1977, 1978, 1981, 1982]
Employ primarily values of soils # 2,6,8 and 12
Talsma [1974], Moore [1939], Brook & Corey [1966] from Eagleson [1978a-g].
Soil class in ( ) corresponds to an overall proposed soil scenario related
to the USDA soil traingle; in figure with
ID-53
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the c value range has been confined between c=12 [Eagleson 1978] and
c=3.7 [see figure ID-21 for clay]. The c. theoretical estimates are
kept as a guidance. The value of soil #6 (clay loam, c-7.5) equals the
average of the two Eagleson studies [1982, 1978]. The same applies to
soil #8 (silt loam). For the remaining soil types rough linear
interpolation is performed, because the changes of c do not affect water
balance estimates strongly. As information becomes available, these
default values will be improved. For site specific application, model
calibration to estimating the independent soil parameters c, k(l), n is
recommended.
3.5 Soil Parameter Calibration
3.5.1 General
A single general relationship for k(l), n and c does not exist, because
the vegetation canopy density and evapotranspiration — both related to
n , k(l) and c — affect the interrelation of the three parameters in an
area. Tellers & Eagleson [1980] and Eagleson & Tellers (1982] have
employed the water balance theory of Eagleson [1978a-g] to estimate the
effective hydrologic properties of soils from observation on vegetation
density. Bonazountas et al [1981] have employed the monthly water
balance of SESOIL to estimate soil moisture contents of soil, where
field data were available.
Three types of input parameters are associated with Eagleson's hydro-
balance routine: climatic, soil and vegetation. The climatic and
vegetal properties are easily obtained from observations; this leaves
the soil parameters to be determined from relationship between climate,
soil and vegetation [Eagleson 1978a-g]. Four soil parameters are
associated with Eagleson1s theory; three independent soil properties
(k(l), n , c) and the soil moisture state variable SQ. In calibrating
the mode?, two methods are of major importance: (1) calibration of the
soil parameters k(l), c via s and n, or (2) calibration of s via k(l),
c and n. The vegetation part of Eagleson1s theory has been eliminated
from SESOIL, however, calibration procedures remain the same.
3.5.2 Calibration of k(l), c via s
The range of values of the porosity, n, is known to be quite small, from
0.25 to about 0.45 (see section 3.3), and does not have a large effect
on solutions of the water balance equation. Assuming a known value for
n , this fact leaves the soil moisture, intrinsic permeability, and pore
disconnectedness index as unknowns. To solve for these variables, two
equations or relationships are needed which incorporate the soil and
climate as well. The first relationship is the water balance, Equation
HY-32, which expresses the soil moisture, s , as an implicit function of
the climate and soil. The second expression used is a rather weakly
correlated regression between k(l) and m (figure ID-21, equation ID-21).
With the information produced by Eagleson & Tellers [1982] for vegetated
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sites, the following calibration procedure can be designed, to estimate
effective soil parameters, given a set of climatic parameters.
(1) A value of n is assumed, in order to estimate E (equation
HY-37). e
(2) The lowest possible value for c, approximately 3.5, is
selected as an initial value.
(3) k(l) is calculated from equation ID-21.
(4) With these values for the three soil parameters, n , k(l), and
c, it can be seen from equation HY-37 that s remains as the
only variable needed for determining E. With E known from
step (1), s is calculated.
(5) Annual precipitation is calculated via equations HY-32 through
HY-43.
(6) If the annual precipitation from the above step is not equal
to the actual mean rainfall, c is incremented upward from its
initially low value and steps (3)-(5) are repeated.
(7) Due to the approximation introduced by using equation ID-21,
the precipitation, P , calculated in step (5) may never
exactly equal the actual mean value, m_ for any value of c.
P will approach dp. as c is increased, coming to within AP
or equality at intermediate c before diverging again for large
c. For low values of c, the calculated k(l) is large, repre-
senting a soil with high permeability and well connected
pores. With evapotranspiration specified at the optimum (i.e.
minimum) value, a large precipitation is therefore calculated
in order to produce the inevitably large groundwater yield of
the highly porous soil. For large c and small k(l), the soil
is extremely impervious and the surface yield will be high.
With minimum evapotranspiration, a large value for precipita-
tion is again needed. Somewhere between these two extremes, a
set of suitable soil parameters is obtained which gives an
annual precipitation, P , which is closest to the actual mean,
nL . This relationship is illustrated in figure ID-22.
Holding c constant at the value which gives the minimum AP ,
k(l) is then deviated from regression equation ID-21 until
another minimum in calculated precipitation is reached. If
this value is above the mean precipitation, c is decreased, if
it is below the mean, c is increased. Another search is done
on k(l) until the minimum precipitation is found. This step
is repeated until the minimum calculated precipitation is
equal to the mean.
(8) If the values obtained for k(l) and c are not consistent with
the assumed porosity, n is adjusted to a more appropriate
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200
80
160
140
120
100
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150
130
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Locus of Solutions
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Figure ID-22 Water Balance Solutions Using Soil Properties from Equation ID-21
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value corresponding to a more pervious or impervious soil type
depending on the values of k(l) and c. Steps (1) through (7)
are repeated.
The soil parameters obtained from steps (1-8) are used to construct the
CDF of annual yield in the same manner as Eagleson [1978g]. The above
procedure can be repeated for 3 input data categories; i.e. climate,
soil and vegetation in case equation HY-32 were not simplified to the
bare soil SESOIL needs (see section ID-3.1).
3.5.3 Calibration of s via k(l), n , c
The concept of procedure previously described can be repeated to cali-
brate SESOIL either via existing s field measurements, or via USGS data
records for basin yields (surface runoff and groundvater runoff)
[Eagleson 1978a-gj. In this particular case
(1) a n , c set is obtained from table ID-1.
e
(2) the model is run, and model yield output (equation HY-42) is
compared to USGS basin yields.
(3) Depending upon the distribution of the surface vs groundwater
runoff yield predictions, parameters n , c, and k(l) are
adjusted to new values, primarily by Adjusting k(l) (see
section ID-3.2) and by following the sensitivity consensus of
figures HY-7 and HY-8.
(A) Above steps are repeated until basin yields and averaged soil
moisture s predict
o
3.5.4 Automated Calibration
moisture s predictions have reached their field values.
o
It is feasible to write a program automatically calibrating SESOIL and
all its input parameters given USGS data records for basin yields and
some basic precompiled information such as the default data of table
ID-1. However, development of such a computer code has been beyond the
scope of the developers involvement.
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4.0 CHEMISTRY INPUT DATA
Chemical parameters, coefficients, etc. may be compiled from the
handbook "Research and Development Methods for Estimating Physicochem-
ical Properties of Organic Compounds of Environmental Concern" [Lyman
et al 1981], or any other handbook. In the future, authors of SESOIL
intend to compile a data base for chemical properties relevant to the
model use and a number of pollutants.
5.0 CANONICAL CLIMATIC-SOIL COMPARTMENTS
Many environmental studies, such as human exposure assessments related
to hazardous waste sites, may require the design of typical or canonical
soil-compartments; and SESOIL is well suited for such simulations
[Bonazountas et al 1981]. The design, however, of a canonical
compartment is a function of both the climate and the soil-type of the
environment; therefore, only climatic or only soil canonical (default)
data sets would not suffice for a model user if he has to describe a
canonical soil-compartment. There may be a way to design for the entire
U.S. canonical soil environments accounting for both climatologic and
soil type default values, but since model developers have not yet
finalized their thinking regarding this issue, and they are not
confident regarding their current technical approach, they have decided
not to present this information in this section. Some information may
follow in the future.
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6.0 REFERENCES
Bear, J. (1979). "Hydraulics of Groundwater," New York: McGraw Hill
International Book Company.
Bonazountas, M.; W. Hawes and W. Tucker (1979). "Heutistic Unsaturated
Flow/Quality Soil Zone Model," American Geophysical Union, Spring
Meeting, Washington, D.C.
Bonazountas, M.; J. Wagner and B. Goodwin (1981). "Evaluation of
Seasonal Soil/Groundwater Pollutant Pathways." EPA Contract No.
68-01-5949, Task 9. Washington, D.C.: Monitoring and Data Support
Division, U.S. EPA.
Bonazountas, M.; J. Wagner; J. Segna; and M. Slimak. (1982). "The
'SESOIL1 Model and Exposure Studies." J. Environ. Monit. & Assessment
(submitted for publication).
Brooks, R.H. and A.T. Corey (1966). "Properties of Porous Media
Affecting Fluid Flow," J. Irrig. Drain. Div. Amer. Soc. Civil Eng., IR2,
61-68.
Buckman, H.O. and N.C. Brady (1969). "The Nature and Properties of
Soils." London: The Macmillan Company, 653 pp.
Burdine, N.T. (1952). "Relative Permeability Calculations from
Pore-size Distribution Data." Petrol. Trans., Am. Inst. Mining, Met.
Petrol. Engrs., Vol. 198, 71-77.
Chan, S. and P.S. Eagleson (1980). "Water Balance Studies of the Bahr
El Ghazal Swamp," Report No. 261, Ralph M. Parsons Laboratory for Water
Resources and Hydrodynamics, Department of Civil Engineering, Massachu-
setts Institute of Technology, Cambridge, Massachusetts.
Chiang, S.L. (1971). "A Runoff Potential Rating Table for Soils." J.
Hydrology Vol. 13, 54-62.
Chow, V.T. (1964). "Runoff." In: Handbook of Applied Hydrology. New
York: McGraw Hill Book Company, Inc.
Corey, A.T. (1977). "Mechanics of Heterogeneous Fluids in Porous
Media." Water Resources Publication, Fort Collins, Colorado.
Eagleson, P.S. (1970). "Dynamic Hydrology," New York: McGraw-Hill Book
Company.
Eagleson, P.S. (1977). "Climate, Soil and the Water Balance: A Frame-
work for Their Analytical Coupling," Department of Civil Engineering,
Massachusetts Institute of Technology, Cambridge, Massachusetts.
ID-64
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Eagleson, P.S. (1978a-g). "Climate, Soil, and Vegetation," Water
Resources Research, 14(5), 705-776.
Eagleson, P.S. (1982). "Ecological Optimality in Water-Limited Natural
Soil-Vegetation Systems. 1. Theory and Hypothesis," Water Resources
Research, 18(2), April 1982; 325-340.
Eagleson, P.S. and I.E. Tellers (1982). "Ecological Optimality in
Water-Limited Natural Soil-Vegetation Systems. 2. Tests and Applica-
tions," Water Resources Research 18(2), April 1982; 341-354.
El-Hemry, I.I. and P.S. Eagleson (1980). "Water Balance Estimates of
the Machar Marshes," Report No. 260, Ralph M. Parsons Laboratory for
Water Resources and Hydrodynamics, Department of Civil Engineering,
Massachusetts Institute of Technology, Cambridge, Massachusetts.
Freeze, R.A. and J.A. Cherry (1979). "Groundwater," Englewood Cliffs,
New Jersey: Prentice-Hall, Inc.
Grayman, W.M. and P.S. Eagleson (1969). "Streamflow Record Length for
Modelling Catchment Dynamics," Report No. 114, Hydrodynamics Labora-
tory, School of Engineering, Massachusetts Institute of Technology,
Cambridge, Massachusetts.
Holton, H.N.; C.B. England and D.E. Whelan (1967). "Hydrologic
Characteristics of Soil Types. J. Irrig. Drainage Div. IR3, 33-39.
Horn, M.E. (1971). "Estimating Soil Permeability Rate," J. Irrigation
and Drainage Div., 97(IR2), p.263.
Libardi, P.L.; K. Reichardt; C. Jose; M. Bazza and D.R. Nielsen (1982).
"An Approximate Method of Estimating Soil Water Diffusivity for Differ-
ent Soil Bulk Densities," Water Resources Research 18(1), February 1982;
177-181.
Lyman, W. et al. (1981). "Research and Development Methods for Esti-
mating Physicochemical Properties of Organic Compounds of Environmental
Concern." Prepared by Arthur D. Little, Inc., Phase II, Final Report
for U.S. Army Medical Bioengineering Research and Development Labora-
tory, Fort Detrick, Maryland. New York: McGraw-Hill Book Company.
McWhorter, D.B. and D.K. Sunada (1977). "Ground-water Hydrology and
Hydraulics," Water Resources Publication, Fort Collins, Colorado.
Metzger, B.H. and P.S. Eagleson (1980). "The Effects of Annual Storage
and Random Potential Evapotranspiration on the One-Dimensional Annual
Water Balance," Report No. 251, Ralph M. Parsons Laboratory for Water
Resources and Hydrodynamics, Department of Civil Engineering,
Massachusetts Institute of Technology, Cambridge, Massachusetts.
Moore, R.E. (1939). "Water Conduction from Shallow Water Tables,"
Hilgardia 12(6), 382-426.
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Nielsen, D.R.; J.W. Biggar and K.T. Erh (1973). "Spatial Variability of
Field Measured Soil-Water Properties." Hilgardia Vol. 42(7), 215-260.
Novotny, V. (1976). "Hydrological and Hydraulical Conceptual Models
Applicable to Overland and River Transport Modeling," Literature Review
No. 4, Water Resources Center, Univeristy of Wisconsin, Madison,
Wisconsin.
Perrier, E.R. and A.C. Gibson (1980). "Hydrologic Simulation on Solid
Waste Disposal Sites (HSSWDS), Contract No. EPA-IAG-D7-01097,
Cincinnati, Ohio: Municipal Environmental Research Laboratory, ORD,
U.S. Environmental Protection Agency.
Talsma, T. (1974). "The Effect of Initial Moisture Content and
Infiltration Quantity on Redistribution of Soil Water," Australia. J.
Soil Res., 12, 15-26.
Tellers, T.E. and P.S. Eagleson (1980). "Estimation of Effective
Hydrologic Properties of Soils from Observations of Vegetation Density,"
Report No. 254, Prepared by Ralph M. Parsons Laboratory for Water
Resources and Hydrodynamics, Department of Civil Engineering,
Massachusetts Institute of Technology, Cambridge, Massachusetts.
Zunker, F. (1930). "Das Verhalten des Bodens zum Wasser." Handbuch der
Bodenlehre, Vol. VI, 66-200.
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OF • data files
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APPENDIX DF
DATA FILES (INPUT/OUTPUT)
Page
1.0 INTRODUCTION DF-3
2.0 INPUT DATA ARRAYS (IDA) DF-5
2.1 General DF-5
2.2 Climatologic IDA Arrays DF-5
2.3 Soil IDA Arrays DF-8
2.4 Chemistry IDA Arrays DF-10
2.5 Geometric IDA Arrays DF-11
2.6 Application Specific IDA Arrays DF-12
3.0 OPERATIONAL/RETRIEVAL ARRAYS (ORA) DF-16
FIGURES
DF-1 — SCHEMATIC OF "SESOIL" DATA FILE/ARRAY.
OVERALL STRUCTURE DF-4
DF-2 — CLIMATOLOGICAL INPUT DATA ARRAYS (IDA) DF-6
DF-3 — SOIL, CHEMISTRY, GEOMETRIC INPUT DATA ARRAYS (IDA) DF-9
DF-4 — APPLICATION SPECIFIC INPUT DATA ARRAYS (IDA) DF-13
DF-5a~ OPERATIONAL/RETRIEVAL ARRAYS (ORA) DF-17
DF-5b~ OPERATIONAL/RETRIEVAL ARRAYS (ORA) DF-18
Dec. 81 DF-1
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1.0 INTRODUCTION
This appendix is intended to guide users through details of the data
management and the computational procedures of the FORTRAN code of
SESOIL. It will also help model developers (Bonazountas and Wagner) in
the future, since model design and development has not been completed.
SESOIL is operational at various levels as discussed in Section 3.0,
User's Manual. To organize data management and provide a quality
assurance control during operations, the input, output and intermediate
data are stored in data files (arrays).
SESOIL is structured around
(1) An input data file system (IDFS), and
(2) A data management array system (DMAS)
The input data file system (IDFS) contains user input or permanently
stored input data (climatic, soil, chemistry; see appendix ID) required
to operate the model. This input data file system consists of 5 input
data files, the GE DATA, LO DATA, LI DATA, L2 DATA and EXEC DATA.
Detailed information regarding these files is given in section 3.4
(Input Data Files), of section 3.0 (User's Manual) of this documenta-
tion; therefore, it is not discussed in this appendix.
The data management array (DMAS) system contains two major types of
arrays:
(2.1) Input data arrays (IDA) and
(2.2) Operational/Retrieval arrays (ORA)
The input data arrays (IDA) contain the input data relevant to a parti-
cular simulation. These data are read from the input data file system
(IDFS) and are stored in the input data arrays (IDA) by subroutine
RFILE (Read FILE). RFILE can access any of the 5 data files: GE DATA,
EXEC DATA, LO DATA, LI DATA, L2 DATA.
Operational/Retrieval arrays (ORA) contains data or results of inter-
mediate calculations, and/or data for transfer to other subroutines.
These arrays can be accessed (from the FORTRAN code) by a programmer or
user to check on the correctness of intermediate computational steps of
the model. As such, ORA-arrays serve as "control nodes" of the model
code.
A schematic presentation of the SESOIL operations via its data file
system is shown on the next page (Figure DF-1). Most of the DMAS
arrays used in SESOIL and their contents are discussed in the following
sections.
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2.0 INPUT DATA ARRAYS (IDA)
2.1 General
The input data arrays contain the input data required for a particular
simulation. Four major imput data arrays are available: climatologic
soil, chemistry, geometric and application specific arrays. The array
name, and the parameters (in FORTRAN code and their units) in each
space of the arrays are given in the following sections.
2.2 Climatologic IDA Arrays
The climatological input data arrays are schematically presented in the
next page (Figure DF-2) and are descirbed below:
CLIMA1(6) — annual climatic parameters of the region
Each line of the array contains one year of data for the following 6
parameters:
1. Latitude; (L;°N)
2. Average annual soil surface temperature; (T;°C)
3. Average annual fraction of sky covered by clouds; (NN;-)
4. Average annual relative humidity (fractional); (S;-)
5. Average annual shortwave albedo of the surface; (A;-)
6. Average daily evapotranspiration; (REP;cm/day)
CLIMA2(6) — annual storm parameters of the region
Each line contains one year's data of six storm-related parameters of
the region:
1. Mean annual precipitation; (MPA;cm)
2. Mean annual storm duration; (MTRjdays)
3. Mean number of storms per year; (MN;-)
4. Mean length of rainy season within a year (MT;days)
5. Empty space in array (no data)
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6. Empty space in array (no data)
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CLIMA3(12) — monthly storm depths (Oct-Sep)
This array contains one year's data of the monthly distribution of storm
depths (MPMrcm) in the area, starting with the month of October
(hydrologic year).
Note: Information contained in this array is not currently used by the
program (see discussion of CLIMM1 and CLIMM2). The array was built
into the code for a previous model version and is maintained for poten-
tial future use.
CLIMM1(6,12,10) — monthly climatic parameters
Each block 6x12 of the 6x12x10 array contains one year of climatic
parameters of a region. Ten years of data may be stored in total
(IYR=1,10).
Each line of the 6x10 block contains 12 values of a particular para-
meter for the 12 months of the hydrologic year (Oct-Sep;IMO=l,12).
These parameters are:
CLIMM1U.1 ,IYR): (L;°N)
CLIMM1(2,IMO,IYR): surface temperature; (T;°C)
CLIMM1(3,IMO,IYR): fraction of sky covered by clouds; (NN;-)
CLIMM1(4,IMO,IYR): relative humidity (fractional); (S;-)
CLIMM1(5,IMO,IYR): shortwave albedo; (A;-)
CLIMM1(6,IMO,IYR): daily evapotranspiration rate; (REP;cm/day)
CLIMM2(6,12,10) — monthly storm parameters of a region
Each 6x12 block of the 6x12x10 array contains one year of storm-related
parameters of the region. Ten years of data may be stored in total
(1YR=1,10).
Each line contains the values of a particular parameter for the twelve
months of the hydrologic year (Oct-Sep;IMO=1,12). The parameters are:
CLIMM2(1,IMO,IYR): mean monthly precipitation; (MPM;cm)
CLIMM2(2,1MO,IYR): mean storm duration; (MTR;days)
CLIMM2(3,1MO,IYR): number of storms per month; (MN;-)
CLIMM2(4,IMO,IYR): mean length of rainy period within the
month; (MT;days)
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CLIMM2(5,IMO,IYR): empty space in array
CLIMM2(6,IMO,IYR): empty space in array
CLIMM3(12,10) — currently an empty array
2.3 Soil IDA Arrays
The soil input data arrays are schematically presented on the next page
(Figure DF-3). They are:
SOIL1(6) — basic regional soil parameters
This array contains the following six basic soil parameters:
1. Soil density; (RS;g/cm3)
2. Intrinsic average (depth) soil permeability; (Kl;cm2)
3. Soil pore disconnectedness index; (c;-)
4. Effective soil porosity; (N;cm^/cni3)
5. Organic carbon content of the soil; (oc;%), and
6. Carbon content of the soil; (cc;%).
SOIL2(6) — other soil related parameters
This array contains additional soil parameters of site specific
simulations.
1. Soil cation exchange capacity; (CECjm.e./lOOg dry w.t. soil)
2. Intrinsic soil permeability of upper soil layer; (KIU;cm2)
3. Intrinsic soil permeability of middle soil layer; (KIM;cm2)
4. Intrinsic soil permeability of lower soil layer; (KIL:cm2)
5. Empty space for future use
6. Empty space for future use
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2.4 Chemistry IDA Arrays
The chemistry arrays (Figure DF-3) are:
CHEM1(18) — chemical specific parameters
This array contains 14 basic parameters of a compound, and has 4 empty
spaces. These parameters are:
1. Solubility of the compound; (SL;ug/mL or mg/L)
2. Adsorption coefficient of the compound based on organic
carbon; (KOC;(ug/g oc)/(ug/mL))
3. Diffusion coefficient of pollutant in air; (DAjcm^/s)
4. Degradation rate in the upper unsaturated soil zone; (KDE;day~*)
5. Henry's Law Constant of the compound; (H;m3-atm/mol)
6. Overall adsorption coefficient of compound on soil;
(K;(ug/g soil)/(ug/mL))
7. Molecular weight of compound; (MWT;g/mol)
8. Valence of compound; (VAL;-)
9. Neutral hydrolysis constant (KNH;day-1)
10. Base hydrolysis constant (KBH;L/(mol-day))
11. Acid hydrolysis constant (KAH;L/(mol-day))
12. Empty space
13. Stability constant of compound-ligand complex; (SK;-)
14. Number of moles of ligand per mole of compound complexed (B;-)
15. Molecular weight of ligand; (MWTLIG;g/mol)
16. Empty space
17. Empty space
18. Empty space
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NUTK6)— nutrient cycle parameters.
The array can contain up to 6 parameters relating to the nutrient cycle.
This array is presently empty, since the nutrient cycle routine is not
operational
2.5 Geometric IDA Arrays
The geometric array (Figure DF-3) is:
GEOM(20) — application related geometric parameters
The array contains 17 parameters of the application geometry and 3
empty spaces. The number of parameters input depends upon the level
of operation. The 17 parameters are:
1. Area of the compartment for all levels; (AR;cm2)
2. Depth to groundwater for all levels; (Z;m)
3. Depth of the upper soil zone for all levels; (DU;cm)
4. Depth of the middle soil zone for level 3 (DM;cm)
5. Depth of the lower soil zone for all levels; (DL;cm)
6. Ratio of biodegradation, middle/upper soil zone;
(A2KDE;-) for level 3
7. Ratio of organic carbon content, middle/upper soil zone
(A20C;-) for level 3
8. Ratio of clay content, middle/upper soil zone
(A2CC;-) for level 3
9. Ratio of biodegradation, lower/upper soil zone for all levels
(AKDE;-)
10. Ratio of organic carbon content, lower/upper soil zone for all
levels; (AOC;-)
11. Ratio of clay content, lower/upper soil zone for all levels;
(ACC;-)
12. Index of pollutant participation in surface runoff for levels
0 and 1; (ISRA:-)
13. Ratio of concentration of pollutant in rainfall to maximum
solubility for levels 0 and 1; (ASL;-)
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14. Freundich coefficient for levels 2 and 3; (FRN;-)
15. pH in upper soil zone for all levels; (PH;-)
16. Ratio ofpH middle/upper for level 3; (A2PH;-)
17. Ratio ofpH, lower/upper for all levels; (APH;-)
18. Ratio of CEC, middle/upper for level 3; (A2CEC;-)
19. Ratio of CEC, lower/upper for all levels;(ACEC;m-)
20. Empty space
2.6 Application Specific IDA Arrays
The application specific arrays (Figure DF-4) are:
RUNLO(6) — LEVELO parameters
The array contains values of 4 parameters required to run LEVELO. It
also has 2 empty spaces. The 4 parameters are:
1. Soil moisture; (THA;-)
2. Infiltration; (Ifi ;Cm)
3. Groundwater runoff; (RGA;cm)
4. Surface runoff; (RSA;cm)
5. Empty space
6. Empty space
LOAD(6) — LEVELO and LEVELl pollutant loadings to compartment
The array contains 4 loading parameters and 2 empty spaces:
2
1. The total loading in the upper zone; (POLINU;ug/cm )
2. The total loading in the lower zone (POLINL;ug/cm2)
3. The total ligand mass input to the upper zone;
(LIGU;ug/ctn^)
4. The total ligand mass input to the lower zone;
(LIGL;ug/cmO
5. Empty space
6. Empty space
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RUNM1(10,12) -- LEVEL2 and LEVEL3 loading parameters
The array contains values of 7 monthly parameters for above levels of
operation. The columns represent months from October to September.
The content of the lines is:
1. Concentration of pollutant in the upper zone soil moisture; (CUM;ug/mL)
2. Concentration of pollutant in the middle zone soil moisture; (CMM;ug/mL)
3. Concentration of the pollutant in the lower zone soil moisture;
(CLM;Ug/mL)
4. Monthly loading in the upper soil zone; (POLINU;ug/cm )
5. Monthly loading in the middle soil zone; (POLINM;ug/cm2)
2
6. Monthly loading in the lower soil zone (POLINL;ug/cm )
7. Multiplier for pollutant in surface runoff by month; (ISRM;-)
8. Empty spaces
9. Empty spaces
10. Empty spaces
RUNM2(10,12) — LEVEL2 and LEVELS pollutant parameters
The array contains 7 monthly pollutant parameters for above levels.
The columns represent the months, from October to September. The lines
contain:
1. Concentration of pollutant as fraction of solubility in the
rainfall; (ASL;ug/mL)
2. Rate of pollutant transformation in the upper zone; (TRANSU;ug/cm )
3. Rate of pollutant transformation in the middle zone; (TRANSMjug/cm2)
4. Rate of pollutant transformation in the lower zone; (TRANSLjug/cm^)
5. Pollutant loss (by processes of source/sink)
in the upper zone (SINKU;ug/cm2)
6. Pollutant loss (by processes of source/sink)
in the middle zone (SINKM;ug/cm2)
7. Pollutant loss (by processes of source/sink)
in the lower zone (SINKL;ug/cm2)
8. Ligand mass input to the upper zone; (LlGU;ug/cm2)
DF-14
Arthur D Little, Inc
-------
9. Ligand mass input to middle zone; (LIGM,ug/cm2)
10. Ligand mass input to lower zone; (LIGL;ug/cm^)
TITLES(5,12A4) — titles of the particular simulation
This alphanumeric array contains all titles of a SESOIL.
1. Line 1 contains the regional title
2. Line 2 contains the soil title
3. Line 3 contains the compound title
4. Line 4 contains the nutrient cycle title, and
5. Line 5 contains the application area title
DF-15
Arthur D Little, Inc
-------
3.0 OPERATIONAL/RETRIEVAL ARRAYS (ORA)
The overall use of the operational/retrieval (ORA) arrays has been
discussed in section 1.0 (Figure DF-1). Important operational arrays
are present in the figures on the next page (Figure DF-5a,b). The para-
meters, the symbols in FORTRAN and the units of each array are presented
below.
HYDBAL(13,10) — hydrologic cycle array
This array is used to store and transfer results of the hydrologic cycle
routine. The first 12 lines contain data for the months of the hydro-
logic year (Oct-Sep). The last line contains the total or the average
over the year. The columns contain:
1. Moisture content; (THA; fractional)
2. Monthly precipitation; (MPM;cm)
3. Monthly infiltration; (IM;cm)
4. Monthly evapotranspiration; (REP;cm/day)
5. Monthly surface runoff; (RSM;cm)
6. Monthly groundwater recharge; (RGM;cm)
7. Convergence function; (GZ;-)
8. Empty spaces
9. Empty spaces
10. Empty spaces
PINP(13,6) — pollutant input parameters array
This array is used to store the pollutant input masses calculated for
each month of the monthly simulations (levels 2 and 3). The first 12
lines contain data for the months of the hydrologic year (Oct-Sep). The
last line contains the total inputs for the year. The columns contain:
1. Pollutant input mass via rainfall; (PINFU;ug/cm2)
2. Pollutant mass input directly to the upper zone; (POLINUjug/cm^)
3. Pollutant mass input directly to the lower zone; (POLINL;ug/cni2)
4. Pollutant mass input directly to the middle zone; (POLINM;ug/cm2)
5. Empty (spaces)
6. Total pollutant input mass for soil column; (PINjug/cm^)
DF-16
Arthur D Little, Inc
-------
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-------
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(oRX\)
-------
PCONC(13,15) — pollutant concentrations array
This array is used to store the pollutant concentrations in the various
media (air, soil, soil moisture) for each month of the monthly simula-
tion (levels 2 and 3). The first 12 lines contain data for the months of
the hydrologic year (Oct-Sep). The last line contains the total inputs
for the year. The columns contain:
1. Pollutant concentration in the upper zone soil moisture; (CUM;ug/mL)
2. Pollutant concentration in the middle zone soil moisture; (CMM;ug/mL)
3. Pollutant concentration in the lower zone soil moisture; (CLM;ug/mL)
4. Pollutant concentration on the soil in the upper zone; (SUM;ug/g)
5. Pollutant concentration on the soil in the middle zone; (SMM;ug/g)
6. Pollutant concentration on the soil in the lower zone (SLM;ug/g)
7. Pollutant concentration in the soil air of the upper soil zone;
(CUSA;ug/mL)
8. Pollutant concentration in the soil air of the middle soil zona;
(CMSA;ug/mL)
9. Pollutant concentration in the soil air of the lower soil zone;
(CLSA;ug/mL)
10. Free Ligand concentration in the soil moisture of the upper zone-
(LIGCUF;ug/mL)
11. Free Ligand concentration in the soil moisture of the middle zone;
(LIGCMF;ug/mL)
12. Free Ligand concentration in the soil moisture of the lower zone;
(LIGCLF;ug/mL)
13. Depth of rainfall''front"; (DPTHjcm)
14. Empty column
15. Empty column
DF-19
Arthur D Little Inc
-------
POLBAL(13,45) — pollutant mass array
This array is used to store the pollutant masses involved in the indivi-
dual fate processes for each month of the monthly simulation for levels 2
and 3. The first 12 lines contain data for the months of the hydrologic
year (Oct-Sep). The last line contains the total or the remaining mass
at the end of the year. The columns contain:
1. Pollutant mass in surface runoff; (PRSMjug)
2. Pollutant mass volatilized from upper zone (PVOLU;ug)
3. Pollutant mass in other sinks from upper zone; (PSINKU;ug)
4. Pollutant mass adsorbed in upper zone (PADSU;ug)
5. Pollutant mass degraded in upper zone (PDEGU;ug)
6. Pollutant mass transformed in upper zone; (PTRANU;ug)
7. Pollutant mass released to groundwater; (PRGM;ug)
8. Pollutant mass in other sinks from lower zone; (PSINKLjug)
9. Pollutant mass adsorbed in lower zone; (PADSL;ug)
10. Pollutant mass degraded in lower zone; (PDEGL;ug)
11. Pollutant mass transformed in lower zone; (PTRANSL;ug)
12. Pollutant mass dissolved in soil moisture in upper zone;
(PMOIU;ug)
13. Pollutant mass dissolved in soil moisture in lower zone;
(PMOILjug)
14. Empty space
15. Empty space
16. Pollutant mass cation exchanged in upper zone; (PCECU;ug)
17. Pollutant mass cation exchanged in lower zone; (PCECL;ug)
18. Pollutant mass hydrolyzed from moisture in upper zone; (PIlYDMUjug)
19. Pollutant mass hydrolyzed fron moisture in lower zone; (PHYDML;ug)
20. Pollutant mass complexed in upper zone; (PCOMU;ug)
DF-20
Arthur D Little, Inc
-------
21. Pollutant mass complexed in middle zone; (PCOMLjug)
22. Pollutant mass in other sinks in middle zone; (PSINKM^ig)
23. Pollutant mass adsorbed in middle zone; (PADSMjug)
24. Pollutant mass degraded in middle zone; (PDEGMjug)
25. Pollutant mass transformed in middle zone; (PTRANM;ug)
26. Pollutant mass in moisture of middle zone; (PMOIMjug)
27. Empty space
28. Pollutant mass cation exchanged in middle zone; (PCECMjug)
29. Pollutant mass hydrolyzed from moisture in middle zone; (PHYDMM;ug)
30. Pollutant mass complexed in middle zone; (PCOMMjug)
31. Pollutant mass volatilized from middle zone; (PVOLM;ug)
32. Pollutant mass volatilized from lower zone; (PVOLLjug)
33. Pollutant mass hydrolyzed from upper soil layer; (PHYDSUjug)
34. Pollutant mass hydrolyzed from middle soil layer; (PHYDSM;ug)
35. Pollutant mass hydrolyzed from lower soil layer; (PHYDSLjug)
36. Pollutant mass hydrolyzed (upper) from cation exchanged
pollutant; (PHYDCU;ug)
37. Pollutant mass hydrolyzed (middle) from cation exchanged
pollutant; (PHYDCM;ug)
38. Pollutant mass hydrolyzed (lower) from cation exchanged
pollutant; (PHYDCLjug)
39. Pollutant mass in soil air of upper layer; (PSAUjug)
40. Pollutant mass in soil air of middle layer; (PSAMjug)
41. Pollutant mass in soil air of lower layer; (PSALjug)
42. Empty space
43 Empty space
44. Empty space
45. Empty space
DF-21
ArthurDLittleJnc
-------
FC - Fortran code
-------
AP - applications
-------
APPENDIX AP
APPLICATION SAMPLES
This section will contain abstracts and executive summaries of applica-
tions discussed in sections 2.0 and 3.0 of this documentation. Eg. see
references Bonazountas et al (1981), Wagner & Bonazountas (1982) in
section 3.0.
A typical data base and typical input/output model results are presented
in the following pages for all levels 0, 1, 2 and 3.
Jan. 82
AP-1
Arthur D Little, Inc
-------
i:l
****** LLVtLO SESOIL MOiJEL OPERATION «*•>***
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-------
YEA* - I ANNUAL SUMMARY IJEPO-.M
fJTAL lNPUrj> (UGI --
SOIL fJIt-
. 1JOE+J*
- r«YU.<.)i.Ur,IC CYCLE CUMPONtNTj --
X) 2'j.(J
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TOT ALYI^LJit'l) ftl.7
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101 AL JtHt.-< I-
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i3Aoc PJcLuT«NT
?
MJl 5Tu-< (UGSG) --
J.JO
-------
========
MONTHLY INCUT PAKAriETLHS
OCT
NOV
JAN
FE.J
MAR
AP4
MAY
JUM
JUL
AUG
SEP
-- CLIMATIC PA^AMETCHS --
LAI 1 TUOtC DLO)
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=s=rs===
MIHTHLY RbSULTM OUTPUT)
-- H Y i>.«0l_ 0 GIC CYCLE tUMPONErfTj --
OCT NOV OtC JAN FtB l>
GOIi_ M(JIaTUI . Mj 2
r 1 _ L U ( £ 4 ) 0.14 j.14 j.14 'j.14 j.14 -j
WAT 1J PA/ 1PA( ji ) 1.00 1.0'J l.OJ l.OJ 1.00 I
<*« APH MAV JUN JUL AUG SEP
3-8 25. B 25. U 2b.M 2i«. 8 2fi.8 £t>.8
.14 t.14 a. 14 t».l4 :>.14 !j.!4
•00 1.00 1.00 1.00 1.00 l.OJ 1.00
-- i'JLLJfANT MASS INPUT TO COLUMN (UG) --"
OTrie.4luP>> .
UCT
0
0
0
NOV
.0
.V
.0
DEC
.0
.0
.0
JAN
.0
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FL6
.0
.0
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MAR
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.0
APR
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.0
.C
MAV
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JUL
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5
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TOTAL !Nr>uT
.0
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-- r'OLL'JlANT C>)l4CtNTHAI IUI4i (UJ/MLI OH (Uli/C) --
MOI -i
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, ,^ •7d'J .021 .062 .'jO'i .45'j .412 .374 .341 .312 .206 .263
3<.3c-v,l .2oVC-Ul .24-jE-Ol .210E-01 .1'JIE-OI .1-J7E-OI .I36E-01 .1I4E-01 .IOSE-OI .V24E-02 .61tlf02
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-------
YEAR - 2 ANNUAL SUMMARY PEPOST
==================================
-- TJTAL INPUTi (UG) --
SUIL
LJ.Er,' SOIL
-- •i»L»-;ui.'j'Jic CYCLE
AVfi^AOC -JJIL •'IJI5TUH£( X) 25.3
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YEAH-
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OUlu MOliTUHEt X)
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OCT
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5^32
2.72
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1.03
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DEC
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2*94
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-------
RE - references
-------
APPENDIX RE*
REFERENCES
Adams, R.T. ; Jurisu, P.M. Simulation of pesticide movement on small
agricultural watersheds. Report No. EPA-600/3-76-006. Athens, GA:
U.S. Environmental Protection Agency Research Laboratory; 1976. Avail-
able from: NTIS, Springfield, VA; PB 259 933.
Benjamin, J.R.; Cornell, C.A. Probability, statistics, and decision for
civil engineers. New York, NY: McGraw-Hill; 1970.
Biggar, J.W.; Nielsen, D.R. Miscible displacement: I. Behavior of
tracers. Soil Sci. Soc. Amer. Proc. 26:125-128; 1962.
Bode, L.E.; Day, C.L.; Gebbart, M.R.; Goering, C.E. Prediction of
trifluralin diffusion coefficients. Weed Sci. 21(5):485-489; 1973.
Crawford, N.H.; Donigian, A.S., Jr. Pesticide transport and runoff
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Davidson, J.M.; Brusewitz, G.H.; Baker, D.R.; Wood, A.L. Use of soil
parameters for describing pesticide movement through soils. Report No.
EPA R-800364. Washington, DC: U.S. Environmental Protection Agency;
1974.
Day, P.R.; Forsythe, W.M. Hydrodynamic dispersion of solute in the soil
moisture stream. Soil Sci. Soc. Amer. Proc. 21:477-480; 1958.
Donigian, A.S., Jr.; et_ a_l. Agricultural Runoff Management (ARM) model
version II. Report No. EPA-600/3-77-098. Athens, GA: U.S. Environ-
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Donigian, A.S., Jr.; Crawford, N.H. Modeling pesticides and nutrients
on agricultural lands. Report No. EPA-600/2-7-76-043. Athens, GA: U.S.
Environmental Protection Agency Research Laboratory; 1976.
Eagleson, P.S. Dynamics of flood frequency. Water Resour. Res.
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Eagleson, P.S. Climate, soil, and the water balance, a framework for
their analytical coupling. Cambridge, MA: Massachusetts Institute of
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Eagleson, P.S. Climate, soil, and vegetation, 1, introduction to water
balance dynamics. Water Resour. Res. 14(5):705-712, Paper 8W0184; 1978.
*
References mainly not contained in the various Appendices.
RE-1
Arthur D Little Inc
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Eagleson, P..S. Climate, soil, and vegetation, 2, the distribution of
annual precipitation derived from observed storm sequences. Water
Resour. Res. 14(5):713-721, Paper 8W0185; 1978.
Eagleson, P.S. Climate, soil, and vegetation, 3, a simplified model of
soil moisture movement in the liquid phase. Water Resour. Res.
14(5):-722-730, Paper 8W0186; 1978.
Eagleson, P.S. Climate, soil, and vegetation, 4, the expected value of
annual evapotranspiration. Water Resour. Res. 14(5):731-740, Paper
8W0188; 1978.
Eagleson, P.S. Climate, soil, and vegetation, 6, dynamics of the annual
water balance. Water Resour. Res. 14(5):749-764, Paper 8W0207; 1978.
Eagleson, P.S. Climate, soil, and vegetation, 7, a derived distribution
of annual water yield. Water Resour. Res. 14(5):765, Paper 8W0189;'1978.
Eagleson, P.S. The annual water balance. J. Boston Soc. Civil
Engineers, Spring issue; 1979.
Eagleson, P.S. The annual water balance. J. ASCE. HY8(105):923-941;
1979.
Eliss, B.C.; Knwzek, B.D. Adsorption reactions of micronutrients in
s.oils. - Mortvedt, J.J.; Giordano, P.M.; Lindsay, W.L. eds. Micro-
nutrients in Agriculture. Madison: Soil Science Society of America: 59-
78; 1972.
Enfield, C.G. Rate of phosphorus sorption by fine Oklahoma 'soils. Soil
Sci. Soc. Amer. Proc. 38:404; 1974.
Fairbridge, R.W.; Finkl, C.S. The encyclopedia of soil science. Part 1.
Pennsylvania, PA: Dowden, Hutchinson and Ross, Inc.; 1979.
Farmer, W.J.; Igu'e, K. ; Spencer, W.F. Effect of bulk density on the
diffusion and volatilization of dieldrin from soil. J. Environ. Quality
2:107-109; .1973.
Farmer, W.J.; Igue, K. ; Spencer, W.F.; Martin, J.P. Volatility of
organochlorine insecticides from soil: I. Effect of concentration,
temperature, air flow rate, and vapor pressure. Soil Sci. Soc. Amer.
Pro,c . 36 :_44-3-447 ; 1972.
Foster, G.R. Soil erosion modeling: special considerations for
nonpoint pollution evaluation of field-sized areas. Overcash, M.R. ;
David son,'.J.M.- eds. Environmental impact of nonpoint source pollution.
Ann. Arbor ,• MI:' Ann Arbor Science Publishers, Inc.; 1980.
Foster, G.R.; Huggins, L.; Meyer, L.D. Simulation of overland flow on
short field plots. Water Resour. Res. 4(6) :1179-1187; 1968.
RE-2
Arthur D Little. Inc
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Foster, G.R.; Lane, L.J.; Nowlin, J.D.; Laflen, J.M.; Young,-R.A. A model
to estimate sediment yield from field-sized areas: development of
model. Report No. A-2361. Laxenburg, Austria: International Institute
for Applied Systems Analysis; 1980.
Foster, G.R.; Meyer, L.D. Mathematical simulation of'upland erosion
using fundamental erosion mechanics. Presented at Sediment Yield
Workshop, November 1972, Oxford, MS; 1972.
Foster, G.R.; Meyer, L.D. A closed-form soil erosion equation for upland
areas. In: Shen, H.W., ed. Sedimentation symposium to honor Professor
Hans Albert Einstein. Fort Collins, CO: Colorado State University, pp.
12-1 to 12-19; 1972.
Foster, G.R.; Meyer, L.D.; Onstand, C.A. A runoff erosinity factor and
variable slope length exponents for soil loss estimates. Transactions
.ASAE, 20(4):683; 1977.
Foster, G.R.; Meyer, L.D.; Onstand, C.A. An erosion equation derived
from basic equation principles. Transactions of ASAE, 20(4):678; 1977.
Gardner, W.R. Some steady-state solutions of the unsaturated moisture
flow equation with application to evaporation from a water table. Soil
Sci. 85(4):228-232; 1958.
, i»
Hamaker, J.W. Decomposition: quantitative aspects1. Goring, C.A.I;
Hamaker, J.W., eds. Organic chemicals in the soil environment, Vol. I.
New York, NY: Marcel Dekker; 1972.
Hamaker, J.W. Diffusion and volatilization. Goring, C.A.I.-; Hamaker,
J.W., eds. Organic chemicals in the soil environment, Vol. I. New York,
NY: Marcel Dekker, 1972.
Hartley, G.S. Evaporation of pesticides. In: Pesuicidal formulations
research, physical and colloidal chemical aspects, advances in chemistry
series, 86. Washington, DC: American Chemical Society; 1969.
Hoi ton, H.N.; e_t al. Moisutre tension data for selected soils on
experimental watersheds. Report No. ARS 41-144. U.S. Department of
Agriculture. 1968.
Igue, K. ; Fanner, W.J.; Spencer, W.F.; Martin, J.P. Volatility of
organochlorine insecticides from soil: II. Effect of re-lative humidity
and soil water content on dieldrin volatility. Soil Sci. Soc. Amer.
Proc. 36:447-450; 1972.
Jurinak, J.J.; Grenney, W.J.; Woodbridge, G.L.; Riley, J.P.;.Wagenet,
R.J. A model on environmental transport of heavy metals originating from
stack derived particulate emission in semi-arid regions. Logan, UT:
Utah State University; 1977.
RE-3
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Jury, W.A.; Grover, R.; Spencer, W.F.; Farmer, W.J. Predicting vapor
losses of so'il-incorporated triallate. Unpublished, undated'manuscript
received as personal communication from W.J. Farmer,• December 4, 1979.
.Kay., B.O.; Elrick, D.E. Adsorption and movement of lindane in'soils.
Soil Sci. 104:314-322; 1967.
Knisel,' W.G.; Foster, G.R. CREAMS—A system for evaluating best-
management practices. Personal correspondence with G.R. Foster; 1979.
Konrad, J.G.; Chester, G.; Bauer, K. Description and calibration of a
pollutant- loading -model—LANDRUN. Report No. EPA-R005142. Inter-
national Joint Commission, Menomonee River Pilot Watershed Study,
Wisconsin Department of Natural Resources, University of Wisconsin;
1978.
Lindsay, W.L. Inorganic phase equilibria of micronutrients in soils.
Mortvedt, J.J.; Geordano, P.M.; Lindsay, W.L., eds. Micronutrients in
agriculture. Madison: Soil Science Society of America, pp. 41-57; 1972.
Lymah,-• W. ; £t-£l- Research and development methods for estimating
physicochemical properties of organic compounds of environmental con-
cern. Arthur D. Little, Inc., Phase II final report to U.S. Army. To be
published^in 1981 by McGraw-Hill, New York, NY.
Mayer, R.; Letey, J.; Farmer, W.J. Models for predicting volatilization
of .s-oil-incorporated -pesticides. Soil Sci. Soc. Am. Proc. , 38, 563-68;
1974.
Meyer, L.D.; Wischmeier, W.H. Mathematical simulation of a process of
soil-erosion by water. Trans. ASAE 12(6):754-762; 1969.
Moe, P.G, Kinetics of the microbial decomposition of the "herbicides IPC
and CIPC. Environ. Sci. and Technol. 4(50}:429-431; 1970.
Moldenhauer, W.C.; Long, D.C. Influence of rainfall energy on so'il loss
and infiltration particles: I. Effect over a range of texture. Soil
Sci. Soc. Amer. Proc. 28(6) :813-817.
Neibling, W.H.; Foster, G.R. Estimating deposition and sediment yield
from overland flow processes. Proceedings of the international sym-
posium on urban hydrology hydraulics and sediment control; Lexington,
Kentucky; 1977.
Novotny, V. Hydrological and hydraulical conceptual models applicable
to overland and water transport modeling. Madison, WI: University of
Wisconsin, Water Resources Center; 1976.
Novotny, V.; Tran, H. ; Simsiman, G.V.; Chester, G. Mathematical
modeling of land runoff contaminated by phosphorus. J. Water Pollution
Control pp. 101-112; 1978.
RE-4
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On stand, C.A.; Foster,, G..R. Erosion modeling on a watershed. Trans-
actions of the ASAE, 18(2):288; 1975.
Penman, H.L. Natural evaporation from open water, bare soil, and grass.
Proc. Roy. Soc. (London), Ser. A. 193:120-145; 1948.
Perry. J.H. Chemical Engineering Handbook, 4th ed. New York, NY:
McGraw-Hill; 1963.
Philip, J.R. Theory of .infiltration. Chow,.,V.T.., ed. Advances in
hydroscience 5:215-296. New York, NY: Academic P.ress; 1969.
Rifai. M..N.E.; Kaufman, W.J.; Todd, O.K. . Dispersion phenomena in
laminar flow porous media. Sanitary Eng. Res. Lab. and Div. C.E. Report
3. Berkeley, CA: University of California; 1956.
Ryden, J.C.; e_t al. Potential of an eroding urban soil for the
ph'osphorus enrichment of streams. J. Environ. Quality 1(4):430; 1972.
Shearer, R.C.; Letey, J.; Farmer, W.J.; JClute, A. Lindane diffusion in
'soil. Soil Sci. Soc. Amer. Proc. 37(2): 189-193; 1"9737
Smith, J.M. Chemical engineering kineti-cs, 2nd ed. New York, NY:
McGraw-Hill; 1970.
Spencer, W.F.; Claith, M.M.; Farmer, W.J. Vapor density of soil-applied
dieldrin as related to soil-water content, temperature and dieldrin
concentration. Soil Sci. Soc. Amer. Proc. 33:509-511; 1969.
Swann, R.L.; McCall, P.J.; Unger, S.M. Volatility of pesticides from
soil surfaces. Unpublished and undated manuscript received as personal
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Yalin, Y.S. An expression for bed-load transportation. J. Hyd. Div.5
Proc. ASCE 89(HY3):221-250; 1963.
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Ml - miscellaneous
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APPENDIX MI
SYMBOLS & MISCELLANEOUS
The appendix will contain sections such as
1.0 INDEX
2.0 DEFINITIONS
2.1 Soil Moisture Content (see next page)
3.0 NOTATIONS (also presented in each scientific appendix separately)
4.0 FORTRAN/NONFORTRAN VARIABLE CORRESPONDENCE
5.0 LIST OF FIGURES (also presented in each appendix)
6.0 LIST OF TABLES (also presented in each appendix)
7.0 TABLE FOR NUMERICAL CALCULATIONS
8.0 TYPICAL INPUT/OUTPUT (attached)
SM-1
Dec. 81
Arthur D Little Inc.
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2.1 SOIL MOISTURE CONTENT
The soil moisture content (0) is defined as
v /v
w t
inmL/mL = cm /cm
where:
V - V + V +V
t s w a
V =- total volume of soil
matrix (mL)
Vg a volume of solid portion (mL)
V = volume of water (mL)
V « volume of air (mL)
air
•water
w
Like the porosity (n), volumetric moisture content is usually reported
as a decimal fraction or a percent. For saturation flow, 0=n; for
unsaturated flow, 9
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MARCOS BONAZPUNTAS
JANET M. WAGNER
;pr/:B6na'zountas, "a 'Giyil 'and environ mental-.engineer., •
".is:''::a'v.s6nipF;/*nV'erh'ber.'' p.f •• the . "Bio'/Envirp Systems,.
'Section;; of "Arthur D.. Little. Inc.' who specializes in.
rnathem'aticai environmental modeling, -f -. '•'. .
Since", joining Arthur D. Little. Inc., in 1977, Drr
Bohazbuntas has- coordinated modeling teams and has,
developed, applied: and validated models for: soi.ls,
,grpundwater, biology, .water resources.-and air; mul-
ti-media- models for pollutant fate in! the envi-
ronment; estuarine..an^hydrodyn^ with a
,;cdntinupus".,em'phasis.;,on;, both .the physics"and.--_the
'5c'hemis.try^pf^f% 'envirohmehtaT systems; >;and wat^r,:
resources' econqmic and'-:optimization models." , Re-^
.'cent '• models- /deyeloped-. include: -/Ian unsaturated
' spil/biQticzone;model, whiph ^can-be interfaced .with
':any 'num'erical:L;finite difference -'or, finite .. 'element
groundw.ater model; a time series water .resource
model; a civiT engineering 'construction containment
.model for hazardous waste sites;'an oceanic oil;slick
. model;: a--Fiver quality and sedimentation model; an
economic .model''for waste underground'"injection; an
environmental exposure/^ risk, model .-for/-toxic sub-
'stanc.esB' and a-river., basin model' for the Maqarin
Qam. and; the Jordan :River;in Jordan. He. recently
headed ,a multi-media (air, water, soil, biptaj mathe-
'matical effort .whose objective was.to describe, fate.,
'••pathways';;"andlexpiosure.::pi':toxics in -the.environmenti;•
The". :"SES,OIL. "model encompasses his ' le'ngthy ex-'
perienee in ;soii, groundwater and",general,environ-
mental • rnodeling. ".. • ••,-. ,'•' •_• ••• ;';.'.-'•''. .•-;-..'-
Dr. Bonazountas received his engineering degree .in;
civil engineering (1969) from the/National'Technical
Universiiy ;of Athens, "Greece; his doctoral degree in
,:river hydromechanics--'and sediment transportation
'(1973) from the .Technical' University ''of Munich.
Germany; ;and • his diploma in. co.mputer- sciences
(^Ggj.froni .the Data Processing Institute in -Athens,
Greece.:7v He :'undertook-; 'further ; studies1:, at".. the
Massachtisetts" Institute of Technology and: :at Har-
.vard University. "X'He is a 'member of the.^. ASCE,-
AGU, AVV7R"Ai :IAIIR, and':- has ..authored several:
-publications concerning his research. • . .
.Ms. iVagner, a chemist and computer scientist, is a
member of the Analytical and Environmental Chem-
istry Section. Her interests focus on the use of
computers for solving environmental and chemical
problems. '
Since joining Arthur D. Little, Inc. in 1978, Ms.
, Wagner has been, involved-in the application of
numerical and mathematical techniques to the mod-
eling of environmental processes, in the development
.of software packages _for data management, and in
the analysis of several toxic substances in the
.environment. L Recent projects, other than SESOIL,
include design "and implementation of a data
management system for a project involving utility
disposal wastes: which is designed to facilitate data
.entry and storage and to perform further statistical
and numerical analyses on-, subsets of r the data;
: analysis pf chemical properties, laboratory ^studies,
and environmental,"models -'to assess: the ienviron-.
mental fate,: of'some of .the priority; pollutants for.
EPA risk -assessment reports; and; a multi-media
.environm.ental - computer.: modeling' effort,^;encQm-..
. passing" iair,--^ soil^ and. water-body; mddeling/:;,'issues,
such as -'air /quality', river flow #hd quality, and
exposure to humans and biota. Ms. Wagner was a
member on the ADLPIPE/DIS project, where she
.contributed to the'development, implementation, and
quality control of large FORTRAN based software
packages used for - piping system design and pipe
stress analysis. Prior to joining Arthur D. Little.
Inc., 'Ms. JVagner participated in the design and
implementation of computer models in the areas of
quantum chemistry and chemical kinetics. :
In her computer applications, Ms. Wagner has em-
ployed the^computer languages of FORTRAN, APL;
BASIC, ALGOL and COBOL; has'.worked on IBM,
VAX, CpC^&NrvAif,:,.and...Data Generalvsysyms;. and;
has developed:- and .wprked, -with computer gVaphics-
packages^.-^f^ '-:' \"-: • '-•-''.,' :'..•'•~':'.-- '•';'.':;V' - . •
Ms. Wagner'received' her ;vB.A. iri •'rChenfistr.y and
Computer Sciences (1980) -from Williams 'College,
Massachusetts. '•' • ."•• . . ...
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