United States
            Environmental Protection
            Agency
             Office of Research and
             Development
             Washington, DC 20460
EPA/600/R-93/184
March 1994
vvEPA
Evaluation of
Unsaturated/Vadose
Zone Models for
Superfund Sites

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                                              EPA/600/R-93/184
                                              March 1994
        EVALUATION OF UNSATURATED/VADOSE ZONE
              MODELS FOR SUPERFUND SITES
                            by
           D. L. Nofziger, Jin-Song Chen, and C. T. Haan
            Oklahoma Agricultural Experiment Station
                   Oklahoma State University
                   Stillwater, Oklahoma 74078
                         CR-818709
                       Project Officer

                     Joseph R. Williams
           Extramural Activities and Assistance Division
         Robert S. Kerr Environmental Research Laboratory
                     Ada, Oklahoma 74820
ROBERT S. KERR ENVIRONMENTAL RESEARCH LABORATORY
        OFFICE OF RESEARCH AND DEVELOPMENT
        U.S. ENVIRONMENTAL PROTECTION AGENCY
                  ADA, OKLAHOMA 74820
                                       ^g> Printed on Recycled Paper

             U S. Environmo:f"! ^otection Agency
             Region 5, Lfrr.    :.-12J)
             77 West Jack;-./. ..o'jlevard, 12th Floor
             Chicago, IL  60604-3590

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                                             DISCLAIMER NOTICE
           The information in this document has been funded wholly or hi part by the United States Environmental
        Protection Agency under cooperative agreement # CR-818709 with the Oklahoma Agricultural Experiment
        Station, Oklahoma State University, Stillwater, Oklahoma.  It has been subjected to the Agency's peer and
        administrative review, and it has been approved for publication as an EPA document. Mention of trade
        names or commercial products does not constitute endorsement or recommendation for use.

           All research projects making conclusions or recommendations based on environmentally related
        measurements and funded by the Environmental Protection Agency are required to participate in the Agency
        Quality Assurance Program. This project did not involve environmentally related measurements and did not
        involve a Quality Assurance Project Plan.
Margins  for  all numbered pages:

 -  J"  foot
 -center  PAGE NUMBER  side to side.

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                                            FOREWORD

    EPA is charged by Congress to protect the Nation's land, air, and water systems. Under a mandate of
national environmental laws focused on air and water quality, solid waste management and the control of
toxic substances, pesticides, noise and radiation, the Agency strives to formulate and implement actions which
lead to a compatible balance between human activities and the ability of natural systems to support and
nurture life.

    The Robert S. Kerr Environmental Research Laboratory is the Agency's center of expertise for
investigation of the soil and subsurface environment.  Personnel at the laboratory are responsible for
management of research programs to: (a) determine the fate, transport and transformation rates of
pollutants in the soil, unsaturated and the saturated zones of the subsurface environment; (b) define the
processes to be used in characterizing the soil and subsurface environment as a receptor of pollutants; (c)
develop techniques for predicting the effect of pollutants on ground water, soil and indigenous organisms;
and (d) define and demonstrate the applicability and limitations of using natural  processes, indigenous to the
soil and subsurface environment, for the protection of this resource.

    Mathematical  models are useful tools for evaluating potential remediation treatments. However, models
require users to specify various parameters characteristic of the site and chemical of interest.  These
parameters are not known without error. Many parameters vary over time and space in manners which  are
unknown. This is  especially true when models  are used to predict future events.  This uncertainty in input
parameters is associated with an uncertainty in model output which should be recognized by the model user.
This research analyzes several transport  models for unsaturated soils and quantifies the sensitivity and
uncertainty of model outputs to changes in input parameters. This information will help users  understand
the importance of different parameters, identify parameters which must be determined at the site, interpret
model results and  apply their findings to specific problems.
                                                              Clinton W. Hall
                                                              Director
                                                              Robert S. Kerr Environmental
                                                              Research Laboratory

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                                             ABSTRACT

    Mathematical models of water and chemical movement in soils are being used as decision aids for
defining ground water protection practices for superfund sites. Numerous transport  models exist for
predicting movement and degradation of hazardous chemicals through soils.  Many of these require extensive
input parameters which include uncertainty due to soil variability and unknown future weather.  The impact
of uncertain model parameters upon the model output is not known.  Model users need an understanding of
this impact so they can measure the appropriate parameters for the site and incorporate the uncertainty in
the model predictions into their decisions. This report summarizes research findings which address the
sensitivity and uncertainty of model output due to uncertain input parameters.

    The objective of the research was to determine the sensitivity and uncertainty of travel tune,
concentration, mass loading and pulse width of contaminants at  the water table.  The four models selected
for this analysis were RITZ, VIP, CMLS and HYDRUS.  All of the models are designed  to estimate
movement of solutes through unsaturated soils.  The  models span a considerable range in detail and intended
use.  This report  presents information on the sensitivity of these models to changes and uncertainties in input
parameters. It does not intend to assess the appropriateness of any model for a particular use nor
uncertainty due to the model chosen.

    Model parameters investigated include soil properties such as organic carbon content, bulk density, water
content, hydraulic conductivity. Chemical properties  examined include organic carbon partition coefficient
and degradation half-life. Site characteristics such as rooting depth, recharge rate, weather,
evapotranspiration and runoff were examined when possible in the models.  Model sensitivity was quantified
in the form of sensitivity and relative sensitivity coefficients.  The sensitivity coefficient is useful when
calculating the  absolute change in output due to  a known change in a single parameter. Relative sensitivity is
useful for determining the relative change in an output corresponding to a specified  relative change in one
input parameter.  Relative sensitivity can also be used to compare the sensitivity of different parameters.
Results are presented in graphical and tabular forms.

    The study found that large uncertainty exists in many model outputs due to the  combination of sensitivity
and high parameter variability.  The study found that predicted movement of contaminants was greater when
the natural variability of rainfall was incorporated into the model than when only average fluxes were used.
This is because major rainstorms  that result in large fluxes of water and high leaching are essentially ignored
when average flux values are used. The study reaffirms that uncertainty is pervasive in natural systems and
that results of modeling efforts presented in a deterministic fashion may be misleading. Rather than
presenting absolute predictions of solute movement, results of model  studies should  present the  probabilities
of various outcomes.

    This report evaluates model sensitivity for a  specific scenario. There is abundant evidence that the
sensitivity and uncertainty are highly dependent on the scenario  being modeled and the parameters used.
Therefore these results will not serve to define sensitivity for the general model user. That need can only be
met by incorporating algorithms into each computer code to enable the user to obtain these sensitivity and
uncertainty estimates for the specific conditions and parameters of interest.

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                                              SYMBOLS
b       Clapp-Hornberger constant
CV     coefficient of variation
Ca      concentration of contaminant in air
C0      concentration of contaminant in oil
Cg      concentration of contaminant adsorbed on soil phase
C^     concentration of contaminant in water
cov(x)  (k x k) covariance matrix of the input parameters
cov(v)  (n x n) covariance matrix of model outputs
var(x')  (k x 1) vector of variances of parameters
D^    effective diffusion-dispersion coefficient of the solute in water
DM     effective diffusion-dispersion coefficient of the solute in air
d       soil depth
f       model output
f(mx)   (n x 1) vector of model outputs where the model is evaluated at jnx
h       soil-water pressure head
lig      osmotic head
hjQ     pressure head at which transpiration is reduced by 50%
K      unsaturated hydraulic conductivity function
Kd     partition coefficient between the solid phase and the water phase
KQJ.     organic carbon partition coefficient
Kj      saturated hydraulic conductivity
Kaw   linear partition coefficients between the  a phase (air, soil, or oil) and the water, w, phase
k       number of model input parameters in uncertainty analysis
L      distance
m      empirical constant, m = 1 - l/£
jn      (n x 1) vector of mean model outputs
jnx     (k x 1) vector of mean parameter values
n       number of model outputs
OC     organic carbon content
PET   potential evapotranspiration
Q      sink or source term
p       power constant in stress response function
q,      flux of air
q       steady-state flux of water
qw     flux of water
R      retardation factor
rw,ra,r0 sink/source terms for contaminant uptake, decay, and production in water, air and oil
S       model sensitivity
j>       (n x k) matrix of sensitivity coefficients of model outputs to input parameters
Sr      relative sensitivity
T      travel time
t       time
v       pore water velocity
v       pure waici vciutuy
x       model input parameter in the matrix x
x       (k x 1) vector of model parameters
z       position coordinate

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                                        SYMBOLS (continued)
a       van Genuchten (shape) parameter
ft       van Genuchten (shape) parameter
Ha      degradation rate constant for the contaminant in a phase (water, soil, air, or oil)
I       pore-connectivity factor
^       porosity
p       soil bulk density
a       stress-response function
6a      volume fraction of air in the soil
6, 6W   water content of soil on a volume basis
6S      saturated water content
6r      residual water content
60      volume fraction of oil in the soil
f       normalized root  uptake distribution function

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                                   CONTENTS

Disclaimer	  ii

Foreword	  iii

Abstract	  iv

Symbols	  v


   1. INTRODUCTION	  1
   2. MODEL DESCRIPTIONS	  2
   3. SENSITIVITY AND UNCERTAINTY	  12
   4. PHYSICAL SETTING	  21
   5. SENSITIVITY RESULTS FOR RITZ MODEL	  23
   6. SENSITIVITY RESULTS FOR VIP MODEL 	  92
   7. SENSITIVITY RESULTS FOR CMLS MODEL  	   101
   8. SENSITIVITY RESULTS FOR HYDRUS MODEL	   125
   9. UNCERTAINTY ANALYSIS	   172

References	   184

Appendix	   187
                                       vii

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                                             SECTION 1

                                          INTRODUCTION

    Mathematical models of water and chemical movement in soils are being used as decision aids for
defining remediation practices for Superfund sites. Numerous transport models exist for predicting
movement and degradation of hazardous chemicals through soils.  Many of these require extensive input
parameters which are often not measured and which include uncertainty due to inherent soil variability at the
site and due to unknown future weather patterns. Little information exists on impact of uncertain input data
on outputs from these models.  Model users want guidelines for the selection and use of models under these
conditions. This  report summarizes research findings which address these issues of uncertainty.

    One objective of this research was to determine the sensitivity of several transport model outputs to
changes in values of input parameters required by the models. Sensitivity as used here refers to the change
in model output resulting from a specified change in an input parameter.  We can observe the sensitivity of
an output by examining differences in graphs of the model outputs for different inputs in the expected range.
If differences in output are large, we conclude the output is sensitive to these changes in inputs.  If
differences in output are small, we conclude the output is not sensitive to these changes in inputs.
Quantitative definitions of sensitivity are given later in this report.

    In order  to use models in making decisions about remediation practices appropriate for Superfund sites,
the model must predict the future behavior of the contaminant. The use of models in a predictive manner
introduces added uncertainty.  For example, chemical leaching depends upon water movement through the
unsaturated soil.  This water movement is dependent upon the amount and distribution of water entering the
soil and hence upon future weather.  Since we do not know future weather, there is an uncertainty in  that
model input.  As  a result, there is an uncertainty in the model output.  Natural variability of the  soil
parameters within the area of interest is another source of input parameter uncertainty. The second part of
this report computes the uncertainty in model  outputs due to uncertainty in one or more model inputs. This
uncertainty can be incorporated into decisions  utilizing model predictions.

    The sensitivity of a particular output to changes in model inputs depends upon the entire set of
parameters used in the model and upon the total system being analyzed. The general scenario modeled in
this study was that of a site containing an initial contaminant layer near the soil surface. The thickness of
that layer is known. None of the contaminant  is present below this layer. No more contaminant enters the
soil profile during the simulation period.  Model outputs of interest include (1)  the time at which the
contaminant reaches the water table, (2) the amount of contaminant entering the saturated zone, (3) the
width of the contaminant pulse at the water table, and (4) the concentration of the contaminant entering the
ground water.

    This report presents results for four models. The models differ substantially in their intended  use,
assumptions and processes included, input data requirements, computer requirements, and  ease of use.
Model selection is a critical step in model use. Each of these models is appropriate for certain uses.  None
of them are appropriate for all uses.  Results of the sensitivity and uncertainty analyses are presented  for the
models. It is not  our intent to compare the predictive ability of the models. The cited references for  each
model should be consulted for detail on the formulation of the various models.

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                                            SECTION 2

                                     MODEL DESCRIPTIONS

    The four models selected for this analysis are RITZ, VIP, CMLS, and HYDRUS.  Overviews of the
models are presented in Tables 2.1 to 2.4. RITZ, VIP, and CMLS were written as management tools.
HYDRUS is better suited for detailed research use by scientists. All four models include sorption of the
contaminant by soil and advection or movement of the contaminant with water.  RITZ and VIP include
sorption on an immobile oil phase as well as a vapor transport component.  RITZ and VIP assume uniform
soil properties and steady water flow.  CMLS and HYDRUS can be used in layered soils and unsteady,
unsaturated water flow. HYDRUS includes hydrodynamic dispersion. This section presents the common
general governing equations which form the framework for the models. The models are then described
along with assumptions inherent in them.

    RITZ and VIP were developed for use at waste disposal  sites where oil can be  mixed with the
contaminant and where movement of the contaminant in the  vapor phase may be significant.  If we assume
the flow and transport processes are one dimensional and the oil phase is immobile, the governing transport
equation in unsaturated soil is given by


                             5Q,      8C&      8C0      3C.
                          ew-2L + p—L  +  *0_2  + 0a_!  ,
                              at       dt       dt        dt          oz.                      (
                                    a2ca      aQ      dc.
                                    - T    w~—    a—
                                     8z2       dz       8z
                                                                      ro
where Cw is the concentration of contaminant in water, Ca is the concentration of contaminant in air, C0 is
the concentration of contaminant in oil, Cs is the concentration of contaminant adsorbed on soil phase, p is
the soil bulk density,  0W is the water content of the soil on a volume basis, 8a is the volume fraction of air in
the soil, 80 is the volume fraction of oil in the soil, qa is the flux of air,  qw is the flux of water, Dew is
effective diffusion-dispersion coefficient of the solute in water, DM is effective diffusion-dispersion coefficient
of the solute in air, and T^ ra, r0 represent sink/source terms for contaminant uptake, decay, and production
in water, air and oil, respectively. In equation 1, z is the position coordinate and t is time.  Partitioning of
the contaminant between the phases is approximated by the equation
                                                                                               (2)
where Ka w is the linear partition coefficients between the a phase (air, soil, or oil) and the water phase.
First-order degradation of the chemical is generally assumed in each phase so



                                           £  - ->"c«

where na is the degradation rate constant for the contaminant in a phase (water, soil, air, or oil).  Physical
constraints imply the sum of the volume fractions of air, water, and oil must equal the porosity of the soil, 4>,
or

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Table 2.1. Characteristics of the Regulatory and Investigative Treatment Zone (RITZ) model
    (Nofziger, Williams, and Short, 1988).               	

    Intended Use:
        Estimate movement and fate of hazardous chemicals during land treatment of oily wastes

    Processes Included:
        Mass flow of chemical with soil water
        Linear reversible sorption of chemical on soil and oil
        Partitioning of chemical to vapor and diffusion from soil
        Degradation of hazardous chemical and oil

    Data Requirements:
        Soil Properties (Assumed constant with depth)
            Organic carbon content
            Bulk density
            Saturated water content
            Saturated hydraulic conductivity
            Clapp - Hornberger constant (water characteristic parameter)
        Site Characteristics
            Plow zone and Treatment zone depths
            Recharge rate (Assumed constant over time)
            Evaporation rate (Assumed constant over time)
            Air  temperature (Assumed constant over time)
            Relative humidity (Assumed constant over time)
            Sludge application rate
            Concentration of pollutant in sludge
            Diffusion coefficient of water vapor in air
        Pollutant Properties
            Organic carbon partition coefficient
            Oil-water partition coefficient
            Henry's  law constant
            Diffusion coefficient in air
            Degradation half-life (Assumed constant with depth and time)
        Properties of Oil
            Concentration of oil in sludge
            Density of oil
            Degradation half-life of oil

    Model Outputs:
        Fraction of pollutant degraded, leached, and volatilized
        Flux density  and total mass of pollutant lost to atmosphere
        Flux density  and total mass of pollutant leached
        Location of pollutant as a function of time
        Concentration  of pollutant in liquid, solid, vapor, and oil phases as functions of time
        Concentration  of oil as a function of time

    Computer Requirements:
        DOS-based computer with math coprocessor. The model requires only a few seconds to simulate
        the movement  and  degradation of the chemical through the plow zone and treatment zone.

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Table 2.2. Characteristics of the Vadose Zone Interactive Processes (VIP) model
    (Stevens, Grenney, and Yan, 1989).
    Intended Use:
        Evaluate the fate of a hazardous substance in the unsaturated zone of the soil for land treatment of
        oily wastes

    Processes Included:
        Transport of the contaminant by advection with soil water
        Transport of the contaminant by advection and dispersion in the air phase (Note: advection was not
            implemented in the source code)
        Transport of the oxygen (diffusion only) in the  air
        Linear reversible sorption of chemical on soil and oil
        Partitioning of the  contaminant between air, oil, soil, and water
        Partitioning of oxygen between air, oil, and water
        Oxygen-limited degradation in air, water, oil, and soil

    Data Requirements:
        Soil Properties
            Soil porosity
            Bulk density
            Saturated hydraulic conductivity
            Clapp and Hornberger constant

        Site Characteristics
            Plow zone depth
            Treatment zone depth
            Mean daily recharge rate during each month
            Temperature during each month in plow zone
            Temperature during each month in treatment zone
            Temperature correction coefficient for  each month of the year
            Sludge application rate
            Pollutant concentration in the sludge
            Weight fraction of oil in waste
            Weight fraction of water in sludge
            Density of sludge
            Application period
            Application frequency within application period

        Pollutant Properties
            Oil-water partition coefficient for plow zone and lower treatment zone
            Air-water partition coefficient for plow zone and lower treatment zone
            Soil-water partition coefficient for plow zone and lower treatment zone
            Degradation constant in oil for plow zone  and lower treatment zone
            Degradation constant in water for plow zone and lower treatment zone
            Dispersion coefficient in unsaturated pore  space
            Adsorption/desorption rate constant between water and soil
            Adsorption/desorption rate constant between water and oil
            Adsorption/desorption rate constant between water and air	

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Table 2.2. Continued.
    Data Requirements (Continued)

        Oxygen Properties
            Oil-air partition coefficient for plow zone and lower treatment zone
            Water-air partition coefficient for plow zone and lower treatment zone
            Oxygen half-saturation constant with respect to the oil degradation
            Oxygen half-saturation constant in air phase in the plow zone
            Oxygen half-saturation constant in air phase in the treatment zone
            Oxygen half-saturation constant in oil phase in the plow zone
            Oxygen half-saturation constant in oil phase in the treatment zone
            Oxygen half-saturation constant in water phase in the plow zone
            Oxygen half-saturation constant in the water phase in treatment zone
            Stoichiometric ratio of the oxygen to the pollutant consumed
            Stoichiometric ratio of the oxygen to the oil consumed
            Oxygen transfer rate coefficient between the oil and air phases
            Oxygen transfer rate coefficient between the water and air phases

        Properties of Oil
            Density of oil
            Degradation rate constant of oil

    Model Outputs:
        Concentration of pollutant in air, water, oil, and soil as function  of depth and time
        Concentration of oxygen in air, water, oil, and soil as function of depth and time
        Concentration of oil in air, water,  and soil as function of depth and time
        Amount of pollutant remaining in the plow zone and treatment zone
        Amount of pollutant leached below treatment zone
        Fraction of pollutant in air, water, oil, and soil phases
        Fraction of pollutant in plow zone and treatment zone

    Computer Requirements:
        DOS-based computer.  The model requires a few seconds to simulate 10 years of movement and
        degradation.

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Table 23. Characteristics of Chemical Movement in Layered Soils (CMLS) model
    (Nofziger and Hornsby, 1986, 1988)	

    Intended Use:
        Estimate the movement and degradation of pesticides through unsaturated soils; Serve as a
        management tool for managing soil applied chemicals.

    Processes Included:
        Mass flow of chemical with soil water
        Sorption of chemical on soil
        Degradation of chemical

    Data Requirements:

        Soil Properties (required for each soil layer)
            Depth of bottom of soil layer
            Organic carbon  content
            Bulk density
            Saturated water content
            Water content at "field capacity"
            Water content at "permanent wilting point"

        Site Characteristics
            Daily infiltration (can be estimated in model from daily weather, supplemental irrigation, and
                SCS curve number)
            Daily evapotranspiration (can be estimated in model from daily weather or pan evaporation)

        Chemical Properties
            Organic carbon  partition coefficient (or actual partition coefficient for each soil layer)
            Degradation half-life for each soil layer
            Amount of chemical applied
            Depth of chemical at application
            Date of chemical application

    Model Outputs:
        Depth of center of mass of chemical as  a function of time
        Amount of chemical in the soil profile as a function of time
        Amount of chemical passing specified depth as function of time
        Travel time of chemical to specified depth
        Probability of exceeding different depths at a specified time
        Probability of exceeding different amounts passing specified depth

    Computer Requirements:
        DOS or UNIX based  computer. Movement and degradation are calculated on a daily time step to
        accommodate dynamic changes in infiltration and evapotranspiration. A single simulation requires
        approximately one second per year on a 80386/387 DOS-based computer.  Computational time may
        increase to several hours when using Monte Carlo techniques and making hundreds of simulations.

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Table 2.4. Characteristics of the HYDRUS model (Kool and van Genuchten. 1991).	

    Intended Use:
        To simulate the movement of water and dissolved solutes in one-dimensional variably saturated and
        layered porous media

    Processes Included:
        Transient, unsaturated water flow with hysteresis in the soil hydraulic properties
        Root water uptake
        Transport of chemical by advection, molecular diffusion and hydrodynamic dispersion
        Linear or non-linear reversible sorption
        First-order degradation

    Data Requirements:
        Soil Properties (for each soil layer)
            Depth of soil layers
            Saturated water content
            Saturated hydraulic conductivity
            Bulk density
            Retention parameters for main water desorption and wetting curves
            Residual water content

    Site Characteristics
        Uniform or step-wise rainfall intensity

    Pollutant Properties (for each soil layer)
        Molecular diffusion coefficient
        Dispersivity
        Decay coefficient for dissolved phase
        Decay coefficient for adsorbed phase
        Freundlich isotherm coefficients

    Root Water Uptake Parameters:
        Power constant in stress-response function
        Pressure head at which transpiration is reduced by 50%
        Root density as a function of depth

    Model Outputs:
        Water content and pressure head distribution with time
        Concentration of chemical as a function of time and depth
        Cumulative infiltration and drainage
        Cumulative root  water uptake from the soil profile
        Cumulative amount of chemical entering the soil profile
        Cumulative amount of chemical leaving the soil profile
        Amount of chemical remaining in the soil

    Computer Requirements:

        DOS-based computer. The numerical solution requires 4 to 24 hours on a 80386/387 based
        computer to simulate transport for ten years.

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    Water flow is described using the equation


                                     ££=  - ±[rf - 1)] - Q                                 (5)
                                      8t     Bz    dz

where K is the unsaturated hydraulic function, h is the water pressure head, and Q is the sink or source
term. Equations 1 to 5 can be used to estimate contaminant fate with advection, dispersion, sorption, root
solute uptake, evaporation, partitioning to oil and vapor phases, degradation, water flow, and
evapotranspiration.  They serve as a general framework for discussing equations used in the RITZ, VIP,
CMLS, and HYDRUS models. The specific governing equation for each model can be derived after
incorporating model-specific assumptions.

RITZ Model:  The conceptual framework of RITZ was developed by Short (1985) and implemented as an
interactive program by Nofriger et al. (1988).  It was created to predict the fate of contaminants mixed with
oily wastes and applied to  land treatment sites. RITZ considers the soil  to be made up of two parts as
shown in Figure 2.1. The  upper region is called the plow zone. The sludge containing contaminant and oil
are mixed uniformly within this depth. Below the plow zone is the treatment zone which contains no oil.
The model simulates movement of the contaminant through both zones.  For this study, the plow zone
represents the portion of soil containing the contaminant at the beginning of the simulation. The bottom of
the treatment zone represents the water table  depth.

    RITZ contains many simplifying assumptions.  (1) Soil properties are assumed to be  uniform throughout
the profile. (2) The flux of water through the soil is assumed to be constant with depth and with time. (3)
Oil is assumed to be immobile so it  does not move out of the plow zone. (4)  Both oil  and contaminant
degrade as first-order processes.  (5) Partitioning of the contaminant between  phases is linear, instantaneous,
and  reversible.  (6) Dispersion in water phase is small and can be ignored.  (7) The soil water content and
unsaturated hydraulic conductivity can be described by  the Clapp and Hornberger equation (1978).

    Assumption 7 above is used to determine  the soil water content, 0^, from the saturated conductivity, K^,
and  the average recharge rate, q, using the equation
                                          0W - t[±]2b * 3                                      (6)


where ^ is the soil porosity or saturated water content and b is the Clapp-Hornberger constant (which
depends on soil properties).  Incorporating these simplifications into equation 1 results in


                              ew—2  +  p_'.  + ee—2  + ea—- =  - q—-                        (7)
                                 dt       dt       dt        dt         dz

Short (1985) derived analytical solutions for the  total concentration in  plow zone, the total concentration in
the treatment zone, the time at which the top and bottom of the solute slug reaches a specific depth, and the
amount lost due to volatilization.

VIP Model: This model was developed by Stevens et al. (1989) to solve the same general problem as that of
RITZ.  Thus Figure 2.1 describes the conceptualized soil system for VIP. Again, a sludge containing a
contaminant and oil are uniformly mixed into the plow zone and the movement of the contaminant is
predicted.  Several assumptions made in RITZ are modified in VIP.  For example, VIP considers the
dynamics of sorption rather than assuming instantaneous equilibrium between phases. It also simulates

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                                   Plow  Zone
                                Treatment Zone
                                                      — Soil  Surface
                                                      — Plow  Zone
                                                           Depth
                                                      —   Treatment
                                                         Zone Depth
   Figure 2.1. Conceptualized soil system for RITZ and VIP models.
oxygen diffusion in the air-phase and oxygen-limited degradation of the contaminant, and diffusion of
contaminant in air phases. When oxygen is not limiting, sorption is instantaneous, and diffusion of
contaminant is negligible, the equations in VIP are essentially the same as those in RITZ. VIP solves the
differential equations numerically.  As  a result, the recharge rate or flux of water passing through the soil can
change with time on a monthly basis.


CMLS Model:  Nofziger and Hornsby  (1986) developed CMLS to describe the movement and degradation of
pesticides in layered soils. The model  was intended as a management tool.  It was designed to utilize
parameters which are readily available to most users.  In CMLS, the soil profile  is composed of up to  20
layers. Soil and chemical properties are constant within a layer, but may change from layer to layer. Water
balance is computed on a daily basis to account for infiltration and evapotranspiration. To apply this model
to the problem of interest in this study, the initial distribution of the chemical was divided into a series of
thin layers.  Movement of each chemical layer was then simulated.  The amount of chemical entering the
water table was the sum of the amounts for all the layers.

    Simplifying assumptions  made in the development of CMLS include: (1) Chemicals move in the liquid
phase with  the soil water only. Movement in the vapor phase can be ignored.  (2) Partitioning of chemicals
between the soil solids and water can be described by the linear, reversible model with instantaneous
equilibrium as in equation 2. (3) Dispersion and diffusion of the chemical can be ignored. (4) Degradation
can be described as a first-order process (Eqn. 3).  The degradation constant can vary with depth, but not
with time.  (5) Water moves through the soil system in a piston-like  manner. All water in the soil is pushed
ahead of new water entering the soil.  (6) The soil drains instantly to the "field capacity" water content after
each infiltration event.  (7) Water is removed from each layer in the root zone in proportion to the available
water stored in that layer. (8) Chemicals move downward in the soil system. Upward movement of
chemicals is ignored.  (9) No oil is present in the soil system.
    The CMLS model estimates the amount of chemical at a particular position as a function of time.  It
does not calculate concentrations.  If concentrations are needed, the user must estimate the mass of water in

-------
which the chemical is mixed and then calculate the concentration from this mass of water and the mass of
chemical leached.

    Incorporating the assumptions listed above into equation 1 we obtain


                                           R*£ = -  *z?£                                      (8)
                                             dt       6  dz
where R = (1 + pK,j)/0w is the retardation factor and qw is the flux of water. Bond and Phylh'ps (1990)
proved that this equation implies that the solute velocity or the rate of change in position of a constant
concentration, dz/dt j^, under unsteady flow conditions is given by

                                          —  I = _   *"
                                           dt  \C  ~6
PK,                                       (9)
or
                                          Ar
                                                                                                (10)
Equation 10 is used in CMLS to calculate the change in position of the contaminant on a daily basis.
The water content, 8^, is replaced by the water content at field capacity, and qw is the daily flux passing the
current solute position.


HYDRUS Model: HYDRUS is a finite element model developed by Kool and van Genuchten (1991).  The
model makes fewer simplifying assumptions than the other models and is the most computationally
demanding.  In this model the soil is described by properties at a series of points. Soil and chemical
properties can vary from one location to another. The user  has great flexibility to define initial conditions to
represent the site of interest. Assumptions incorporated into HYDRUS include the following:  (1)
Partitioning  of chemical between solid and water can be described by the linear, reversible model with
instantaneous equilibrium between phases; (2) Movement  in the vapor phase can be ignored; (3) No oil is
present in the system.

    Applying these assumptions to equation 1 yields


                                              D  ^ - vfS:                                (ii)
                                         8t      ew a;2       bz

where C^ is the concentration of the contaminant in water at time t and position z, R is the retardation
factor defined previously and v is the pore water velocity (v  = qw/0w).
                                                 10

-------
    The root water uptake, Q, (Eqn. 5) for HYDRUS is given by

                                                                                               (12)
where f (z) is a normalized root uptake distribution function,  PET(t) is the potential evapotranspiration and
a is the stress-response function. The stress response function is given by
                                               \(h
                                                                                               (13)
where h^ is the pressure head at which transpiration is reduced by 50%, ^ is the osmotic head, and p, is a
power constant.  The osmotic head is proportional to the solute concentration, C^ HYDRUS solves
equations 11-13 with equation 5 using a finite element method with mass-lumping and upstream-weighting
techniques (Kool and van Genuchten, 1991).
                                                 11

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                                            SECTION 3

                                SENSITIVITY AND UNCERTAINTY

Sensitivity:  As explained in the introduction, the sensitivity of a model refers to the change in a selected
model output resulting from a specified change in an input parameter.  Mathematically the sensitivity
coefficient, S, is defined  as
                                               S-                                             (14)
                                                   Sx


where f represents the output of interest and x represents the input parameter (McCuen, 1973).  If the model
output can be written in a nice symbolic form, the sensitivity can be applied by differentiating f symbolically.
Often the modeb are too complex for this approach.  In that case the sensitivity can be calculated using the
difference equation                    '
                                              S  =                                              (15)
                                                   A*


Model sensitivity, S, as defined by equations 14 and 15 is the change in model response per unit change in
the input parameter. The change in model output due to a small change in input parameter is given by
                                             A / = SA x                                         (16)
where Af is the change in output f due to a change of Ax in the input parameter. That is, the product of the
sensitivity, S, and the change in input parameter is the change in model output.

     The value of S calculated from these equations has units associated with it.  This makes it difficult to
compare sensitivities for different input parameters.  This problem can be overcome by using the relative
sensitivity, S,, given by


                                          s  - *L £ - s £                                    (17)
                                           1 * 3x f '   f
or
                                                 12

-------
where f is the value of the model output and x is the value of the input parameter. The relative sensitivity
can be used to estimate the relative change in model output, Af/f, from the relative change in input
parameter, Ax/x, using the equation


                                             */ - 5r^                                       (19)
So the relative sensitivity is a measure of the relative change in model output corresponding to a relative
change in the input parameter.  In other words, Sf gives the percentage change in model response for each
one percent change in the input parameter. If the absolute value of Sr is greater than 1, the absolute value
of the  relative change in model output will be greater than the absolute value of the relative change in input
parameter.  If the absolute value of Sr is less than 1, the absolute value of the relative change in model
output will be less than the absolute value of the relative change in input.  Note that the sensitivity coefficient
reflects the change in output function due to a single input parameter.  Uncertainty analysis is used to
incorporate simultaneous changes in more than one parameter and variability of the parameters.


Uncertainty: Two approaches are frequently used for determining model uncertainty.  The first approach, a
deterministic approach, is most applicable to models in which explicit equations can be written for model
outputs as functions of input parameters. The first-order second-moment uncertainty analysis is the most
used technique in this approach.  It provides a method of calculating the mean, variance, and covariance of
model outputs from means, variances, covariances and sensitivity coefficients for the model inputs.  The
following equations are used to determine these quantities  (Dettinger and Wilson, 1981).

                                                                                                (2°)
                                                                                                (21)
                                        cov(v) = S CQvfr)f5]T                                    (22)


where n is the number of model outputs, k is the number of model input parameters, .y. is a (n x 1) vector of
model outputs, f(x) is the (n x 1) vector of model outputs with inputs of x, x is a (k x 1) vector of model
parameters, nv, is a (n x 1) vector of mean model outputs, ffm^ is a (n x 1) vector of model outputs where
the model is evaluated at tn^ jnx is a (k x 1) vector of mean parameter values, 9 f/flx2 is a (n x k) matrix of
2nd partial derivatives of KnvJ, covfx') is a (k x k) covariance matrix of the input parameters, covfy) is a (n x
n) covariance matrix of model outputs, var(x) is a (k xl) vector of variances of parameters, and .S is a (n x k)
matrix of sensitivity coefficients of model outputs to input parameters.  First-order second-moment analysis is
most  appropriate when the model is not too  nonlinear in its parameters and the coefficients of variation of
the parameters are small.

The second  approach is a stochastic approach.  It is often used when the explicit formula for a complex
system can not be  obtained or the equations are too cumbersome.  Monte Carlo simulation is an example of
this approach. The Monte Carlo technique requires knowledge of the frequency distribution of each input
parameter and the correlations among these  parameters.  Input parameters are generated at random from

                                                 13

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the parameter populations so that means and correlations are preserved.  Each set of inputs is used in the
model to compute the outputs of interest. This process is repeated many times until the probability
distribution of the model outputs is defined. Summary statistics of the outputs are then computed or the
entire distribution is used in the analysis.

Previous Work:  Knopman and Voss (1987, 1988) conducted a sensitivity analysis of one-dimensional  solute
transport in steady water flow.  They presented implications for parameter estimation and sampling design.
Jarvis (1991)  developed a deterministic model of non-steady state water flow and solute transport in soils
containing  macropores.  He found that pesticide leaching was sensitive to soil hydraulic properties defining
the macropore region and to pesticide properties.  Recently, Cawlfield and Wu (1993) used probabilistic
approach to examine the sensitivity to transport parameters in 1-d steady water flow. They indicated  that the
probabilistic outcome is most sensitive to likely changes in flow velocity and the reaction terms.  Diffusion
coefficient  can also be an important uncertain variable but only when it has significantly higher uncertainty
than any other variables. Skyes et al. (1985) determined the relative sensitivity of performance to various
parameters.  Sensitivity analyses have been performed to  guide a gradient search algorithm  for parameter
estimation  (Newman, 1980). Dettinger and Wilson (1981) used a sensitivity analysis as the framework for
first and second-order, second-moment uncertainty analysis.

    While  the sensitivity of model output to the input parameters is of importance, the overall uncertainty of
the model  prediction is of concern to model users. Burges and Lettenmaier (1975) subdivided uncertainty
into two categories.  Type I uncertainty is the result of the use of an incorrect model which has correct
(deterministic) parameters.  This uncertainty can be subdivided into inappropriate model selection  and
inherent modeling error. Type II uncertainty results from the choice of the correct model with  incorrect, or
uncertain parameters (including data used for estimating  parameters, initial and boundary conditions, and
sink/source terms).  These two types of uncertainty define the total uncertainty of the model, measured by
the mean square error or variance in output variable. The uncertainty analysis incorporated in  this report is
primarily limited to Type II uncertainty.  This is particularly relevant when using models as decision-making
tools for remediation practices appropriate for Superfund sites since the model must predict the future
behavior of the contaminant when inputs such as future weather at the site are unknown.

    Dettinger and Wilson (1981) used the first-order second-moment techniques to estimate the uncertainty
of ground-water flow due to uncertain flow parameters. League et al. (1990) used the same technique to
investigate the impact of data  uncertainty in soil, climatic, and chemical information on assessment of
pesticide leaching.  Zhang et al. (1993) used the Monte Carlo method to characterize  the uncertainty of
solute movement through soils.  They found the uncertainty resulting from weather variability at a  site was
approximately the same as that due to uncertainty in soil and chemical  parameters.


Illustration:  This section illustrates the use of the  sensitivity coefficient, S, and the relative  sensitivity, Sr by
applying them to a simplified transport equation. The illustration is informative in itself and it forms a basis
for understanding results for more complex models which follow. If we assume that the soil is uniform, that
it contains no oil, that dispersion and movement in the vapor phase are negligible, and that water is flowing
at a constant rate through the soil, the time, T, required for a solute to move a distance L is given by
                                                  (6                                              ,-.,,.
                                            T = L- - — -                                       C23)
 where q is the steady-state flux of water, p is the bulk density, Kd is the partition coefficient (Kj is the
 product of the organic carbon partition coefficient, K^, and the organic carbon content, OC, or Kj =
 Kj^OC), and 6 is the soil water content. Table 3.1 lists the sensitivity and relative sensitivity of the travel
 time to the parameters in the model. These expressions were obtained by applying equations 14 and 17 to

                                                  14

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Table 3.1. Sensitivity and relative sensitivity of predicted travel time to different variables based
on equation 23.
     Parameter
Sensitivity, S
  Relative
Sensitivity, 5r
                                                                    -1
                                 LK^OC
                                  LpOC

                                    Q.
        oc
                                         15

-------
equation 23.  Examination of Table 3.1 reveals that the relative sensitivity for bulk density, p, partition
coefficient, Kj, organic carbon partition coefficient, K^, and organic carbon content, OC, are identical.

    Figure 3.1 shows graphs of travel time, sensitivity, and relative sensitivity of the travel time to the flux of
water, q (Equations in Table 3.1).  The lower graph is a plot of equation 23 for different values of recharge
rate.  The middle graph is a plot of sensitivity to recharge rate.  The upper figure is a plot of the relative
sensitivity which has a value of -1 for all recharge rates. This relative sensitivity implies that the relative
change in travel time is equal in magnitude to the relative change in recharge, but it is opposite in sign.  So,
if the recharge rate increases by 10%, the travel time decreases by 10%. Figures 3.2 and 33 show similar
graphs for water content and partition coefficient. In those cases, the relative sensitivities increase as the
parameters increase. In both cases the relative sensitivities are less than 1 so the relative change in travel
time is less than the relative change in either of these parameters. In each figure, model input parameters
were held constant except for the parameter of interest. The standard values used were 1 mm day"1 for q,
1.65 Mg nf3 for p, 80 cm3 g'1 for K^., 0.14 % for OC,  and 0.242 m3 nf3 for 6. The value of Kd was 0.112
cm3 g . The distance, L, was 1.5 m.
    Since Sr is dimensionless, it can be used to compare model sensitivity to parameters having different
units.  For instance, Sr is -1 for recharge rate; Sr is 0.567 for water content, Sr is 0.071 for partition
coefficient.  So the travel time for the standard input values stated above is most sensitive to recharge rate,
and least sensitive to partition coefficient.  These results are applicable to the set of input parameters used.
Large  changes in sensitivity occur as parameters change.

    Relative sensitivity can also be used to approximate the required accuracy of a model parameter if the
desired accuracy in the model response is  known.  By rewriting equation 18 as


                                             £f = !£/                                       (24)


we can calculate the required accuracy (Ax/x) of the input parameter x given the relative sensitivity for x and
the required accuracy in the model output (Af/f).  For example, if we want to estimate T to within 10% of
its actual value,  then the required accuracy (Ax/x) for q, 6, and Kd are 10%, 17.6% and 140.8% respectively.
Clearly q is the  one parameter must be known the most accurately of these three parameters.  Note that
each of these  percentages assume that the other parameters in the model are entered without error.  Zhang
et al. (1993) demonstrated a technique based on uncertainty analysis, sampling theory, and knowledge of
parameter variability for estimating sample size requirements when measuring parameters for simulation
models.

    Uncertainty analyses of this simplified model was carried out using both first-order second moment and
Monte Carlo techniques.  The parameters were assumed to be normally distributed and not correlated.
Coefficients of variation (CV) of  0.05 for  q, 0.05 for p, 0.20 for K^, 0.40 for OC, and 0.10 for  6 were used.
The estimated mean for travel time from  equation 21 is 641.0 days with a standard deviation of 134 days.
Monte Carlo simulation with 500 runs resulted in a mean value of 642.8 days and standard  deviation of 135
days.  The two methods are in good agreement for this model and these parameters.

    When the sensitivity for each parameter and the covariance matrix cov(x') is known, the ratio of the
relative contribution of each parameter to total variance can be used to rank the importance of the input
parameter. We illustrate  this by  using our simplified transport  model with five  input parameters, q, 8, p,
OC, and K^..  Expanding equation 22  for this case yields
                                                   16

-------
          Var(T)
                                                         covfo.p)    covfooc)
cov(p,e)   eov(p,p)   cov(p,oc)

          cov(oc,p)  cov(oc,oe)

                 p)  covtfT^oc)
(25)
where Var(T) is the overall uncertainty or variance of travel time, Sx is the sensitivity of T with respect to
parameter x, and cov(x}, x^) is the covariance between parameter x1 and Xj.  The expression
                                     cov(g,e)  + cov(g.p)  •*• covfooc)
                                                 Var(T)
                                                                                                  (26)
represents the relative contribution of q to the overall uncertainty of travel time. Using the standard
parameter values and CV's listed above, Var(T) is 17902 day2. The relative contributions of p, q, 6, K^, and
OC to this overall uncertainty are 0.011, 0.057, 0.074, 0.172 and 0.687, respectively.  In other words, organic
carbon accounts for 68.7% of the total uncertainty, organic carbon partition coefficient 17.2%, water content
7.4%, flux 5.7%, and bulk density 1.1% for this set of parameters and covariances.  These results incorporate
both sensitivity and parameter variability. Note the much greater contribution of organic carbon than  bulk
density to the total uncertainty even though the two parameters have the same relative sensitivities.  This is
due to the much larger natural variation in organic carbon than in bulk density.  Nichols and Freshley (1993)
used analysis of variance as an alternative method to partition total uncertainty to different parameters in a
model.
                                                   17

-------
H


o
§
i
Cn

s,
s.
s
I

I
            Travel  Time (days)   ,
                                         Sensitivity
                01
                o
                o
o
o
o
en
o
o
o o
2 °
o o
      
      o.
      a
                                                            Relative  Sensitivity
 i
•
o
 I
p
bo
 I
p
en
 I
O

-------
                 1.0


                 0.8


            1   0.6


            W   0.4
                0.2
             Q>
            ct:
             2000
              1500
           E 1000
           W
           c
           0)

           w  500
           (0
           >.

           -o  750
           £  500
           o
               250
                             0.1       0.2       0.3

                         Water  Content  (m5  nf3)
0.4
Figure 3.2. Sensitivity of travel time for different values of water contents for a simplified model (Eqn. 23).
                                    19

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                  0.8
             2   0.6
             75
              0)
             a   0.2
             ^O
              0)
             *     0
               3000
               2000
           §   1000
          tn
               2000
            -§1500
            E 1000
            E
                500
                                  0.1           0.2
                                   KH  (crrf  g'
0.3
Rgure 3.3. Sensitivity of travel time for different values of partition coefficient for a simplified model (Eqn.
23).
                                     20

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                                             SECTION 4

                                        PHYSICAL SETTING

    Site Characteristics: The general case study considered was the fate of benzene spilled near Perdido,
Alabama. The soil in the area was the Norfolk sand (fine-loamy, siliceous, thermic Typic Paleudult).  At the
beginning of the simulation, 100 g m"2 benzene was assumed to be uniformly distributed in the top 0.5 m of
soil. A water table was assumed to be present at a depth of 2 m.  The initial water content throughout the
soil profile was internally calculated by the RITZ and VIP models from the specified recharge rate, the
saturated conductivity, and the Clapp-Hornberger constant. CMLS assumes the initial water content of each
soil layer is the field capacity value. An initial water content of 0.15 cm  cm  throughout the soil profile was
used as the initial condition in HYDRUS. No benzene entered the soil during the simulation.

    Soil properties  for the top 2 meters of the Norfolk sand were obtained from Quisenberry et al. (1987)
for the same soil in Blackville, South Carolina.  The basic soil properties used are shown in Table 4.1. Data
on the organic carbon content (OC) of the soil were  not available in the report. Percent organic carbon
content was assumed to decrease with depth according to the  equation
                                          OC(d) -US*-4'0"                                    (27)
where d is the soil depth (m). The organic carbon content determined for the middle of each soil layer was
used for that entire layer. Table 4.1 also contains depth-weighted average values used in models requiring
uniform soil properties.

     The parameters for the van Genuchten closed-form hydraulic functions (van Genuchten, 1980) were
obtained from the soil water retention data and unsaturated hydraulic conductivity for sites 5 and 6 found in
Tables N53 - N6.ll of Quisenberry et al. (1987).  The RETC software of van Genuchten et al. (1991) was
used to estimate the parameters.  Soil porosity was computed from the bulk density. The Clapp-Hornberger
constant (Clapp and Hornberger, 1978) required in the RITZ and VIP models was determined by regression.
These hydraulic properties are shown in Table 4.2.

     Climatological data from the Perdido area of Alabama were  obtained for the nearby sites  of Fairhope
from the SE Regional Climate Center. The only evaporation (ET) data available were from Fairhope.  The
record period was from 1983 to 1991.  Daily weather data from the Fairhope site were used in the simulation
runs for HYDRUS and CMLS models.  Average recharge rates required for RITZ and VIP were calculated
from total rainfall and total evaporation data at these sites. Average rainfall for the area was 5 mm per day.
Average evaporation was 4 mm per day.  Daily weather data from Caddo County,  Oklahoma was also used
for some of the analyses using CMLS since the data available for Perdido were not sufficient for the Monte
Carlo simulations.
    Chemical Properties: The organic carbon partition coefficient for benzene was obtained from K^ values
in the literature.  Karickhoff and Brown (1979) reported a value of 83 cm3 g"1 for benzene in sediment;
Rogers et al. (1980) reported 92 cm3 g'1: Stuart et al. (1991) reported 18 cm3 g'1; and Chen et al. (1992)
reported 207 cm3 g"1. A value of 80 cm  g"1 was used in this report.

    A pseudo zero-order biodegradation rate of benzene has been reported  to be 25 mg L*1 d"1 for a sandy
aquifer material by Alvarez and Vogel (1991). Zoetman et  al., (1981) published a value of 0.006 d"1 (half-life
of 116 days) for the first-order coefficient for biodegradation using substrate disappearance in landfill
leachate.  Goldsmith and Balderson (1988) reported the maximum biokinetic utilization rate (first-order rate)
of 0.00667 d"1 (half-life of 104 days) in the batch culture.  For a modeling study of BTX (benzene, toluene,
and xylenes) at a  field site, a first-order degradation constant of 0.003 d"* (half-life 231 days) was used by
Rifai et al. (1988). A half-life of 100 days was used in this report.

                                                 21

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Table 4.1. Soil properties of Norfolk Soil.
Depth of
Bottom
m
0.27
0.40
0.58
0.76
1.06
137
2.00
Bulk Density
Mgm'3

1.74
1.79
1.70
1.57
1.52
1.62
1.66
Organic Carbon
%

0.740
0.270
0.130
0.062
0.035
0.010
0.002
Field Capacity
m m

0.109
0.230
0.300
0.242
0.300
0.275
0.242
Wilting Point
m3 m"3

0.014
0.104
0.114
0.027
0.114
0.104
0.027
Depth-Weighted
    Average
                               1.65
               0.142
                   0.242
                        0.063
Table 4.2. Soil hydraulic properties of Norfolk Soil.
Depth of
Bottom
m
0.27
0.40
0.58
0.76
1.06
1.37
2.00
a1
m-1
4.9
2.8
1.8
1.9
1.8
1.9
1.9
ft1
1.64
1.18
1.22
1.54
1.22
1.22
1.54
n/m-3
0.290
0.284
0.364
0.375
0.364
0.335
0.375
nA-3
0.0098
0.0104
0.0083
0.0098
0.0083
0.0077
0.0098
md'1
0.433
0.116
0.296
0.126
0.2%
0.293
0.126
Clapp
Hornberger
Constant
2.4
4.2
8.7
8.4
14.6
11.7
9.3
Depth-Weighted
    Average
                    2.3
1.40
0.349
0.0092
                                                                  0.184
9.1
1. Used in hydraulic functions of van Genuchten (van Genuchten et al, 1991) for

     Water content, 6:  (6 - 6I)/(6S - 0r) = [1 + (ah/]""

     Conductivity, K(h): K(h)=Ks{l-(ah)m^(l + (ah/]-m}2/[l + (ah)'3ft

                             m = 1 -1/0;    t = 0.5

2. Equivalent saturated conductivity (Swartzendruber, 1960).
                                                 22

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                                             SECTION 5

                             SENSITIVITY RESULTS FOR RITZ MODEL

General Impact of Input Parameters

    Figures 5.1 to 5.12 illustrate the dependence of chemical concentration in water at the bottom of the
treatment zone and the dependence of the position of the pollutant in the soil profile upon different model
parameters.  The upper graphs in each figure show the concentration of the pollutant in water at a depth of 2
m as a function of time.  The lower graphs show the position of the upper and lower edges of the pollutant
as functions of time. These bounds define the position of the chemical as it moves through the soil. The
solid lines represent estimates from RITZ for benzene movement through the Norfolk soil in Alabama
(ignoring movement in the vapor phase). The input parameters are shown in Table 5.1 for the solid lines.
These input parameters are the same for all 12 figures.  Other lines on a particular figure result from
changing only the one parameter listed on the figure.  Examining these figures leads us to the following
observations:

    1. The time required for the pollutant to reach the bottom of the treatment zone is quite dependent
upon the recharge rate (Figure 5.1).  Decreasing the  recharge rate from 1 to 0.5 mm  day1 increases the time
at which the pollutant reaches the water table from approximately 700 days to 1200 days. The duration of
the pulse increases from approximately 900 to 1400 days due to this decrease. The concentration of the
pollutant in water decreases 100-fold over this range  of recharge rates.  As the recharge rate decreases, the
travel time increases, the duration of the contaminant pulse increases, the maximum concentration decreases,
and the amount of chemical leaching to the ground water decreases.

    2. Figure 5.2 shows that increasing the organic carbon partition coefficient, JQ,,, increases  sorption of the
chemical on the soil solids and increases the time required for the chemical to reach the 2-m  depth. This
increase in travel time results in an increase in degradation  and a decrease in the concentration of the
pollutant in water.  Little change in the width of the contaminant pulse  is visible for these K^ values.  The
range of values of K^ used in Figure 5.2 is somewhat less than the range found in the literature for benzene.

    3. Organic carbon content of the soil has a large  impact upon travel time and maximum concentration.
This is illustrated in Figure 5.3. Here the solid line for an organic carbon value of 0.14% represents the
average organic carbon value for the top 2 meters of the soil.  The line for a fraction of 0.8% represents the
organic carbon content of the surface horizon.  So the difference shown represents the difference between
using an average value and the value for the surface layer. The time required for the pulse to reach the
water table changes from about 2 years to 6 years due to this change in organic carbon. That corresponds to
a 10000-fold difference in concentration.  Clearly organic carbon content has a very large and a very
significant impact upon chemical movement because of its impact upon sorption and the wide range of
organic carbon values which exist in soils.

    4. Soil bulk density values seem to have little impact on the parameters of interest (Figure 5.4). Rarely
would the uncertainty in bulk density at a site exceed the 0.30 Mg m3  range  shown in the figure.

    5. One hundred-fold changes in saturated hydraulic conductivity change the travel time by only about 100
days (Figure 5.5). The Clapp-Hornberger constant also has a small impact upon the predictions as  seen in
Figure 5.6.  This is reasonable in that RITZ uses these parameters only to estimate the water content of the
soil for a particular recharge rate.
                                                 23

-------
Table S.I.  Values of input parameters used for sensidvity analysb in RITZ model.

Soil Properdes
    Organic Carbon (%)                                            0.14
    Bulk Density (Mg nf3)                                         1.650
    Saturated Water Content (m3 m"3)                              0378
    Saturated Hydraulic Conductivity (m day"1)                       0.19
    Clapp and Hornberger Constant (--)                              4.9

Site Characteristics
    Plow zone depth (m)                                            0.5
    Treatment zone depth (m)                                       2.0
    Recharge Rate (mm day"1)                                       1.0
    Evaporation Rate (mm day"1)                                    4.0
    Air temperature (degrees C)                                      25
    Relative humidity (--)                                            0.5
    Sludge application rate (Mg ha'1)                                 250
    Concentration of pollutant hi the sludge (g kg"1)                   4.0
    Diffusion coefficient of water vapor in air (m  day"1)               2.0

Pollutant properties
    Organic carbon partition constant (cm3 kg"1)                      801
    Octanol-water partition coefficient (--)                            700
    Henry's law constant (-)                                      5.0E-9
    Diffusion coefficient in air (m2 day"1)                             2.0
    Degradation half-life (days)                                      104

Properdes of Oil
    Concentration of oil in the sludge (g kg"1)                         250
    Density of the oil (kg m"3)                                       800
    Half-life of the oil (days)                                         200
1. This partition coefficient was used for the solid lines. The short dashed line represents results for
20 cm g" ; the long dashed line represents results for K^ =  110 cm3 g"1.
                                                   24

-------
    6. The evaporation rate has no detectable impact on the fate of the pollutant in this scenario (Figure 5.7)
 since the evaporation rate is used in RITZ only to estimate volatile losses of the chemical.  If the model
 parameters were such that volatile losses were appreciable, differences due to evaporation rate would be
 observed.

    7. Figure 5.8 illustrates that decreases in degradation half-life of the pollutant result in large decreases in
 the concentration of chemical reaching the ground water, but do not effect the rate of chemical movement.
 RITZ assumes the half-life does not change with depth. Since half-life has a large impact upon
 concentration and since half-life generally changes with depth, this assumption may produce large errors in
 predicted concentrations and amounts leached.

    8. Henry's constant determines the partitioning of the pollutant between water and air. Figure 5.9 shows
 its impact upon concentration and pollutant position. As Henry's constant increases above  10  , RITZ
 predicts a substantial decrease in pulse width due to a large increase in loss of pollutant to the vapor phase.
 The predicted amount of chemical volatilized is so large the pollutant does not reach the water table when
 Henry's constant is equal to 0.24. The impact of Henry's constant is highly dependent upon the diffusion
 coefficient of the pollutant.

    9. Figures 5.10 and 5.11 illustrate the manner in which the pollutant concentration and pollutant
 movement depend upon the diffusion coefficient of the pollutant in air.   In Figure 5.10, we  see no change in
 predicted concentration and travel time due to changes in diffusion coefficients. In Figure 5.10, Henry's
 constant is very small so essentially no pollutant is present  in the air phase.  Therefore changes in the way
 the pollutant diffuses in air have no impact.  The value of Henry's constant used in Figure 5.11 is a
 reasonable estimate of that for benzene. It is much larger than the value used in Figure 5.10.  Figure 5.11
 indicates that the diffusion coefficient does not influence the time the pollutant arrives at the water table, but
 it significantly influences the duration of the pulse and the  amount leached.  In this case the RITZ model
 predicts that none of the pollutant will reach the water table if the diffusion coefficient is 2 m2 day"1. The
 curves in Figure 5.11  look quite similar to those in Figure 5.9.  This is expected since the equations of RITZ
 generally include the product of these two parameters.  The differences between Figures 5.10 and 5.11
 illustrate that all the results of this report are valid for only the set of input parameters used.

    10. Figure 5.12 shows predicted results for different oil contents in the sludge. The oil  content has  no
 impact upon the time at which the leading edge of the chemical reaches  the water table, but it changes  the
 pulse width substantially.  The  presence of oil in the sludge retards the movement of chemical through the
 portion of the soil containing oil  (the plow zone).  This retardation and resulting increase in degradation
 time causes the concentration of the pollutant at the water table to be much less than  that for an oil-free
 sludge. In Figure 5.12 this change hi concentration is approximately 100-fold. The duration of the pulse is
 greatly reduced when the oil content is reduced.

 Sensitivity Coefficients

    Figures 5.13 to 5.24 show the travel time and its sensitivity coefficients for different input parameters of
the RITZ model.  Each of the  figures contains three graphs. The lower  graph shows the travel time as a
function of the parameter being analyzed. The middle graph shows the sensitivity coefficient, S, (defined in
equation 15)  as a function of the parameter being analyzed. The upper graph shows the relative sensitivity,
Sr as defined in equation 18.  Different lines in  each graph represent chemicals with different organic carbon
partition coefficients as shown on the graph.  Input parameters used for these graphs are listed in Table 5.1.

    Figure 5.1 illustrated that the pulse of chemical enters ground water  at earlier times as  the recharge rate
increases. This  dependency of travel time upon recharge rate is shown in Figure 5.13 for a large range  of
recharge rates.  (We have defined the travel time as the time midway between the tune the pollutant reaches
the water table and the time  all of the  pollutant  has entered the water table.  That is, travel time refers to

                                                  25

-------
the time at the middle of the concentration pulse shown in Figure 5.1.)  The middle graph of Figure 5.13 is a
graph of the sensitivity coefficient for travel time to recharge rate.  This is a graph of the slope of the line in
the lower graph.  For a recharge rate of 1 mm day1, the sensitivity coefficient is about -1000.  This means
that an increase in recharge rate of 0.5 mm day1 (recharge goes from 0.75 to 1.25 mm day1) corresponds to
a decrease in travel time of -1000 * 0.5 or 500 days. The upper graph of Figure 5.13 shows the relative
sensitivity as a function of recharge rate.  The relative sensitivity to recharge rate is nearly constant with a
value of approximately -0.7 over the range of rates shown. This means that doubling the recharge rate
decreases the travel time by a factor of 1.4 (0.7 x 2).  If we are concerned about relative changes in travel
time, the relative sensitivity is the parameter of interest; if we are interested in absolute  changes in travel
time, the sensitivity coefficient is the appropriate factor. Since the three lines on each of these graphs are
close together, differences between chemicals with K^ values in the range of 20 to 110 cm3 g1  are small. Note
that these results are similar to those for the simple case shown in Figure 3.1. Differences are primarily the
result of oil in the upper portion of the soil.

    Figures 5.14 to 5.24 can be related to Figures 5.2 to 5.12 as was done above.  Figures 5.14, 5.15,  and 5.16
show that travel time increases as K^., organic carbon content, and bulk density increase just as was observed
in the simplified case shown in Figure 5.3. The increase in travel time is nearly linear.  The curves are very
similar since the product of these factors is the retardation factor, R  (Eqn 8), and travel time increases  as R
increases. Since organic carbon contents commonly vary from near zero to more  than 2%, it is a very
important parameter for predicting travel time of adsorbed materials.

    Figures 5.22 and 5.23 show the sensitivity of travel time to diffusion coefficients. Figure 5.22 shows the
travel time is insensitive when Henry's constant  is very small just as was shown in Figure 5.10. In Figure 5.23,
we see that increasing  diffusion coefficients decreases travel time when a larger value of Henry's constant is
used.

    Travel time predicted by RITZ is not sensitive to evaporation rate, half-life, saturated conductivity, and
Clapp-Hornberger constant.  Relative sensitivities for travel time are less than 0.20 in absolute value for these
scenarios, indicating that the relative change in travel time will be less than 20% of the relative change in the
input parameter.

    Sensitivities for the concentration of pollutant in water (Figures 5.25 to 5.36) and for the total amount  of
pollutant leached to ground water (Figures 5.37 to 5.48) are similar in shape but have different scales. Both
quantities increase with increasing recharge rate and degradation half-life. The concentration  and amount
leached decrease with increasing organic carbon content, K,,,., Henry's constant,  Clapp-Hornberger constant,
and oil content.  Evaporation rate and bulk density have little impact on these predictions. Relative
sensitivities are generally greater than 1 in magnitude for recharge rate, organic carbon content, K^, and
half-life.

    Figures 5.49 to 5.60 present sensitivity graphs for pulse width or the duration  of the chemical pulse  at the
bottom of the treatment zone.  This model output is most sensitive to recharge rate,  Henry's constant, and
oil content for the parameters used here.  Relative sensitivities for pulse width are less than 1  in absolute
value except for Henry's constant and the diffusion coefficient when the pulse width approaches zero.

    Figures 5.61 and 5.62 show the sensitivity of the amount of pollutant volatilized and lost to the
atmosphere as functions of Henry's constant and the diffusion coefficient of the pollutant. Clearly RITZ is
capable of predicting large losses in the vapor phase. It is interesting to note that  differences in K,,c do not
appear to influence the amount volatilized for the range of parameters shown.

    A list of the parameters of RITZ and summaries of sensitivities of travel time, pulse width, and  amount
leached are given in Tables 5.2, 5.3, and  5.4, respectively.  The complete range of values analyzed is broken
                                                   26

-------
Table 5.2. Sensitivity coefficients for travel time using RITZ.
                     Input Parameter
                                 Travel Time (days)
Name

Organic Carbon (%)
Bulk Density (Mg m"3)
Saturated Water Content (m3 m"3)
Saturated Conductivity (m day"1)
Clapp and Hornberger Constant

Plow zone depth (m)
Treatment zone depth (m)
Recharge Rate (mm day)

Evaporation Rate (mm day"1)

Air temperature (degrees C)
Relative humidity
Sludge application rate (Mg ha"1)
Cone, pollutant in sludge (g kg"1)
Range

0.02-0.54
1.35-1.80
0.28-0.48
0.04-0.59
2.9-14.9

0.1-0.6
1-2.5
0.5-2.2
2.2-5.5
1-7

15-35
0.2-0.8
50-450
1.5-6.5
Diffusion coef. water vapor in air (m2 day'1)   0.4-3.6
Partition coefficient (cm3 g'1)                 10-150
Oil-water partition coefficient                 100-1300
Henry's law constant                        0-0.4
Value

  0.3
 1.55
 0.38
 0.34
  4.9

  0.5
  2.0
  1.0
  3.0
  3.0

   20
  0.5
  250
  4.0

  2.0
   80
  700
 0.05
Value

1500
1130
1146
1130
1150

1150
1150
1150
  538
1150

1150
1150
1120
1146

1146
1150
1120
  816
2190
 184
1094
  -91
 26.5

 -310
 435
 -820
 -121
  0.0

  0.0
  0.0
 0.64
  0.0

  0.0
 3.81
 0.24
 -823
   Sr

  0.44
  0.25
  0.36
-0.027
  0.11

 -0.14
  0.76
 •0.72
 -0.67
   0.0

   0.0
   0.0
  0.14
   0.0

   0.0
  0.27
  0.15
-0.050
Diffusion coef. in air (m2 day'1)
Degradation half-life (day)
Cone, oil in sludge (g kg'1)
Density of oil (Mg m )
Half-life of oil (day)
0.4-3.6
24-304
50-450
0.4-1.2
25-400
2.0
104
250
0.8
200
1146
1150
1150
1150
1150
0.0
0.0
0.54
180
1.47
0.0
0.0
0.12
-0.13
0.26
into more than one part for parameters with highly nonlinear sensitivity functions.  Relative sensitivities for
travel time and pulse width are less than 1 in absolute value indicating that a relative change in any
parameter will result in a smaller relative change in the travel time or pulse width. Sensitivities for travel
time are positive for most input parameters indicating that the travel time increases as those parameters
increase. Sensitivities are negative only for saturated  hydraulic conductivity, plow zone depth, recharge rate,
and Henry's law constant so travel  times decrease as each of these parameters increase.  The sensitivities for
pulse width have the same sign for each parameter as their respective sensitivities for travel time with the
exception of plow zone depth.  Increasing the plow zone depth increases the pulse width but decreases the
travel time for the range of parameters studied here. Relative sensitivities for  amount leached are greater in
absolute value for many parameters.
                                                 27

-------
Table 5.3. Sensitivity coefficients for pulse width using RITZ.
Input Parameter
Name
Organic Carbon (%)
Bulk Density (Mg m"3)
Saturated Water Content (m3 m"3)
Saturated Conductivity (m day'1)
Clapp and Homberger Constant
Plow zone depth (m)
Treatment zone depth (m)
Recharge Rate (mm day )

Evaporation Rate (mm day'1)
Air temperature (degrees C)
Relative humidity
Sludge application rate (Mg ha'1)
Cone, pollutant in sludge (g kg'1)
Diffusion coef. water vapor in air (m2 day"1)
Partition coefficient (cm g"1)
Oil-water partition coefficient
Henry's law constant
Diffusion coef. in air (m2 day'1)
Degradation half -life (day)
Cone, oil in sludge (g kg"1)
Density of oil (Mg m )
Half-life of oil (day)
Pulse Width (davs\
Range
0.02-0.54
1.35-1.80
0.28-0.48
0.04-0.59
2.9-14.9
0.1-0.6
1.0-2.5
0.5-2.2
2.2-5.5
1-7
15-35
0.2-0.8
50-450
1.5-6.5
0.4-3.6
10-150
100-1300
0-0.4
0.4-3.6
24-304
50-450
0.4-1.2
25-400
Value
0.3
1.55
0.38
0.34
4.9
0.5
2.0
1.0
3.0
3.0
20
0.50
200
4.0
2.0
80
700
0.05
2.0
104
250
0.80
200
Value
1050
982
986
982
986
986
986
986
619
986
986
986
942
986
986
986
927
306
986
986
986
1023
986
S
412
331
195
-16.3
4.76
250
0.0
-392
-96
0.0
0.0
0.0
1.29
0.0
0.0
0.685
0.488
-2026
0.0
0.0
1.07
-361
2.94
sr
0.12
0.052
0.075
-0.006
0.024
0.13
0.0
-0.40
-0.46
0.0
0.0
0.0
0.34
0.0
0.0
0.056
0.37
-0.33
0.0
0.0
0.27
-0.29
0.60
                                                    28

-------
Table 5.4. Sensitivity coefficients for amount leached using RITZ.
Incut Parameter
Name
Organic Carbon (%)


Bulk Density (Mg m'3)
Saturated Water Content (m3 m'3)
Saturated Conductivity (m day*1)
Clapp and Homberger Constant

Plow zone depth (m)
Treatment zone depth (m)

Recharge Rate (m day"1)
Evaporation Rate (mm day"1)
Air temperature (degrees C)
Relative humidity
Sludge application rate (Mg ha"1)

Cone, pollutant in sludge (g kg"1)
Diffusion coef. water vapor in air (m2 day"1)
Partition coefficient (ml3 g"1)

Oil-water partition coefficient


Henry's law constant

Diffusion coef. in air (m2 day"1)
Degradation half-life (day)
Cone, oil in sludge (g kg"1)

Density of oil (Mg m"3)
Half-life of oil (day)

Amount Leached (%)
Range
0.02-0.14
0.14-0.34
0.34-0.54
1.35-1.80
0.28-0.48
0.04-0.59
2.9-6.9
6.9-14.9
0.1-0.6
1.0-1.5
1.5-2.5
0.5-5.5
1-7
15-35
0.2-0.8
50-200
200-450
1.5-6.5
0.4-3.6
10-70
70-150
100-500
500-1300
250-1300
0.0-0.17
0.17-0.4
0.4-3.6
24-304
50-150
150-450
0.4-1.2
25-120
120-400
Value
0.10
0.26
0.46
1.55
0.38
0.34
4.9
8.9
0.5
1.25
2.0
3.0
3.0
20
0.5
100
300
4.0
2.0
40
110
300
800
800
0.10
0.30
2.0
104
100
300
0.8
75
250
Value
1.1E-1
1.2E-2
8.4E-4
7.0E-2
6.8E-2
7.0E-2
6.2E-2
4.0E-2
6.3E-2
6.5E-1
1.0E-1
2.9E+0
6.2E-2
6.2E-2
6.2E-2
5.1E-2
6.3E-2
6.2E-2
6.2E-2
1.6E-1
3.1E-2
1.6E-1
6.0E-2
6.6E-2
2.6E-2
O.OE+0
6.2E-2
6.2E-2
1.3E-1
5.3E-2
6.2E-2
1.4E-1
5.4E-2
S
-1.4E+0
-1.7E-1
-1.1 E-2
-8.0E-2
-4.4E-1
3.9E-2
-1.0E-2
-2.9E-3
1.2E-1
-1.7E+0
-2.4E-1
2.3E+0
O.OE + 0
O.OE+0
O.OE + 0
1.1E-7
2.2E-8
1.6E-2
O.OE+0
-3.8E-3
-7.2E-4
-4.6E-4
-5.8E-5
-8.4E-5
-4.1E-1
O.OE+0
O.OE+0
3.6E-3
-1.0E-3
-1.6E-4
6.8E-5
-1.8E-3
-1.1 E-4
sr
-1.66
-3.50
-6.19
-1.77
-2.47
0.19
-0.80
-0.65
0.94
-3.34
-4.79
2.33
0.00
0.00
0.00
0.22
0.10
1.00
0.00
-0.94
-2.59
-0.87
-0.77
-1.01
-1.56
0.00
0.00
5.98
-0.77
-0.89
0.89
-0.94
-0.53
                                               29

-------
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                              1000          2000
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 3000
                                            Recharge  Rate
                                                  mm day"1
                                                    0.5
                                                    1.0
                                             	2.0
                             1000           2000
                                Time  (days)
3000
Figure 5.1. Predicted concentration of pollutant in water at 2.0 m and position of the pollutant slug as
functions of time for different recharge rates.
                                    30

-------
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                              1000           2000
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Figure 5.2. Predicted concentration of pollutant in water at 2.0 m and position of the pollutant slug as
functions of time for different organic carbon partition coefficients.
                                    31

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Figure 53. Predicted concentration of pollutant in water at 2.0 m and position of the pollutant slug as
functions of time for different amounts of organic carbon.
                                   32

-------
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Figure 5.4. Predicted concentration of pollutant in water at 2.0 m and position of the pollutant slug as
functions of time for different bulk density values.
                                   33

-------
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                               1000          2000
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 3000
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                              1000           2000
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3000
Figure 5.5. Predicted concentration of pollutant in water at 2.0 m and position of the pollutant slug as
functions of time for different saturated hydraulic conductivities.
                                     34

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                              1000           2000
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Figure 5.6. Predicted concentration of pollutant in water at 2.0 m and position of the pollutant slug as
functions of time for different values of the Clapp-Hornberger constant.
                                    35

-------
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Figure 5.7. Predicted concentration of pollutant ia water at 2.0 m and position of the pollutant slug as
functions of time for different evaporation rates.
                                  36

-------
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Figure 5.8. Predicted concentration of pollutant in water at 2.0 m and position of the pollutant slug as
functions of time for different values of pollutant half-life.
                                   37

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Figure 5.9. Predicted concentration of pollutant in water at 2.0 m and position of the pollutant slug as

functions of time for different values of Henry's constant.
                                     38

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Figure 5.10. Predicted concentration of pollutant in water at 2.0 m and position of the pollutant slug as
functions of time for different diffusion coefficients of pollutant in air and a small value of Henry's constant.
                                     39

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                                          Time  (days)
Figure 5.11. Predicted concentration of pollutant in water at 2.0 m and position of the pollutant slug as
functions of time for different diffusion coefficients of pollutant in air for Henry's constant for benzene.
                                               40

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Hgure 5.13. Sensitivity of travel time to recharge rate for chemicals with different organic carbon partition
coefficients.
                                 42

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Figure 5.14. Sensitivity of travel time to organic carbon partition coefficient.
                                    43

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Figure 5.15. Sensitivity of travel time to organic carbon content for chemicals with different organic carbon
partition coefficients.
                                   44

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Figure 5.19. Sensitivity of travel time to evaporation rate for chemicals with different carbon partition
coefficients.
                                  48

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Figure 5.21. Sensitivity of travel time to Henry's constant for chemicals with different organic carbon
partition coefficients.
                                           50

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Figure 5.22. Sensitivity of travel time to the diffusion coefficient of the pollutant in air for chemicals with

different organic carbon partition coefficients and very small Henry's constant.
                                      51

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Figure 5.24. Sensitivity of travel tune to concentration of oil in the sludge for chemicals with different organic
carbon partition coefficients.
                                    53

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                       0123456
                            Recharge  Rate (mm  day"1)
Figure S.2S. Sensitivity of concentration of pollutant in water to recharge rate for chemicals with different
organic carbon partition coefficients.
                                           54

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Figure 5.26. Sensitivity of concentration of pollutant in water to organic carbon partition coefficient.
                                             55

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Organic  Carbon
Figure 521. Sensitivity of concentration of pollutant in water to organic carbon content for chemicals with

different organic carbon partition coefficients.
                                            56

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Figure 5.28. Sensitivity of concentration of pollutant in water to soil bulk density for chemicals with different

organic carbon partition coefficients.
                                     57

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Figure 5.29. Sensitivity of concentration of pollutant in water to soil saturated hydraulic conductivity for

chemicals with different organic carbon partition coefficients.
                                        58

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Figure 532. Sensitivity of concentration of pollutant in water to degradation half-life of the pollutant for
chemicals with different organic carbon partition coefficients.
                                       61

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Figure 533. Sensitivity of concentration of pollutant in water to Henry's constant for chemicals with different
organic carbon partition coefficients.
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Figure 534. Sensitivity of concentration of pollutant in water to the diffusion coefficient of the pollutant in
air for chemicals with different organic carbon partition coefficients and very small Henry's constant.
                                             63

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Figure 535. Sensitivity of concentration of pollutant in water to the diffusion coefficient of the pollutant in

air for chemicals with different organic carbon partition coefficients and Henry's constant of benzene.
                                         64

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Figure 5.36. Sensidvity of concentration of pollutant in water to concentration of oil in the sludge for

chemicals with different organic carbon partition coefficients.
                                     65

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Hgure 537. Sensitivity of amount leached to recharge rate for chemicals with different organic carbon
partition coefficients.
                                        66

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200
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Figure 538. Sensitivity of amount leached to organic carbon partition coefficient.
                                         67

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Sensitivity
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Figure 5.41. Sensitivity of amount leached to soil saturated hydraulic conductivity for chemicals with different
carbon partition coefficients.
                                        70

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Figure S.42. Sensitivity of amount leached to Clapp-Hornberger constant for chemicals with different carbon
partition coefficients.
                                  71

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Figure 5.43. Sensitivity of amount leached to evaporation rate for chemicals with different carbon partition
coefficients.
                                  72

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Figure 5.44. Sensitivity of amount leached to degradation half-life of the pollutant for chemicals with different

carbon partition coefficients.
                                     73

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Figure 5.4S. Sensitivity of amount leached to Henry's constant for chemicals with different carbon partition
coefficients.
                                     74

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Figure 5.46. Sensitivity of amount leached to the diffusion coefficient of the pollutant in air for chemicals
with different carbon partition coefficients and very small Henry's constant.
                                      75

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Figure 5.47. Sensitivity of amount leached to the diffusion coefficient of the pollutant in air for chemicals
with different carbon partition coefficients and Henry's constant of benzene.
                                      76

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                          	   20
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0      100    200    300    400    500
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Figure 5.48. Sensitivity of amount leached to concentration of oil in the sludge for chemicals with different
carbon partition coefficients.
                                   77

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Figure 5.49. Sensitivity of pulse width to recharge rate for chemicals with different organic carbon partition
coefficients.
                                   78

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Figure 5^1. Sensitivity of pulse width to organic carbon content for chemicals with different organic carbon
partition coefficients.
                                      80

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Figure 532. Sensitivity of pulse width to soil bulk density for chemicals with different carbon partition
coefficients.
                                       81

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                    0     0.1    0.2   0.3    0.4   0.5    0.6

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Figure 5,53. Sensidvity of pulse width to soil saturated hydraulic conductivity for chemicals with different
carbon partition coefficients.
                                   82

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Figure 554. Sensitivity of pulse width to Clapp-Hornberger constant for chemicals with different carbon

partition coefficients.
                                   83

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Hgure 5.55. Sensitivity of pulse width to evaporation rate for chemicals with different carbon partition

coefficients.
                                  84

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Figure 536. Sensitivity of pulse width to degradation half-life of the pollutant for chemicals with different
carbon partition coefficients.
                                    85

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Figure 5.57. Sensitivity of pulse width to Henry's constant for chemicals with different carbon partition
coefficients.
                                        86

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                                   	   20

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Hgure 5.58. Sensitivity of pulse width to the diffusion coefficient of the pollutant in air for chemicals with

different carbon partition coefficients and very small Henry's constant.
                                      87

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Rgure 5,59. Sensitivity of pulse width to the diffusion coefficient of the pollutant in air for chemicals with
different carbon partition coefficients and Henry's constant of benzene.

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Figure 5.60. Sensitivity of pulse width to concentration of oil in the sludge for chemicals with different carbon
partition coefficients.
                                     89

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                                                    0.4
Figure 5.61. Sensitivity of the amount of pollutant lost in the vapor phase to Henry's constant for chemicals
with different carbon partition coefficients.
                                       90

-------
B-31
i. L
er j
 ? •
  "
 J:    Amount Volatilized   (*)
g o

11
§ 2,


II


H
Is
 I
  §
  s
  n
Sensitivity
Relative  Sensitivity


      o   o
                                                           o
                                                           •
                                                           rO
                                  o
                                  •

                                  00

-------
                                             SECTION 6

                             SENSITIVITY RESULTS FOR VIP MODEL

    VIP was written to model movement of a chemical in a system similar to that used in RITZ.  VIP
includes oxygen transport, exchange, and loss which are not present in RITZ. It also incorporates chemical
movement in the vapor phase for the pollutant.  The resulting equations are solved numerically. Table 6.1
contains the input parameters used in this analysis of VIP.

    Figure 6.1 shows the predicted concentration of pollutant at the 2-m depth as a function of time for both
VIP and RITZ. The conditions modeled here represent conditions for which vapor movement is minimal
and oxygen is not limited so the two models would be expected to agree. The time at which the pollutant
reaches 2 m and the concentration in water at that time are in good agreement  between the models.  The
end of the contaminant pulse is much more gradual for VIP than for RITZ. Also, the concentration of
pollutant in water during the duration of the pulse decreases more rapidly in VIP than in RITZ.  As the
mesh size in depth decreases from 15.3 to 1.5 cm, the end of the pulse moves to earlier times and
approaches the time predicted by RITZ. This suggests that the gradual decline at the end of the pulse may
be due to the numerical techniques used in solving the problem. We were not able to test VIP for smaller
mesh sizes since a maximum of 150 mesh points in depth  can be used.

    Figure 6.2 shows the concentration of pollutant in  water at  the 2-m depth as a function of  time for 3
recharge rates. These results show that the travel time and pulse width increase as the recharge rate
increases as was observed in the analysis of RITZ.  Figures 6.3  to 6.12 show concentration of  pollutant in
water as functions of time for different values of partition coefficients, organic carbon contents, bulk density,
saturated hydraulic  conductivity, Clapp-Hornberger constant, half-life of pollutant, Henry's constant, diffusion
coefficient, and oil content. The impact of these parameters upon concentration are  nearly identical to those
discussed for RITZ with the following exceptions:

    1. The rate of decrease in concentration as a function of time during the duration of the pulse is greater
than that predicted  by RITZ. This is surprising since the two models predict the  same concentration at the
leading edge of the pulse.

    2. The pulse width predicted by VIP is somewhat greater than that predicted  by  RITZ due to the
gradual decline in concentration at the trailing edge of the pulse.

    3. When model parameters are such that substantial movement takes place in the vapor phase, radically
different concentration functions are predicted by VIP. Figure  6.9 shows this behavior for different values of
Henry's constant with a large diffusion coefficient.  VIP predicts low concentrations of pollutant at the 2-m
depth at very small times for simulations with Henry's constants exceeding 0.005.  RITZ does not predict this
early arrival of the  contaminant (see Figure 5.9). Also, although VIP predicts the end of the pulse will occur
at an earlier time, the change is not as large as  that predicted by RITZ.  Figures  6.11 and 5.11 also illustrate
substantial differences in predicted pollutant movement.   While VIP shows a rapid increase in  concentration
at 2 m to a  concentration of 0.01 g m"3, RITZ predicts the pollutant never reaches that depth.

    These results imply that sensitivity coefficients for VIP are approximately those of RITZ for conditions
when vapor movement is of minor importance and oxygen-limiting conditions do  not exist. A thorough
examination of the  sensitivities under oxygen-limiting conditions was not carried out.
                                                  92

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Table 6.1. Values of input parameters used for sensitivity analysis in VIP model.


Soil Properties
    Soil porosity (--)                                                                 0378
    Bulk density (Mg nf3)                                                            1.65
    Saturated hydraulic conductivity (m day )                                          0.19
    Clapp and Hornberger constant (--)                                                4.9

Site Characteristics
    Plow zone depth (m)                                                              0.5
    Treatment zone depth (m)                                                        2.0
    Mean daily recharge rate during each month (mm day"1)                            1.0
    Temperature during each month in plow zone (°C)                                  25
    Temperature during each month in treatment zone (°C)                             25
    Temperature correction coefficient for each month (--)                               1
    Sludge application rate (g/lOOg soil)                                               3.03
    Pollutant concentration in the sludge (g Mg"1)                                      4000
    Weight fraction of oil in waste (kg kg  )                                            0.25
    Weight fraction of water in sludge (kg kg"1)                                         0.01
    Density of sludge (Mg m"3)                                                        1.0
    Application  period (days)                                                         100000
    Application  frequency within application period (days)                              10000

Pollutant Properties
    Oil-water partition coefficient in plow zone (g m"3)                                  700
    Oil-water partition coefficient in lower treatment zone (g m  )                        700
    Air-water partition coefficient in plow zone (g m"3)                                 5.0E-9
    Air-water partition coefficient in lower treatment zone (g m  )                       5.0E-9
    Soil-water partition coefficient in plow zone (cm3 g"1)                              0.112
    Soil-water partition coefficient in lower treatment zone (cm  g"1)                    0.112
    Degradation constant within oil in plow zone  (day"1)                                0.00667
    Degradation constant within oil in lower treatment zone (day "J)                    0.00667
    Degradation constant within water in plow zone (day"1)                             0.00667
    Degradation constant within water in lower treatment zone (day"1)                  0.00667
    Dispersion coefficient for pollutant in unsat. pore  space (m2  day"1)                   2.0
    Adsorption/desorption rate constant water/soil (day"1)                               1000
    Adsorption/desorption rate constant water/oil (day"1)                               1000
    Adsorption/desorption rate constant water/air (day"1)                               1000
                                                  93

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Table 6.1. Continued.
Oxygen Properties
    Oil-air partition coefficient in plow zone (g g"1)                                    l.OE-7
    Oil-air partition coefficient in lower treatment zone (g g*1)                          l.OE-7
    Water-air partition coefficient in plow zone (g g"1)                                  l.OE-7
    Water-air partition coefficient in lower treatment zone (g g*1)                       l.OE-7
    Oxygen half-saturation constant with respect to oil degradation (g m*3)               l.OE-9
    Oxygen half-saturation constant within air phase in plow zone (g m'3)                l.OE-7
    Oxygen half-saturation constant within air phase in treatment zone  (g m*3)          l.OE-7
    Oxygen half-saturation constant within oil phase in plow zone (g m"^               l.OE-7
    Oxygen half-saturation constant within oil phase in treatment zone (g m*3)           l.OE-7
    Oxygen half-saturation constant within water phase in plow zone (g m"3)            l.OE-7
    Oxygen half-saturation constant within water phase in treatment zone  (g m*3)        l.OE-7
    Stoichiometric ratio of oxygen to pollutant consumed                                 3
    Stoichiometric ratio of oxygen to oil consumed                                       3
    Oxygen transfer rate coefficient between oil and air phases (day"1)                    1000
    Oxygen transfer rate coefficient between water and air phases (day'1)                 1000

Properties of Oil
    Density of oil (Mg m'3)                                                             0.8
    Degradation rate constant of oil (day"1)                                           0.003467
                                                   94

-------
<*-N
7E 10-°
CD
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•2
o 10"4
c
- 10-*
^
o
c
3 10-
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_ 	 RITZ
	 \nofi K\

	 VIP(3.5)
- - - VIP(6.06)
Im
	 VIP(8.00)
	 	 VIP(15.3)
-
—


—
1
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^^.^^^ Benzene
^^^•^^^
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0 500 1000 1500 2000
                                     Time  (days)
Figure 6.1. Predicted concentration of pollutant in water at the 2-m depth as a function of time using the
RITZ model and using the VIP model with different mesh sizes. Numbers in parentheses are mesh sizes in
centimeters.
                                   1000           2000
                                     Time  (days)
3000
Figure 6.2. Concentration of pollutant in water at the 2-m depth as a function of time for three recharge
rates.
                                          95

-------
                               1000
                                 Time
       2000
(days)
                                                    3000
Figure 63. Concentration of pollutant in water at the 2-m depth as a function of time for three organic
carbon partition coefficients.                              4
        e
        a>
        V.
        0)
   1

10-*

10-4

10-6
        a

       J
        Organic  Carbon
                (*)
          	  0.1
          	o.u
          	0.2
          	0.8
              iV
                           1000      2000      3000
                                 Time  (days)
                       4000
Figure 6.4. Concentration of pollutant in water at the 2-m depth as a function of time for different organic
carbon contents.

-------
                                1000
                                  Time
       2000
(days)
3000
Figure 6.5. Concentration of pollutant in water at the 2-m depth as a function of time for different bulk
density values.
                                            Saturated Conductivity.
                                                          m day"1
                                                           0.019
                                                           0.19
                                                    	1.9
                                1000           2000
                                  Time  (days)
                        3000
Figure 6.6. Concentration of pollutant in water at the 2-m depth as a function of time for different values of
saturated hydraulic conductivity.
                                       97

-------
        £
        D>
   1

10~2

10-4

io-«
        o
        c
        o
       o
Clapp-Hornberger
         Constant
    	 4.0
    	 4.9
    	8.0
                                             \
                                              \
                               1000          2000
                                 Time  (days)
                  3000
Figure 6.7. Concentration of pollutant in water at the 2-m depth as a function of time for different values of
the Clapp-Hornberger constant.
                                              Half-Life of
                                              Pollutant  (days)
                                                  	   50
                               1000           2000
                                 Time  (days)
                  3000
Figure 6.8. Concentration of pollutant in water at the 2-m depth as a function of time different values of
degradation half-life.
                                      98

-------
                      Diffusion Coefficient
                             2.0 it?  day'1
      Henry's Constant
                                1000           2000
                                  Time  (days)
                       3000
Figure 6.9. Concentration of pollutant in water at the 2-m depth as a function of time for different values of
Henry's constant.
              10
             10
               -2
             10-
         V

        <§
Diffusion  coefficient
               nf  day'1
        	  10-6
        	  0.02
        	0.76
        	2.00
       Henry's Constanf-
           5.0x10-9
                                1000           2000
                                  Time  (days)
                       3000
Figure 6.10. Concentration of pollutant in water at the 2-m depth as a function of time for different diffusion
coefficients and a small Henry's constant.
                                       99

-------
               10
                                           Diffusion  coefficient
                                                          rr? day-1
                                                   	  0.0001
                                                   	0.76
                                                   	  2.00
                                                  Henry's Constant-
                                                       0.24
                                 1000           2000
                                  Time  (days)
3000
Figure 6.11. Concentration of pollutant in water at the 2-m depth as a function of time for different diffusion
coefficients and a large Henry's constant for benzene.
                                                 Oil Concentration
                                 1000           2000
                                   Time  (days)
3000
Figure 6.12. Concentration of pollutant in water at the 2-m depth as a function of time for different
concentrations of oil in the sludge.
                                       100

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                                             SECTION 7

                            SENSITIVITY RESULTS FOR CMLS MODEL

Impact of Model Simplifications

    The predicted position of the chemical in the soil profile as a function of time is shown in Figure 7.1 for
three simulations. (Input parameters for soil properties are given in Table 4.2). The first case is predicted by
RITZ when no oil is present in the plow zone so the soil and chemical properties are uniform with depth.
The second case is predicted by CMLS using the same uniform soil properties used in RITZ and using
average daily infiltration and evapotranspiration values as used in RITZ.  The third  case is predicted by
CMLS using layered soil properties of Norfolk  but still using average daily infiltration and evapotranspiration.
A root depth of 0-5  m was used in the CMLS simulations.  When totally uniform systems are simulated, the
predicted positions of the bottom of the chemical pulse are in good agreement between RITZ and CMLS.
CMLS predicts that the top of the chemical moves more rapidly through the shallow soil layers  than does
RITZ. Hence the duration of the pulse entering the water table is less for CMLS than for RITZ. This
difference is because RITZ assumes that the flux of water at every depth in the soil is the same. Therefore
the top and bottom  of the chemical move at the same velocity (when no oil is present).  In CMLS the flux of
water passing any depth on a particular day is the difference between  the flux entering the soil surface and
the amount of water stored in the soil profile above that depth.  Therefore, the flux of water in  the root zone
decreases with depth so chemicals near the  soil surface move more rapidly than chemicals below the root
zone.  (CMLS predicts that the top and  bottom of the chemical pulse move at the same speed when the root
zone depth is zero and the soil properties are uniform with depth.)

    CMLS allows the user to model movement through layered soils where soil-water and chemical
properties change with depth.  The third set of lines in Figure 7.1 shows the predicted movement of benzene
when the soil is considered a layered system rather than a uniform one. In this case, the chemical reaches
the 2-m depth approximately 150 days earlier than when average soil properties are used. The duration of
the chemical pulse entering the water table is greater for the layered soil than for the uniform soil.  This is
primarily due to a lower velocity of chemical in the shallow soil layers where  the sorption coefficient is
greater than in the uniform case. For this soil, the use of uniform soil properties causes CMLS to
overestimate the travel time and  to underestimate the amount leached.

    The simulations above using CMLS and RITZ  assume the daily infiltration and evapotranspiration are
equal to their long term average  values for 1983 to  1991.  CMLS  was used to estimate benzene movement
using daily water fluxes for starting dates of January 1 of 1983 to 1990. Results are shown in Table 7.1.
Using layered soils with uniform  fluxes results in a 23% lower travel time than the totally uniform system.
Using layered soils and daily fluxes gives a mean travel time which is 47% less than the uniform soil -
uniform flux case. The amounts leached for the layered soil with uniform flux and the layered soil with daily
flux are 4 and 18 times greater than the uniform case,  respectively.  These leaching  amounts are based on a
half-life of 100 days. If the half-life were less than  100 days these factors would be larger. When average
infiltration and evapotranspiration rates  are used in CMLS, solute leaching is underestimated since the
impact of large rainfall events  and the resulting large water fluxes are essentially ignored.


General Impact of Input Parameters

    Figure 7.2 shows the positions of the top and bottom of the chemical pulse as functions of time.  The
different lines represent predicted depths for infiltration and evapotranspiration data beginning January 1 of
1983,1985, and 1987. Rainfall distributions for three year periods beginning on these dates are  shown in
Figure 73.  Clearly  the water fluxes or the weather sequences used to drive the model have a large impact

                                                 101

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Table 7.1. Comparison of predicted travel time, duration of loading, and amount leached for benzene the
Norfolk soil with different levels of simplification. Weather for Fairhope, Alabama.  Model used was
CMLS.               	

                                        Travel Time      Duration   Amount Leached
	  (days)          (Days)           (%)
Uniform Soil/Uniform Water Fluxes

Layered Soil/Uniform Water Fluxes

Layered Soil/Daily Water Fluxes

              Beginning Year
                   1983
                   1984
                   1985
                   1986
                   1987
                   1988
                   1989
                   1990

                   Mean
699

541
327
573
374
423
224
276
370
395

370.2
 70

115
242
152
 72
  5
 87
 28
 58
320

120.5
 1.0

 3.8
32.9
 3.6
 9.9
 5.4
29.9
16.3
 9.6
33.0

17.6
upon the predictions.  Therefore, weather will have a large impact upon the sensitivity coefficients.  Since it
is desired to get an understanding of the sensitivity for any weather sequence, the model was run many times
for different weather sequences characteristic of a site.  Results from all of the different simulations were
summarized and used in the sensitivity analysis. The site chosen is near Fort Cobb, Oklahoma.  Annual
rainfall there varied from 398 to 1034 mm during the 1948 to 1975 time period. Average annual rainfall was
709 mm during that time period.  Weather sequences were generated using the weather generator developed
by Richardson and Wright (1984) which is incorporated into the current version of CMLS. Probability
distributions of travel time and amount leached to ground water were obtained and used in subsequent
analyses.

    Figure 7.4 shows a histogram of travel time for the top of the  chemical to reach a depth  of 2 meters and
a second histogram of the relative amount of chemical originating  at the soil surface which passes the 2.0
meter depth. The different values shown are due only to different weather sequences, each of which is
equally likely at the Fort Cobb site. Each histogram is based on 100 simulations. Predicted travel times vary
from 707 days to 5056 days.  The corresponding values for the amount  of chemical leached below 2 m range
from more than 10"2 to less than  10"15 percent of that applied.  Figure 7.5  shows the distribution of travel
times expressed as cumulative probability distributions. Lines are shown for both the top and the bottom of
the chemical pulse.

    Since the weather has such a large impact upon travel time and amount leached, the results in this
section are presented as cumulative probability plots each based on 100 simulations with different lines
                                                102

-------
representing results for different input parameters of interest. For example, Figure 7.6 shows probability
distributions for travel time for 4 partition coefficients.  The travel times increase as the partition coefficient,
KQJ., increases as expected from equations 9 and 23. At a probability level of 0.50, travel times increase from
1375 days to 2250 days as K^ increases from 0 to 160 cm3/g. That corresponds to a 400-fold decrease in
amount leached for the 100-day half-He that was used.

    Figure 7.7 shows the dependence of travel time upon organic carbon content.  Here the solid line
represents the distribution of travel times for the Norfolk soil.  Other lines on the graph represent results
when the organic carbon content of each soil layer is increased by 0.1%, 0.5% and 1%. The travel time  at a
particular probability level increases greatly as organic carbon content increases (see Eqn  23).  The increase
appears to be greater at the probability level of 0.90 than it does at the 0.10 level. That is, the increase in
travel time per unit increase in organic carbon content is larger for weather sequences producing lower
leaching rates than in weather producing larger leaching rates.

    The travel time is shown to increase as the field capacity of the soil increases in Figure 7.8. This is
expected since increasing  the field capacity increases the soils capacity to store water and  reduces the flux of
water moving below the root zone. The travel time was found to decrease with an increase in water content
at wilting point (Figure 7.9). This is true since a decrease in the wilting point value will increase water
storage capacity.  The impact of both of these parameters is greater at high probability levels which
correspond to greater  travel times and generally lower infiltration.

    Figure 7.10 contains curves for three different bulk  densities. Differences between  the curves are  small
indicating the travel time depends only slightly upon soil bulk density.  This is consistent with results
observed for RITZ (Figure  5.4) and those observed for  the steady state model (Figure 3.3).

    CMLS computes the flux of water moving past the chemical each day after performing a water balance
for infiltration and evapotranspiration. This water balance depends upon the depth to  which water is
extracted from the soil (or the root depth), the evapotranspiration and the infiltration.  Potential
evapotranspiration is estimated from weather data using the Blaney-Criddle technique  (Blaney and Criddle,
1962). Actual evapotranspiration is related to potential  evapotranspiration with a proportional constant,
called crop coefficient.  Infiltration in CMLS is estimated from daily rainfall using the SCS curve number
method (USDA-SCS, 1972). As the curve number increases, the amount of runoff increases and infiltration
decreases.  Figures 7.11, 7.12, and 7.13 show the cumulative probability  distributions of travel time for
different root depths, crop coefficients, and curve numbers, respectively. Travel times increase as root depth
increases since the soil is capable of storing more water in  the root zone leaving less to percolate deeply into
the profile and leach the chemical. Travel times increase as crop coefficients increase  since added
evapotranspiration results in dryer root zones which can store a larger portion of infiltrating water. Travel
times increase as the curve number increases since daily infiltration decreases  as curve numbers increase
(especially for curve numbers above 70).  The impact of each of these parameters increases as the probability
level increases.

Sensitivity Coefficients

    Figures 7.6 to 7.13 provide an overview of the dependence of travel time upon different input parameters
and upon weather. This section presents sensitivity coefficients computed for the travel time, pulse width,
and amount leached.  Figure 7.14 shows  the median travel time, pulse width, and amount  leached as
functions of the organic carbon partition coefficient, K^.. Results are shown for three soils. (Points plotted
for travel time in the Norfolk soil correspond to the 4 travel times shown on Figure 7.6 at a probability level
of 0.50). Results could also be shown  for other probability levels of interest. Figure 7.15 shows the travel
time and its sensitivity coefficients for three levels of probability and a K^. = 80 cm3 g"1 in the Norfolk soil.
In the lower graph of Figure 7.15 the  line labeled 10% shows the travel time which is not  exceeded in 10%
of the simulations at each value  of K^. The line labeled 50% shows the travel time which is not exceeded in

                                                  103

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50% of the simulations. That line represents the median travel time for each value of K^. The line labeled
90% shows the time which is not exceeded in 90% of the simulations. The middle graph of Figure 7.15
shows the sensitivity for each line in the lower graph.  Since travel time increases approximately linearly with
KO,., the sensitivity coefficient, S, for travel time is nearly constant. The upper graph shows the relative
sensitivity for each line. Table 12 summarizes these sensitivities for travel times.  In a similar manner,
Tables 73 and 7.4 summarize the sensitivities for pulse width and amount leached, respectively.

    Figures 7.16 to 7.19 show median travel time, pulse width, and amount  leached (as a percent of the
inkial amount) as functions of organic carbon  content, bulk density, water content at field capacity, and water
content at wilting point, respectively.  The median travel time, pulse width,  and amount leached are shown as
functions of root depth, crop coefficient, and curve number in Figures 720  to 722. The sensitivity
coefficients for these input parameters are also shown in Tables 7.2, 73, and 7.4.

    Travel time and pulse width appear to be  linear functions of the parameters shown in Tables 7.2 and 7.3
except for the curve number.  Thus the sensitivity coefficient, S, is constant for the range of data used.
Figure 7.22 shows that the travel time and pulse width are approximately linear for curve numbers in the
range of 0 to 80 and in the range from 80 to 90. Therefore the coefficients in Tables 14 and  15 contain
values for each of these ranges.

    The logarithm of the amount of chemical  leached past  2 meters changes linearly with the parameters
analyzed (except for curve number).  That means the S is proportional to the amount  leached or S divided by
the amount leached is a constant. This fact can be used to estimate S  for any amount from the values shown
in Table 7.4.  Two sets of coefficients are present in Table  7.4 for curve numbers at each K^ since the range
is broken up  into two parts as discussed above.

    From Table 7.2 we can see that the sensitivity coefficients are positive for all parameters  except water
content at wilting point.  Relative sensitivities generally increase in absolute value in the order of curve
number (for values less than 80), K^, bulk density, water content at wilting point, organic carbon content,
root depth, crop coefficient, water content at field  capacity, and curve number for values above 80.  Within a
particular input parameter, the sensitivity coefficient, S, tends to increase as the probability level increases.
A 3-fold increase is not uncommon for several parameters. Relative sensitivities are generally constant or
decrease somewhat as probability levels increase.  For  many of the  parameters shown, the difference in travel
times between the 10% and 90% probability lines is greater than the difference due to the parameter being
analyzed.  This illustrates again that uncertainty in water fluxes due to unknown daily weather in the future is
a major component of the total uncertainty in a predicted value.

    Results shown in Table 73 indicate that the pulse width increases greatly as the probability level
increases.  Those increases are 50-fold or more in many cases. Sensitivity coefficients generally increase with
probability as well, although  relative sensitivities remain approximately unchanged.

    Table 7.4 shows that relative sensitivities for amount leached are generally negative  since the  amount
leached decreases as the parameter value increases. The magnitudes of these relative sensitivities are much
greater than  those for travel time or pulse width.  The magnitudes of these relative sensitivities are greater
than 1 which means the relative change in predicted amount  leached will be greater than the  relative change
in the parameter itself. A partial explanation for these large values of relative sensitivity is that the amount
leached is a small number so small absolute changes in the amount leached represent large relative changes.

    It is noteworthy that all  of the relative sensitivity coefficients shown in  Tables 7.2-7.4 are  larger than 0.54
in absolute value for some range of the parameters and some probability level. This indicates that all of the
CMLS parameters are important.
                                                  104

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Table 7.2. Sensitivity coefficients for travel time (days) which are not exceeded in 10%, 50%, and 90% of the simulations
performed.  Weather is for Caddo County, Oklahoma. Model used was CMLS.
Probability
Parameter

Partition Coefficient
- Norfolk soil
• Mdain soil
- Cobb soil
Organic Carbon
• Koc« 80 ml/g OC
• Koc- 40 ml/g OC
Bulk Density
- Koc- 80 ml/g OC
• Koc* 40 ml/g OC
Field Capacity
• Koc* 80 ml/g OC
-Koc- 40 ml/g OC
Wilting Point
-Koc= 80 ml/g OC
• Koc* 40 ml/g OC
Root Depth
- Koc =160 ml/g OC
- Koc- 80 ml/g OC
- Koc* 40 ml/g OC
Crop Coefficient
- Koc* 80 ml/g OC
- Koc- 40 ml/g OC
Curve Number
•Koc- 160 ml/g OC
• Koc- 80 ml/g OC
- Koc* 40 ml/g OC
- Koc = 160 ml/g OC
- Koc* 80 ml/g OC
- Koc* 40 ml/g OC
Parameter
Value

80.0
80.0
80.0

0.64
0.64

1.60
1.60

0.242
0.242

0.068
0.068

0.600
0.600
0.600

1.00
1.00

40
40
40
85
85
85

Time

1040
2880
2300

4310
2480

1130
972

1130
935

722
638

1490
1220
943

1100
822

1660
1150
957
3420
2740
2220
10%
S

4.8
25.0
16.2

6180
3010

627
0.0

9800
7100

-4570
-1530

1260
1630
1420

1270
907

4.9
5.3
3.7
268
237
195

sr

0.37
0.70
0.56

0.92
0.78

0.89
0.0

2.10
1.84

0.43
0.16

0.51
0.80
0.90

1.16
1.10

0.12
0.18
0.15
6.65
7.35
7.48

Time

1820
3630
3710

5520
3490

1870
1610

1920
1590

1410
1330

2300
1900
1670

1820
1560

2510
1940
1750
5010
4090
3740
50%
S

5.6
28.5
21.3

7160
3750

573
767

19900
17500

-11300
-6700

2890
3050
3170

1970
1730

7.8
6.8
5.5
366
317
304

sr

0.25 -
0.63
0.46

0.83
0.69

0.49
0.76

2.51
2.68

•0.54
•0.34

0.75
0.96
1.14

1.08
1.10

0.12
0.14
0.13
6.21
6.59
6.91

Time

2830
4360
5240

7020
4783

2860
2620

2770
2630

2280
2140

3280
2780
2550

2800
2400

3520
3010
2710
6540
5870
5490
90%
S

4.8
29.6
22.9

8420
3970

467
3.3

26700
22900

-11700
-11800

5190
5520
5200

3130
3220

8.8
8.6
7.3
446
426
425

sr

0.14
0.54
0.35

0.77
0.53

0.26
0.00

2.33
2.10

-0.35
•O.37

0.95
1.19
1.23

1.12
1.34

0.10
0.12
0.11
5.80
6.16
6.58
                                                     105

-------
Table 7.3. Sensitivity coefficients for pulse width (days) which are not exceeded in 10%, 50%, and 90% of the simulations
performed.  Weather is for Caddo County, Oklahoma. Model used was CMLS.
Probability
Parameter

Partition Coefficient
- Norfolk soil
- Mclain soil
• Cobb soil
Organic Carbon
- Koc= 80 ml/g OC
- Koc= 40 ml/g OC
Bulk Density
- Koc> 80 ml/g OC
- Koc- 40 ml/fl OC
Reid Capacity
- Koc* 80 ml/g OC
- Koc« 40 ml/g OC
Wilting Point
- Koc = 80 ml/g OC
- Koc = 40 ml/g OC
Root Depth
- Koc =160 ml/g OC
-Koc= 80 ml/g OC
- Koc = 40 ml/g OC
Crop Coefficient
-Koc- 80 ml/g OC
- Koc = 40 ml/g OC
Curve Number
-Koc= 160 ml/g OC
- Koc= 80 ml/g OC
-Koc= 40 ml/g OC
• Koc =160 ml/g OC
- Koc- 80 ml/g OC
- Koc = 40 ml/g OC
Parameter
Value

80.0
80.0
80.0

0.64
0.64

1.60
1.60

0.242
0.272

0.068
0.068

0.600
0.600
0.600

1.00
1.00

40
40
40
85
85
85

Width

37
546
42

122
58

14
1

14
1

17
0.5

237
85
31

14
1

84
12
1
82
14
2
10%
s

0.46
6.62
0.52

215
117

-37
0

-250
0

800
33.3

-1170
-425
-155

-35
-7.5

1.01
0.20
0.29
-9.70
-1.90
-0.30

sr

1.00
0.97
1.00

1.13
1.28

-4.3
0.0

-4.2
0.0

3.2
4.5

-2.95
-3.00
-3.00

-2.50
-5.00

0.48
0.68
1.63
-10.1
-11.1
-17.0

Width

292
885
359

659
382

329
138

330
137

267
154

578
307
140

281
136

594
247
82
791
345
126
50%
S

3.63
9.44
4.17

747
374

247
93

-1100
1300

-1100
-1170

-1180
-550
-570

392
60

1.72
1.47
0.45
14.6
3.60
0.40

sr

0.99
0.85
0.93

0.72
0.63

1.20
1.08

-0.81
2.30

-0.28
-0.51

-1.22
-1.07
-2.44

1.40
0.44

0.12
0.24
0.22
1.57
0.89
0.27

Width

707
1460
1130

1500
846

1040
567

968
704

779
603

1420
893
492

838
610

1440
893
564
2090
1240
952
90%
S

6.42
13.2
8.53

1040
501

357
-130

1160
1240

-6800
-3730

1150
888
385

1450
1160

3.37
1.90
3.14
99.2
37.4
31.5

sr

0.73
0.72
0.60

0.45
0.38

0.55
-0.37

2.89
4.25

-0.59
-0.42

0.49
0.60
0.47

1.72
1.90

0.09
0.08
0.22
4.03
2.57
2.81
                                                        106

-------
Table 7.4. Sensitivity coefficients for amount leached (% of initial amount) which was exceeded in 10%, 50%, and 90% of the
simulations. Weather is for Caddo County, Oklahoma. Model used was CMLS.
(Note: S/Amount is nearly constant for the range of parameters tested.)

Parameter




Parameter

Value
Amount

10%
S


sr


Amount
Probability
50%
S


sr


Amount

90%
S


sr
Partition Coefficient
-Norfolk soil
-Mdain soil
-Cobb soil
Organic Carbon
-Koc= 80 ml/g
-Koc= 40 mt/g
Bulk Density
-Koc= 80 ml/g
-K6c« 40 ml/g
Reid Capacity
-Koc- 80 ml/g
-Koc= 40 ml/g
Wilting Point
•Koc- 80 ml/g
-Koc= 40 ml/g
Root Depth
-Koc= 160 ml/g
-Koc- 80 ml/g
-Koc» 40 ml/g
Crop Coefficient
-Koc= 80 ml/g
-Koc= 40 ml/g
Curve Number
-Koc =160 ml/g
-Koc= 80 ml/g
-Koc- 40 ml/g
-Koc - 160 ml/g
-Koc= 80 ml/g
-Koc= 40 ml/g




OC
OC

OC
OC

OC
OC

OC
OC

OC
OC
OC

OC
OC

OC
OC
OC
OC
OC
OC
80.0
80.0
80.0

0.64
0.64

1.60
1.60

0.242
0.242

0.068
0.068

0.60
0.60
0.60

1.00
1.00

40
40
40
85
85
85
3.0E-1
9.2E-5
2.3E-4

2.0E-9
7.1E-5

1.6E-1
2.5E-1

2.0E-H
4.0E+1

4.2E+1
5.8E+2

4.5E-1
6.9E-1
9.5E-1

3.4E-1
5.9E-1

5.9E-2
1.2E-1
2.6E-1
3.7E-6
6.2E-5
1.9E-4
-4.7E-3
-l.OE-5
-2.1 E-5

-7.7E-8
-1.3E-3

-9.0E-2
-1.5E-2

-1.3E-t-3
-3.7E-f3

1.1E+3
5.7E+4

-2.2E+0
-3.4E-fO
-4.5E+0

-2.5E+0
•3.5E+0

-1.8E-3
-2.0E-3
-6.9E-3
-5.3E-6
-7.8E-5
-2.0E-4
-1.24
-9.17
-7.14

-24.5
-11.4

-0.88
-0.10

-15.3
-22.6

1.80
6.67

-2.97
-2.93
-2.85

-7.45
-5.90

-1.24
-0.65
•1.07
-121
-108
-92
2.7E-03
7.4E-07
1.9E-08

2.6E-13
3.3E-08

3.0E-03
4.1E-OE

2.5E-01
4.5E-01

3.8E-01
1.3E-t-01

5.0E-02
8.2E-02
1.1E-01

3AE-03
8.8E-03

2.9E-04
8.6E-04
1.5E-03
5.9E-11
1.4E-09
4.9E-09
-4.2E-05
•9.4E-08
-2^E-09

-1.2E-12
-7.9E-07

-1.6E-03
-1.7E-03

-2.4E+01
•4.4E+01

2.8E+01
2.2E+03

-2.5E-01
-4.1E-01
-5.6E-01

-3.1E-02
•7.3E-02

-1.2E-05
•3.3E-05
-4.8E-05
-1.4E-10
-2.8E-09
•9.7E-09
-1.24
•1.02
•9.07

-29.2
-15.2

•0.87
-0.65

-23.6
-23.6

5.1
11.4

-3.00
-3.00
•3.00

-8.96
-8.38

-1.70
-1.53
-1.28
-196
-172
-169
1.0E-06
2.4E-09
1.7E-13

4.7E-19
4.0E-12

2.1E-06
3.8E-06

1.8E-04
4.1E-04

8.2E-04
1.1E-01

2.4E-03
4.6E-03
6.2E-03

1.9E-06
8.8E-06

1.2E-07
4.8E-07
1.0E-06
1.4E-16
2.5E-15
8.4E-15
-2.0E-08
-3.4E-10
-2.0E-14

-2.8E-17
-1.0E-10

-1.1E-06
O.OE-t-00

-3.7E-02
-8.5E-02

7.4E-02
2.8E + 01

-1.2E-02
-2.3E-02
-3.1E-02

-3.5E-05
-1.9E-O4

-5.9E-09
-2.1E-08
-4.4E-08
-4.7E-16
-7.5E-15
-2.5E-14
-15.9
-11.3
-9.5

-38.6
-16.9

•0.83
0.00

•49.6
-50.1

6.2
16.7

•3.00
-3.00
-3.00

-18.3
-2.11

-1.89
-1.80
-1.76
-277
-257
-249
                                                      107

-------
         -C
         "a.
          
         O
    0


0.50


1.00


1.50


2.00
                               100         200         300
                                       Time  (days)
                                                         400
Figure 12. Predicted position of the top and bottom of the pollutant as functions of time for daily infiltration
and evapotranspiration values and three different dates for the simulation.
                                         108

-------
     200
   E
   E
   E
   E
150

100

 50

   0
200

150

100

 50

   0
           1985-1987
I
, i
ill.

                                i
I
           1987-1989
              .i
      1.1

                     L

                200     400     600     800
                       Time  (days)
                               l,im
                                      1000
Figure 73. Daily rainfall distributions for three-year periods starting January 1 at the Fairhope site in
Alabama.
                          109

-------
           0.50
        g  0.40
        0)

        g"  0.30
       U.
        
       5^
       •5  0.10
       QL
                                              = 80  g crrt*
                          1500       3000      4500
                           Travel  Time (days)
                                  6000
            0.50
            0.40
        a>
        I"  0.30
        
        • MM

        •i  0.10
                  -16
10H2       10"6       10
  Amount  Leached
               10
Figure 7.4. Upper graph is a histogram of the travel time for a chemical to move from the soil surface to a
depth of 2 m. for different weather sequences equally likely to occur in Caddo County, Oklahoma. Lower
graph is a histogram of the amount leached as a percent of the amount applied.
                                    110

-------
                            1500      3000       4500
                               Travel  Time  (days)
                                        6000
Figure 7.5. The probability that different travel times for the top and bottom of the pollutant to reach a
depth of 2m. will not be exceeded.
             1.00
1000    2000    3000    4000
     Travel  Time  (days)
                                                                 5000
Figure 7.6. The probability that different travel times for the top of the pollutant to reach a depth of 2m. will
not be exceeded for organic carbon partition coefficients of 0, 40, 80, and 160 cm3 g"1.
                                      Ill

-------
            1.00

            0.80
            0.60
        XI
        o
        •§  0.40
        QL.
            0.20
         oc
	  Std
	+.1  *
	+.5*
	+  1*
                                 5000          10000
                               Travel  Time  (days)
              15000
Figure 7.7. The probability that different travel times for the top of the pollutant to reach a depth of 2m. will
not be exceeded for organic carbon contents which are 0%, 0.1%, 0.5%, and 1% greater than the standard
Norfolk soil.
        .0
         O
         o
        £
                                 2000            4000
                                Travel  Time  (days)
               6000
Figure 7.8. The probability that different travel times for the top of the pollutant to reach a depth of 2m. will
not be exceeded for field capacity values which are 0, -0.01, and 0.01 m  m"3 greater than the standard
Norfolk soil.
                                        112

-------
                                   2000            4000
                                 Travel   Time  (days)
6000
Figure 7.9. The probability that different travel times for the top of the pollutant to reach a depth of 2m. will
not be exceeded for wilting point values which are 0, -0.01, 0.01, and 0.02 m3 m'3 greater than the standard
Norfolk soil.
                                   2000            4000
                                 Travel  Time  (days)
6000
Figure 7.10. The probability that different travel times for the top of the pollutant to reach a depth of 2m.
will not be exceeded for bulk density values which are 0, -0.2, and 0.1 Mg m*3 greater than the standard
Norfolk soil.

                                          113

-------
            1.00
                                                     Root Depth
                                                     —   0.4  m
                                                     --•   0.6  m
                                                     	   0.8  m
                                2000           4000
                               Travel  Time  (days)
6000
Figure 7.11. The probability that different travel times for the top of the pollutant to reach a depth of 2m.
will not be exceeded for root depths of 0.4, 0.6 and 0.8 m.
             1.00

             0.80
        HE  0.60
        JD
        D
        •§  0.40
            0.20

                0
                                2000           4000
                               Travel  Time  (days)
6000
Figure 7.12. The probability that different travel times for the top of the pollutant to reach a depth of 2m.
will not be exceeded for crop coefficients of 0.8,1.0 and 1.2.
                                       114

-------
                           2500       5000       7500
                              Travel  Time  (days)
10000
Figure 7.13. The probability that different travel times for the top of the pollutant to reach a depth of 2m.
will not be exceeded for curve numbers of SO, 70, 80, and 90.
                                      115

-------
                15000
10000
                                  McLaln
                                  Norfolk
                                  Cobb#1
                                                                      200
Figure 7.14. Median travel time, pulse width, and amount leached as functions of organic carbon partition
coefficient for three soils.
                                          116

-------
                    0.50
50
                                                  100         150
                                                    (9  cnf*)
200
Figure 7.15. Travel time which is not exceeded in 10%, 50%, and 90% of the simulations as functions of
organic carbon panition coefficient. Middle and upper figures show the sensitivity and relative sensitivity for
each function.
                                             117

-------
             15000
             10000
           -5  5000

           o
                   0
               2000
             W
              -1500
              I	1
            £ 1000


             o  500

            OL
                   0
                   1

           £  10-4
           •o
            2   10"8
            o
            §  10~12
           _j

           •£  10-"

            |  KT"

           <  10-24
                                          1       I
I	I
                    0      0.2    0.4    0.6    0.8    1,0    1.2
                               Organic  Carbon   (*)


Figure 7.16. Median travel time, pulse width, and amount leached as functions of organic carbon content for
three K,^ values.
                                     118

-------
             91
  4000



  3000



  2000



  1000



       0

    500



    375
             £  250
             o   125
             J2
             3
             O_
                    0

             x-^    1
             K
             O
             a
                io
                   -1
"c  10-2
 o

<
    10-*
                               K   =
                                oc
              G	
                                               -QJ-
                                                           a
                                                          -o
                     1.4
1.5
1.6
                                         1.7
1.8
                                 Bulk  Density    (Mg  nf5)
Figure 7.17. Median travel time, pulse width, and amount leached as functions of bulk density for two

values.
                                      119

-------
           to
           >*
           0
              3000
              2000
          •   1000

                   0

                500
                400
                             .0 ---- -a
            o
            •o
                300
|  200



J  100
3
Q_
       0

      1
                       a-
            •o 10'1
            ®
               io
            I  10"*
            o



            <  10-*
                 -e-
                        -&•
                  KOC =80

                  K  =40
                                          , .et ..... O
-©-.
                                            EJ
                   0.23          0.24          0.25          0.26

                Water  Content at Field  Capacity   (IT? nT3)



Figure 7.18. Median travel time, pulse width, and amount leached as functions of water content at field

capacity for two K^. values.
                                     120

-------
              2500
           >*  2000
              1500
              1000


          1
           P   500
                   0

                500
            OT
            >.
            o
            vt

            3
            0.
400



300



200



100



   0

   1
            .c
            o
            o
            O
                       Q-
                                          • -B
                                  =80

                                  =40
10~2




10-8



10-*
    0.05      0.06      0.07      0.08      0.09

Water Content  at  Wilting Point     (ni5  nr5)
Figure 7.19. Median travel time, pulse width, and amount leached as functions of water content at permanent

wilting point for two K^ values.
                                     121

-------
              5000

              4000

           „  3000
           E
           p  2000
           o   1000
=  80
                            0.20    0.40    0.60    0.80     1,00
                                   Root  Depth  (m)
Figure 7.20. Median travel time, pulse width, and amount leached as funcdons of root depth for three
values.
                                      122

-------
              5000
              4000
           „  3000
           E
           p  2000
           g  1000
           1-
                   0
                500
                400
                300

            ~  200

            J  100
            CL
                   0
                  1
               10'2
            0
            "O
            o
            o
            I 10-
            O

            < 10-«
=  80
=  40
                   0.50      0.75       1.00      1.25       1.50
                               Crop  Coefficient

Figure 721. Median travel time, pulse width, and amount leached as functions of crop coefficient for two
values.
                                    123

-------

             10000
              8000
              6000
          ^  4000


          1
           P  2000
                      -- K
                            M
            (0
            >»

            T31000
               500
                  0*
           •g  io-8
            o

           £  10-12
           "c

            o  10-"
K
                            ,.
=160


=  80
=  40
                     O"
                                    -~S-~Ar
20      40     60      80

      Curve Number
                                                           100
Figure 7.22. Median travel time, pulse width, and amount leached as functions of curve number for three

values.
                                   124

-------
                                             SECTION 8

                          SENSITIVITY RESULTS FOR HYDRUS MODEL

General Impact of Model Parameters

    Figure 8.1 shows the predicted concentration of pollutant in water at a depth of 2 m for simulations with
daily water fluxes.  Results are shown for simulations beginning January 1,1983, 1985, and 1987. Rainfall
distributions following those dates are shown in Figure 73.  As was observed in the case of CMLS, travel
time, pulse width, and amount leached vary greatly with the different starting dates. The concentration
curves are not smooth bell-shaped curves but have greatly different shapes due to different rainfall
distributions. Pulse widths for these simulations are approximately 400 days. The predicted amounts of
pollutant leached below the 2-m depth were 27%, 3%, and 10% for 1983,1985, and 1987, respectively.  The
results for 1983 are in good agreement with those from CMLS (Figure 12 and Table 7.1). For 1985 and
1987, CMLS predicts more rapid movement to the 2-m depth and greater amounts leached.

    The results presented in Figure 8.1 again indicate the large impact of weather variability upon predicted
pollutant leaching. As a result, model sensitivity is dependent upon weather used. Ideally, we could run
HYDRUS many times for different weather and incorporate probabilities into the analysis as was done with
CMLS. That approach was not feasible in the time frame and funding of this project because of the
computational time required. It would be worthwhile for future work. Instead, we chose to calculate model
sensitivity using uniform soil properties and uniform water fluxes.  This is a serious compromise since these
assumptions simplify the flow and transport problem  to the  degree that many of the sophisticated features of
HYDRUS do not enter into the solution.  Table 8.1 contains the basic input parameters used in the
sensitivity analysis which follows.

    Figures 8.2 shows the concentration of pollutant at the 2-m depth as a function of time for different
values of half-life.  The concentration decreases substantially as the half-life decreases.  The peak of the
pulse in Figure 8.2 appears to move slightly to the left as half-life decreases. By comparing  the curve in
Figure 8.2 for a half-life of 104 days to those in Figure 8.1 we see that simulations using uniform soil and
uniform flux results in a larger travel time and a lower concentration than predicted with daily fluxes and
non-uniform soil properties.

    Figure 83 shows the impact of different partition coefficients of chemicals in soil upon the concentration
of pollutant at the 2-m depth as a function of time. This result is very similar to that obtained for organic
carbon partition coefficient and organic carbon content in the  previous models.  This is  reasonable since  the
partition coefficient is often approximated as the product of the organic carbon content  and  the organic
carbon partition coefficient.

    Figures 8.4 to 8.14 illustrate the dependence of concentration  upon other model parameters. Note that
the concentration scale shown on Figures 8.2, 83, 8.12, and  8.13 extends to 0.50 g m  while its limit is 0.25 g
m"3 for the remaining figures. Figures 8.4 shows that the time at which the maximum concentration reaches
a depth of 2 m decreases as the saturated hydraulic conductivity increases. The  maximum concentration
increases with increasing saturated hydraulic conductivity. The travel time increases and maximum
concentration decreases as the bulk density of  the soil increases as shown in Figure 8.5.  The residual water
content (see footnote in Table 4.2) has only a slight impact  upon the concentration function (Figure 8.6).
Figure 8.7 shows that the travel time increases somewhat as the saturated water  content increases from 0.32
to 0.44 m3 m'3.  The maximum concentration decreases by a factor of 2 over this range  of water contents.
Pollutant concentration changes substantially as the van Genuchten hydraulic parameter ft changes (Figure
8.8). A change from 0.02 to 0.04 cm*1 in the van Genuchten parameter a produces a large change in travel
time but an additional increase to 0.04 cm*1 has little effect  on the prediction (Figure 8.9).  The impact of

                                                  125

-------
Table 8.1. Values of input parameters used for sensitivity analysis in HYDRUS models.

Soil Properties (assumed uniform for each soil layer)
     Depth of soil layers (m)                                                   2.0
     Saturated water content (m3 m"3)                                          0.38
     Saturated hydraulic conductivity (m day"1)                                  0.19
     Bulk density (Mg m'3)                                                   1.637
     van Genuchten's a                                                        0.04
     van Genuchten's ft                                                       1.637
     Residual water content (m3 m"3)                                          0.04
Site Characteristics
     Uniform rainfall intensity (mm day"1)                                      5.12
     Uniform potential evapotranspiration (mm day*1)                           4.09
Pollutant Properties (assumed uniform for each soil layer)
     Molecular diffusion coefficient (m2 day"1)                                0.00004
     Dispersivity (m)                                                         0.027
     Decay coefficient for dissolved phase (day"1)                               0.0067
     Decay coefficient for adsorbed phase (day"1)                               0.0067
     Leading Freundlich isotherm coefficient (cm3 g"1)                          0.1136
     Freundlich isotherm exponent                                             1.0
Root Water Uptake Parameters:
     Power constant in stress-response function                                 3.0
     Pressure head at which transpiration is reduced by 50% (cm)                -200
     Root  density/effectiveness value                                          0.333
different values of dispersivity upon the concentration is shown in Figure 8.10.  The width of the pulse
increases and the maximum concentration decreases as the dispersivity increases.  Recall that dispersion is
one process which is ignored in RITZ, VIP and CMLS.  No effect of diffusion coefficient was observed for
the parameters used in this simulation (Figure 8.11).

     The dependence of pollutant concentration upon water uptake parameters of the roots is shown in
Figures 8.12 and 8.13.  The travel time and  concentration change appreciably as these parameters change.
That is expected since these parameters determine the amount of infiltrating water lost to the atmosphere
and therefore they have a direct impact upon the leaching of the pollutant below the  root depth.  Figure 8.14
shows that the travel time decreases and amount leached increases as the root depth  increases.  This
behavior is unexpected and it does not persist to a depth of zero since the travel  time is only 135 days for a
root depth of zero.


Sensitivity Coefficients

     Figures 8.15 to 8.26 show the travel time as a function of different input parameters.  The figures also
show the sensitivity coefficients calculated using equation 15 and relative sensitivities from equation 18. The
relative sensitivities are summarized in Table 8.2.  Figures 8.27 - 8.50 show the curves for pulse width and
amount leached.  Recall that positive relative sensitivities imply that the relative change in output is positive
when the relative change in input parameter is positive.  These results indicate the travel time is quite
sensitive to the vanGenuchten ft, the saturated water content, the partition coefficient, the root uptake
potential, and the bulk density.  Relative sensitivities for pulse width are quite high for saturated water
                                                  126

-------
Table 8.2. Summary of relative sensitivities for travel time, pulse width, and amount leached for the
HYDRUS model.
Input Parameter
Travel Time
Pulse Width
Amount Leached
Partition coefficient
Saturated conductivity
Bulk density
Residual water content
Saturated water content
vanGenuchten £
vanQenuchten a
Dispersivity
Diffusion coefficient
Root uptake pot. h^
Root uptake exponent
Root depth
0.12 to 0.42
-0.06 to -0.10
0.32 to 0.36
0.01 to 0.04
0.45 to 0.55
-0.52 to -0.25
0.19 to 0
•0.05 to -0.12
-0.001 to -0.015
0.02 to -0.42
0.25 to -0.1 5
-0.04 to -0.2
0.3 to -0.25
-0.05 to -0.08
0.32 to 0.36
0.03 to 0.045
0.42 to 0.45
-0.45 to -0.18
0.1 8 to -0.01
0.25 to 0.24
0.004 to 0.03
0.01 to 0.43
0.26 to 0.1 5
-0.04 to -0.25
-0.4 to -3.5
0.25 to -0.41
-1.3 to -1.6
•0.07 to -0.1 7
-2.0 to -2.6
2.2 to 1.0
-0.8 to 0.1
0.06 to 0.1 6
0.003 to 0.035
-0.01 to -1.1
-1.0 to -0.6
0.3 to 0.8
content, bulk density, dispersivity, and the vanGenuchten ft coefficient.  Relative sensitivities to the partition
coefficient vary continuously for relatively large positive values to large negative values. Relative sensitivities
for amount leached are generally larger in magnitude than those for travel time and pulse width. Sensitivities
for amount leached are opposite in sign to those for travel time. All three output parameters are quite
insensitive to residual water content and diffusion coefficient.
                                                 127

-------
            0)
    1.20
    1.00
    0.80
    0.60
    0.40
    0.20
       0
    1.20
    1.00
    0.80
           I  0.60
           £  0.40
g  0.20
o
o     o
    1.20
    1.00
    0.80
    0.60
    0.40
    0.20
                                               1983-1985
                                               1985-1987
                                               1987-1989
                           200     400     600     800
                                   Time  (days)
                                                 1000
Figure 8.1. Concentration of pollutant in water at the 2-m depth as a function of time using HYDRUS with
daily rainfall and daily evaporation. Different graphs show predictions for different starting dates.
                                     128

-------
        o>
0.50
           0.40
           0.20

                          1 - 1
                   Half Life  (days)
                    -  104
                    --   208
                        200      400     600      800
                                 Time  (days)
                                                  1000
Figure 82. Concentration of pollutant in water at a depth of 2 meters for different values of half-life.
            0.50

            0.40
            0.20
        o

        J
                              <<  (err?  g-1
                              ...   0.018
                              	   0.114
                               -   0.284

              200     400     600      800
                      Time  (days)
                                                              1000
Figure 83. Concentration of pollutant in water at a depth of 2 meters for different values of partition
coefficient.
                                    129

-------
           0.25
         ^

        E  0.20
        Q>
       "5
           0.15
           0.10
            0.05
        o
       o
  Saturated  Conductivity  (m day"1)
               	   0.09
               	  0.19
               	0.39
200     400      600     800
         Time  (days)
                                                             1000
Figure 8.4. Concentration of pollutant in water at a depth of 2 meters for different values of saturated
hydraulic conductivity.
            0.25

            0.20

        £   0.15
       "5
       ^   0.10

        d   0.05

       I      o
              Bulk  Density  (Mg  nT3)
               	  1,35
               	  1.65
               	1.85
                         200     400     600      800     1000
                                 Time  (days)
Figure 8.5. Concentration of pollutant in water at a depth of 2 meters for different values of bulk density.

                                    130

-------
u.zo
/-•x
t
E 0.20
o>
^^^^
v. 0.15
"o
£ 0.10
c
^••w
. 0.05
o
c
0 0
i i i i
6r ( rf irT8)
	 A A?
_ ..... V/.U4. —
	 0.04
	 0.10

-
* * »
* J^~l ^.
/^V
// N.
.// ^*
^ , ^"^ 	













0 200 400 600 800 1000
Time (days)
Figure 8.6. Concentration of pollutant in water at a depth of 2 meters for different values of residual water
content.
0.25
/••s
'E 0.20
o>
^^^
u 0.15
-2
"o
£ 0.10


c
»^
. 0.05
o
c
<

•' /^^^^V
' / •/* "~" "^^"v
.' y/ / '*^^s.
i .-^S*'' i ^^fe.^
















200      400     600
          Time  (days)
                                                         800     1000
Figure 8.7. Concentration of pollutant in water at a depth of 2 meters for different values of saturated water
content.

                                       131

-------
        u>
            0.25
            0.20
            0.15
            0.10
         .   0.05
        o
       O
                                       1.64
                                       2.54
                         200     400     600      800     1000
                                 Time  (days)
Figure 8.8. Concentration of pollutant in water at a depth of 2 meters for different values of van Genuchten
/9 parameter.
 CD
^_x


£
*O
            0.25
            0.20
            0.15
            0.10
        £
        ~  0.05
        o
        c
        ^     0
    a   (cm"1
	  0.02
	  0.04
	0.08
                 200      400     600      800
                          Time  (days)
                                                              1000
Figure 8.10. Concentration of pollutant in water at a depth of 2 meters for different values of van Genuchten
a parameter.
                                    132

-------
        o>
    0.25

    0.20

fe  0.15
"S
^  0.10

o  0.05

<§      0
Dispersivity (m)
 	   0.0113
 	   0.0273
 	0.0433
                        200      400     600     800     1000
                                 Time  (days)
Figure 8.10. Concentration of pollutant in water at a depth of 2 meters for different values of dispersivity.
        o>
            0.25
            0.20
            0.15
            0.10
        
-------

c
E

D>
^^^X
L.
-2
"5
^

c
*«•
*
o
c
o
r •>
u.ou

0.x ft
• *"T^/


0.30


0.20



0.10


0
i i i i
hM (cm)
eft
DU -
	 -100
* «
; \ 	 -200
; \ 	 -500
9 •
1 •
— 1 * —
1 »
9 »
V •
* * ^ ™ ^v
* / * _^,
* y * .x^*^ ^*^s^
/i ^ x^^f^i ^ <*^^**-l_
                         200      400     600     800
                                  Time  (days)
                                      1000
Figure 8.12. Concentration of pollutant in water at a depth of 2 meters for different values of root uptake
potential h^.
            0.50
            0.
            0.30
            0.20
         .  0.10
        o
        c
        o
        o
  Root Water Uptake Exponent

               	2

               	    4
200      400     600      800
         Time  (days)
                                                               1000
Figure 8.13. Concentration of pollutant in water at a depth of 2 meters for different values of root uptake
exponents.
                                     134

-------
           0.25

           0.20

           0.15

           0.10
       £
        „•  0.05

       <§      0

Root  Depth (m)
	   0.2
	  0.6
	1.0
                        200     400      600     800
                                 Time  (days)
                      1000
Figure 8.14. Concentration of pollutant in water at a depth of 2 meters for different values to root depth.
                                   135

-------
on
o
 '
£?
o
r+
o
3

8-
a
             Travel Time  (days)
           Senstlvlty
                            o>
                            o
00
o
en
o
o
o    01
o    o
o    o
ro
o
o
o
                                   Relative Senstlvlty
O

O)
       O

       Ol

-------
           w
           c
           0

          o:
-0.05



-0.10



-0.15



-0.20

    0


-100



-200



-300



-400


-500

 800
            -§  600
               400
               200
          £
          ]>
          yz
           CO
           c
           fl>
                           0.1      0.2     0.3     0.4     0.5

                      Saturated  Conductivity  (m  day"1)
Figure 8.16. Sensitivity of travel time to saturated hydraulic conductivity.
                                   137

-------
U.4U
> 0.30
CO
c
& 0.20
I
"o 0.10
o>
on
0
200
160
1*120
g 80
CO
40
0
800
co
5, 600
1 400
U
g 200
i_
0
1 1

-

_
1 1

1 1

~ *
-
1 1


, 	 	 	 - -
-

1 1
                     1.2
   1.4            1.6            1.8
Bulk  Density    (Mg  nT5)
Figure 8.17. Sensitivity of travel time to bulk density.
                                         138

-------
              0.06
           ?  0.04
           c
           9
           £ 0.02
           15
           0
           cc

                  0

              500


              400


           I* 300
w
g
               200
               100


                  0

               800
           (0
           •§  600
           o>
           E
   400
               200
                  0.02      0.04      0.06      0.08      0.10
                      Residual Water  Content  (n?  nf5)
Figure 8.18. Sensitivity of travel time to residual water content.
                                    139

-------
                0.6
            I  0.4
             c
             o
             ®
             >  0.2
                  0

             1000



               800
               600
g
               400
               200



                  0

               800
           OT
           >
           •o  600
           S—'


           
-------
             c
             0)
            CO
    0



 -0.2



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 -0.6
                -0.8

                   0
            w
            c
            0)
           CO
               -100
-200
               -300

                800
            x-s
             V)
             >.

            •§  600
            .1  400


            1>

             n  200
                    1.2
                1.6
2.0
2.4
2.8
Figure 8.20. Sensitivity of travel time to the van Genuchten ft parameter.
                                      141

-------
               0.20
           ?  0.10
            c
            0)
           ,>     0
           or
              -0.10
              4000

              3000

              2000
1
              1000
            -1000
               800
            X
           •§  600
               400
               200
0.02      0.04
                            0.05
                            a
                                                 0.06      0.08
Figure 8.21. Sensitivity of travel time to the van Genuchten a parameter.
                                    142

-------
o

p°
C/5
n

B.
ft
51
o
*•+•
o




q
3.
             T    , „    ,„   v
             Travel Time (days)
                          *   •  '
                       Senstlvtty
                                                           Re(at|v9  Senstlvlh,

                                                                             '
        O

        °
O

°
O
o
OO
oo
O
o
O
o
                                                                      I
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p
b
    •o
     o
     - 8
     —• 10
       o
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       O

       b
                                                                     l
                                                                     o
 I
p

b
en

-------
              0.02
              0.01
          c
          «
         v>
          £•
          j>

          "w
          c
-0.01




-0.02

    0



-100



-200



-300



-400



-500

 800
           (0
           >s


           -D  600
           o>

           .i  400
               200
                   0       0.005     0.010    0.015    0.020

                       Diffusion  Coefficient    (rrf day-1)
Figure 8.23. Sensitivity of travel time to diffusion coefficient.
                                   144

-------
oo
C/J
O

g.
c.
a,
n
I
n
Travel  Time (days)
                                             Senstivlty
                                       Relative  Sensttvfty
        I o

        o
        o
        I

     IT Is*
     o

     3
        O
        o
ro

S
0
                      S
                      0
55

S
0
                     oo

                     S
                     0
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o o    —
o   o   o   o
•     *    *    *
K)   O<   *>   Ul

-------
                0.4
            £•
            *>  0.3
            Ti»
             c
            $  0.2
            I
             0)
            o:
               120
               100
                80
             I  60
             I  40
                20
               800
            w
           •§  600
           >-x
            O
           |  400
               200
                                2.0          4.0           6.0
                         Root Water  Uptake  Exponent
Figure 8.25. Sensitivity of travel time to root uptake exponent.
                                    146

-------
o

00
i1
f
5

a.
n


1

K
o
o
             Travel Time  (days)
N>
o
o
                      o
                      o
o>     oo
o     o
o     o
     TO


     S°
     O
     
-------
            w
            c
            0>
   0.4



   0.2



    0



 -0.2



 -0.4

2000
            ^1000

            *>
            c
            0)
             -10001	L

                500
            >.  400
            o


           ^  300



           g   200



           -|   100

           CL

                   0
                                 0.1            0.2

                                    Kd (en?  g'
                                                0.3
Figure 8.27. Sensitivity of pulse width to partition coefficient.
                                     148

-------
              -0.00
          £•  -0.02
           w
           c  -0.04 -

              -0.06
          •5  -0.08
              -0,10
          £•

          T

          "w
           c
    -50




  -100




  -150




  -200

    500



  '  400



    300



5  200



5  100

Q.

      0
            o
           •u
                   0      0.1     0.2     0.3     0.4     0.5

                      Saturated Conductivity  (m day"1)
Figure 828. Sensitivity of pulse width to hydraulic conductivity.
                                  149

-------
   0.40




>  0.30




   0.20
            w
            c
           I

           o  0.10

           o:

                  0

               100


                80



             I* 60



             1  40



                20



                  0

               500


           It  400
           D


           ^  300


           ^
           g  200



           |  100

           Q.
                   1.2
                     1.4           1.6

                   Bulk  Density    (Mg
1.8
Figure 8.29. Sensitivity of pulse width to bulk density.
                                    150

-------
1
0>
o
"w
c
o
0
i
jj
OL
U.Ut)
0.04

0.02
0
300
200
100
0
500
400
300
200
100
0
• i i
x^
-


1 1 1

1 1 1
-
-
_
1 1 1
                   0.02       0.04      0.06      0.08      0.10
                       Residual Water Content  (n?  nf3)
Figure 830. Sensitivity of pulse width to residual water content.
                                      151

-------
    0.50
5*  0.40
c  0.30
o>
 «  0.20



•f  0.10
CK

       0

    500
    375
I  250

«
w
    125
       0

    800
 o  600
•o
*=  400

£

 S  200
                  0.30      0.35      0.40      0.45

                     Saturated Water Content  (m*



Figure 831. Sensitivity of pulse width to saturated water content.
                                                0.50
                         152

-------
            c
            0)
            5
-0.2



-0.4-



-0.6
                -0.8

                   0
                -50

           £

           ^  -100
           c


              -150
              -200

                500
            w

            o  375
            5  250
            •^



            8  125
                    1.2
               1.6
2.0
2.4
2.8
Figure 832. Sensitivity of pulse width to the van Genuchten ft parameter.
                                    153

-------
           w
           c

   0.2



   0.1



    0



 -0.1



 -0.2

3000



2000
           ^1000
           c
           9
           V)
            -1000

               500
               400
               300
           g  200


           J2  100

           a.

                  0
                  0.02      0.04      0.05      0.06

                                      a


Figure 833. Sensitivity of pulse width to the van Genuchten a parameter.
                                              0.08
                                    154

-------

               0.40


               0.30



               0.20



               0.10
              8000


              6000



          =g  4000
           c


              2000


                  0

               500


           'E 400


               300


           g  200


           .2  100
           Q_
                            0.01       0.02      0.03
                                 Dispersivity  (m)
0.04
Figure 834. Sensitivity of pulse width to dispersivity.
                                    155

-------
              0.04




          ]>  0.03

          "w
           c

              0.02




              0.01




                 0

              800




              600
              400

           c
           0)
           
-------
TJ
                400

                300

                200
            .2  100
            Q.
                   -400
                 -300
-200
-100
                                          hM (cm)
Figure 836. Sensitivity of pulse width to root uptake potential, h^.
                                     157

-------
                0.4
                0.3
                0.2
            I
             o  0.1
            &
                  0
               100
                80
                60
             g  40
            V)

                20
   0
500

400

300

200
               100
           o.
                  0
            D
           •o
                   0            2.0           4.0           6.0
                         Root  Water Uptake Exponent
Figure 837. Sensitivity of pulse width to root uptake exponent.
                                    158

-------
           500
           400
           300


       g  200

        o
       •|  100
       Q_
               0
                         0.2      0.4      0.6      0.8
                               Root  Depth  (m)
1.0
Figure 8.38. Pulse width of pollutant at 2-m depth as a function of root depth.
                                  159

-------
            w
            c
            0)


           5

           a:
               -1.0-
               -2.0
    -3.0-
               -4.01
£>
]>

"»»
c
®
               -20




               -40




               -60
               -80

                 8.0
                 6.0
             §   4.0
             c  2.0

             o


             <   0
                      0.1
                                     ,  (cm5
                                               0.2
Hgure 839. Sensitivity of amount leached to partition coefficient.
0.3
                                     160

-------
                 0.5
               *  0.4
             «o
             c  0.3
             o
             o  0.2


             •5  0.1
             on

                   0

                 4.0
                 3.0
             I  2.0
              c
              9
             V)

                 1.0
                   0

                 8.0
              ®

              o
                 6.0
                 4.0
              c  2.0
              o

             I    o
0.1
0.2
0.3
0.4
                                                                 0.5
                        Saturated  Conductivity  (m  day"1)
Figure 8.40. Sensitivity of amount leached to saturated hydraulic conductivity.
                                       161

-------
w
c

V)  -
                 0.5



                 1.0

            0)
            o:
    -1.5



    -2.0

       0
            c
    -1.0




    -1.5



    -2.0

     8.0



     6.0
              0)


             1  4.0
              o
              c  2.0

              o

             I    o
                    1.2
                       1.4           1.6            1.8

                    Bulk  Density   (Mg nf3)
Figure 8.41. Sensitivity of amount leached to bulk density.
                                      162

-------
          f
          "w

    0

-0.05


-0.10


-0.15


-0.20
    0
               -1.0-



           ?  -3'°

           &  -4.0-

               -5.0-
               -6.0
                8.0
               »

                6.0


                4.0
             c  2.0
             o
                  0.02      0.04      0.06      0.08      0.10
                      Residual Water  Content  (n?  nr5)
Figure 8.42. Sensitivity of amount leached to residual water content.
                                   163

-------
           c
           o
           I
           35
           «
           a:
               -1.0
               -2.0
-3.0-
                4.0

                  0
                -5

           £


           ^  -10
           c



               -15
               -20


                8.0

              b


              ' 6.0
             8  4.0
             c  2.0

             o


            <    0
                  0.30      0.35      0.40      0.45      0.50

                     Saturated Water Content  (nf m"3)
Figure 8.43. Sensidvity of amount leached to saturated water content.
                                    164

-------
                   4.0
               w
               c

                   2.0
                     0

                   4.0




                   3.0




               I  2.0




                   1.0
               o

               o
  0

8.0




6.0




4.0
               c   2.0

               o

              I     o
                      1.2
               1.6
2.0
2.4
2.8
Figure 8.44. Sensitivity of amount leached to the van Genuchten ft parameter.
                                           165

-------
                 0.5
            o
           ,>   -0.5-
            o
           oc
                 I.O

                 50
           £>
           ]>

           "w
            c
              9


              O
 -50






•100

  8.0




  6.0




  4.0
              3  2.0
              o
                   0.02      0.04       0.05       0.06      0.08

                                          a


Figure 8.45. Sensitivity of amount leached to the van Genuchten a parameter.
                                       166

-------
                0.20
            o
0.10

0.05
                   0
                10.0

                 8.0

             ~  6.0
             "Si
              g  4.0

                 2.0

                   0
                8.00
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            ^  6.00
            •o
            o
            o  4.00
            c  2.00
            o
            <     0
                              0.01       0.02      0.03      0.04
                                   Dispersivity (m)
Figure 8.46. Sensitivity of amount leached to dispersivity.
                                       167

-------
   0.04
w
c
               0.03




               0.02
5  0.01
5>
e

       0

     4.0




     3.0




 H  2.0




     1.0




       0

     8.0
     6.0
 "§  4.0
 §  2.0

 o


 I    o
                   0       0.005     0.010

                       Diffusion Coefficient



Figure 8.47. Sensitivity of amount leached to diffusion coefficient.
                                       0.015     0.020

                                       (nf day'1)
                          168

-------
            •s  -1.0-
             C
             o

             >  -2.0-
              T3
              O
                12.0
              "   8.0
              c  4.0

              o

              I    o
                   -400     -300
-200      -100

      (cm)
                                           50
Figure 8.48. Sensitivity of amount leached to root uptake potential,
                                     169

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           !>  -o.5L
            c
               -1.0

            o  -1.5-

               -2.0
                  0
            M
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 -2.0



 -4.0


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  8.0
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' 6.0
                4.0
             c  2.0
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                                4.0
                                                            6.0
                         Root Water  Uptake  Exponent
Figure 8.49. Sensitivity of amount leached to root uptake exponent.
                                    170

-------
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00
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t
         Amount Leached (*)
              10
              *

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       09

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                                             SECTION 9

                                     UNCERTAINTY ANALYSIS

    The first part of this report deals with the sensitivity of model output to changes in single input
parameters.- This section will show overall model uncertainty due to combined uncertainty in model
parameters. Monte Carlo techniques were used in this analysis.  This approach characterizes model
uncertainty by making many simulations with the model using different input parameters selected at random
from distributions of the real parameters.  This results in many model outputs which can then be
summarized probabilistically to provide insight on model uncertainty. The technique can be applied to any
model, but it requires many computations. This section includes results for RITZ.  Figures 7.5 to 7.13 show
uncertainty in travel time due to uncertainty  in weather for CMLS.

Uncertainty Analysis for RITZ Model

    In order to conduct Monte Carlo simulations for estimating model uncertainty, we need to  generate
many sets of model input parameters with means, standard deviations, and correlations characteristic of the
actual distributions for these parameters. A  multivariate data generating procedure using principle
components (Haan, 1977; Zhang et al., 1993) was used.

    Since a uniform soil profile is assumed in RITZ, the depth weighted average soil properties for the
Norfolk soil were used. The probability distributions of the soil parameters were determined using soil data
from 87 soil profiles and ten soil series of sand from Florida.  The bulk density, saturated conductivity,
organic carbon content, saturated water content,  and Clapp-Hornberger constant were best described by a
log normal distributions. The means and standard deviations of soil properties from the analysis are given in
Table 9.1.  Statistics for bulk density, saturated water content, and Clapp-Hornberger constant for Norfolk
sand obtained from undisturbed soil cores (Quisenberry et al., 1987) are included in Table 9.1 along with
values from Jury (1986). The  depth weighted saturated hydraulic conductivity values from in-situ field data
show a large variability with a coefficient of variation of 2.07.  This variability includes variability across
depths and sites as well as experimental error.

    The range of values for the partition coefficient and half-life of benzene  are also shown in Table 9.1. A
wide range of values for these properties were found in the literature. Normal distributions were assumed
for these two parameters.

    The statistical characteristics of the soil and chemical parameters used in the Monte Carlo analysis are
shown in Table 9.2.  Soil properties and chemical properties were assumed to be uncorrelated.   If the
generated saturated water content exceeded  the soil porosity based on the generated bulk density, the set of
generated parameters was rejected and another set was generated. One hundred sets  of input parameters
were generated for Monte Carlo simulation.

    Results of incorporating the variability and uncertainty of soil parameters into RITZ for the standard
scenario defined in Table 5.1 are shown in Figure 9.1.  This figure shows the concentration of the pollutant
in water as a function of time for three probability levels.  Consider the curve labeled 95% probability.  At
any instant of time, the predicted concentration of pollutant at the 2-m depth was less than the plotted value
for 95%  of the simulations.  Likewise, the predicted concentration of the pollutant in water was less than the
plotted values for 50% and 5% of the simulations for the lines labeled 50% probability and 5% probability,
respectively.  These curves indicate that the maximum concentration has values in the  range of 0.06 to 0.64 g
m  for 90% of the  simulations.  Five percent of the predicted values are greater than  0.64 g m'3 and 5% are
less then 0.06 g m*3. Figure 9.2, 93, and 9.4 are cumulative probability plots for  travel time, pulse width, and
amount leached below the 2-m depth.  Figure 9.2 shows the probability that the travel time will be less than

                                                  172

-------
Table 9.1. Variability of soil properties.
Parameter
Bulk Density (Mg m3)
Bulk Density (Mg m3)
Bulk Density (Mg m3)
Bulk Density (Mg m3)
Saturated Conductivity
(m day'1)
Saturated Conductivity
(m day1)
Saturated Conductivity
(m day'1)
Saturated Conductivity
(m da/1)
Organic Carbon (%)
Organic Carbon (%)
Saturated Water Content
(m3 nf3)
Saturated Water Content
(m3 nf3)
Saturated Water Content
(m3 of1)
Porosity
Clapp-Hornberger
Constant
Clapp Hornberger
Mean
1.59
120-1.67
138-1.47
1.64
0.67-143
0.04-3.16
1.5-2.56
0.26
0.21-1.23
0.04-2.59
0.36-0.47
0.38
0.35
037-0.53
2.06-4.69
11.6
CV
0.05-0.06
0.03-0.26
0.08-0.20
0.02
0.73-14.9
0.48-3.20
1.10-1.30
2.07
0.30-0.74
5.75-0.60
0.04-0.11
0.03
0.05
0.11-0.07
0.08-0.17
0.19
Source
Florida soils1
Jury, 1986
Staffer, 1988
Norfolk sand,undisturbed
Quisenberry et. al., 1987
Florida soils1
Jury, 1986
Staffer, 1988
Norfolk sand,in-situ
Quisenberry et. al., 1987
Florida soils1
Staffer, 1988
Florida soils1
Norfolk sand,undisturbed
Quisenberry et. al., 1987
Norfolk sand,in-situ
Quisenberry et. al., 1987
Jury, 1986
Florida soils1
Norfolk sand, undisturbed
 Constant
Quisenberry et. al., 1987
                                                   173

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Table 9.1. Continued.
Parameter
Koc (cm3 g1)
Koc (cm3 g'1)
Koc (cm3 g'1)
Koc (cm3 g1)
Koc (cm3 g1)
Mean
19000
23000
120000
83000
83,92,107
cv
0.65
0.73
0.00
0.16
Oil2
Source
Pyrone in sand sediments
Karickhoff and Brown, 1979
Methoxychlor in sand fraction
Karickhoff and Brown, 1979
Pyrone in clay fraction
Karickhoff and Brown, 1979
Methoxychlor in clay fraction
Karickhoff and Brown, 1979
Benzene in soils
Half Life (days)
Half Life (days)
104,106
  231
            Karickhoff and Brown, 1979
                Rogers et al., 1980
                 Chen et al., 1992

                benzene in solution
               Zoetman et al., 1981
          Goldsmith and Balderson, 1988

                  benzene in soil
                 Rifai et al., 1988
Kd (cm3 g1)
 2.01
0.31
Jury, 1986
1. Ten Florida soil series are: Albany sand, Blanton sand, Bonifay fine sand, Chobee sandy loam, Manatee
sandy loam, Myakka sand, Orangeburg sandy loam, Pomona sand, Wauchula sand, and Winder loamy sand.

2. Calculated  from three values at the left.
                                                174

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Table 9.2. Statistics of parameters used in RITZ uncertainty analysis

Mean
Coef. of Variation, CV
Log mean
LogCV
Correlation Matrix1

Bulk Density, p
Sat. Conductivity, Y^
Organic Carbon, OC
Sat. Water Content, 8S
Clapp-Hornberger Const, CH
Partition Coefficient, K^
Pollutant Half-life, t1/2
P
1.65
0.05
0.4995
0.10

P
1.00
-0.761
-0.189
-0.872
0.726
0.0
0.0
KS
0.19
2.00
-2.465
0.593

KS

1.00
0.012
0.572
-0.731
0.0
0.0
OC
0.14
0.40
-2.040
-0.189

OC


1.00
0.227
-0.374
0.0
0.0
«.
0378
0.05
-0.974
-0.051

».



1.00
-0.695
0.0
0.0
CH K^
4.9 80
0.14 0.20
1.580
0.088

CH K^




1.00
0.0 1.00
0.0 0.0
V
104
0.20
-
-

tl/2






1.00
1. Correlation matrix for soil properties was obtained from log transformed data of Blanton Sand, FL.
                                                  175

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the travel time plotted.  The figure indicates that the travel time for the pollutant ranges from approximately
940 to 1460 days with 90% of the values falling in the 980 to 1370 day range. Figure 9.3 shows the
probability that the pulse width will be less than the pulse width plotted.  The computed pulse width varies
from 950 to 1050 days with 90% of the values in the between 960 and 1020 days.  Figure 9.4 shows the
probability that the amount leached will be less than amounts plotted.  The predicted leaching varies from
0.009% to 0.2% of the amount applied with 90% of the values in the range of 0.02% to 0.2% of the amount
applied.  Clearly, there is a large uncertainty in model predictions due to only soil properties.

    Figures 9.5, 9.6, 9.7, and 9.8 show results of the uncertainty analysis due to uncertainty in the partition
coefficient and half-life of the pollutant. The maximum concentrations on the 95%, 50%,  and 5% probability
curves are 0.7, 0.21, and 0.008 g m*3, respectively. This  range is slightly larger than those for soil properties.
Figure 5.6 shows  that the travel time varies from 970 to 1310 days for these simulations with 90% of the
values in the range of 1050 to 1220 days. Pulse width takes on values of 950 to 1010 days  due to uncertainty
in these chemical properties.  Ninety percent  of the values are in the range of 970 to 1000 days.  The amount
leached varies over more than 4 orders of magnitude with 90% of the leaching amounts in the range of 0.004
to 0.4 % of the amount applied (Figure 9.8).  In this case the uncertainty b amount leached due to chemical
properties exceeds that due to soil properties.

    Simulations for systems incorporating uncertainty in both soil and chemical properties produced results
shown in Figures 9.9, 9.10, 9.11, and 9.12.  The ranges of values predicted here exceed those for  soil and
chemical properties individually. Large differences in predicted  concentrations are shown  in Figure 9.9 with
nearly 150-fold differences in concentration between the 5% and 95% lines.  Travel times  take on values
from 950 to 1540 days with 90% of the values b the 960 to 1350 day range.  Pulse widths  vary from 950 to
1060 days with 90% of the simulations between 955 to 1020 days. Calculated amounts  leached beyond the 2-
m depth have values of 0.0003 to 0.8%. Ninety percent of the values lie b the range of 0.004 to 0.5%.


Summary

    The uncertainties presented come  as a result of uncertainties b soil properties, organic carbon  partition
coefficient, and half-life of the pollutant. These uncertainties would increase if all of the chemical properties,
oil properties, and site characteristics were bcluded in the analysis. One site characteristic with  a large
degree of uncertainty is the weather and hence the infiltration and evapotranspiration at a site.  Results
shown for CMLS (Figures 7.2 to 7.13)  and for HYDRUS (Figure 8.1) indicate the significance of weather
uncertainty on the predictions.  Haan and Nofziger (1991) presented the results of a detailed simulation
study that evaluated the impact of variations in weather sequences on the transport of a solute through the
soil profile. They demonstrated that large differences in the times required for a solute to reach a given
depth b the  soil profile and b the concentrations of the solute that at that depth exist  due entirely  to
differences in weather sequences at the specific site.  Zhang et  al (1993) presents an analysis of  uncertainty
for CMLS as well as  implications of this uncertainty for model use and soil sampling. They suggest  that
results from field experiments and modeling studies involving only one weather sequence are of  little value in
making decisions about future behavior of a chemical in a soil system.

    The fact that these uncertainties exist must be incorporated into our use of models. It is more realistic
to think b terms of the probability that a certain type of behavior will take place rather than attempting to
say whether or not that behavior will occur.  Moreover, the fact that soil properties vary spatially within a
mapping unit must be acknowledged.  We will be better served to simulate movement in that unit for the
many different sets of properties expected and to summarize the model predictions than to attempt to derive
some representative set of parameters for the region hoping that the model output for  that set will  describe
the entire region. By simulating results for many sets of parameters expected b the area, we  can determine
the contaminant leaching for the area and gab knowledge of the likely range of leaching possible.  All of this
                                                  176

-------
information can then be used in the decision-making process. Uncertainties must also be included when
validating models experimentally.

    Finally, the uncertainty in model predictions due to uncertainty in input parameters represents only part
of the overall uncertainty. This analysis does not incorporate uncertainty due to model simplifications of real
phenomena, errors in understanding that phenomena, or errors in solving the simplified problem.
                                                 177

-------
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^ Tr^i-^A*-^-
Probablllty
Probability
Probability
Properties


_




_



i
                               1000
2000
                                                  3000
                                  Time  (days)
Figure 9.1. Concentration of pollutant at the 2-m depth which is not exceeded for 5%, 50%, and 95% of the
simulations which incorporate uncertainty in soil properties.
1600


1400


1200


1000


 800
                        Soil Properties
                                 I	I	I
       J	I
                    .001   .01 .05 0.2    0.5 0.8 .95 .99  .999
                             Cumulative  Probability
Figure 92. Probability that different travel times will not be exceeded based on uncertainty in soil properties.
                                     178

-------
           1100
         §•1050
         o
        £1000
        T
         8   95°
         3
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             900
            i     i    i     i     r

             Soil Properties
                               J	I
                  .001   .01 .05 0.2   0.5 0.8 .95 .99  .999

                           Cumulative Probability



Figure 93. Probability that different pulse widths will not be exceeded based on uncertabty in soil properties.
o
o
    io-2
             10
o  10-*


   io-5
                                            Soil Properties
                                                   i    i     i
                  .001   .01.05 0.2   0.5 0.8 .95 .99  .999

                          Cumulative  Probability
Figure 9.4. Probability that different amounts leached will not be exceeded based on uncertainty in soil

properties.
                                   179

-------
            1.00
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          	SO* Probability

          	95* Probability




                Koc  and  Half-Life
                              1000
                  2000
3000
                                 Time  (days)
Figure 9.5. Concentration of pollutant at the 2-m depth which is not exceeded for 5%, 50%, and 95% of the

simulations which incorporate uncertainty in selected chemical properties.
            1600
            1400
         o
        TJ
             1200
         o
             1000
              800
\    r
                                                          \     I
                        Koc,  and  Half-Life
                             J	I
                    .001   .01.05 0.2   0.5 0.8 .95 .99  .999

                            Cumulative  Probability
Figure 9.6. Probability that different travel times will not be exceeded based on uncertainty in selected

chemical properties.
                                    180

-------
           1100
           1050
           1000
         3
        0.
             950
             900
                       Koc, and Half-Life
J	I
j	i	i	i     i
                  .001  .01 .05 0.2    0.5 0.8 .95 .99  .999
                           Cumulative  Probability
Figure 9.7. Probability that different pulse widths will not be exceeded based on uncertainty in selected
chemical properties.
             io-1
         •g  io-2
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             10-
         c
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                  r
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r
: 0
1 1 1
Koc and Half-Life :
•!
•
1 1 1 1 1 1
                  .001   .01 .05 0.2    0.5 0.8 .95 .99  .999
                           Cumulative  Probability
Figure 9.8. Probability that different amounts leached will not be exceeded based on uncertainty in selected
chemical properties.
                                    181

-------
            1.00
            0.80
       £   0.60
       I
            0.40
            0.20
        o
       0
                              	5*  Probability
                              	50*  Probability
                              	95*  Probability
                                    Soil  Properties,
                                    Koc, and Half-Life
                              1000          2000
                                 Time  (days)
                                                      3000
Figure 9.9. Concentration of pollutant at the 2-m depth which is not exceeded for 5%, 50%, and 95% of the
simulations which incorporate uncertainty in soil and chemical properties.
 >*
 o
•o
         S
            1600
            1400
             1200
             1000
              800
                        Soil Properties,
                        Koc,  and  Half-Life
                    ,001   .01.05  0.2   0.5 0.8 .95 .99  .999
                            Cumulative  Probability
Figure 9.10. Probability that different travel times will not be exceeded based on uncertainty in soil and
chemical properties.
                                    182

-------
           1100
         >*
         D
        £  1000
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             950
             900
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                       Sol! Properties,
                       Koc,  and  Half-Life
I     I    I	I
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                   .001   .01 .05  0.2    0.5 0.8  .95 .99  .999
                           Cumulative  Probability
Figure 9.11. Probability that different pulse widths will not be exceeded based on uncertainty in soil and
chemical properties.
         O
         D
         
-------
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                                                                                            •

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Zoetman B.CJ, E. De Greef, and FJ J. Brikmann. 1981. Persistency of organic chemicals in ground water,
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                                            APPENDIX
                                Problems Encountered in Using Models

This section describes some problems we encountered in using the computer programs.  We did our best to
verify that these problems are real and are not just the result of our inability to correctly use the models.

VIP

    VIP is distributed as an executable interactive program. To facilitate the many simulations we needed to
make for this analysis we requested and obtained source code for  a batch version of the program.  This was
compiled into a batch program. We found the batch version produced results in agreement with the
interactive version when the oil content of the sludge was zero, but it failed when oil was present.  With  oil
present, degradation rapidly decreased to zero and oxygen became limiting even though  parameter values
defined a system in which oxygen was not limiting. This suggests that the source code provided was not  the
latest version and included errors not present in  the interactive program.

    An error was detected in the source code where  the definition of subroutine OUT did not include the
same number of parameters as the code calling this subroutine. This did not produce a compiler error, but
it could produce unexpected results at run time.  We cannot determine if this error exists in the interactive
code.

    The VIP manual states that advection of air is included in  the model and an input parameter is provided
for the advection velocity in the unsaturated pore space. Our examination of the source code revealed that
this component is not implemented and this variable  is not used. Also no differences in output from the
interactive program  were observed for a wide range of values of this input parameter.

    Because of the first problem mentioned, we  were forced to use the interactive program for our analysis.
This program worked as intended, but our efforts were hampered in two ways. First, the program  supports a
maximum of 150 nodes on the  space grid.  This limited the size of the grids we could use (See Figure 6.1).
The interactive code also limits the number of times  at which results can be generated to 50.  This was a
problem in our analysis since we did not know in advance  what times to specify. These  limitations may be
more evident to us than to general VIP users due to  the analysis we were performing.

    Finally, we would like to know if the gradual decline in concentration shown in Figure 6.1 is a  result of
discretization error or if it represents the true solution to the problem.  In addition, we would like  to know
why the concentration decreases more rapidly than that predicted  by RITZ (See Figure 6.1 and the
discussion of it). Possibly an error exists in RITZ or VIP.
HYDRUS

    HYDRUS supports upper boundary conditions which change in a step-wise manner in time, but only 50
changes can be made during a simulation.  This limitation prevents changing boundary conditions on a daily
basis if the duration of the time simulated exceeds 50 days.  This is a significant limitation for long-term fate
studies.

    HYDRUS supports different types of boundary conditions at the upper soil surface.  We attempted to
use a constant flux boundary condition to simulate infiltration of daily rainfall amounts. HYDRUS solved

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the flow equation satisfactorily when the specified flux density did not exceed 15% of the saturated
conductivity.  When this value was exceeded, the model would not converge and would stop.  To simulate
these daily rainfall amounts, it was necessary to preprocess the rainfall data to guarantee that the flux on any
day did not exceed 15% of the saturated conductivity.  If the rainfall exceeded that amount, the excess was
carried over to the following days.

    When making the sensitivity analysis, we often encountered combinations of parameters for  which the
program would terminate abnormally even though the parameter values appeared to be reasonable and
physically consistent.
                           *D.S. GOVERNMENT PRINTING OFFICE:1994-550-001/80361
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