vvEPA
United States
Environmental Protection
Agency
Region V
Great Lakes National
Program Office
536 South Clark Street, Room 932
Chicago, IL 60605
EPA-9O5/9-82-O01
ANSWERS -
USERS MANUAL
I
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ANSWERS
(Areal Nonpoint Source Watershed Environment Response Simulation)
User's Manual
David B. Beasley, PhD, PE and Larry F. Huggins, PhD, PE
Agricultural Engineering Department, Purdue University, West Lafayette, Indiana
Assisted by:
U.S. Environmental Protection Agency, Region V
230 South Dearborn St., Chicago, IL 60604
Agricultural Experiment Station, Purdue University
U.S. Department of Agriculture (ARS, SCS, and ASCS)
Allen County Soil and Water Conservation District, Ft. Wayne, Indiana
Indiana Heartland Coordinating Commission, Indianapolis, Indiana
U S Environmental Protection Agency
Region 5, Library (PL-12J)
77 West Jackson Boulevard, 12th Floor
Chicago, IL 60604-3590
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Contents
I. Introduction 1
Acknowledgment 1
Disclaimer 1
II. Concepts 3
Philosophy 3
Model Structure 4
Hydrplogic Considerations 5
Applicability 6
III. Component Relationships 7
Flow Characterization 7
Rainfall Rate 9
Infiltration 10
Sediment Detachment and Movement 12
Best Management Practices 15
Programming Overview 15
IV. Data Preparation for Answers 17
General 17
Data File Construction 17
Simulation Requirements 17
Rainfall Information 19
Soils Information 19
Land Use and Surface Information 21
Channel Descriptions 21
Individual Element Information 22
V. Answers Output 24
General 24
Input Information "Echo" 24
Watershed Characteristics 24
Flow and Sediment Information and BMP Effectiveness 24
Net Transported Sediment Yield or Deposition 26
Channel Deposition 27
Graphical Output 27
List of References 30
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Appendices
A. Soil Parameters 33
Section A.1 33
Total Porosity (TP) 33
Field Capacity (FP) 33
Infiltration Control Zone Depth (DF) 34
Antecedent Soil Moisture (ASM) 34
Section A.2 35
Infiltration Rate Descriptors (FC and A) 35
Infiltration Exponent (P) 37
Section A.3 37
Soil Erodibility-USLE "K" (K) 37
Subsurface Drainage Characteristics 38
Section A.4 38
B. Land Use and Surface Parameters 39
Section B.1 39
Interception Parameters (PIT and PER) 39
Manning's n (N) 39
Relative Erosiveness (C) 39
Section B.2 40
Surface Storage Descriptors (HU and RC) 40
C. Individual Element Information 41
Section C.1 41
Simplified Data File Construction 41
Data File Construction Using Topographic Maps 42
Section C.2 43
D. Enhanced Sediment Model 45
General 45
Model Development 45
Input and Output Format Changes 51
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CHAPTER I: INTRODUCTION
This manual is intended to present the theory behind the ANSWERS simulation model, a broad
overview of the computational algorithms employed in the current implementation of the model and,
most importantly, a practical guide for persons who want to use the model as a tool in developing
nonpoint source pollution control measures. Depending upon the intended application, only certain
sections of the manual may be relevant.
Chapter II gives a broad overview of the model and should generally be read by anyone considering
its use. Chapter III goes into computational details of the component relationships and is necessary
reading only if a thorough understanding of the internal workings of the model is desired. Two
different sediment detachment/transport sub-models are presented in this manual. Chapter III
details the current, "production" version of the model, while Appendix D describes the new, more
detailed model capable of providing information on particle-size distributions. Chapters IV and V,
together with Appendices A, B, and C, detail procedures for simulating watershed behavior and
interpreting the results.
Finally, it must be noted that developmental work on improving the utility of ANSWERS is still
on-going. A listing of the ANSWERS computer program was deliberately excluded from this
publication in order that interested users would obtain the latest version of the model rather than
attempt to manually reproduce a possibly obsolete listing. In particular, developmental work is
nearing completion on a version which includes direct simulation of nutrient losses in addition to the
sediment yield discussed herein. A supplement to this manual will be distributed with all releases of
the expanded version of the model.
Acknowledgments
The ANSWERS simulation model development was financed with Federal funds from the U.S.
Environmental Protection Agency under Sections 108a and 208 of PL 92-500 and by the Purdue
Agricultural Experiment Station. The EPA grants were administered by the Soil and Water Cpnserva-
tion District of Allen County, Indiana and by the Indiana Heartland Coordinating Commission in
Indianapolis. Special recognition is due the U.S. Dept. of Agriculture, Agriculture Research Service,
for technical assistance with field rainujator experiments conducted in cooperation with the
Department of Agronomy, Purdue University. These field tests, together with other plot data and
professional consultation made available by ARS personnel, provided the basic information for
development of the erosion and sediment transport components of the ANSWERS model. Earlier
research supported in part by the Dept. of Interior, Office of Water Resources Research provide a
foundation for the hydrologic portion of the mode!.
Numerous graduate students of the Department of Agricultural Engineering and professional col-
leagues have contributed greatly to various components and programming algorithms. Individuals
deserving special mention include: J.R. Burney, T.A. Dillaha, III, G.R. Foster, H.M. Galloway, J.V.
Mannering, T.D. McCain, E.J. Monke, D.W. Nelson, and W.H. Wischmeier.
Disclaimer
The contents of this publication do not necessarily reflect the views and policies of the U.S.
Environmental Protection Agency, nor does mention of trade names or commerical products consti-
tute endorsement or recommendation for use. While every reasonable effort has been made in the
development of the ANSWERS model to provide a computer program free of logical errors, no
absolute assurance can be given that this effort has been entirely successful. Furthermore, neither
the U.S. Environmental Protection Agency, the Allen County Soil and Water Conservation District,
the Indiana Heartland Coordinating Commission or Purdue University assumes any responsibility
for liability, either direct or indirect, as a result of actions predicated on model simulation results.
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In order to assure that modeling results are as reliable as possible, always use the latest release
of ANSWERS. Contact Dr. David B. Beasley in order to determine the most recent version of the
ANSWERS model and to obtain information concerning acquisition of ANSWERS and related pro-
grams.
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CHAPTER II: CONCEPTS
Philosophy
ANSWERS is a model intended to simulate the behavior of watersheds having agriculture as their
primary land use, during and immediately following a rainfall event. Its primary application was
envisioned to be planning and evaluating various strategies for controlling nonpoint source pollu-
tion from intensively cropped areas. For such situations, a watershed's hydrologic response to a
storm event is the controlling mechanism for transporting pollutants to the drainage network.
A fundamental characteristic of the ANSWERS model is its distributed parameter approach as
contrasted to the more common lumped parameter modeling efforts. While this approach is gener-
ally more computationally intensive, its inherent advantages were deemed to more than offset this
factor.
A distributed parameter watershed model incorporates the influences of the spatially variable,
controlling parameters, e.g., topography, soils, land use, etc., in a manner internal to its computa-
tional algorithms. In contrast, lumped parameter models incorporate, to whatever degree they do
not ignore, these effects by an a priori analysis of a watershed's spatially variable characteristics.
In other words, the lumped approach uses some type of averaging technique to generate an
"effective" coefficient(s) for characterizing the influence of specific, non-uniform distributions of
each parameter. The influence of this distribution is then represented by the "lumped" coefficients,
and the resulting model is treated as a mathematical transformation of input into output, i.e., a
"black box", for the subsequent simulation.
A primary advantage of a distributed parameter analysis is its potential for providing a more
accurate simulation of natural catchment behavior. The term potential is used because increased
accuracy is by no means a direct consequence of using a distributed analysis; rather, it is realized
only if the model is designed to avoid the constraints imposed by lumped parameters.
Lumped models almost invariably employ some weighting function to account for the spatial
variability of watershed parameters such as soil type, cover and slope steepness. Such weighting
functions, regardless of how elaborate, are applied to the catchment prior to modeling runoff. This
constrains the parameter values to be independent of the magnitude and temporal distribution of the
storm event. Such a constraint is valid only for linear systems. Thus, the assumptions and limita-
tions of behaving, at least to some degree, as a linear system are subtly imposed on lumped models.
Another linear system assumption implicit to almost all weighting functions used with lumped
models results from ignoring the influence of geographic placement of spatially varying factors
within the watershed boundaries. The magnitude of error associated with such approximations has
been demonstrated by Muggins, et al. (1973).
A second major advantage of a distributed model is its inherent ability to simultaneously simulate
conditions at all points within the watershed. This ability to depict what is happening throughout the
watershed greatly increases the amount and utility of information provided. In addition, it permits
simulation of processes that change both spatially and temporally throughout the watershed. The
accuracy with which interacting processes can be modeled is thereby increased.
Finally, distributed models greatly facijitate incorporation of relationships developed from small
scale "plot-size" studies to yield predictions on a watershed scale. It is much easier to formulate the
individual processes being modeled as independent equations applicable at a point, letting the
subsequent integration process incorporate effects of spatial and temporal variability, than to
develop an elaborate weighting function for each process. This approach also directly accounts for
process interactions that would otherwise be ignored or require complex modifications of weighting
functions.
A complete discussion of the concepts and chronologic development of the ANSWERS model can be
found in Muggins and Monke (1966), Beasley (1977), Beasley, et al. (1980), and Dillaha (1981).
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Model Structure
ANSWERS is a deterministic model based upon the fundamental hypothesis that:
"At every point within a watershed, functional relationships exist between water flow
rates and those hydmlogic parameters which govern them, e.g., rainfall intensity, infiltra-
tion, topography, soil type, etc. Furthermore, these flow rates can be utilized in conjunc-
tion with appropriate component relationships as the basis for modeling other transport-
related phenomenon such as soil erosion and chemical movement within that watershed."
An important feature of the above hypothesis is its applicability on a "point" basis.
In order to apply this approach on a practical scale, the point concept is relaxed to refer instead to a
watershed "element". An element is defined to be an area within which all hydrologically significant
parameters are uniform. Of course, this process of going from a point to an elemental area could be
extended indefinitely until one assumed the entire watershed was composed of a single element with
"averaged" parameter values, i.e., a lumped model. The actual geometric size of an element is not
critical because there is no finite-sized area within which some degree of variation in one or more
parameters does not exist. The crucial concept is that an element must be sufficiently small that
arbitrary changes pf parameter values for a single element have a negligible influence upon the
response of the entire watershed.
A watershed to be modeled is assumed to be composed of "elements" as shown in Figure 2-1. A
square element shape was chosen to ease the task of data file preparation and to facilitate
computational convenience. It is this user supplied elemental data file, listing the physical charac-
teristics of each watershed element, which permits ANSWERS to simulate the unique behavior of any
particular watershed.
Figure 2-1. Watershed Divided into Elements with Channel Elements Shaded.
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Component relationships characterizing water and pollutant production need only simulate the
behavior of a small, uniform elemental area. Parameter values are allowed to vary in an unrestricted
manner between elements; thus, any degree of spatial variability within a watershed is easily
represented. Individual elements collectively act as a composite system because of supplied
topographic data for each element delineating flow directions in a manner consistent with the
topography of the watershed being modeled. Element interaction occurs because surface flow
(overland and channel), flow in tile lines and groundwater flow from each element becomes inflow to
its adjacent elements. Pollutants are generated and transported by these flows and by raindrop
impact.
It is the distributed model structure, which inherently provides the ability to simulate the fate of any
type of pollutant and to integrate the response of individual elements to yield a composite watershed
simulation, that is the foundation of ANSWERS. The component relationships included in a specific
release of the model will determine which pollutant processes are described and to what extent.
Specific relationships included have no effect whatsoever on the integration algorithm or distributed
model concepts. Of course, relationships chosen have a marked impact upon the accuracy with
which the model can characterize real watershed behavior. The significant consequence is that to
substitute one component relationship for another when subsequent research develops improved
relationships is a relatively trivial task.
Hytlroiogie Considerations
As indicated earlier, hydrologic processes are the driving force within the model. Consequently, a
conceptual understanding of those processes, as they apply to each independent watershed ele-
ment, is a prerequisite to studying component algorithms.
Hydrologic processes, for which component relationships have been incorporated within ANSWERS,
are shown qualitatively in Figure2-2. After rainfall begins, some is intercepted by the vegetal canopy
until such time as the interception storage potential is met. When the rainfall rate exceeds the
interception rate, infiltration into the soil begins. Since the infiltration rate decreases in an exponen-
tial manner as the soil water storage increases, a point may be reached when the rainfall rate
exceeds the combined infiltration and interception rates. When this occurs, water begins to accumu-
late on the surface in micro-depressions.
INTERCEPTION
INFILTRATION
LU
Ct
h-
2
ID
CC
LJ
a.
LJ
h-
QC
SUBSURFACE DRAINAGE
Figure 2-2. Water Movement Relationships for Small Watershed Elements.
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Once surface retention exceeds the capacity of the micro-depressions, runoff begins. The accumu-
lated water, when in excess of surface retention capacity, produces surface runoff and is termed
surface detention. Subsurface drainage begins when the pressure potential of the groundwater
surrounding a tile drain exceeds atmospheric potential. A steady-state infiltration rate may be
reached if the duration and intensity of the rainfall event are sufficiently large.
When rainfall ceases, the surface detention storage begins to dissipate until surface runoff ceases
altogether. However, infiltration continues until depressional water is no longer available. Subsur-
face drainage continues as long as there is excess soil water surrounding the drains. The long
recession curve on the outflow hydrograph, typical of tile drained areas, is then produced. Slowly
falling recession limbs are also produced by interflow, the emergence of groundwater into the
surface drainage network.
Soil detachment, transport, and deposition are very closely related to concurrent hydrologic
processes in a watershed. Detachment and transport can both be accomplished by either raindrop
impact or overland flow. Detachment by rainfall occurs throughout a storm even though overland
flow may not occur. Thus, most of the soil particles detached prior to flow initiation are deposited
and to some extent, reattached. Detachment of soil particles by overland flow occurs when the shear
stress at the surface is sufficient to overcome the gravitational and cohesive forces of the particles.
Whether or not a detached soil particle moves, however, depends upon the sediment load in the flow
and its capacity for sediment transport.
The transport of chemical pollutants from a land area is also highly related to the hydrologic
behavior of a catchment and, for certain chemicals, e.g., phosphorus, to the soil erosion that occurs.
These processes can be readily incorporated into a distributed model by developing component
relationships that characterize what happens within an individual watershed element. These pro-
cesses may be much simpler than those that must work on the watershed scale required by a lumped
approach.
Natural rainfall events do not exhibit the steady appearance shown in Figure 2-2. Furthermore,
uniformity of coverage over a watershed will usually vary during an event. In addition, hydrologic
responses of various areas within a watershed may vary greatly. Hence, the resultant hydrograph
for the entire watershed will contain at least some of the effects of all of these highly complex,
unsteady, non-uniform interactions. The distributed approach provides a straightforward and
accurate method of simulating such a complex situation.
All materials leaving an element are assumed to be transported with one of the various flow
components. Overland flow either moves into an element's shadow channel element, if a channel is
specified for that element, or onto its adjacent elements. Tile and groundwater flows are assumed to
outlet directly into the specified channel network. It is this network of interacting flows which causes
the "independent" watershed elements to act together as a composite system.
Applicability
The distributed nature of the ANSWERS model is both its strength and ultimate limiting factor. As will
be shown with subsequent examples, the degree of information provided to decision making bodies
and program planners is extraordinary. However, costs for preparing an elemental data file and for
computer time increase with the number of elements required. Thus, economics and the size of
computer available limit the feasible number of elements and, consequently, the size of watershed
which can be simulated. Of course, selection of a larger element size permits simulation of a larger
area for a given number of elements. However, this comes at the expense of inaccuracy in
representing the spatial diversity of a watershed and of component relationships within the model.
As a practical matter, element sizes normally range from 1 to 4 ha. with watershed sizes commonly
less than 10,000 ha. Additionally, the utilization of the expanded capability sediment transport
model (which allows particle-size calculations) requires additional computer resources and time.
Hence, all other things being equal, the expanded model will not simulate as large an area and it will
cost more (as much as two times) on a unit area basis.
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CHAPTER III: COMPONENT RELATIONSHIPS
This chapter outlines the specific mathematical relationships currently used to quantify the various
model component processes and also gives an overview of the programming algorithms employed.
jt is intended primarily for the person who is doing research in model development or who is
interested in modifying some features of the current release of the model. Parameter names which
are given in all capital letters correspond to the programming names used for those variables.
The specific component relationships selected for the current version of ANSWERS are separately
discussed below. All except the time integration of the continuity equation are incorporated on a
modular basis. Modification or replacement of component relations such as infiltration or sediment
production does not affect the algorithms for other components. In other words, the component
relationships are sufficiently independent from each other that user-supplied subroutines may be
substituted for those supplied with the "official" release of the model. This framework also permits
users to append additional component relationships to simulate other processes important to
specific applications.
Flow Characterization
Mathematically, each element's hydraulic response is computed, as a function of time, by an
explicit, backward difference solution of the continuity equation:
z _ Q = dS (3-1)
where: I = inflow rate to an element from rainfall and adjacent elements,
Q = outflow rate,
S = volume of water stored in an element,
t = time.
This equation may be solved when it is combined with a stage-discharge relationship. Manning's
equation, with appropriately different coefficients, is used as the stage-discharge equation for both
overland and channel flow routing.
Within its topographic boundary, a catchment is divided into an irregular matrix of square elements,
as shown in Figure 2-1. Every element acts as an overland flow plane having a user specified slope
and direction of steepest descent. Channel flow is analyzed by a separate pattern of channel
elements (referred to hereafter as channel segments) which underlie i.e., are in the shadow of, the
grid of overland flow elements.
Elements designated to have channel flow may be viewed as dual elements. These elements act as
ordinary overland flow elements, with the exception that all overland flow out of that element goes
into its "shadow" channel segment. Flow from a channel segment goes into the next downstream
channel segment. This downstream channel segment will also receive flow from any other channel
segments which are directed toward it and from its own overland flow element.
Overland and tile outflow from an element flows into neighboring elements according to the direction
of the element's slope. The slope direction is designated on input as the angle, in degrees, counter-
clockwise from the positive horizontal (row) axis. For the example shown in Figure 3-1 below, slope
direction is in the fourth quadrant. The slope direction angle equals 270 degrees plus angle ANG.
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Direction of
steepest slope
Al + A2
Figure 3-1. Partitioning of Overland Flow.
The fraction of outflow going into the adjacent row element, RFL, is:
RFL =
tan (ANG)
2
if ANG < 45 deg.
(3-2a)
RFL = 1 -
tan (90-ANG)
2
if 45 deg. < ANG <90 deg.
(3-2b)
with the remaining outflow going into the adjacent column element. Since everything, including
surface slope, within an element is assumed to be constant, this method of partitioning overland
flow seems intuitively obvious.
The most appropriate manner to partition tile flow is not as obvious as is overland flow. In general,
records are seldom available which delineate the layout of tile systems. However, limitations on
feasible installation depths mean that tile slopes must, with only temporary deviations, follow the
general topography. Therefore, the use of an element's slope properties was chosen as a close
approximation which has the secondary benefit of eliminating the need for additional input informa-
tion.
Baseflow, the emergence of groundwater into the channel system, is simulated only crudely in the
current release of ANSWERS. All infiltrated water which moves past the zone of tile drainage is
assumed to enter a single groundwater storage reservoir. Water is then released evenly into all
channel segments at a rate proportional to the volume of accumulated storage.
The flow relationship utilized in conjunction with the continuity equation to perform the overland
flow routing is Manning's equation. The hydraulic radius is assumed equal to the average detention
depth in an element. The flow width is assumed to be the maximum width for that element, i.e., the
length measured in a direction perpendicular to the overland flow direction.
Surface detention is the water volume which must build up to sustain overland flow. Detention depth
is calculated as the total volume of surface water in an element, minus the retention volume (which
can only infiltrate), divided by the area of the element. This implies that the entire specified retention
volume of an element be f il led before any water becomes available for surface detention and runoff.
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Surface detention is a component that can have a pronounced effect on surface runoff and drainage
characteristics of a watershed. Rough ground can store large amounts of water. Muggins and Monke
(1966), using several field surfaces, developed a relationship describing the surface storage poten-
tial of a surface as a function of the water depth in the zone of micro-relief. The form of that equation
used by ANSWERS is:
H 1./ROUGH (3_3)
DEP = HU * ROUGH * (
where: DEP = volume of stored water, in depth units,
H = height above datum,
HU = height of maximum micro-relief,
ROUGH = a surface characteristic parameter.
The specified surface roughness determines the volume of surface storage and also influences
infiltration rates during the recession limb of a hydrograph, as explained later.
Although the channel flow system is unrestricted in direction and branching, it is necessary that it be
continuous and that each element contain only one channel segment. To achieve greater definition it
is necessary to assume a smaller element size for all elements, with a consequent increase in core
storage and computer execution time.
As all overland flow from a dual element is constrained to enter its shadow channel segment, the
surface slope direction of a dual element is irrelevant for partitioning overland flow to adjacent
elements. Therefore, instead of specifying the direction of surface slppe for a dual element, this
parameter position in the data file is used to specify the f^w direction for the shadow channel
segment. This slope direction is of vital importance in establishing channel continuity. All outflow
from a channel segment must enter a single adjacent channel segment located in one of the eight
directions of the cardinal axes or the diagonals. Thus, only 45 degree increments in slope direction
should be specified for dual elements.
It is permissible to specify the slope, width and Manning's roughness coefficient for each channel
segment independent of the corresponding values for its overland flow element. Typically, rather
than having a unique set of values for each channel segment, they are grouped into reaches with
similar coefficients. Manning's equation is again used as the flow relationship necessary, in
conjunction with the continuity equation, to perform the routing calculations.
Much programming effort has been expended to develop computational algorithms which solve the
flow routing equations very efficiently. For example, a piece-wise linear segmented curve is used to
approximate Manning's equation and thereby eliminate the iteration process that would otherwise
be necessary when solving the continuity equation. Unfortunately, this computational optimization
has resulted in some very complex programming logic. Therefore, it is recommended that only
someone intimately familiar with all aspects of the ANSWERS mode! attempt to modify this portion
of the computer program.
Rainfall Rate
The net rainfall rate, that which reaches the ground surface, is dependent on the user specified
pluviograph(s) and on the rate of interception by vegetation. The net rainfajl rate for each rain gauge
and crop is calculated by FUNCTION RAIN. Since a rain gauge identifier is specified for each
watershed element, it is theoretically possible to have each element subjected to a different storm
pattern. As a practical matter, the standard release of the model is dimensioned to permit only 4
gauges.
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Interception is that water extracted from the incoming rainfall upon contact with and retention by the
vegetal canopy. Water retained by the vegetation, i.e., interception storage, is held primarily by
surface tension forces. This initial interception volume is quickly satisfied, particularly in more
intense storms. Since a dense vegetal cover can expose an immense surface area to rainfall, the
amount of moisture evaporating during a long duration storm can be appreciable. Intercepted water
which evaporates will be replenished during the storm. This creates a low level of interception
demand throughout a storm. However, for the high intensities of primary interest from the stand-
point of nonpoint source pollution from cropland, interception is a relatively minor hydrologic
component. In order to reduce simulation costs, interception was assumed to be uniform in rate and
total volume over each type of vegetation. Evaporation losses during a storm were assumed to be
negligible.
Horton (1919) did a great deal of work in the area of estimating the amount and mechanisms
controlling interception. He studied the water intercepted by several species of trees as well as some
economically important crops. Values from 0.5 millimeter to 1.8 millimeters of interception storage
volume were found to exist for trees and nearly as much for well developed crops. Values for
potential interception storage, PIT, are based primarily on his recommended relationship.
The maximum potential interception (PIT), supplied as an input value, represents the available leaf
moisture storage in depth units (volume per unit land area). In each time increment in which
interception storage remains unsatisfied, rainfall supplied to interception storage is calculated as
incremental intercepton (RIT), i.e., the product of the rainfall amount (RATE) and the portion of the
element covered by foliage (PER). The value of potential interception (PIT) and the net rainfall (RAIN)
are correspondingly decreased until all interception storage is satisfied. At this stage, PIT is set
equal to zero and the net rainfall rate is subsequently equal to the gauge rainfall rate for the
remainder of the simulation.
Infiltration
Infiltration is one of the components to which ANSWERS is most sensitive, especially during low to
medium runoff storms. Although many years of research have been conducted on infiltration
phenomena, there is still no universally accepted method for describing infiltration on a watershed
scale. The widely used, time-dependent equations 9? Horton (1939) and Philip (1957) presume a
continuous water supply rate adequate to meet all infiltration demands. This approach does not
readily allow for the observed recovery in soil infiltration capacity during periods of light or zero
rainfall. To avoid this difficulty, the infiltration relation chosen for ANSWERS was the one developed
by Holtan (1961) and Overton (1965). In a dimensionally homogeneous form it can be expressed as:
FMAX = FC + A * (P™/ (3-4)
where: FMAX = infiltration capacity with surface inundated,
FC = final or steady state infiltration capacity,
A = maximum infiltration capacity in excess of FC,
TP = total volume of pore space within the control depth,
PIV = volume of water that can be stored within the control
volume prior to its becoming saturated,
P = dimensionless coefficient relating the rate of decrease
in infiltration rate with increasing soil moisture
content.
This form uses the soil water content, rather than time, as the independent variable.
10
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During periods of zero rainfall rate, any infiltration which occurs must be supplied by water stored
as either retention or detention. Since the surface of an element is seldom entirely inundated, the
computed infiltration capacity is reduced in direct proportion to the percent of the soil surface not
submerged. Thus, the specified surface micro-relief parameter also can reduce the infiltration
capacity during these recession periods.
According to Holtan's conceptualization of the infiltration process, a "control zone" depth of soil
determines the infiltration rate at the surface. He defined the depth of this control zone as the
shallower of the depth to an impeding soil layer or that required for the hydraulic gradient to reach
unity. Extending this same concept somewhat, the ANSWERS model maintains an accounting of
water that leaves this control zone.
Holtan's equation requires six infiltration parameters to be specified fpr a given soil type: total
porosity, field capacity, depth of the control zone, steady-state infiltration rate (FC), and the two
unsteady-state coefficients (A and P). Data from both large, plot-sized simulated rainfall tests
(Skaggs, et al., 1969) and field rainulator tests conducted in cooperation with USDA-ARS as a part of
the Black Creek Project have been used to estimate parameter values. All of these tests indicated
that surface crusting conditions have a major impact on the observed infiltration relationship.
Experience with Holtan's equation has indicated the influence of crusting can be modeled by
adjustment of the specified depth of the control zone. Crusting requires the use of a much shallower
control zone.
The rate of water movement from the control zone is a function of the moisture content of that zone.
The two conditions which can exist are handled according the following rules:
1. when the moisture content of the control zone is less than field capacity, no water
moves from this zone,
2. when the control zone moisture exceeds field capacity, the water moves from this
zone according to the equation:
PIV 3 (3-5)
np = pr * M _ r •*•'
UK hi, U
where: DR = drainage rate of water from control zone,
GWC = gravitational water capacity of the control zone
(total porosity minus field capacity).
This relationship satisfies the continuity requirement that at saturation, when PIV=0, the drainage
rate from the control zone equals the steady state infiltration rate, FC. In addition, it exhibits
intuitively desirable properties of rapidly decreasing moisture movement as the soil dries from
saturation and of asymptotically approaching a zero drainage rate.
Water leaving the control zone contributes to tile drainage, if the element is tiled, or to baseflow. In
both cases the water is assumed to re-emerge into the channel segments. Water moves from the
infiltration control zone into the "pools" available for tile and/or baseflow at a rate equal to DRA.
Individual elements may selectively be designated as being tile drained. In addition to water coming
from the control zone, tile inflow may be occurring from adjacent tiled elements. The sum of these
two rates constitutes the rate of subsurface inflow into an element. Subsurface water moves out the
element's tile at this inflow rate up to a maximum outflow rate equal to the tile drainage coefficient.
Whenever the rate of subsurface inflow to an element exceeds its drainage coefficient, that excess
water is diverted to baseflow storage. Elements which are not tiled have a drainage coefficient of
zero.
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Subsurface water entering an element at rates in excess 9f its drainage coefficient is stored in a
single "pool." To simulate baseflow it is released directly into channel segments at a rate propor-
tional to the volume of water in storage. Water is released at an equal rate to each channel segment.
For small catchments having no defined channels, only overland flow will appear at the outlet.
Sediment Detachment and Movement
Soil erosion, as it relates to nonpoint source pollution, can be viewed as two separate processes,
detachment of particles from the soil mass and transport of these particles into the streams and
lakes. Detachment of either primary soil particles or aggregates can result from either rainfall or
flowing water. These same factors can cause detached particles to be transported to the water
supply network. Thus, there are four processes for which quantifying relationships must be deve-
loped, as shown in Figure 3-2. Two different transport models are available for use in ANSWERS. The
simpler, less descriptive transport relationship is presented in this chapter. A more detailed trans-
port model, which predicts particle size distributions and differential deposition, is presented in
Appendix D.
TRANSPORT BY FLOW
DETACHMENT BY
RAINDROP IMPACT
DETACHMENT
BY FLOW
6
Figure 3-2. Sediment Detachment and Transport.
The detachment of soil particles by water is accomplished by two processes. The first involves
dislodging soil as a result of the kinetic energy of rainfall. Rainfall is the major detachment process
on relatively flat watersheds. The second process involves the separation of particles from the soil
mass by shear and lift forces generated by overland flow.
Detachment of soil particles by raindrop impact is calculated using the relationship described by
Meyer and Wischmeier (1969):
DETR = .108 * CDR * SKDR * A. *
(3-6)
where: DETR = rainfall detachment rate, kg/min,
CDR = cropping and management factor, C (from Universal Soil
Loss Equation - Wischmeier and Smith, 1978),
SKDR = soil erosivity factor, K (from Universal Soil Loss
Equation), r.
A. = area increment, m ,
R = rainfall intensity during a time interval, mm/min.
12
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The detachment of soil particles by overland flow was described by Meyer and Wischmeier (1969)
and modified by Foster (1976) as follows:
DETF = .90 * CDR * SKDR * A. * SL * Q
(3-7)
where: DETF = overland flow detachment rate, kg/min,
SL = slope steepness,
Q = flow rate per unit width, m/min.
Once a soil particle has been detached, sufficient energy must be available to transport it or the
particle will be deposited. The transport of sediment by overland flow is self-regulating, i.e., soil
particle detachment by overland flow does not occur unless there is excess energy available in
addition to the amount required to transport suspended sediments. However, detachment by rainfall
impact often occurs when there is little or no flow available for transport.
After a literature study which included Yalin (1963), Meyer and Wischmeier (1969), Foster and Meyer
(1972), and Curtis (1976), as well as an inspection of soils data, a relationship for particle transport in
overland flow was chosen as shown in Figure 3-3. The two portions of the curve generally represent
the laminar and turbulent flow regions. Obviously, the transport capacity does not continue to
increase as the square of f jow forever. However, within the range of flows generally encountered in
ANSWERS simulations, this generalized relationship (based in part on Yalin's work and in part on
observed data) has produced reasonable results. Equations and their region of application are:
TF = 161 * SL * Q'5 if Q <_ .046 m2/min (3-8a)
TF = 16,320 * SL * Q2 if Q > .046 m2/min (3-8b)
where: TF = potential transport rate of sediment, kg/min-m.
The erosion portion of the ANSWERS model was simplified further by the following assumptions:
1. Subsurface or tile drainage produces no sediment. (Data indicate around two percent
of the average annual loading originated from subsurface systems on the Black
Creek Watershed).
2. Sediment detached at one point and deposited at another is reattached to the soil
surface.
3. Re-detachment of sediment requires the same amount of energy as required for the
original detachment.
4. For channel segments rainfall detachment is assumed to be zero and only deposited
sediment is made available for flow detachment, i.e., original channel linings are not
erodible.
Although these assumptions were made primarily to reduce the computational cost of using the
model, some were also required because little or no data were available in the literature to quantify
the particular process. Also, after consideration of the relative magnitude of the four detachment/-
transport processes, the transport of soil particles by rainfall was assumed negligible.
13
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TURBULENT FLOW
2
10
q = m /min
Figure 3-3. Transport Relationship Used in the ANSWERS Model.
14
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Combining the above equations and assumptions gives a composite soil movement model wherein
soil particles are dislodged from the soil mass by both rainfall and flowing water. Detached solids
then become available for transport by overland flow. Within an element the material available for
transport is the combination of that detached within the element and that which enters with inflow
from adjacent elements.
Once the available detached sediment within an element is known, the transport capacity is
computed. If it is insufficient to carry the available material, the excess is deposited in the element.
The overall accounting relationship for this pmcess is the differential form of the continuity equation
as applied ab9ve to water flow. Sediment carried out of an element is apportioned between adjacent
elements in direct relation to overland flow.
Best Management Practices
Land use changes, tillage techniques and management procedures which qualify as Best Manage-
ment Practices (BMPs) for controlling nonpoint source pollution are simulated with ANSWERS by
using appropriate parameter values for the component relationships discussed above. For example,
conservation tillage generally results in a rougher surface, reduced C-factor and increased infiltra-
tion. Gully stabilization structures such a drop spillways or chutes may be simulated by reducing the
slope steepness of the associated channel segments. Certain structural BMPs cannot be adequately
accommodated with these component relationships. Currently, four specific BMPs which require
special computational provision have been included: ponds, parallel tile-outlet terraces, grass
waterways and field borders.
The four special structural BMPs are dealt with by a subroutine named STRUCT. The programming
philosophy for STRUCT was to have it adjust "standard" parameter values for those elements which
contain a structural BMP. These modifications are made when subroutine DATA is called. This
approach permits simulating the important impacts of the BMP without major modification to the
fundamental computational logic of the entire computer program.
Both ponds and PTOs are handled in a similar manner using a trap efficiency concept. Sediment
trapped from the water flowing into a pond or PTO is diverted into a special, psuedp element which
provides a means of tabulating the combined effectiveness of all such BMPs. Water is 3)59 assumed
to be diverted, in the same ratio as sediment is trapped, into the tile drainage system. In this manner,
effects of both reduced sediment loads and downstream overland flow rates are simulated.
Grass waterways and field border strips are also treated similarly to one another. It is assumed that
the vegetated area within the affected element is no longer subject to any sediment detachment.
Computationally, this is accomplished by adjusting the specified slope steepness by an amount
which produces the desired change in sediment detachment rate for the element. Deposition within
the vegetation of a grass waterway is deliberately prohibited, since any waterway that effectively
traps sediment would soon fill and become ineffective. Specifying that an element has a grassed
waterway forces the presence of a shadow channel element if none was already present.
Programming Overview
ANSWERS is programmed with a MAIN section which includes all the logic to simulate the various
component processes each one of which is structured as an independent subroutine. Prior to
beginning any simulation calculations, which follow the descriptions given above, MAIN calls a
large subroutine named DATA.
It is the responsibility of DATA to read the user supplied data file and convert that parametric and
geographic information into a structure which maximizes the computational efficiency of the
lengthy simulation calculations. Specifically, it converts the gridded watershed into a one-
dimensional array structure. This is done to avoid wasting machine memory with incomplete
two-dimensional arrays that would result from irregularly shaped watersheds. Computational
15
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speed is also significantly improved by this process. The process of transforming the two-
dimensional layout of a watershed elemental map into one-dimensional computational arrays is
primarily accomplished by subroutine RELEM.
Subroutine RELEM is designed to utilize three adjacent rows of elements in a watershed file to
determine position sequence numbers for all elements. The three-row system is utilized in order to be
able to account for discontinuous rows of elements. The subroutine operates in such a manner that it
can detect whenever the specified stope direction of an element would direct any portion of the
runoff from that element into a non-existent element, i.e., out of the catchment. A warning message
is printed for each offending element.
Specifically, subroutine RELEM returns to subroutine DATA a 3-dimensional array, IEL. The first
subscript refers to the row's position in the 3-row array. Eventually, each row of watershed elements
"ripple through" all three row positions in IEL. The second subscript in IEL refers to the element's
watershed column number. The third subscript corresponds to the parameter number for that
watershed element according to:
1. — contains the element's watershed row number,
2. — contains its column, except for IEL(i,1,2) which contains the column no. of the last
element in a given row,
3. — contains the position sequence number for the element,
4. — contains the element's slope steepness,
5. — contains the flow direction for the element,
6. — contains the channel designator and soil type,
7. — contains the crop type,
8. — contains the rain gauge name,
9. — contains the tile flow designator,
10. — contains the slope steepness of any shadow channel element,
11. — contains the identifier number for a structural BMP,
12. — contains size information about any structural BMP,
13. — contains size information about any structural BMP.
Array ITEMP is used to temporarily hold parameter values for the most recently read element.
Subroutine RELEM must be entered with array ITEMP loaded with parameter values for the very first
element of the catchment. The first task of RELEM is to transfer row-2 values for array IEL into row-1
and row-3 values into row-2. Once entered, execution continues within RELEM until an entire row of
watershed elemental parameters has been read and stored in row-3 of IEL.
Upon return to subroutine DATA from RELEM, DATA works with row-2 of IEL to transfer its parameter
data into the single dimension, sequential arrays that will ultimately be used for simulation
computations. After an entire watershed row has been so set up, it again returns to subroutine
RELEM which "ripples" the data in array IEL so it is ready to accept the next row of watershed
elemental parameter values.
After all watershed elements have been set up by RELEM and DATA, the shadow channel elements
that have been detected are moved to occur sequentially at the end of the regular elements.
Parameter values for each element are next combined into computationally efficient coefficients and
control is returned to MAIN for the actual simulation.
16
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CHAPTER IV: DATA PREPARATION FOR ANSWERS
General
The data file used by the ANSWERS model provides a detailed description of the watershed
topography, drainage networks, soils, land uses, and BMPs. Most of the information can be readjly
gleaned from USDA-SCS Soil Surveys and land use and cropping surveys or summaries. Also, aerial
photographs of the area, USGS topographic maps, and BMP construction or implementation data is
quite useful in developing descriptions of actual watershed areas. This chapter will detail the
techniques used in putting together the data files necessary for running ANSWERS. In addition,
information describing various surface conditions, soil responses, and BMP data is included in the
Appendices. The formats shown in this section are for the current release of the ANSWERS program.
The expanded sediment detachment/transport model, detailed in Appendix D, utilizes additional
information which is described in that section.
Input information for the ANSWERS model contains six general types of data:
1. Simulation requirements (measurement units and output control),
2. Rainfall information (times and intensities),
3. Soils information (antecedent moisture, infiltration, drainage response and potential
erodibility),
4. Land use and surface information (crop type, surface roughness and storage
characteristics),
5. Channel descriptions (width and roughness),
6. Individual element information (location, topography, drainage, soils, land use and
BMPs).
The individual element information is the largest body of data and the most time consuming to
collect. However, once the topography, soils, land use and drainage patterns have been determined
for all of the elements, changes in watershed management or BMPs can be added very easily without
having to totally reconstruct the input file.
Figure 4-1 shows the configuration of a typical ANSWERS data file. Each of the six data areas listed
above are noted and will be covered individually in succeeding sections. The ANSWERS data file was
designed to be self explanatory. The information contained in the soils, land use, and individual
element information sections are physically measurable and can be checked for validity without
having to go through a complicated process of differentiating one or more lumped parameters.
Data File Construction
The configuration oi an ANSWERS input data file allows the file to be constructed in two parts. All
data except for the individual element data can be contained in a separate file. This first or "predata"
file contains all of the general information necessary to describe the various soils, Jand uses, and
management systems in a given county, planning region, state, etc. This "predata" file can be used
with numerous elemental data files which describe greatly differing watersheds. Therefore, once a
"predata" file has been constructed for a given area, subsequent simulations, even on different
watersheds, may be possible with very little or no additional general information collection.
Simulation requirements. Figure 4-2 depicts the portion of the ANSWERS input file that supplies
data on simulation requirements. The first line of this two-line portion of the "predata" file contains
an alpha-numeric header used to describe which "predata" file is being used. All 80 columns of the
card are used, and this information will be reprinted at execution time. Metric or English units are
acceptable for input/output. The system of units used must be specified in columns 2-8 (left justified)
on the second card. Inches and feet are both used when ENGLISH units are specified. Millimeters and
17
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STANDARD PREDATA FILE FOR
ALLEN CO.
, INDIANA— 800823 1 •!
ENGLISH UNITS ARE USED ON INPUT/OUTPUT
PRINT 1 '
RAINFALL DATA FOR 2 GAUGE(S)
GAUGE NUMBER Rl
0 0. 0.00
0 9. .52
0 15. 1.55
0 20. 2.40
0 30. 1.59
0 35. .85
0 45. .50
1 300. 0.00
GAUGE NUMBER R2
0 0. 0.00
0 7. .45
0 14. 1.25
0 18. 2.66
0 25. 1.65
0 33. .60
0 42. .35
1 300. 0.00
FOR EVENT
OF: — TEST— -
2
SOIL INFILTRATION, DRAINAGE
NUMBER OF SOILS = 8
S 1, TP =.46, FP =.75, PC =
S 2, TP =.46, FP =.65, PC =
S 3, TP =.46, FP =.70, FC =
S 4, TP =.42, FP =.70, FC =
S 5, TP =.44, FP =.80, FC =
S 6, TP =.46, FP =.75, FC =
S 7, TP =.46, FP =.75, PC =
S 8, TP =.35, FP =.65, PC =
AND GRDUNDWATER CONSTANTS FOLLOW
.40, A =
.40, A =
.40, A =
.60, A =
.60, A =
.60, A =
.40, A =
.90, A =
DRAINAGE COEFFICIENT FOR TILE DRAINS =
GRDUNDWATER RELEASE FRACTION
.005
.80, P
.80, P
.80, P
1.0, P
1.0, P
1.0, P
.80, P
1.6, P
=.65, DF = 4.0, ASM =.70
=.65, DF = 3.0, ASM =.70
=.75, DF = 3.0, ASM =.70
=.65, DF = 4.0, ASM =.70
=.65, DF = 5.0, ASM =.70
=.65, DF = 5.0, ASM =.70
=.65, DF = 3.0, ASM =.70
=.60, DF = 6.0, ASM =.70
K =.36
K =.32
K =.17
K =.36
K =.32
, K =.36
K =.38
K =.35
0.25 IN/24HR
SURFACE ROUGHNESS AND CROP CONSTANTS
NUMBER OF CROPS AND SURFACES
C 1, CRDP= SI CORN, PIT=.01,
C 2, CROP= CORN-NT, PIT=.06,
C 3, CHOP=BEANS TP, PIT=.01,
C 4, CROP=S. GRAINS, PIT=.04,
C 5, CROP= PASTURE, PIT=.03,
CIO, CROP= WOODS , PIT=.10,
= 6
PER=0.0,
PER=. 75,
PER=.45,
PER=.90,
PER=1.0,
PER=.90,
FOLLOW
RC=.47,
RC=.55,
RC=.47,
RC=.55,
RC=.40,
RO.55,
HU= 2.0, N=.075, C=.50
HU= 3.5, N=.150, C=.30
HU= 1.5, N=.070, C=.60
HU= 2.0, N=.150, C=.15
HU= 1.5, N=.200, C=.04
HU= 3.5, N=.250, C=.15
4
CHANNEL SPECIFICATIONS FOLLOW
NUMBER OF TYPES OF CHANNELS = 4,
CHANNEL 1 WIDTH =15.0 FT, ROUGHNESS COEFF. (N) = .035"
CHANNEL 2 WIDTH =10.0 FT, ROUGHNESS COEFF. (N) = .040
CHANNEL 3 WIDTH = 7.5 FT, ROUGHNESS COEFF. (N) = .045
CHANNEL 4 WIDTH = 5.0 FT, ROUGHNESS COEFF. (N) = .070
ELEMENT SPECIFICATIONS FOR MIDDLETOWN WATERSHED
EACH ELEMENT IS 528.0ft SQUARE
' OUTFLOW FROM ROW 21 COLUMN 3
1 15 4 270 1 1 Rl 0
1
7
7
7
8
8
8
8
20
20
21
21
22
22
16
20
22
23
11
12
13
14
19
20
3
4
13
14
5
9
2
3
20
17
16
12
8
8
9
28
2
9 5
259
186
135
180
270
180
180
148
180
180
270
180
0
90
3
2
1
3
201
302
303
1
1
"l
102
108
3
1
1
1
2
5
2
2
1
1
2
2
1
1
4
4
Rl
Rl
Rl
Rl
R2
R2
R2
R2
R2
R2
R2
R2
R2
R2
•
TILE
TILE
TILE
TILE
TILE
TILE
TILE
TILE
TILE
0
0
0
0
5
5
5
0
0
0
3
3
0
0
2
4 32
4 20
4 20
1
3 20
4 40
4 40
5
827.8
828.8
822.8
835.3
835.3
799.7
799.3
802.2
809.2
802.0
803.0
766.5
762.0
799.5
798.0
Figure 4-1. Typical ANSWERS Input Data File.
18
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meters are used when METRIC units are chosen. The presence of the word PRINT in the second line
of the "predata" file in columns 58-62 causes ANSWERS to produce a detailed listing of all predata
information. The absence of the word PRINT on line 2 suppresses this output.
STANDARD EKEDATA FILE FOR ALLEN CXI., INDIANA—800823
ENGLISH UNITS ARE USED ON INPUT/OUTPUT PRINT
Figure 4-2. Simulation Requirements.
Rainfall information. Figure 4-3 shows the portion of the "predata" file dedicated to the descrip-
tion of the precipitation event to be simulated. The first line must contain the word RAINFALL
beginning in column 2. The number of gauges used in the simulation are inserted in column 20.
ANSWERS permits up to four rain gauges to be used. Beginning in column 47, an eight character
identifier of the particular storm being modeled is inserted. Each new rain gauge file contains a two
character identifier for the gauge in columns 17-18.
The Thiessen polygonal method is used to determine which areas of a watershed are affected by
specific rain gauges. For hypothetical situations, the various gauges can be used,to simulate the
movement of a storm across the watershed.
The three columns contain the following data:
1. Data column 1 - last entry? (indicated by 1),
2. Data columns 3-10 - time (in minutes),
3. Data columns 11-20 - precipitation intensity (in inches/hour or millimeters/hour,
depending on units chosen) which ended at corresponding time (Column 2).
in this example, the intensity was 0.52 iph from 0 to 9 minutes and 1.55 iph from 9 to 15 minutes for
gauge R1. During a similar time interval, the rates were 0.45 iph from 0 to 7 minutes and 1.25 iph from
7 to 14 minutes at gauge R2. The last entry for both gauges, at 300 minutes, indicates the end of
simulation us, although the precipitation ended at approximately 45 minutes, ANSWERS would
continue simulating the watershed response until the time was equal to or greater than 300 minutes.
RAINFALL DATA
GAUGE NUMBER
0 0.
0 9.
0 15.
0 20.
0 30.
0 35.
0 45.
1 300.
GAUGE NUMBER
0 0.
0 7.
0 14.
0 18.
0 25.
0 33.
0 42.
1 300.
FOR 2 GAUGE(S) FOR EVENT OF: — TEST—
Rl
0.00
.52
1.55
2.40
1.59
.85
.50
O.OO
R2
0.00
.45
1.25
2.66
1.65
.60
.35
0.00
Figure 4-3. Rainfall Information.
Soils information. Figure 4-4 lists the information necessary to describe the response of the
various soils to precipitation inputs. The word SOIL must be found in columns 3-6 of the first data
card. The number of identified soil groups or types is entered in columns 19-22 (right justified) of the
second card. ANSWERS is normally dimensioned to handle up to 20 different soils. If additional soils
are present, the model can be easily set up to accept as many soils as are needed.
19
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SOIL INFILTRATION, DRAINAGE AND GROUNDWATER CONSTANTS FOLLOW
NUMBER OF SOILS = 8
S 1, TP
S 2, TP
S 3, TP
S 4, TP
S 5, TP
S 6, TP
S 7, TP
S 8, TP
=.46,
=.46,
=.46,
=.42,
=.44,
=.46,
=.46,
=.35,
FP =.75,
FP =.65,
FP =.70,
FP =.70,
FP =.80,
FP =.75,
FP =.75,
FP =.65,
FC = .
FC = .
FC = .
PC = .
FC = .
FC = .
FC = .
FC = .
DRAINAGE COEFFICIENT FOR TILE
GROUNDWATER RELEASE FRACTION =
40, A =
40, A =
40, A =
60, A =
60, A =
60, A =
40, A =
90, A =
DRAINS =
.005
.80,
.80,
.80,
1.0,
1.0,
1.0,
.80,
1.6,
0.25
P =.65,
P =.65,
P =.75,
P =.65,
P =.65,
P =.65,
P =.65,
P =.60,
IN/24HR
DF =
DF =
DF =
DF =
DF =
DF =
DF =
DF =
4.0,
3.0,
3.0,
4.0,
5.0,
5.0,
3.0,
6.0,
ASM
ASM
ASM
ASM
ASM
ASM
ASM
ASM
=.70,
=.70,
=.70,
=.70,
=.70,
=.70,
=.70,
=.70,
K =.36
K =.32
K =.17
K =.36
K =.32
K =.36
K =.38
K =.35
Figure 4-4. Soils Information.
The infiltration descriptors, antecedent moisture content, and the potential credibility of the various
soils are listed in this section. Table4-1 describes each parameter and gives its location on the data
card. Methods for determining the values of TP, FP, FC, A, P, DF, and ASM are presented in Appendix
A. The K parameter is identical to the K parameter in the Universal Soil Loss Equation. Because the
soil parameters may be used to describe the response of several similar soil types, the listed K value
is usually an effective or average value.
The next two user-selectable constants are used to help describe the contribution of subsurface
drainage to the total water yield in the watershed. The tile drainage coefficient indicates the design
coefficient (inches/day or millimeters/day) of tile drains in those areas designated as having tile
drainage. Generally, this value is 0.25 to 0.5 inches/day (6.4 to 12.7 millimeters/day). The ground-
water release fraction is a measure of the contribution of lateral groundwater movement or interflow
to total runoff. Appendix A contains information to be used in the selection of a release fraction.
The tile drainage coefficient is contained in columns 40-44 (right justified). The groundwater release
fraction is contained in columns 32-41 (right justified).
Table 4-1. Soils Information File Construction.
Parameter
Definition
Column(s) Appendix
TP
FP
FC
A
P
DF
ASM
K
Total porosity (percent volume)
Field capacity (percent saturation)
Steady state infiltration rate
Difference between steady state and
maximum infiltration rate
Exponent in infiltration equation
Infiltration control zone depth
Antecedent soil moisture (percent saturation)
USLE "K"
11-13
20-22
29-33
39-43
49-51
58-62
70-72
78-80
A.I
A.I
A. 2
A. 2
A. 2
A.I
A.I
A. 3
All entries are right justified.
20
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Land use and surface information. The layout of the land use and surface description portion of
the "predata" file is given in Figure 4-5. Line one should C9ntain the word SURFACE in columns 3-9.
The number of different land uses defined in this section is contained in columns 32-34 (right
justified) of the second card. ANSWERS is normally set up to handle up to 20 different combinations
of land use, management, and surface conditions. The model can be easily re-dimensioned to accept
more entries, if necessary.
The particular land use and, in some cases, the management system used are noted in the crop
section. The potential interception (PIT), percentage cover (PER), surface storage (RC and HU),
surface roughness (N), and relative erosiveness (C) parameters are listed and described in Table4-2.
Methods for determining the values of these descriptors are given in Appendix B. The C value used in
this section is a seasonally-adjusted combination of the C and P factors used in the Universal Soil
Loss Equation.
SURFACE ROUGHNESS AND CHOP CONSTANTS FOUCW
NIMBER OF CROPS AND SURFACES = 6
C 1, CBOP= SI CORN, PIT=.01, PER=0.0, RC=.47, HU= 2.0, N=.075, C=.50
C 2, CROP= CORN-NT, PIT=.06, PER=. 75, RO.55, HU= 3.5, N=.150, C=.30
C 3, CROP=*EANS TP, PIT=.01, PER=.45, RC=.47, HU= 1.5, N=.070, C=.60
C 4, CROP=S.GRAINS, PIT=.04, EER=.90, RC=.55, HU= 2.0, N=.150, C=.15
C 5, CROP= PASTURE, PIT=.03, PER=1.0, RC=.40, HU= 1.5, N=.200, O.04
CIO, CROP= WOODS , PIT=.10, PER=.90, RC=.55, HU= 3.5, N=.250, O.15
Figure 4-5. Land Use and Surface Information.
Table 4-2. Land Use and Surface Condition File Construction.
Parameter Definition Column(s) Appendix
CROP
PIT
PER
Specific land use and management
Potential interception volume
Percentage of surface covered by
12-19
26-28
B.I
B.I
specific land use (CROP) 35-37 B.I
RC Roughness coefficient (a shape factor) 43-45 B.2
HU Maximum roughness height 51-54 B.2
N Manning's n 59-62 B.I
C Relative erosiveness of a particular
land use (function of time and
USLE "C" and "P") 67-69 B.I
All entries are right justified.
Channel descriptions. The part of the "predata" file used to describe the channels in the
watershed is shown in Figure 4-6. The first line must contain the word CHANNEL in columns 3-9. The
number of different channel configurations (width or roughness) is listed in columns 31-33 (right
justified) on the second line. The assumption is made that the channel is rectangular in cross-
21
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section. The width of the channel is noted in columns 19-22 and the value of Manning's n is listed in
columns 50-54 (both right justified). The channel is also assumed to be sufficiently deep to handle the
runoff. ANSWERS does not predict flooding, nor does it presently use variable geometry in the
channel cross-section.
CHANNEL SPECIFICATIONS FOLLOW
NUMBER OF,TYPES OF CHANNELS = 4,- "" '
CHANNEL 1 Wl*±H =15"6 FT, ROUSHNEltS*COEFF. (N) = .035
CHANNEL 2 WIOTH =10.0 FT, ROUGHNESS COEFF. (N) = .040
CHANNEL 3 WIDTH = 7.5 FT, TOUGHNESS COEFF. (N) = .045
CHANNEL 4 WIDTH = 5.0 FT, ROUGHNESS COEFF. (N) = .070
Figure 4-6. Channel Descriptions.
Individual element information. This file allows the user to describe, in detail, the particular
watershed and its special characteristics. Information on topography, soils, land use, drainage and
BMPs is included in this section. Figure 4-7 shows the configuration of the individual element
information file.
ELEMENT SPECIFICATIONS FOR MIDDLETOWN WATERSHED
EACH ELEMENT IS 528.0ft SQUARE
OUTFLOW FROM ROW 21 COLUMN 3
1
1
7
7
7
8
8
8
8
20
20
21
21
22
22
15
16
20
22
23
11
12
13
14
19
20
3
4
13
14
4
5
9
2
3
20
17
16
12
8
8
9
28
2
9 5
270
259
186
135
180
270
180
180
148
180
180
270
180
0
90
1
3
2
1
3
201
302
303
1
1
1
102
108
3
1
1
1
1
2
5
2
2
1
1
2
2
1
1
4
4
Rl
Rl
Rl
Rl
Rl
R2
R2
R2
R2
R2
R2
R2
R2
R2
B2
TILE
TILE
TILE
TILE
TILE
TILE
TILE
TILE
TILE
•
0
0
0
0
0
5
5
5
0
0
0
3
3
0
0
2
4 32
4 20
4 20
1
3 20
4 40
4 40
827
828
822
835
835
'799
799
802
809
802
803
766
762
799
798
.8
.8
.8
.3
.3
.7
.3
.2
.2
.0
.0
.5
.0
.5
.0
Figure 4-7. Individual Element Information.
The top three lines of this file are header informatipn. The first card contains the watershed name or
identifier in columns 29-72. The size of the element is shown in columns 17-22 on the second card. The
third card contains the row and column coordinates for the outlet element in columns 18-21 (row) and
30-33 (column). All information is right justified.
Each subsequent line of this file contains the information necessary to characterize the physical
configuration of each element. The position and definition pf all of the parameters used in describing
each element are shown in Table 4-3. Appendix C describes various methods for setting up the
elemental data file.
22
-------
Table 4-3. Element Information File Construction.
Parameter Definition Column(s) Appendix
Row number of element 1-3
Column number of element 4-6
Last element flag, this field should be blank
except for the last watershed element; that
element should have a value of 9 entered here 7-8
Slope steepness of the element, entered in
tenths of a percent, e.g., an element with a
slope of 2.9 percent would be entered as 29 9-11 C.I
Direction of steepest slope, entered in
degrees counterclockwise referenced to a
horizontal line from the center of
the element and directed to the right 12-15 C.I
Channel size category, if this element has a
well defined channel flowing through it, other-
wise these columns should be blank 16-17
Soil type number 18-19 A
Crop/management type number 20-23 B
Rain gauge designator (alpha-numeric) 27-28
Tile flag; presence of the letters "TI" indicate
tile drainage, anything else indicates no tile 30-31
Channel slope steepness in tenths of a percent;
when no value is present and a channel exists,
the slope will be taken to be equal to the over-
land slope 34-37
BMP identification number 39-40 C.2
First BMP descriptor 41-44 C.2
Second BMP descriptor 45-48 C.2
Mean elevation of element (optional) 64-70 C.2
All entries are right justified.
23
-------
CHAPTER V: ANSWERS OUTPUT
General
By using a very descriptive data file and the distributed parameter concept, the ANSWERS model is
capable of producing a detailed accounting of the erosion and hydrologic response of a watershed
subjected to a precipitation event. Figure 5-1 displays a condensed version of the typical ANSWERS
output. The output listing consists of five basic sections:
1. An "echo" of the input data (can be suppressed by removing PRINT parameter in line
2 of input data),
2. Watershed characteristics (calculated from elemental data),
3. Flow and sediment information at the watershed outlet and effectiveness of structu-
ral BMPs,
4. Net transported sediment yield or deposition for each element,
5. Channel deposition.
The various tabular output sections of the ANSWERS model can be used with several plotting
programs to yield graphical depictions of the watershed's hydrologic and erosion response.
This chapter will describe the five sections of the ANSWERS tabular output as listed above. In
addition, examples of graphical representation of the output (to lend spatial significance) will be
presented.
Input information "echo". This portion of the ANSWERS, when enabled with the PRINT parameter
in line 2 of the input file, essentially reprints the "predata" file. It can be quite useful in tracking down
problems with input formats, since the output will be exactly what it read.
Watershed characteristics. Included in this section is the header information from the elemental
data file. The size of the elements is calculated from the side length and the area of the watershed is
displayed, based on the total number of elements. Also, a count of the number of channel elements is
made to give some feeling for drainage density. Information on the minimum, average and maximum
slopes for both overland flow and channels is collected. Information on subsurface drainage, mean
antecedent moisture and outlet element location is given.
The second section of this portion of the output contains a short synopsis of each of the land uses
and soils that are actually present in the watershed. Percentage of area occupied as well as several
pertinent descriptors for each soil or land use are displayed.
The final section of the watershed characteristics involves the number of elements containing those
BMPs which involve structures or land use changes (identified in elemental data file). If no BMPs of
this type are present, this section will not appear.
Flow and sediment information and BMP effectiveness. This portion of the output most
nearly resembles the "normal" output from most watershed models. A flow hydrograph, along with
associated sediment concentration and accumulative yield, is displayed. The time interval between
print points is determined by the number of hydrograph print points (set internally to 101). This
parameter can be changed easily.
An accounting of total rainfall, total flow and average sediment yield is presented at the end of the
hydrograph. Also, the amount of sediment trapped by each structural BMP (if any) is noted.
Although the only hydrograph printed is that of the outlet element, it is possible to access the output
information from any element(s) within the watershed. A rather minor modification to the output
section of the ANSWERS model is all that is required to produce a hydrograph and associated
sediment information for any point in the basin.
24
-------
DISTRIBUTED HYDROLOGIC AND WATER QUALITY SIMULATION
BY ANSWERS UER 4.800326
STANDARD PREDATA FILE FOR ALLEN CO., INDIANA—800423
RAINFALL HYETOGRAPH FOR EUENT OF B-DIST
GAGE NUMBER GA
TIME - MIN.
0.0
9.0
18.0
23.0
29.7
37.6
45.0
54.0
63.0
72=0
90.0
350.0
RAINFALL RATE - 1N./HR.
0.00
0.52
0.76
0.92
1.59
5.52
.63
1.15
0.83
0.72
0.60
0.00
SOIL PROPERTIES
SOIL POROSITY FIELD CAP. INFILTRATION CONSTANTS CONTROL ANTECEDENT EROSION
(PERCENT (PERCENT
1
2
3
4
5
6
7
8
UOL.)
46.0
46.0
46.0
42.0
44.0
46.0
46.0
35.0
SAT.)
75.0
65.0
70.0
70.0
80.0
75.0
75.0
65.0
FC
IN./HR.
0.4
0.4
0.4
0.6
0.6
0.6
0.4
0.9
ft
IIS./HR
0.8
0.3
0.3
1.0
1.0
1.0
0.8
1.6
0.65
0.65
0.75
0.65
0.65
0.65
0.65
0.60
ZONE
IN.
4.0
3.0
3.0
4.0
5.0
5.0
3.0
6.0
TILE DRAINAGE COEFF. = 0.25 IN./24H
GROUNBWATER RELEASE FRACTION = 0.500E-03
COUER/MANAGEMENT PRACTICES
CROP MAX. POT.
INTERCEPTION
1 FALLOW
2 51 CORN
3 S2 CORN
4 CORN-NT
5 BEANS TP
6 BEANS FC
7 S. GRAINS
8 PASTURE
9 WOOES
11 HOMESITE
IN.
0.00
0.02
0.04
0.06
0.03
0.03
C . 04
o.os
0.10
0.02
PERCENT
CQUER
0.
20.
60.
85.
75,
75.
95.
100.
90.
100.
ROUGH
COEFF
0.47
0.47
0.55
0.55
0.47
0.53
0.55
g.CO
0.55
0.40
.8
,4
ROUGH.
HEIGHT
IN.
2,5
2.
2.
4.
2.
2.G
3.0
0.4
5.1
2.4
MANNINGS
N
0.100
0.075
0.070
0.150
0.060
O.OS5
0.090
0.100
0.200
0.090
MOISTURE CONST.
(PERCENT SAT)
70.0 0.36
70.0 0.32
70.0 0.17
70.0 0.36
70.0 0.32
70.0 0.36
70,0 0.38
70.0 0.35
EROSION
CONST.
1.00
0.50
0.50
0.30
0.60
0.55
0.15
04
15
O.SO
CHANNEL PROPERTIES
TYPE MIDTH MANNINGS M
FT.
1 10.0 0.035
2 8.0 0,040
3 6.0 0.040
4 5.0 0.050
5 3.0 O.OSO
BKUNSON ~ 1980 PRACTICES
WftTbRSHED CHARACTERISTICS
NUMBER OF 6.40 AC. OUEELAND FLOW ELEMENTS =
NUMBER OF CHANNEL SEGMENTS = 41
AREA OF CATCHMENT = 1644.8 AC.
CATCHMENT SLOPE: MIN = 0.2" AUE = 1.35
CHANNEL SLOPE: MIN = 0.45 AUE = 1.63
PERCENT OF AREA TILED = 100.0 WITH A D.C. OF
MEAN ANTECEDENT SOIL MOISTURE = 70,, FIELD CAPACITY = 70. PERCENT SATURATION
GROUNDWATER RELEASE FRACTION = 0.0005
OUTLET IS ELEMENT 2b5 AT ROW 18 COL 2
257
MAX =
MAX =
0.25 IN./24H
4.00 PERCENT
2.50 PERCENT
Figure 5-1. Typical ANSWERS Output Listing.
25
-------
SURFACE COUER/NANAGEMENT CONDITIONS
CROP PERCENT PERCENT N
SOIL ASSOCIATION PROPERTIES
PRESENT
S2 CORM 87,5
PASTURE 0.4
WOODS 3.3
HOMESITE 2.7
COUER
SO. 0.070
100. 0,100
90. O.SOO
100. 0.090
MO. PERCENT FC
INITIAL CONTROL K
0.50
0,04
0,15
0.20
1
2
3
6
7
8
PRESENT IN./HR. IN./HR.' DEPTH IN.
23.4
35.4
18,
S.
10.
.7
.a
.5
0.8
STRUCTURAL MEASURES INCLUDED
TYPE NUMBER
1 PTO TERRACES 17
3 G. WATERUftYS 15
4 FIELD BORDER 5
OUTLET HYDROGRftPHS — UER
TIME
S1IN.
0.0
3.5
7.0
10.5
14.0
17.5
21.0
24.5
28.0
31.5
35.0
38.5
42.0
45.5
43.0
52.5
56.0
53.5
63.0
66.5
70.0
73.5
77.0
80.5
84.0
87.5
31. 0
34.5
«
276.5
280.0
283.5
287.0
336.6
339.5
343.0
346.5
350.0
RAINFALL
IN./HR.
0.00
0.52
0.52
0.76
0.76
0.76
0.92
1,59
1.59
5.52
5.52
1.63
1.63
1.15
1.15
1.15
0.83
0.83
0.83
0.72
0.72
0.60
0.60
0.60
0.60
0.60
0,00
0,00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
RUNOFF
IM./HR.
0.0000
0.0000
0.0000
0.0000
0.0000
0.0001
0.0001
0.0001
0.0002
0.0004
0.0019
0.0126
0.0554
0.1705
0.3071
0.3877
0.4237
0.4403
0.4479
0.4495
0.44C9
0.4411
0.4325
0.4217
0.4032
0.3357
0.3820
0 . 3663
0.0160
0.0159
0.0158
0.0157
V
0.0155
0.0155
0.0155
0.0155
0.0155
YIELD
SEDIMENT
LB.
0.
0.
0.
0.
0,
0.
0.
0.
3.
19.
139.
1247.
7200.
S6052.
63336.
114398.
172411.
233857.
295959.
360548.
423912.
486639.
548335.
608331.
667707.
724795.
780001.
833187.
1503945!
1504636.
1505257.
1505810.
1508849'
1508879.
1508901.
1508916.
15089H6.
4.300326
CONC.
SEDIMENT
PPM
0.
0.
0.
0.
0.
0.
3.
200.
1179.
3524.
6097.
8150.
8226.
7138.
6SS3.
6517.
6500.
6520.
6520.
6508.
6502.
6506.
65.15.
6527.
6538.
6547.
6551.
6560.
•
2105!
1913.
1725.
1544.
•
107!
78.
56.
39.
27.
0.4
0,4
0.8
0.8
4.0
3.0
1.7
0.36
0.32
0.17
.36
.38
6.0 0.35
RUNOFF UOLUME PREDICTED FROM 1.96 IN. OF RAINFALL = 0.625 IN.
AUERftGE SOIL LOSS = 317. LB./AC
STRUCTURAL PRACTICE 1 REDUCED TOTAL SEDIMENT YIELD BY 56384.1. LB.
Figure 5-1, cont.
Net transported sediment yield or deposition. Statistics are kept, throughout the simulation,
on the actual amount of soil removed from or deposited on each element. Although this soil actually
leaves the element (in the case of a negative number), it may or may not reach the channel system.
This is due to the fact that deposition may occur further down slope.
Another problem with treating "hot spots" identified with this information is that the removal of one
"hot spot" may actually cause another one. If the management practice removes sediment, yet still
allows nearly the same amount of water to flow downslope, the detachment rate will increase in the
26
-------
ELEMENT SEDIMENT
NO.
1
5
3
137
141
145
149
153
£41
245
249
253
257
LB./AC
-301.
-839.
-980.
-109.
-2160.
-5GB,
-1762.
-2255.
-1S58.
-1663.
-1993.
-1653.
-1884.
MAX EROSION-RATE =
NO.
43
72
31
AMOUNT
0.
1S5.
324.
INDIUIDUAL ELEMENT SEDIMENTATION
ELEMENT SEDIMENT ELEMEI*
NO. LB./AC NO.
2 40. 3
6 -909. 7
10 -887. 11
138 -1779. 139
142 -1832. 143
146 -183. 147
150 2203. 151
154 21. 155
242 -839, 243
246 -1S84, 247
250 -1882, 251
254 -2018. 255
2948. LB./AC
STD. BEU. =
IEDIMENT
LB./AC
-189.
-2214.
-1744.
e
-1072^
-2QB6.
-333.
56.
-1895..
a
-851 1
-1745.
-1137.
-1137.
ELEMENT
ISO.
4
8
12
0
140
144
148
152
156
244
248
252
256
SEDIMENT
LB./AC
-2201.
-1063.
151.
-isss!
-32S.
-1S25.
-615.
-1654.
0
-149]
-1410.
-1434.
-1333.
MAX DEPOSITION RATE =
893. LB./AC
CHANNEL DEPOSITION — LB.
NO. AMOUNT (SO. fi[10UNT
57 0. ISO 0.
75 0. 73 0.
32 79. 33 234.
2203. LE./fiC
NO.
64
83
108
ftMCUNT
0.
467.
' 661.
134
206
255
37.
0.
0.
193
207
Oo
27.
290
PPP
0.
0.
Figure 5-1, cont.
201
E39
94.
0.
downhill elements, since the load is less from above. In most cases, however, practices which
reduce the sediment load also reduce the runoff rate in the downslope area.
Channel deposition. This section of the output information details the amount of sediment
deposited in each of the "shadow" or channel elements. ANSWERS does not presently predict
channel erosion. It does allow the channel flow to entrain deposited sediment if the flow regains
enough excess transport capacity to do so.
Graphical Output
Several plotting programs have been constructed to use the input to and the output from the
ANSWERS model to provide visual enhancement and better understanding of the information
provided by this program. The QCKPLT program, mentioned in a previous section, uses the elemental
data portion of the input file to produce the map shown in Figure 5-2. The arrows indicate the flow
direction for each element. The shaded areas indicate "dual" elements or overland elements with
companion channel elements. This map can be produced so that it will fit any scale. This feature
allows one to check input data on maps with different scales by producing overlays at the specific
scale needed. The grid is also very useful in physically locating the predicted "hot spot" areas.
Figure 5-3 shows the graphic output from the HYPLT program. HYPLT uses standard CALCOMP-
compatible calls and plots the rainfall hyetograph, the runoff hydrograph and the sediment concen-
tration curve. The program directly uses the hydrograph portion of the output listing.
27
-------
1 ? 5 4 5 6 7 P S 12 1 1 \2 13 14 IS 18 17 18 1S2021 222524
1 -1
2 -7
5 -IS
4 -IS
S -28
6 -58
7 -48
8 -60
S -75
10 -S2
11 -115
12 -154
15 -157
14 -180
IS -205
16 -226
17 -2G0
18 -275
IS -2S4
20 -512
21 -550
22 -542
vF^
Figure 5-2. Example Elemental Map Produced by QCKPLT Program.
.OOO-i
4.000-
6.000 ->
1.200-
.800-
.400-
Intensity
Runoff
BRUNSON DITCH
8 YR. - 1.5 HR. STORM
.Sediment Concentration
18.00
- 12.00
- 9.00
- 3.00
.000-4 - ' — -f - 1 - 1 - : - 1 — r " T
.0 40.0 80.0 120.0 160.0 200.0 240.0 280.0 320.0
TIME - MINUTES
.00
Figure 5-3. Example Output of HYPLT Plotting Program.
28
-------
The information presented in Figure 5-4 comes directly from the net transported sediment yield or
deposition section of the ANSWERS output. Several programming steps are required to "recon-
struct" an elemental data format (row and column coordinates) and input the individual element
information to a pmgram called CONTUR. CONTUR allows the user to set the levels of sediment yield
or deposition at which contours are desired. The program produces a map at any desired scale (up to
the maximum size the plotter allows). The shading in Figure 5-4 is for additional visual effect. The
portions of the watershed with closely spaced contqurs show areas with excessive transported soil
loss or deposition. In general, high transported soil loss areas will be found near high deposition
areas. This is due to the fact that steep slopes blend into flat slopes near the channels.
CONSTRUCTION SETE
WATERSHED
Indiana MIP
Erosion> 20 M.T./ha
Deposition 10 M.T./ha
Figure 5-4. Example Output from CONTUR Program.
29
-------
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Barfield, B.J. 1968. Studies of turbulence in shallow sediment laden flow with superimposed
rainfall. Technical Report No. 11. Water Resources Institute, Texas A&M University. College Station,
TX.
Beasley, D.B. 1977. ANSWERS: A mathematical model for simulating the effects of land use and
management on water quality. Ph.D. Thesis. Purdue University. West Lafayette, IN. 266 p.
Beasley, D.B., L.F. Huggins and E.J. Monke. 1980. ANSWERS: A model for watershed planning.
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Yalin, Y.S. 1963. An expression for bed-load transportation. Journal of Hydraulics Division,
Proceedings of the ASCE. 89(HY3):221-250.
Young, R.A. and C.K. Mutchler. 1969. So/7 movement on irregular slopes. Water Resources
Research. 5(5): 1084-1089.
31
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APPENDIX A - SOIL PARAMETERS
Section A.I
The parameters described in this section are concerned with the physical description of the soil
condition. The parameters do have some seasonal variation, since the bulk density of a 59!! does
vary somewhat throughout the year. The total porosity (TP) is a measure of the bulk density. The
field capacity (FP) describes the upper limit of available water in the soil. It also quantifies that
portion of the pore volume which can contain only gravitational water (above the moisture holding
capacity of the soil). The control zone depth (DF) identifies the volume of soil (depth) that actually
influences the rate of infiltration at the surface. The antecedent soil moisture (ASM) quantifies the
starting point for the soil moisture-based infiltration equation. Methods for determining each of
these important parameters will be presented in this section.
Total Porosity (TP).The volume of pore space within the soil is directly related to the bulk density
(weight per unit volume) of the soil. The total porosity (percent pore space) of a soil is defined as:
TP = 100 - (>) * 100 (A-1)
where: TP = total porosity, percent,
BD = bulk density,
PD = particle density (assumed to be 2.65).
In some cases, comprehensive soil surveys will contain information on the bulk density of the
mapped soil types. However, most soil surveys, even the newer ones, do not contain this kind of
data. One bit of information that is available in all soil surveys is the textural class of the individual
soil types. Without specific information on the bulk density of a particular soil, the modeler can still
make a reasonabjy good estimate of the bulk density, and thus the total porosity, by utilizing the
textural class definition.
Table A-1 lists bulk densities and other soil physical properties for several different soil textural
classes. For those classes not listed, an interpolation can be performed. Very sandy soils or organic
soils have much larger ranges of values.
Field Capacity (FPJ. As the moisture content of the soil is increased, a point is reached when water
begins to drain due to gravitational forces. Another way of describing this phenomenon is to say that
the moisture holding tension within the soil becomes less than 1 /3 atmosphere. The point at which
this gravitational drainage begins is called field capacity (FP) and is expressed as a percentage of
saturation. Saturation occurs when the total pore space within the soil is filled with water. Thus, a
soil with a total porosity of 50 percent and a field capacity of 70 percent contains 35 percent water (by
volume) at field capacity.
Although some soil surveys contain information about the actual field capacity of the individual soil
types, most soil surveys only state what the available water capacity of the soil is. Using the
information in Table A-1 and the available water capacity of the individual soijs (A horizon), the
modeler can easily estimate the field capacity (percent saturation) when that information is not
available. By definition, the available water capacity of a soil is that water held within the pores
between field capacity (tension of 1 /3 atmosphere) and the wilting point (tension of 15 atmospheres).
In addition, the assumption is made that approximately one half of the water in the soil is
33
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Table A-1. Some Representative Physical Properties of Soils.
Soil
Texture
Sandy
Sandy loam
Loam
Clay loam
Silty clay
Clay
Bulk
Density*
(9/cc)
1.65
(1.55-1.80)
1.50
(1.40-1.60)
1.40
(1.35-1.50)
1.35
(1.30-1.40)
1.30
(1.25-1.35)
1.25
(1.20-1.30)
Total
Porosity*
(% volume)
38
(32-42)
43
(40-47)
47
(43-49)
49
(47-51)
51
(49-53)
53
(51-55)
Field
Capacity*
(% saturation)
39
(31-47)
49
(38-57)
66
(59-74)
74
(66-82)
79
(72-86)
83
(76-89)
Wilting
Point*
(% saturation)
17
(10-24
21
(15-26)
30
(26-34)
36
(32-40)
38
(34-42)
40
(37-43)
*Numbers in parentheses indicate normal range.
Adapted from: (Israelsen and Hansen, 1962).
unavailable. Thus, if the available water is listed as .15 inches/inch (15 percent by volume), the field
capacity of the soil is twice that amount or .30 inches/inch (30 percent by volume). Further, if the
total porosity has been listed as 50 percent, that means that the field capacity of the soil is 30 percent
divided by 50 percent or 60 percent of saturation.
Infiltration Control Zone Depth (DF). Of all of the parameters used in the ANSWERS, this one is
the least well defined and most arbitrary. Essentially, it describes the volume of soil (depth) that
influences the infiltration rate at the surface of the soil. Experimental data and simulation experience
have lead to the conclusion that the control zone depth (DF) varies with time. However, not enough
information exists to describe a seasonal influence exactly. In general, the control zone depth is
equal to or less than the depth of the A horizon. For most of the soils that have been modeled in the
Midwest, the control depth (DF) has been assumed to be equal to .25 to .75 of the depth of the A
horizon. In general, a starting value of one half of the A horizon has been used.
Antecedent Soil Moisture (ASM).The infiltration equation in the ANSWERS model is based on the
moisture content of the soil. Since the infiltration rate will be much greater when the soil is "dry" than
when it is "wet", it is very crucial that the correct antecedent moisture content be used when
simulating actual situations. For hypothetical or "wet weather" simulations, moisture contents at or
above field capacity will generally be used.
34
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This section details a simple moisture balance approach for determining the antecedent moisture
content in each soil. The form of the moisture balance equation is:
ASM = ASML + RAIN - ET - RO - PERC (A'2)
where: ASM = antecedent soil moisture,
ASML = last known (initial) soil moisture,
RAIN = daily rainfall,
ET = evapotranspiration,
RO = runoff,
PERC = percolation.
In this equation, percolation refers to drainage of gravitational water (water in excess of field
capacity). In order to simplify the moisture balance calculations, several assumptions are made:
1. The depth of the soil layer that influences the moisture content is equal to the control
zone depth (DF),
2. The evapotranspiration rate is one half of normal on days that have rainfall in excess
of 0.2 inches,
3. The soil drains down to field capacity within 1 day at the steady state infiltration rate
(FC),
4. When the soil moisture content reaches the wilting point, no additional moisture is
lost due to ET,
5. On days when rainfall is less than 0.3 inches, RO (runoff) is zero,
6. On days when rainfall is between 0.3 and 0.8 inches, RO 0.10*RAIN,
7. On days when rainfall is between 0.8 and 1.5 inches, RO 0.15*RAIN,
8. On days when rainfall is greater than 1.5 inches, RO 0.20*RAIN.
The rate of evapotranspiration can be calculated using any of several different equations. Each
method entails certain assumptions and the user must determine which equation best serves his
purposes and utilizes his data. The average monthly rates shown in the following example are
representative of cropland rates in northern Indiana.
The antecedent moisture calculations should be started approximately one month prior to the time to
be simulated. Field capacity or any other reasonable moisture content can be assumed as a starting
point. During the period of calculation, the soil moisture is not allowed to go below the wilting point.
Once enough rainfall has occurred within the calculation period to equal or exceed field capacity, the
previous history is wiped out. Table A-2 shows example moisture calculations for a soil with a total
porosity of 50 percent, control depth (DF) of 6 inches, field capacity of 70 percent saturation (wilting
point of 35 percent saturation) and a steady state infiltration rate (see Section A.2) of 0.3 inches per
hour. Using the above information and assuming that an ANSWERS simulation is to be started on
June 14, the ASM value for this soil type would be 67 percent.
Section A.2
The parameters which specifically describe a soil's infiltration response as described by the
modified form of Holtan's equation used in ANSWERS are defined in this section. The steady state
infiltration rate (FC) indicates the rate at which the soil will absorb water when the soil is saturated.
The difference between the maximum and steady state infiltration rates (A) combined with the
infiltration exponent (P) helps to describe the typical exponential "drawdown" of the infiltration rate.
Infiltration Rate Descriptors (FC and AJ. A simple procedure for selecting values for the steady
state infiltration rate (FC) and the difference between maximum and steady state rates (A) is
described here. The user is, of course, free to use any information he has concerning these values.
Soil survey information is used in this procedure due to its general nature and ready availability.
35
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Table A-2. Antecedent Soil Moisture (ASM) Calculation Example.
Day
1 (5/15)
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18 (6/1)
19
20
21
22
23
24
25
26
27
28
29
30
31 (6/14)
Soil Moisture
(% saturation)
70
69
67
65
64
62
100
94
93
69
67
76
68
67
65
65
73
78
76
77
79
81
85
69
67
65
63
62
92
69
67
Rain
(in.)
.01
0
0
0
0
3.16
.90
.80
.02
0
.29
0
0
0
.05
.27
.27
.21
.25
.35
.39
.53
.03
0
0
0
.02
1.11
.04
0
ET
(in.)
.05
.05
.05
.05
.05
.03
.03
.03
.05
.05
.02
.05
.05
.05
.05
.03
.03
.03
.03
.03
.03
.03
.06
.06
.06
.06
.06
.03
.06
.06
Runoff
(in.)
0
0
0
0
0
.63
.14
.08
0
0
0
0
0
0
0
0
0
0
0
.04
.04
.05
0
0
0
0
0
.17
0
0
Percolation
(in.)
0
0
0
0
0
0
2.26
.73
.69
0
0
.18
0
0
0
0
.09
.24
.18
.22
.28
.32
.45
0
0
0
0
0
.66
0
The range of permeabilities for a given soil type (as listed in the USDA Soil Survey format) are used in
the following manner:
1. The midpoint of the lower 1/3 of the range is used for FC,
2. The midpoint of the upper 2/3 of the range is assumed to be the maximum rate,
3. The value of A is equal to the maximum rate minus FC.
Assuming a permeability range of 0.2 to 1.5 inches per hour, the following example illustrates the
technique:
The total range =1.3 inches per hour
1/3 of range = 1.3/3 = .43 inches per hour
Thus, FC equals the midpoint of the lower 1/3 of range
FC = .2. + (.43/2) = .42 inches per hour
36
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The maximum rate is the midpoint of the upper 2/3 of the range
maximum rate = ((.2 + .43) +1.5)/2 = 1.07 inches per hour
The A value equals the maximum rate minus FC
A^ = 1.07 - .42 = .65 inches per hour
Using the entire range, FC would be 0.2 iph and A would be 1.3 iph. The method detailed above
appears to give more realistic numbers.
Infiltration Exponent (P). As stated in the section on component relationships, the infiltration
exponent (P) relates the rate of decrease of infiltration capacity to increasing moisture content. This
property varies among soil types and is most closely related to the textural class of the soil. The
heavier the texture (more clay), the larger the value of P. Conversely, sandy soils show little change
in infiltration rate with increasing soil moisture content and, thus, have a much smaller value of P.
Table A-3 lists some starting point values for several textural classes.
Table A-3. "P" Values for Various Soil Testures.
Soil Texture Suggested Values for "P1
Clay
Silty clay
Clay loam
Loam
Sandy loam
Sand
.75 -
.65 -
.60 -
.55 -
.50 -
.35 -
.80
.75
.70
.65
.60
.50
Section A.3
Two different types of information are included in this section. The USLE "K" factor or soil erodibility
of each soil type is described. The general subsurface drainage characteristics of the watershed are
described by the combination of the tile drainage coefficient and the groundwater release fraction.
Both of these drainage terms are defined and methods of parameter value assignment are discussed.
Soil Erodibility - USLE "K" (K). Most of the newest USDA Soil Surveys contain information pn the
"K" factor for each soil type mapped. Other sources of this information include statewide soil loss
handbooks or brochures which are published by most state SCS offices. Wischmeier et al. (1971)
have produced a nomograph technique for determining the USLE "K" factor based on textural class
and other soil characteristics.
Section A.4 details a method for simplifying the soils description file presented in this Appendix.
Essentially, the technique involves the grouping of soils by similarities in drainage response. When
soils are grouped in this manner, the (K) parameter for the various individual soils may not be equal.
If they are not, one of two methods can be used to arrive at an "effective" (K).
1. Use an area weighted average of "K" values within a drainage class, or
2. Use the value of "K" for the predominant soil(s).
37
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Subsurface Drainage Characteristics. The two parameters which describe the rate of
subsurface water movement are the tile drainage coefficient and the groundwater release fraction.
The tile drainage coefficient is simply the design value for tile drainage. Interflow or groundwater
release is described by putting a fraction of the water in the subsurface reservoir into the channel
system at each time step. Experience has shown that the value of the fraction varies from as little as
zero to approximately 0.01. Small values of the fraction may actually cause an increase in the flow
rate on the recession limb of the hydrograph due to the fact that the drainage rate from the control
zone is greater than the groundwater movement rate. Thus, the subsurface reservoir of water
increases, and the interflow rate rises accordingly. Higher values of the fraction will cause the
hydrograph to "level off" for a period of time and then decrease as the rate of subsurface drainage
becomes less than the interflow rate.
Section A.4
In order to reduce the number of soils that must be described in the "predata" file, a technique has
been developed for identifying soils with similar drainage characteristics. The similar soils are then
placed in a general group with drainage and erosion characteristics which describe the "average"
response of the soils making up the group.
The procedure requires information about the drainage classification and hydrologic soil group of
each soil type. The technique involves the following:
1. Soils are listed by their drainage classification (i.e., well drained, poorly drained,
very poorly drained, etc.) and by hydrologic group (i.e., A, B, C or D).
2. The soils are first grouped by drainage classification. Then, those soils are examined
for hydrologic group. Soils that have the same drainage classification and hydrologic
group are considered to have similar responses. It is possible that within one
drainage classification there may be soils with two or more hydrologic groups. The
soils in each hydrologic group should be considered as a separate soil group.
3. The soil(s) that predominate the area in each soil group are chosen as representative.
A more complex method would be to select the descriptive parameters based on area
weighting.
38
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APPENDIX B - LAND USE AND SURFACE PARAMETERS
Section B.I
The information presented in this section involves the extent of crop cover, the flow retardance of the
surface and the relative erosiveness of the various crops or land uses. The specific land use or crop
(CROP) is simply an identifier that is printed during output. The potential interception (PIT) and
percent cover (PER) are used to describe the interception of rainfall. Manning's n (N) describes the
surface roughness or retardance to flow. The relative erosiveness parameter (C) is actually a
combinatio_n of the USLE "C" and "P" values with seasonal adjustment.
Interception Parameters (PIT and PER). A certain amount of the precipitation during any event
never reaches the soil surface. Contact with and storage on vegetation accounts for this removal
and is called interception. The potential interception volume (PIT) describes the volume of moisture
that could be removed if the area were completely covered by that crop or land use. The actual
percentage of cover (PER) assumes the non-covered area has no interception. Table B-1 lists some
example values for PIT.
Table B-1. Potential Interception Values.
Crop PIT
Oats .5 - 1.0
Corn .3 - 1.3
Grass .5 - 1.0
Pasture and Meadow .3 - .5
Wheat, Rye and Barley .3 - 1.0
Beans, Potatoes and Cabbage .5 - 1.5
Woods 1.0 - 2.5
Manning's n (N).The measure of surface roughness or flow retardance used in the flow equation in
ANSWERS is Manning's n. This information, when combined with element slopes, rainfall, intercep-
tion, infiltration and routing considerations, helps yield the solution to the continuity equation,
which is the basis of ANSWERS. There are numerous sources for obtaining reasonable values of n for
channel and overland flow situations.
Relative Erosiveness (C).This parameter is used in determining how much soil could potentially
erode due to a particular crop or land use, when compared to fallow ground under identical
conditions. It is a direct combination of the USLE "C" and "P" parameters with a seasonal adjust-
ment. Thus, conventionally tilled corn at crop stage 1 will have a higher (more erosive) C value than
the same corn at crop stage 2, when there is more foliage and root structure. Agriculture Handbook
No. 537 (Wischmeier and Smith, 1978) contains information for determining the USLE "C" and "P"
values throughout the year for numerous crops and management systems.
39
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Section B.2
Figure B-1 shows a profile of a section of the soil surface. The combination of the peaks and valleys
yields a certain depressional storage volume. In addition, the amount of the surface that area that is
inundated at any time is a direct function of the depth of water on the surface. The infiltration rate
within an element is greatly affected by the amount of pondage within the area.
Figure B-1. Soil Surface Profile.
Surface Storage Descriptors (HUand RC). The ANSWERS model uses the maximum roughness
height (HU) and a roughness coefficient (RC) to describe the surface storage characteristics and the
ponded surface area. The roughness coefficient (RC) is, essentially, a shape factor which describes
the frequency and severity of the roughness. The maximum roughness height (HU) is used to
establish the upper limits of the surface roughness and is physically measurable. Table B-2 shows
some typical values for both HU and RC.
Table B-2. Typical Surface Storage Coefficients.
Surface Condition
RC
Plowed Ground:
Spring - smooth
Spring - normal
Spring - rough
Fall - smooth
Fall - normal
Fall - rough
(mm)
100
130
130
60
70
130
.53
.48
.59
.37
.33
.45
Disked and Harrowed:
Very smooth
Rather rough
Corn Stubble
30
60
110
.42
.43
.59
40
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APPENDIX C - INDIVIDUAL ELEMENT INFORMATION
Section G.I
One of the strengths of the ANSWERS model is its ability to describe spatially those processes which
affect the hydrologic and erosion responses of a watershed. In order to accomplish this, the
topographic influences of the various sub-areas within the watershed must be quantified. By
applying a square grid to a soils or topographic map, the element pattern is defined. Once done,
additional information concerning specific soils, land use, drainage and BMPs can be added easily.
In the rather rare situation in which the necessary watershed data is available on machine readable
media, the only requirement is to develop a simple computer program to reformat the data in a
manner compatible with the above definitions. Unfortunately, the more common situation is to have
only maps available from which the necessary information must be manually extracted. Because the
format outlined in Chapter IV is rather tedious, a series of programs have been written to facilitate
the manual transcription of map information into the file format required by ANSWERS.
It is recommended that a transparent overlay be prepared with a grid of squares drawn to the
map-scale size desired for watershed elements. It is further suggested that this grid have its rows
and columns numbered beginning in the upper left-hand corner with number 1 for the rows and for
the columns of elements. This overlay can then be superimposed on topographic and soils maps to
delineate the elements of which the catchment is composed. The map should be oriented in such a
manner that the direction of predominate water flow is from the top (row 1) to the bottom of the map,
i.e., the watershed outlet should be as near to the highest numbered row of elements as possible
while still maintaining an orientation which is compatible with most field boundaries. This often
means that the rows will be oriented in one of the four cardinal directions. Although not an absolute
necessity, this arrangement does facilitate computation.
Available data formatting programs are written with the expectation that separate files will be
manualjy prepared for each different physical parameter in the element file (i.e., soil, crop, channel
type, rain gauge). Data for these programs may be prepared in a free-format style with each numeric
entry separated by a comma. Any number of data entries may be entered on a single line. For those
locations which do not have a FORTRAN compiler which accepts free-format input, it is a simple
matter to modify the input format statements in whatever manner desired.
The method for describing the direction of slope applies to both overland and channel flow direc-
tions. In those elements which contain channels, the direction is in 45 degree increments which
contribute all of the flow to one of the eight surrounding (and touching) elements. The channel
direction takes precedence over the overland direction.
Simplified Data File Construction. The basis of the simplified data file construction technique is
the use of USDA-SCS Soil Survey information to provide a map base for the grid and slope
information from the mapping units themselves. Although the mapping units used in modern Soil
Surveys give a range of slopes for each defined area, there is no information provided on slope
direction. Therefore, directions must be chosen using a "common sense" approach in conjunction
with topographic information.
An additional degree of slope descriptiveness can be obtained by using the surrounding elements to
determine which part of the slope range should be used. For example, when a soil with a range of 3-6
percent is surrounded by soils with steeper slopes, the high end of the range (approximately 6
percent) should be used. On the other hand, a soil with 6-12 percent slopes surrounded by lesser
slopes would use the low end of the range. An element surrounded by soils with similar slopes would
use the midpoint of the range.
41
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Data File Construction Using Topographic Maps. ANSWERS requires that the average slope
steepness and direction of steepest slope be specified for each element in the catchment. Rather than
attempt to obtain this information directly from a topo map a program, called ELEVAA, has been
written which requires instead that the elevations of the corners of each element be input. That
program calculates the slope steepness and flow direction of each element and then sets up the
complete format for the elemental data file. That file is subsequently updated to add inf9rmation
concerning the soil type and crop/management practice for each element and to identify those
elements which contain a well defined channel.
ELEVAA is organized so that the identification of the location of the elevation data requires a slight
mental transposition of the element's row and column number to refer to the elevation at the upper
left-hand corner of the element. For example, position 4,6 for an elevation actually refers to the
upper-left corner elevation for the element in row 4 and column 6 of the watershed. The elevation in
the lower right-hand corner of element 4,6 would be identified by the position numbers5,7 (note that
this elevation is also the elevation of the upper left-hand corner of element 5,7; thus, since a single
point elevation is normally used to help compute the slppe direction and steepness of four different
elements, one never needs to be concerned with specifying the location of anything except the upper
left-hand corner elevation for each element).
Begin preparing the input data file for ELEVAA by starting with the upper corner elevations of the top
row of elements in the catchment. Generally this will be row number 1. The first two entries on a data
line must be, respectively, the corresponding row number and the column number of the first
elevation that will appear on that line. The remaining entries on that line will be the elevations of
sequential elements in that given row. Any number of elevations, up to a maximum of 28, may be
entered on a single line, but they must be for sequential columns. Thus, if a row is discontinuous
(watershed boundaries are irregular and often exclude some element positions) or whenever all
elements in a given row have been specified, it is necessary to start a new line of data. The end of
data input to ELEVAA is signified by including a blank line after all elevation data has been specified.
There are some difficulties that arise as a result of trying to generate the elemental data file from
corner elevations. It is almost certain that some slope directions calculated on the basis of corner
elevations will be unsatisfactory and will need to be manually edited. This is especially true for
boundary elements of the catchment. They will often be computed in a direction which would result
in some of their outflow moving out of the watershed. Also, it is mandatory that all of the outflow
from the outlet element move directly out of the catchment, i.e., it should have one of the cardinal (0,
90,180 or270) directions and will usually be specified as a channel element as discussed below. It is
also likely that elements located near to stream channels will not have appropriate slope directions
of slope steepness returned from ELEVAA due to topographic irregularities along a channel. Most of
these difficulties will be automatically corrected when the channel data file is processed. In any
case, it is recommended that all manual editing of the elemental data file be postponed until after the
basic soils and channel data have also been processed.
One final warning should be given concerning possible difficulties with the output of ELEVAA for
cases where the watershed of concern has substantial areas which are relatively flat or even
depressional. For such situations, it is likely that ELEVAA will return element flow directions for a
group of elements which results in a computational ponding of water, i.e., the flow pattern for the
of elements has no outlet for surface flows. These areas, due to the cumulative flow depths that
result from the circulating runoff, will often show a false very high erosion rate. There are at least
two ways to discover such problem areas. One is to plot an elemental map with the flow direction
show for each element and to visually inspect it for such regions. A GCS (Graphics Compatibility
System)-based plotting program, called QCKPLT has been devised for this purpose (see Chapter V for
an example). Even if that procedure is followed, the second method is recommended as afinal check.
This second method involves running an initial watershed simulation assuming a fallow (no
vegetation) condition and then making a critical examination of all regions which show high erosion
rates to make sure they are not the result of circulatory regions caused by erroneous element slope
42
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directions. Once such regions are detected it is necessary to manually correct the flow directions to
provide a drainage outlet for the region. An interactive editing program for this purpose has been
written in the "C" language for use on computers utilizing the UNIX operating system. A FORTRAN-
based version of this editor is planned.
Section G.2
In order to fully utilize the ANSWERS model as a planning or evaluation tool, it must be able to
simulate the particular practices that users might apply to a watershed. ANSWERS handles BMPs in
two different ways. Practices which are strictly tillage-oriented are described in both the soils and
land use files. This is due to the fact that tillage-based management changes can affect both the
infiltration response and the surface condition of the soil. On the other hand, those BMPs which are
structural in nature or which require a change in land use (row crop to grass for waterways or field
borders, for example) are described in the individual element data file.
The primary tillage based BMPs considered by ANSWERS are:
1. Change from conventional tillage (fall turning plow) to chisel plowing,
2. Change from conventional tillage to minimum tillage,
3. Change from conventional tillage to no-till.
Each of these changes has similar effects, but to a different degree upon both the soils and land use
(surface) descriptors. This necessitates describing both "new" soils and land uses.
When conventional tillage is replaced by chisel plowing (#1), the infiltration components (A and FC)
should be increased approximately 20 percent. At the same time, the surface descriptors (HU and N)
should be increased by approximately 15 percent. In changing from conventional tillage to minimum
tillage techniques (#2), the infiltration and surface parameters should be increased by approxi-
mately 25 percent and 20 percent, respectively. The change from conventional to no-till (#3) requires
increases of approximately 25 percent for both infiltration and surface parameters.
Table C-1 lists the BMPs which are based on structures or land use changes. Each BMP, its code
number, additional descriptors required and any pertinent assumptions are listed.
Table C-1. Structural and Land Use Change BMP Descriptions.
Additional
BMP Code No. Information Assumptions
Tile Outlet Terraces 1 Trap efficiency of 90%
Only lowermost terraces
are described
Sedimentation Pond 2 Trap efficiency of 95%
Only ponds in upland
areas should be defined,
instream structures are
treated differently
Grassed Waterways 3 Width Decreases credibility
Field Borders 4 Total width Decreases credibility
43
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If a terrace or pond exists only in a portion of the element, the assumption is made that all incoming
flow is influenced by that BMP. Thus, elements which have only a small portion of a practice within
their boundaries should not be given credit for that practice. The most effective BMP found in an
element should be the one described. As an example, in an element with a pond and a grassed
waterway, the pond, with its very effective sediment trapping characteristics, should be chosen for
description.
44
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APPENDIX D - ENHANCED SEDIMENT MODEL
general
In order to better understand the complex processes of sediment and nutrient movement on a
watershed scale, it is necessary to have a transport model capable of determining not only the
magnitude of the material in movement but also the makeup. Since phosphorus transport is highly
influenced by the amount of fine material in the sediment load, a model which can predict the actual
"enrichment" of fines in the sediment load should be a very positive addition to a total "water
quality" model.
An expanded capability sediment transport model is available as part of the ANSWERS package
which can produce information on the differential detachment and transport of the various particles
which make up the soil surface and sediment load. This model utilizes many of the assumptions that
the original detachment/transport model within ANSWERS uses. It is based on the Yalin (1963)
model with modifications for multiple particle classes and for varying densities.
The component relationships, additional input information required, and output formats are des-
cribed in this section. The general release of the ANSWERS model does not contain this version of
the sediment model. It is significantly slower and requires more computer resources than the
original sediment algorithms. A complete discussion of the development and testing of this section
of ANSWERS can be found in Dillaha (1981). A modified version of ANSWERS, incorporating this
model, can be obtained by contacting the Agricultural Engineering Department, Purdue University,
West Lafayette, IN 47907.
Model Development
Sediment transported by overland flow occurs in two related forms: bedload and suspended load.
Bedload is that portion of the load which moves along the bottom of the flow by saltation, rolling and
sliding. Bedload is generally composed of the larger soil particles (sand, gravel and aggregates).
Bedload movement is highly transport dependent. A decrease in transport capacity causes the
immediate deposition of the excess bedload.
Suspended load is much more uniformly distributed throughout the flow depth as contrasted with
bedload. A decrease in the transport capacity will not result in the immediate deposition of
suspended sediment. This delay is the result of the small fall velocities of most suspended particles
which prevents them from depositing immediately. Part of the suspended load has such small fall
velocities (see Table D-1) that they are effectively permanently suspended, when compared with the
larger sediment particles. In this research the smallest particles, primary clay and silt less than 10
microns in diameter, were considered to be washload and were not allowed to deposit unless the
overland flow rate was zero. This means that their yield was determined entirely by their weight
fraction in the original soil masses and the total amount of detachment.
Table D-1. Typical Sediment Characteristics.
Particle Type Size Specific Fall Velocity Time to Settle
(mm) Gravity (mm/s) 1.0 mm
Primary Clay 0.002
Primary Silt 0.010
Small Aggregate 0.030
Primary Sand 0.200
Large Aggregate 0.500
2.65
2.65
1.80
2.65
1.60
0.003
0.080
0.349
24.
40.
5. min
13. s
3. s
.04 s
.03 s
45
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The fraction of particles larger than 10 microns which were deposited when there was a transport
capacity deficit was defined as:
RE. = FVi * . (if REi > 1, then RE. = 1) (D"1}
where: RE = fraction of particles of partiqle size class i
depositing,
FV. = fall velocity of particle i, m/s, ?
AREA = area of an overland flow or channel element, m ,
Q = flow rate, m /sec.
This is the classic relation describing the settling efficiency of particles in water (Weber, 1972). This
equation is not strictly true for the case of overland flow since it was developed assuming that:
1. The settling is occurring under quiescent conditions.
2. Flow is steady and the concentration of suspended particles of each size is initially
distributed uniformly throughout the flow.
3. Once the particles are deposited they are not resuspended.
Although overland flow conditions violate some of these assumptions (resulting in a possible
overestimation of the removal efficiency), it was decided to use the equation anyway. It was chosen
because it is an improvement over the normal procedure which assumes that all excess sediment is
deposited immediately and because the overestimation of removal efficiency due to turbulence is
potentially offset by the high concentration of the large particles in the lower flow region.
The fall velocity, FVi, in Equation (D-1) was calculated as (Fair, et al., 1968):
4 * AGRAV * (SG-l) * DIA. *5 (D-2)
FVi = ( r^TD L)
o
where: AGRAV = acceleration due to gravity, m/s ,
SG. = particle density, g/cm ,
DIA. = diameter of particle class i, mg,
CD = Newton's drag coefficient.
Newton's drag coefficient, CD, is defined as:
CD = 18 * VISCOS for REYN < .1 (D-3a)
CD = lL + 3 + .34 for REYN > .1 (D-3b)
where: VISCOS = kinematic viscosity of water, m2/s,
REYN = Reynolds number = FVi * DIA1 * VISCOS.
46
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For Reynold's numbers less than or equal to 0.1 the fall velocity calculation was direct; but for values
greater than 0.1, an iterative solution was required. If experimentally determined fall velocities are
available for the actual particle classes being modeled, they should be input directly and the model
will not have to estimate the fall velocities.
The rate at which sediment is transported by flow is a function of both the sediment supply rate and
the transport capacity of the flow. The net rate of movement is proportional to the lesser of the
transport or the rate at which the particles are available for transport.
The selection of a transport equation for the overland flow regime is probably the most critical
component of a sediment yield model. It is very difficult because all accepted transport models,
developed to date, were developed for streamflow conditions. The differences between deeper
channel flows and shallow overland flows are significant. Shallow flow undulates constantly,
resulting in flow regime changes; rainfall drastically increases the turbulence of the flow (Barfield,
1968); the ratio of particle diameter to flow may be high; surface tension may affect flow conditions;
(Young and Mutchler, 1969); and the slope of the energy gradeline is difficult to estimate (Foster,
1982). In spite of these differences, streamflow transport relations must be used because of the lack
of any relations developed from overland flow data.
Foster and Meyer (1972), Davis (1978), Alonso, et al. (1981) and Foster (1982) have done considerable
work in studying the use of streamflow equations for modeling the overland flow situation. Their
general concensus is that the Yalin (1963) equation best fits experimental overland flow data,
especially when one is modeling the particle size distribution of the eroded sediment. Based upon
their success with the equation it was decided to use the Yalin equation in this work.
Yalin (1963) developed an expression for the bedload transport of uniform, cohesionless grains over
a movable bed for steady, uniform flow of a viscous fluid. His derivation is based upon dimensional
analysis and upon the mechanics of the average motion of a grain. The flow was assumed to be
turbulent with a laminar sublayer not exceeding the thickness of the grains. Grain motion was
assumed to be by saltation and a critical tractive force was assumed. The critical tractive force as a
function of the laminar sublayer thickness was assumed to be demonstrated by the Shields' curve.
The Yalin equation is:
TF = PS * SG * * DIA * VSTAR * AGRAV (D'4a)
where:
PS = YALCON * DELTA * (1 - 1n (1 * S.IGMA))
SIGMA
SIGMA = 2.45 * SG~'4 * Y™ * DELTA (D-4c)
l/K
DELTA = JL - I (when Y < YrD, DELTA = 0) (D-4d)
ICR CK
VSTAR2 (D-4e)
(SG - 1) * AGRAV * DIA
47
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VSTAR = (AGRAV * r * SI)
.5 (D-4f)
TF = transport capacity,
e = mass density of fluid,
VSTAR = shear velocity,
YpR = critical shear stress from Shield's diagram,
5C = slope of the energy grade! ine,
r = hydraulic radius,
YALCON = an empirically derived factor = 0.635.
In the new sediment model, the hydraulic radius, r, was assumed to be equal to the flow depth
(actually depth of stored water less the depth of retention storage).
Foster and Meyer (1972) developed a method by which Yalin's equation could be used to predict the
transport capacity of each particle size class in a mixed sediment. Yalin assumed that the number of
particles in transpprt was equal to DELTA. Foster and Meyer, therefore, assumed that for a mixture,
the number of particles of a size i is proportional to DELTAj. Values of DELTAj for each particle class
were summed to give the total transportability, SDEL:
NPART
SDEL = £ DELTA. (°-5)
where: NPART = number of particle size classes,
DELTA. = DELTA as defined by Equation (D-4d) for
1 particle class.
The number of transported particles of class i in a mixture, (Ne)j was taken to be:
_ N1 * DELTA. (D.6)
v Vi S~D"ET
where: N. = the number of particles transported in a uniform
sediment for DELTA..
In a similar manner, PS was assumed to be proportional to DELTA, so:
PS, * DELTAi (D.7)
1 e'1 5DEC
where: (P ). = the effective PS for particle class i in a
mixture,
PS = the PS calculated for a uniform sediment of class i.
48
-------
The actual transport rate TFj of each particle class in a mixture can then be expressed as:
TFi = (lVi * SGi * PW * AGRAV * DIAi * VSTAR
(D-8)
Yalin's method, as originally derived, was developed from laboratory flume studies of the transport
of sand and gravel with flows much deeper than those encountered in overland flow. The constant
0.635 was determined from these flume studies. Davis (1978) found that 0.88 was a better value for
sand with a diameter of 342 microns and that 0.47 was better for coal particles with diameters of 156
microns and 342 microns and specific gravities of 1.67 and 1.60 respectively. No other information is
available concerning the value to use for YALCON unless one determines it by calibration. It was
decided to leave it fixed at 0.635 in this study.
The original Shields' diagram used by Yalin was not developed for sediment particles of low specific
gravity and small size. Fortunately, the Shields' diagram was extended for small particles by Mantz
(1977) and Figure D-1 can be used to estimate YCR. In the model, Shields' diagram, as extended by
Mantz, was broken down into the 5 regions listed in Table D-2.
0.1 1.0 tO 100
PARTICLE REYNOLDS NO. , REYN = VSTAR • DIA/VISCOS
Figure D-1. Shield's Diagram as Extended by Mantz (1977).
Table D-2. Critical Shear Stress Relations Used in Transport Model.
Region
Reynolds
number
Critical shear stress relation
I 0.03 j 450.
YCR = 0.1 * REYN
-0.3
YCR = EXP (-2.3026 - .5546 * log (REYN))
YCR = 0.033
YCR = EXP (-3.9793 + .19212 * logg (REYN))
YCR = 0.06
49
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A flow diagram of the model is presented in Figure D-2 which gives an overall picture of the
interactions between the various parts of the model.
HYDRAULIC AND SEDIMENT INFLOW
DATA FROM MAIN MODEL
1
DOES FLOW RATE EQUAL ZERO?
WASHLOAD
\
/
YES
LARGER
PARTICLES
CALCULATE TRANSPORT CAPACITY
OF SUSPENDED SEDIMENT
GROSS TRANSPORT CAPACITY
CALCULATE DETACHMENT RATES
AND POTENTIAL SEDIMENT OUTFLOWS
DISTRIBUTE TRANSPORT CAPACITY
EXCESSES TO PARTICLES WITH
TRANSPORT CAPACITY DEFICITS
IS THE TRANSPORT CAPACITY
GREATER THAN THE MAXIMUM
POTENTIAL SEDIMENT LOAD?
NO
IS TRANSPORT CAPACITY LESS
THAN THE POTENTIAL SEDIMENT LOAD J
WITH NO FLOW DETACHMENT?
NO
NO DEPOSITION, MAXIMUM RAINFALL
DETACHMENT WITH PARTIAL
FLOW DETACHMENT
APPLY CONTINUNITY EQUATION TO
ROUTE SEDIMENT AND COMPUTE
CUMULATIVE AGGRADATION
YES
YES
PARTITION SEDIMENT OUTFLOW
TO ADJACENT ELEMENT
NEXT ELEMENT
Figure D-2. Flow Diagram.
50
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A brief summary of the basic assumptions on which the model is based follows:
1. The particle size distribution of detached sediment is the same as the weight fractions
of the soil particles in the original soil mass (no enrichment during detachment).
2. Rainfall detachment is not limited by the transport capacity of the flow.
3. Flow detachment occurs only if there is excess transport capacity and can never
exceed the transport capacity excess.
4. Deposition and flow detachment never occur at the same time for the same particle.
5. Washload transport is independent of the transport capacity of the flow and does not
influence the transport of the larger particles.
6. Deposited sediment requires the same amount of energy as in the original
detachment to become redetached.
7. Enrichment is controlled by the deposition process.
8. The rate at which a particle will deposit is proportional to its fall velocity.
9. Channel erosion does not occur.
10. Subsurface or tile drainage produces no sediment.
Input and Output Format Changes
Figure D-3 depicts the additional information required to run the expanded version of the ANSWERS
sediment model. The data block is inserted just after the soils information and before the drainage
and groundwater release information. It includes a description of each particle class (size, specific
gravity, and fall velocity—if known) and the make-up (in terms of the defined size classes) of each
of the listed soil types. In this example, there were five total size classes with two (the first two)
defined as washload classes. Additionally, there were ten soil types. Soil number three was
composed of the following percentages of the five size classes:
1. 10 percent of class 1 (.002 mm),
2. 18 percent of class 2 (.010 mm),
3. 50 percent of class 3 (.030 mm),
4. 17 percent of class 4 (.500 mm),
5. 5 percent of class 5 (.200 mm).
PARTICLE SIZE AND TRANSPORT DATA FOLLOWS
NUMBER OF PARTICLE SIZE CLASSES = 5
NUMBEF< OF WASH LOAD CLASSES = 2
SIZE SPECIFIC GRAVITY FALL VELOCITY
0.002
0.010
0.010
0.50
0.20
.JOO
.100
.160
.080
.160
.100
.160
.024
.200
.200
2.65
2.65
i.ro
1.60
2.65
0.0
0.0
0.0
0.0
0.0
.180
.180
,160
.120
.) 60
.180
.160
.031
.200
.20u
.500
.500
.530
.350
. 530
.500
.530
.240
.200
.200
.170
.170
.110
.150
.110
.170
.110
.239
.200
.200
.050
.050
.040
.300
.040
.050
.040
.466
.200
.200
3a
DRAINAGE COEFFICIENT FOR TILE DRAINS =6.35 MM/24HR
GROUNDWATER RELEASE FRACTION = .001
Figure D-3. Additional Input Information.
51
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Classes 1,2, and 5 are defined as primary clay, silt, and sand, respectively. Classes 3 and4, as noted
by their lower specific gravity and larger sizes, are small and large aggregates, respectively.
The input data "echo" for the expanded model shows the newly calculated fall velocity (unless
previously defined) for each size class and the "sand equivalent" diameter of particles with specific
gravities less than 2.65. Figure D-4 shows the data "echo" which is displayed immediately following
the soils information.
q
10
55.0
1.0
po.n
100.0
38.1
0
127.0
25.4
.60
1.00
203.0
.1
70.0
100.0
.20
0
PARTICLE SIZE DISTRIBUTION DATA
NUMBER OF PARTICLE SIZE CLASSES = 5
NUMBER OF WASHLOAD CLASSES = 2
CLASS
1
2
->
A
5
PARTICLE
CLASS
SOIL 1
SOIL 2
SOIL 3
SOIL 4
SOIL 5
SOIL 6
SOIL 7
SOIL 8
SOIL 9
SOIL10
DIA,MM
.002
.010
.•030
.500
.200
EQ3AND,MM
SIZE DISTRIBUTION
1 2
.100 .IPO
. 100 . 1RO
.160 .160
.080 .120
. 160 . 160
.100 .180
. IbO .160
.024 .031
.200 .200
. 200 . 200
3
.500
.500
.530
.350
.530
.500
.530
.240
.200
.200
.002
.010
.021
.278
.200
OF SOILS .AS
4
.170
.170
.110
.150
.110
.170
.110
.239
.200
.200
5
.050
.050
.040
.300
.040
.050
.040
.466
.200
.2.00
SG FALL VELOCITY, M /S
2.650
2.650
1.800
1.600
2. 650
DETACFIED
6 7
.0000036
.0000896
.0003910
.0432082
.0263375
P
TILE DRAINAGE COEFF. = 6.35 MM/24H
GROUNDWATER RELEASE FRACTION = l.OOOE-03
Figure D-4. Data "Echo" in Output.
Immediately following the statistics on total rainfall and runoff and average sediment yield (at the
end of the printed hydrograph), statistics on the composition of the sediment leaving the watershed
are presented. Figure D-5 indicates that both of the washload classes (clay and silt) were
significantly enriched during this particular event.
52
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3487.0
RUNOFF VOL
0 .1633 532016. 0.
JME PREDICTED FROM 63.40 MM OF RAINFALL
AVERAGE SOIL LOSS = 745. KG/HA
PARTICLE SIZE DISTRIBUTION
OF ERODED SEDIMENT
PARTICLE CLASS 1 = 24.4fi PERCENT
PARTICLE CLASS 2 = 38.85 PERCENT
PARTICLE CLASS 3 = 28.13 PERCENT
PARTICLE CIASS 4 = 3.45 PERCENT
PARTICLE CLASS 5 = 5.12 PERCENT
14.708 MM
INDIVIDUAL ELEMENT NET SEDIMENTATION
ELEMENT SEDIMENT ELEMENT SEDIMENT ELEMENT SEDIMENT ELEMENT SEDIMENT
Figure D-5. Sediment Sizes Exiting Watershed.
53
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TECHNICAL REPORT DATA
(Please read Instructions on the reverse before completing)
1. REPORT NO. 2.
EPA-905/9-82-001
4. TITLE AND SUBTITLE
ANSWERS Users Manual
7. AUTHOR(S)
David B. Beasley and Larry F. Huggins
9. PERFORMING ORGANIZATION NAME AND ADDRESS
Agricultural Engineering Department
Purdue University
West Lafayette, IN 47907
12. SPONSORING AGENCY NAME AND ADDRESS
U.S. Environmental Protection Agency
Great Lakes National Program Office
536 South Clark Street, Room 932
Chicago, IL 60605
3 RECIPIENT'S ACCESSION-NO.
5. REPORT DATE
December, 1981
6. PERFORMING ORGANIZATION
8, PERFORMING ORGANIZATION
CODE
REPORT NO
10. PROGRAM ELEMENT NO.
11. CONTRACT/GRANT NO.
EPA-G005335
13. TYPE OF REPORT AND PERIOD COVERED
Computer Model Users Manual
14. SPONSORING AGENCY CODE
15. SUPPLEMENTARY NOTES
This report is an expanded and edited version of the Users Manual for
the ANSWERS (Areal Nonpoint Source Watershed Environment Response Simulation) model,
first published in September, 1980. ANSWERS is a distributed parameter model
capable of predicting the hydrologic and erosion response of primarily
agricultural watersheds. Particle-size distributions of the eroded sediment
(at all points in the watershed, as well as the outlet) are available. The
manual provides insights into model concepts, input requirements, output
interpretation, and planning applications.
17. KEY WORDS AND DOCUMENT ANALYSIS
a. DESCRIPTORS
Water quality model
Hydrology
Sediment yield
Particle-size distributions
Best Management Practices
Runoff model
tS. DISTRIBUTION STATEMENT
Document is available from U.S. EPA,
Chicago and Agr. Engr. Dept. , Purdue Univ.,
West Lafayette, IN.
b. IDENTIFIERS/OPEN ENDED TERMS
19. SECURITY CLASS (This Report}
20. SECURITY CLASS f This page)
c. COSATI Field/Group
21. NO. OF PAGES
54
22. PRICE
EPA Form 2220-1 (9-73)
54
U S. Uovernmont Printing Office 1981 750-79S
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