CHEMFLO
One-Dimensional Water and Chemical
Movement in Unsaturated Soils
by
D.L. Nofziger, K. Rajender,
Sivaram K. Nayudu, and Pei-Yao Su
Department of Agronomy
Oklahoma State University
Stillwater, Oklahoma 74078
CR-812808
Project Officer
J.R. Williams
Extramural Activities and Assistance Division
Robert S. Kerr Environmental Research Laboratory
Ada, Oklahoma 74820
ROBERT S. KERR ENVIRONMENTAL RESEARCH LABORATORY
OFFICE OF RESEARCH AND DEVELOPMENT
U.S. ENVIRONMENTAL PROTECTION AGENCY
ADA, OKLAHOMA 74820
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Disclaimer
This is a scanned reproduction of the original document for distribution purposes via electronic
format. Effort has been made to provide an accurate and correct document. The document is
supplied "as-is" without guarantee or warranty, expressed or implied. A hard copy of the original
can be provided upon request.
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DISCLAIMER
The information in this document has been funded wholly or in part by the United States
Environmental Protection Agency under cooperative agreement No. CR-812808 to the National
Center for Ground Water Research. It has been subjected to the Agency's peer and
administrative review, and it has been approved for publication as an EPA document. Mention
of trade names or commercial products does not constitute endorsement or recommendation for
use.
11
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FOREWORD
EPA is charged by Congress to protect the Nation's land, air and waters ystems. Under a
mandate of national environmental laws focused on air and water quality, solid waste
management and control of toxic substances, pesticides, noise and radiation, the agency strives to
formulate and implement actions which lead to a compatible balance between human activities
and the ability of natural systems to support and nurture life.
The Robert S. Kerr Environmental Research Laboratory is the Agency's center of
expertise for investigation of the soil and subsurface environment. Personnel at the laboratory
are responsible for management of research programs to: (a) determine the fate, transport and
transformation rates of pollutants in the soil, the unsaturated and the saturated zones of the
subsurface environment; (b) define the processes to be used in characterizing the soil and
subsurface environment as a receptor of pollutants; (c) develop techniques for predicting the
effect of pollutants on ground water, soil, and indigenous organisms; (d) define and demonstrate
the applicability and limitations of using natural processes, indigenous to the soil and subsurface
environment, for the protection of this resource.
This user's guide serves the purpose of instructing the user in the execution of a software
package CHEMFLO for simulating water and chemical movement in unsaturated soils. The
guide should allow easy access to information critical to the development of an understanding of
the transport and fate of chemicals for point and non-point sources.
Clinton W. Hall
Director
Robert S. Kerr Environmental
Research Laboratory
in
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ABSTRACT
An interactive software system was developed to enable decision-makers, regulators,
policy-makers, scientists, consultants, and students to simulate the movement water and
chemicals in unsaturated soils. Water movement is modeled using Richards (1931) equation.
Chemical transport is modeled by means of the convection-dispersion equation. These equations
are solved numerically for one-dimensional flow and transport using finite differences. Results of
the water model can be displayed in the form of graphs of water content, matric potential, driving
force, conductivity, and flux density of water versus distance or time. Graphs of concentration,
and flux density of chemical as functions of distance or time can also be displayed. Cumulative
fluxes of water and chemical and total mass of chemical in the soil can be displayed as functions
of time. Tabular outputs are also available. This manual presents the mathematical equations and
the numerical techniques used in the software. Limitations of the model are presented.
Instructions for installing the software on your computer are given along with illustrations of its
use. Finally, a set of numerical experiments are presented to enable the user to gain an
understanding of the dynamic processes involved in water movement and chemical transport in
soils. The software was written for usewith IBM compatible microcomputers with 640 K bytes of
random access memory, two floppy disk drives or one floppy disk and one fixed disk, or CGA,
EGA, or VGA graphics cards, and an 80x87 math coprocessor.
IV
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TABLE OF CONTENTS
Introduction 1
Mathematical Models 2
Computational Methods 9
Limitation of Models 20
Hardware and Sofware Requirements 22
Getting Started 23
Operating Conventions 26
Illustrations of Software Features 29
Water Movement 29
Water and Chemical Movement 56
Non-Uniform Initial Conditions 70
Continue Simulation From Disk File 74
Enter, Modify, or Print Soil Parameters 75
Numerical Experiments for Water Movement 80
Infiltration of Water Ponded on the Soil Surface 80
Infiltration of Water from Rainfall or Sprinkler Irrigation 81
Water Content and Matric Potential Distributions during Infiltration 82
Comparison of Horizontal and Vertical Water Movement in Unsaturated Soils .... 84
Redistribution of Soil Water Following Infiltration 85
Redistribution and Evaporation of Soil Water Following Infiltration 86
Influence of Rainfall Rate upon Infiltration Rate and Depth of Wetting 88
Influence of Initial Water Content upon Water Movement 89
Steady-State Water Movement in Unsaturated Soils 90
Numerical Experiments for Water and Chemical Movement 91
Chemical Movement during Infiltration Due to Rainfall 91
Influence of Initial Soil Wetness upon Depth of Chemical Movement 92
Influence of Adsorption on Chemical Movement 94
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Chemical Movement Without Water Movement 94
Degradation and Production of Chemicals 95
References 96
VI
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INTRODUCTION
Understanding the movement of water and chemicals into and through soils is of great
importance in managing, utilizing, and protecting our natural resources.These processes are very
dynamic, changing dramatically over time and space. Soil properties, chemical properties, and
water and chemical application rates interact in complex ways within the soil system to
determine the direction and rate of movement of these materials. Researchers have worked many
years to understand the physical and chemical mechanisms responsible for the movement of
these materials. They have developed mathematical models describing these processes and
compared the predictions of these models with field and laboratory measurements. The resulting
mathematical models form a basis for predicting the behavior of water and chemicals in soils.
This manual describes a software system designed to enable persons to define water and
chemical movement systems, to solve the mathematical models, and to display the results of the
simulations in graphical and tabular forms. This software expands on that of Nofziger (1985) by
reducing limitations in simulating water movement, adding chemical movement, and expanding
the graphical and tabular output options. The manual describes the mathematical models used in
the software and their limitations. The computer hardware andsoftware required are then
described. Simulations for several flow systems are included as the use of the software is
described. Other features of the software are then illustrated. Finally, a set of numerical
experiments is included. These experiments are designed to illustrate flow and transport in
different types of soil systems and to enable users to assess the importance of different soil
properties and other physical and chemical parameters upon water and chemical movement.
The software is intended for use by students, regulators, consultants, scientists, and
persons involved in managing water and chemicals in soil who are interested in understanding
unsaturated flow and transport processes. A limited amount of technical terminology is used in
the software and manual, but the user need not understand the mathematics of the model in order
to effectively use the software. As is the case in any model, the useris urged to become familiar
with the limitations of the model and to assess their significance for the situation of interest
before using it for decision making.
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MATHEMATICAL MODELS
This section of the manual lists and describes the mathematical equations which form the
basis for this software. The next section describes the numerical techniques used to solve these
equations. A summary of the symbols used and theunits associated with them is shown in Table 1
following the description of the numerical techniques. Finally, a description of the limitations of
the model is presented.
Two partial differential equations are used in this software to describe water movement
and chemical transport. These equations appear on the following pages. The definition of the
flow problems must also include specification of the initial conditions or the water and chemical
conditions before the simulation begins. The types of initial conditions supported by this
software are described. Finally, boundary conditions must be specified. The boundary conditions
describe the behavior of the water and chemicals at the surfaces or boundaries of the soil system.
Governing Partial Differential Equation for Water: The partial differential equation used
to describe one-dimensional water movement is that of L. A. Richards (1931):
., x dh d rT,,,, ,dh , ..
B(h)— = —[K(h)( cosOO)]
dt dz dz (1)
where h = h(z,t) is the matric potential; z is the distance coordinate parallel to the direction of
flow; t is the time; cos(A) is the cosine of the angle A between the direction of flow and the
vertical downward direction; K(h) is the hydraulic conductivity as a function of the matric
potential; and B(h) is the specific water capacity (i.e. B(h) = d6/dh> where 6 is the volumetric
water content). Figure 1 illustrates the flow system for vertical downward and horizontal
orientations and the corresponding values of A.
Figure 1. Vertical and horizontal soil systems and the corresponding values of the angle A.
Initial Condition for Water: This software can simulate water movement in soil columns
of finite length with uniform or non-uniform initial conditions. It can simulate water movement
in semi-infinite soils with uniform initial conditions. That is, for a finite soil of length L, the
initial condition is
h(z,t) = h(z,0) for t = 0 and 0 < z < L (2a)
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In the semi-infinite case, the initial condition is
h(z,t) = hiniti
initial
for t = 0 and 0 < z
(2b)
Boundary Conditions for Water: Three types of boundary conditions can be applied at the
soil surfaces. These conditions can be imposed at any time.They may also be changed at any time
to simulate complicated flow problems. At z = 0 (the upper surface if A = 0) the boundary
conditions are
1.
Constant Potential, h0 : h(0,t) = ho
(3)
2. Constant Flux, q0: -K(h)
dh , ,,
cos (A)
dz
(4)
3. Mixed Type:
dh , ,.
-- cos(A)
dz
h (0,0 = ho
for t <. t
o
fort>t
(5)
where h0 and q0 represent the specified potential and flux at the soil surface (z = 0), respectively,
and t0 is the time at which the soil at z = 0 reaches a potential h0 (i.e. h(0, t0) = h0). NOTE: h0 and
q0 are specified by the user; ^ is determined by the system.
4. Rainfall: An additional boundary condition, called the rainfall boundary condition, is
provided in the model. This is simply a mixed-type boundary condition with q, equal to
the rainfall rate and h0 equal to zero.
For a finite soil system, one of the following boundary conditions can be imposed at z = L
(the lower boundary if A = 0):
1. Constant Potential, hL: h(L,t) = hL
2. Constant Flux, qL: -K(h)
/,<•>
cos(A)
dz
(6)
(7)
Z-L
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Mixed Type:
-K(h)
dz
h(L,t) - hL
dh f A^
— - cos(^4)
'z-i
for t <, t.
Li
for t > tL (8)
where hL and c^ represent the specified potential and flux at the soil surface (z = L), respectively,
and tL is the time at which the soil at z = L reaches a potential hL (i.e. h(L, ^) = hL).
The Richards equation (Eqn. 1) subject to appropriate initial and boundary conditions
defines the water flow problem. The required soil hydraulic properties are defined by specifying
the 6(h) and K(h) functions. The solution to equation 1 is h(z,t). From this function and the input
6(h) and K(h) functions, other quantities of interest can be determined. Equations for calculating
other parameters of interest are described on the following pages.
Additional Equations: The flux density of water is the volume of water flowing past a
certain point in the soil per unit cross-sectional area (normal to the flow direction) of soil per unit
time. It is positive in the direction of the z-axis. If A = 0 as shown in Figure 1, the flux density is
positive for downward flow and negative for upward flow. In this manual and software, flux
density and flux will be used interchangeably, although they are technically different. The
infiltration rate is the flux of water at the soil surface (z = 0). It is positive as water enters this
surface and negative as water leaves this soil surface as in evaporation. In this model, the flux of
water, q(z,t), is given by the Darcy-Buckingham equation
q(z,t) = -K(h)dH/dz (9)
where K(h) is the hydraulic conductivity of the unsaturated soil as a function of the matric
potential of the soil, H is the total potential of the soil water per unit weight, and z is the position
coordinate defined earlier. The total potential. H, is related to the matric potential, h, and the
position coordinate by the expression
(10)
H = h - zcos(A)
where A is the angle defined previously.
The cumulative flux of water is the volume of water flowing past the position of interest,
per unit cross-sectional area of soil from time t =0, to the time of interest. This is often used to
find the total amount of water flowing past the inlet or outlet of the soil system during the
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simulation. The cumulative flux, Q(z,t) is given by
a
Q(z,r) = q(z,t)dt (11)
where q(z,t) is the flux of water.
Sometimes it is convenient to think of the flux of water as the product of the conductivity
of the soil and the driving force causing water to move. The Darcy-Buckingham equation thus
implies that the driving force, df, is given by
df = - vH/M
(12)
Governing Partial Differential Equation for Chemicals: Movement and degradation of
chemicals in this model is described by the convection-dispersion equation.
^(2C + »S) = —(2D(^ - qC) - t , C - y *S + «r i
M sz M (13)
where C is the concentration of chemical in the liquid phase, S is the concentration of chemical
in the solid phase, D is the dispersion coefficient^ is the volumetric water content, q is the flux
of water, p is the soil bulk density, a is the first-order degradation rate constant in the liquid
phase, B is the first-order degradation rate constant in the solid phase, and i is the zero-order rate
constant in the liquid phase.
If the concentration of the chemical adsorbed on the solid phase is assumed to be directly
proportional to the concentration in the liquid phase, then
(14)
S = kC
where k is the partition coefficient. Incorporating this relationship into equation 13 yields
M
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where R = 1 + pk/6 is the retardation factor for the chemical in the soil. In this model, the
concentration of a chemical in the liquid phase at any location and time is determined by solving
equation 15 coupled with equation 1 for water movement. (Values of 6(z,t) and q(z,t) from the
solution of equation 1 are used in equation 15.) Equation 14 is then used to determine the
concentration adsorbed on the solid phase.
Initial Condition for Chemical: This software can be used to simulate chemical movement
in soil columns of finite length with uniform or non-uniform initial conditions. That is, the initial
condition is
C(z,t) = C(z,0) for t = 0 and 0 < z < L (16)
where C(z,0) is specified.
Boundary Conditions for Chemical: Two types of boundary conditions can be imposed at
the soil surfaces. These conditions can be imposed at any time. They can also be modified at any
time so complex flow problems can be simulated. At z = 0 (the upper surface if A = 0) the
boundary conditions supported are as follows:
1. Constant Concentration of Inflowing Solution: This boundary condition is used to
simulate movement of chemicals when the solution entering the soil has a known and
constant concentration, Cs. The amount of chemical entering the soil depends upon
the flux of water entering the soil. Moreover, if water is moving out of the soil at z =
0 (as in evaporation), no chemical moves with it. Mathematically, this boundary
condition implies
^ + q(0,t)C - q(0,t)Cs if q(0,t) > 0
-0D — + ?(0,OC = 0 if 4(0,0 <; 0
dz
The expressions on the left side of the equal signs in equation 17 are evaluated at z =
0.
2. Constant Concentration in Surface Soil (z = 0): This boundary condition specifies that
the concentration C(z,t) at z = 0 is a specified valueC0. That is
C(0,t) = C0 (18)
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Note that equation 18 approximates a system in which the concentration in the soil is abruptly
forced to take on a certain value and to remain at that value. This would likely be difficult to
carry out experimentally. Equation 17 will likely be a better approximation to real soil systems.
The boundary conditions supported at z = L are described below.
1. Mass Flow Without Dispersion: This boundary condition is used to simulate soil
systems in which the chemical moves out of the soil with the moving soil water, but
dispersion and diffusion do not contribute to this movement. This condition is
equivalent to the requirement that the gradient of the concentration is zero at z = L.
That is,
— = 0 at z = L
Bz
(19)
2. Constant Concentration at Soil Surface (z = L): This boundary conditionspecifies that
the concentration C(z,t) at z = L is a specified valued^. That is
C(L,t) = CL (20)
The boundary condition specified by equation 20 is of limited utility. It can serve as an
approximation for simulating upward movement of water from a water table with a constant
concentration of chemical.
Additional Equations: The flux density of chemical is the mass of chemical passing a
certain point in the soil per unit cross-sectional area per unit time. It is positive in the direction of
the z-axis, as explained for flux of water. As in the case of water, flux density and flux of
chemical are used interchangeably in the manual. The flux of chemical, j(z,t), at location z and
time t, is given by
+ qC
The cumulative flux of chemical is the mass of chemical moving past the position of
interest per unit cross-sectional area of soil from tme t = 0 to the time of interest. That is, the
cumulative fluxof chemical, J(z,t) is given by
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J(z,t) - [j(z,t)dt
(22)
where j(z,t) is the flux of chemical.
The total mass of chemical (per unit cross-sectional area) in the soil at time t is the sum of
the mass of chemical in the liquid and solid phases. (Partitioning of the chemical to the vapor
phase is ignored in this model.) That is,
ms(t)
(23)
where the mass of chemical in the liquid phase, mL(t) is
m{(t) - f 0(0,OC(z,0 dz
(24)
and the mass of chemical on the solid phase, ms(t) is
z,f) dz
(25)
The dispersion coefficient. D in previous equations is approximated by the relation
q(z,t)
(26)
where D0 is the molecular diffusion coefficient, T is the tortuosity factor for the soil, A is the
dispersivity, q(z,t) is the flux of water, and 6(z,t) is the volumetric water content{o/3The tortuosity,
T is approximated by the equation of Millington and Quirk (1961) where T = and 4) is the
porosity of the soil. ^
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COMPUTATIONAL METHODS
In this model, the governing partial differential equations for water and chemicals are
solved numerically using finite difference techniques. This was done to facilitate the use of
non-uniform initial conditions and boundary conditions which change with time. The cost of this
flexibility is additional computational time. This time is usually on the order of 5 - 15 minutes for
the simulation of water and 15-60 minutes for simulation of water and chemicals on IBM AT
type microcomputers. As is illustrated later in themanual, the software provides methods of
viewing results as they are computed and of storing the solution so the user can quickly view the
results at alater time. The following pages summarize the numerical procedures.
Solution of Richards Equation: An implicit finite difference scheme with explicit
linearization described as model 3 by Haverkamp et al.(1977) was used. In this scheme the
partial differential equation takes the form
(27)
where
K,
2'J
and At and Az are the mesh sizes in time and depth, respectively. The indices i and j take on
values of 0, 1,2, .... The finite difference equation (Eqn. 27) is used for all interior mesh points
in depth (i = 1, 2, 3, ... ) for the soil system. Special forms of this equation are used to represent
mesh points on the boundaries of the soil.
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Equations for Soil Boundaries:
1. Constant Potential h0 at z = 0: Equation 3 states that h(0,t) = h0. This translates to the
h(0,j) = h0 for all j. Therefore, h(0,j) is known for each time step. Equation 27 at mesh
point i = 1 then becomes
At
J_
Az
- cos (A)
(28)
2. Constant Flux q0 at z = 0: The matric potential h(0,t) or h(0,j) must be determined for
each time step. In this case it is convenient to use a different form of equation 1 which
is
at
dz
where q is the flux of water (Eqn. 9). This equation for mesh point i = 0 was
approximated by
Az
- cos(A)
(29)
3. Mixed Type: Equation 5 indicates that the mixed type boundary condition is a flux
boundary condition for t < t0. During this time, equation 29 isused. For t > !<,, equation
28 is used.
4. Constant Potential hL at z = L: Equation 6 states that h(L,t) = hL, or h(I,j) = t^ for all j
(lAz = L). Therefore, h(I,j) is known for each time step. Equation 27 at mesh point i =
1-1 then becomes
10
-------
J_
Az
/ A \ S
cos(A)
-lj) JMi-U+D-Mi-2,;) _ COS(A)1
2 / I Az J.
(30)
5. Constant Flux qLat z = L: The matric potential h(L,t) or h(I,j) must be determined for each
time step (lAz = L). As in the case at z = 0, the equation for mesh point i = I becomes
Az
- cos(A)
(31)
6. Mixed Type: As in the case for z = 0, equation 31 is used for t < tL and equation 30 is
used for t > tL.
7. Semi-infinite Soil Systems: If the soil is semi-infinite, there exists a location z such that
h(z,t) = hinitial. As t increases, larger and larger values of z will be required to satisfy the
above relationship. Recognizing this, one can simulate movement into a semi-infinite
media using equation 30 at the lower boundary with hL = h^ai and I large enough so that
h(I,j)= burial- In this model, the default value of I is 10 initially. After each iteration, the
values of h(i,j) are analyzed and the value of I is increased if needed.
Equation 27 and the equations appropriate for the selected boundary conditions result in a
system of simultaneous equations which must be solved for each time step At. One equation applies
to each mesh point in depth. Since each equation involves only three unknowns, the system of
equations defines a tridiagonal matrix which is relatively easily solved. (This version of the software
limits the number of mesh points and equations to 200.) All floating point calculations are
performed in double precision (about 16 decimal digits).
Additional Computations: The flux, cumulative flux, and driving force are calculated as
needed by numerical approximations to equations 9, 11, and 12, respectively. When possible,
derivatives are approximated by central difference equations. One-sided differences are used as
needed on the boundaries. Trapezoidal integration is used to approximate integrals.
One estimate of the computational error due to approximating the differential equation with a
finite difference equation is the mass balance error. Since the mass of water must be conserved in the
11
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soil system, the accumulation of water in the soil should be equal to the difference between the
amount entering and the amount leaving the soil surfaces. The mass balance error. MBEW, is given by
MBEw= M0(z,0- - . - .
The first integral represents the change in water stored in the soil between time t-At and time
t. The second integral represents the amount of water entering the soil at z = 0. The third term
represents the amount of water leaving the soil at z = L. The mass balance error must be small for
the solution to be valid.
The software contains an algorithm to determine the initial mesh sizes in time and depth. The
user has the option of entering other values as well. Frequently the mesh size in time and depth can
be increased as the time increases. The model contains an algorithm to adjust the mesh size based on
the mass balance and the depth of wetting. The user can specify a fixed mesh size for all times as
well as the desired precision before adjusting mesh sizes. See the section on program execution for
details.
12
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Solution of Convection-Dispersion Equation: The numerical solution to equation 15 is based
on that of van Genuchten (1978). In that work, he derived a correction for numerical dispersion. That
equation was
{0RC}(i,y+l)-{0RC}(f,y) + j_ _3_
A t 2\dz
0D --
•D- f -,C
I dz j
(oc0
(33)
where
{0RC}(/,y) = 0(iAz,;AOR(/Az,yAr)C(/Az,yAr),
D -
602R
602R
0D* —
- C (i,j ) [ 0 (/,- 1 ,y ) D * (/- 1 ,y ) + 2 0 (i ,y ) D * (/,y ) + 0 (/+ 1 ,y ) D * (/+ 1 ,y ) ]
(6Az)
(/,y) = |c(zM,y
y) [(a0
13
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and At and Az are mesh sizes in time and depth, respectively. Similar expressions are written for
terms involving D". Equation 33 is used for interior mesh points in depth (i = 1,2,3,...) for the soil
system. Values of 6(i,j) and q(i,j) are obtained from the solution to the water flow equation. Special
forms of the convection-dispersion equation are used on the boundaries of the soil.
Equations on Soil Boundaries:
1. Constant Concentration of Inflowing Solution: For this boundary condition, the
concentration of the inflowing solution Cs is known but the concentration at z = 0 in the
soil must be found. That is C(0,j) must be determined for each time step. Using logic
similar to that used in the case of a constant flux of water, the equation for i = 0 can be
shown to be
[{0RC}(0,7 +
Az
(2AO
Azy 0(0,7 +
7(0- 0.5J) -7(0.5,7)
AzYe(o,7)\ /2
2 I/
where
(34)
7(OJ) = <7(0,7)CS,
[{60} (OJ)
,f05 n
and
2
-------
3. Mass Flow without Dispersion at z = L: Equation 19 implies that the flux of chemical at z
= L, j(L,t) = q(L,t)C(L,t) where q(L,t) is the flux of water and C(L,t) is the concentration
of chemical. The concentration of the outflowing solution C(L,t) (or C(I,j) where lAt = L)
must be determined for each time step. Equation 33 for i = I then becomes
[{0RC}(I,7 + 1)-{6RC}(I,,
Az
(2AO
(1-0.5,7 + 1) -7(IJ+1)
Az(tt6+pp£) (1,7+ 1)C (IJ+1) + Azy 6 (IJ+1)
2 + 2
{y(i- 0.5,7) -y(iJ)
Az(a6+pp£)(I,7)C(I,7) + Azy 6 (O.y) \ I 2
1 2)1
where
(35)
,fl 05 n [{60} (I- 1J)
'
(2Az)
2q(l-1,7) C (I- 1J) / 6 ,
and
4. Constant Concentration at Soil Surface, z = L: If this boundary condition is specified, the
concentration at z = L, C(I,j), where IA)t = L is known for all time steps. Therefore, no
equation for i = L is included in the set of equations.
Additional Equations: The flux, cumulative flux, and mass of chemical are calculated as
needed by numerical approximations to equations 21, 22, and 23, respectively. When possible,
derivatives are approximated by central difference equations. One-sided differences are used as
needed on the boundaries. Trapezoidal integration is used to approximate integrals.
15
-------
A mass balance error for the chemical is calculated for the purpose of detecting
computational error. The logic here is similar to that used in the equation for water. Since the mass
of chemical must be conserved, the accumulation of chemical in the soil should be equal to the
difference between the amount entering the soil surfaces or produced within the soil and the amount
leaving the soil surfaces or degraded within the soil. The mass balance error for the chemical MBES,
is given by
L
MBEs = f {mT(z,0 - mT(z,t
Q(z,t)dz
ms(Y-AO(l-exp(-pAO)
n^ 0-AO(l-exp(-aAO)
The first integral represents the change in mass of chemical in the soil between time t-At and
time t. The second integral represents the amount of chemical entering the soil at z = 0. The third
term represents the amount of chemical leaving the soil at z = L. The fourth term represents the
massof chemical produced by zero-order processes. The fifth and sixth terms represent the mass of
chemical lost by degradation in the solid and liquid phases, respectively. The mass balance error
must be small for the solution to be valid.
16
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TABLE 1. List of symbols, descriptions and units used in text.
Symbol Description Units
A - angle between the direction of flow and the vertical deg
downward direction
B(h) - specific water capacity, d6/dh cm"1
C(z,t) - concentration of chemical in liquid phase at position jig/cm3
z and time t
Cs - concentration of inflowing solution at z=0 for constant |ig/cm3
concentration of inflowing solution boundary condition
C0 - concentration in surface soil at z = 0 for constant |ig/cm3
concentration in surface soil boundary condition
CL - concentration in surface soil at z = L for constant |ig/cm3
concentration at surface soil boundary condition
df - driving force for water
D - dispersion coefficient cm2/hr
D0 - molecular diffusion coefficient cm2/hr
h(z,t) - matric potential at position z and time t cm
hinitial - matric potential at t = 0 for semi-infinite soil cm
h0 - matric potential at z = 0 for constant potential boundary cm
condition
hL - matric potential at z = L for constant potential boundary cm
condition and finite soil column
H(z,t) - total potential at position z and time t cm
i - index of mesh points in depth
I - number of mesh points in depth in finite soil (IAz=L)
j - index of mesh points in time
j(z,t) - flux of chemical at position z and time t |ig/cm2/hr
17
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Table 1. Continued.
Symbol
Description
Units
J(z,t)
k
K(h)
L
mT
m,
ms
MBEW
MBES
q0
qS
Q(z,t)
R
S(z,t)
t
At
to
tL
z
Az
a
- cumulative flux of chemical at position z and time t |ig/cm2
- partition coefficient
- hydraulic conductivity as a function of matric potential cm/hr
- length of soil cm
- mass of chemical (per sq. cm) in soil system jig
- mass of chemical (per sq. cm) in liquid phase jig
- mass of chemical (per sq. cm) in solid phase jig
- "mass" balance error for water cm
- mass balance error for chemical jig
- flux of water at position z and time t cm/hr
- flux of water at z=0 for constant flux boundary condition cm/hr
- flux of water at z=L for constant flux boundary condition cm/hr
and finite soil column
- cumulative flux of water at position z and time t cm
- retardation factor
- concentration of chemical in solid phase |ig/g
- time hr
- mesh size in t direction hr
- time at which matric potential at z = 0 reaches limiting hr
potential in mixed-type boundary condition
- time at which matric potential at z = L reaches limiting hr
potential in mixed-type boundary condition
- distance in the direction of flow cm
- mesh size in z direction cm
- first-order rate constant in the liquid phase hr4
18
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Table 1. Continued.
Symbol Description Units
B - first-order rate constant in the solid phase hr"1
T - zero-order rate constant in the liquid phase
A - dispersivity
6(z,t) - volumetric water content at position z and time t cm3/cm3
p - bulk density of soil g/cm3
T - tortuosity factor of soil
c|> - porosity of soil
19
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LIMITATIONS OF MODELS
Although this software is based on common mathematical models for describing water and
chemical transport in unsaturated soils, the results may not agree with experimental observations.
This lack of agreement may be due to a large number of reasons (Jury, 1986). Among them are the
following:
1. One-dimensional water and chemical movement: This software is based on mathematical
models for water and chemical movement in one dimension. In nature this will seldom take
place due to spatial variability in soil properties or boundary conditions. Although these
processes have been modeled in two or three dimensions, the required soil properties are
seldom known and the computational time is much greater. This model also does not include
source and sink terms so it cannot be used to simulate uptake of water by roots at different
depths in the soil.
2. Homogeneous soil profiles: This software assumes the soil and chemical properties are
homogeneous with depth. The validity of this assumption will depend upon the specific site
of interest. In general, these properties will vary with depth. This assumption could be
removed from this software. The user would then need to provide much more detailed soil
and chemical parameters for the site. An estimate of the significance of this assumption can
be obtained by comparing results of several simulations with a range of soil and chemical
parameters representative of the site.
3. Inappropriate water flow equation: The Richards equation for water movement is based on
the Darcy-Buckingham equation for water movement in unsaturated soils. This equation is
usually a good descriptor of water movement in agricultural soils, but exceptions exist. No
provision is made in the model for swelling soils. No provision is made in this model for
preferential flow of water through large pores in contact with free water. Therefore, it will not
accurately represent flow in soils with large cracks which are irrigated by flooding. The
model assumes that hysteresis in the wetting and drying processes is negligible and can be
ignored. It also assumes that the hydraulic properties of the soil are not changed by the
presence of the chemical.
4. Inappropriate chemical transport equation: Limitations in the convection-dispersion equation
have been observed. Clearly, any inadequacy in simulating water movement will impact the
simulation of chemicals. In addition, partitioning of the chemical between the solid and liquid
phases may not be proportional as assumed in equation 14. The model also assumes that this
partitioning is instantaneous and reversible. Partitioning and movement of the chemical in the
vapor phase is ignored in this model.
5. Inappropriate initial conditions: The simulated results depend upon the initial conditions
specified. If the specified initial conditions do not match the real conditions, the calculated
values may be incorrect. The user may want to compare simulations with a range of initial
conditions.
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6. Inappropriate boundary conditions: The predictions of the model are quite sensitive to the
specified boundary conditions. If the specified ones do not match the actual conditions, large
errors may be made. In some cases, the errors may be due to a lack of knowledge of the real
boundary conditions. In other cases, the software may not be flexible enough to accommodate
the real conditions. Hopefully this will not be a major problem since boundary conditions can
be changed during a simulation.
7. Inappropriate soil or chemical properties: Many of the soil and chemical parameters are
difficult to measure experimentally. Moreover, soil hydraulic properties can vary by large
amounts over small areas. This means that the input parameter values involve uncertainty.
Repeated simulations with different parameters can be used to assess the influence of this
uncertainty upon predictions.
8. Discretization errors: Limitations in the software due to approximating derivatives by finite
differences as well as other approximations used in solving the partial differential equations
are subtle and may be difficult to detect. Mass balance errors for water and chemicals are
calculated to detect net computational error. Small mass balance errors are simply essential
conditions for a valid solution, but they do not guarantee accurate solutions. In general,
discretization errors tend to decrease as the mesh sizes decrease, so the user may want to
compare solutions for different mesh sizes.
9. Special Case of Drying a Saturated Soil: Another limitation of the numerical techniques
employed here is exhibited when one attempts to simulate the drainage or drying of a soil
with a uniform initial matric potential greater than -2 cm. This results in a predicted matric
potential which is linear for the entire length of the soil system (as would be the case for
saturated flow conditions). This problem has not been observed for initial matric potentials
less than -2 cm nor for non-uniform initial distributions resulting from infiltration. The user
can approximate movement from a soil initially saturated with water by specifying an initial
condition of -2 cm or less instead of zero.
Due to the wide range of flow and transport problems which may be simulated with this
software and the highly nonlinear form of Richards equation, ALWAYS BE ALERT FOR
ABNORMALITIES IN THE SOLUTION. If results look suspicious (as indicated by poor mass
balance or unexpected water content, water potential,or concentration profiles), compare the results
with those for additional simulations with mesh sizes having smaller At/Az2 ratios. If the solution is
important to you, simulate the flow with another model using a different solution method and
compare the results.
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HARDWARE AND SOFTWARE REQUIREMENTS
The software requires an IBM PC, AT, PS/2 or a compatible computer with at least 640K
bytes of random access memory, two floppy disk drives or one floppy disk drive and one fixed disk,
a graphics card compatible with IBM CGA, EGA,or VGA graphics, and a compatible monitor. An
80x87 math coprocessor is highly recommended. A printer is useful, but it is not essential.
The operating system must be MS-DOS or PC-DOS 2.01 or later. The ANSI.SYS device
driver must be installed for proper screen operation of the software. (See GETTING STARTED for
instructions on installing this device driver). The GRAPHICS.COM program must be executed
before this software is executed if the user wants to print graphics on a printer using the
keys.
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GETTING STARTED
Files on Distribution Diskette: The software is distributed on one floppy diskette. It contains
the following files:
This file contains the executable program.
This file contains soil hydraulic data for several soils. These can be
used to become familiar with the software. You may then add data for
other soils of interest to you.
This file contains notices regarding the operation of the current version
of the software which are not included in this manual.
This file may be used to install the ANSI. SYS device driver, provided
you are not presently using any CONFIG.SYS file on your
boot-updisk. If you already have a CONFIG.SYS file on your system,
it should be modified to install the ANSI. SYS device as explained in
the DOS manual.
Software Installation:
Installation instructions are given below for systems with a fixed disk
and systems with only floppy disks.
Fixed-Disk Systems:
1. Make a new sub-directory for the CHEMFLO software using the
MKDIR command of DOS.
2. Change to that sub-directory using the CUDIR command of DOS.
3. Place the distribution diskette in drive A: and copy its contents to
this sub-directory by means of the COPY command of DOS.
4. Store the distribution diskette in a safe place.
5. If the root directory of the fixed disk contains a CONFIG.SYS file,
be sure that it contains the line DEVICE=ANSI. SYS. If it does not,
you will need to use an editor to add this line to the file. The file
ANSI. SYS will also need to be in the root directory if this line is
23
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added. (Note: If you have all of your DOS programs in a separate
directory, you may specify the path and name in the CONFIG. SYS
file.For example, if the DOS programs are in a directory called
DOS, the line in CONFIG.SYS would be
DEVICE=\DOS\ANSI.SYS. In this case, the file ANSI.SYS need
not be in the root directory.)
Floppy-Disk Systems:
1. Format a working diskette with the /S option of the DOS
FORMAT command so the system can boot up from this diskette.
That is, place a new diskette in drive B: and enter FORMAT B:/S
.
2. Copy the file ANSI.SYS file from the DOS diskette to the working
diskette.
3. Copy the GRAPHICS.COM file from the DOS diskette to the
working diskette.
4. Copy the entire distribution diskette to the working diskette.
5. Store the distribution diskette in a safe place.
Program Execution: The program is supplied as an executable file called CHEMFLO.EXE.
Follow these steps to execute the program.
1. Make the disk drive and directory containing the CHEMFLO software the default
directory.
2. If printed copies of the graphs will be made by means of the keys, execute
the GRAPHICS.COM file by entering GRAPHICS .
3. Execute the program by entering CHEMFLO [options] where the command-line
options in the square brackets may be used to change default parameters in the software.
Command-line options include the following:
Fixed mesh size, F
This option causes the model to use only a fixed mesh size in time and
depth. The internal algorithm used to adjust mesh size based on mass
balance and depth of penetration is ignored. This option is
implemented by executing the program by entering CHEMFLO F
24
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Precision, P
This option is used to set the relative precision in mass balance
required before the mesh size in time can be increased. The default
value for this precision is 0.01. The user can set it to .05 by entering
CHEMFLO P.05
Initial Number of Mesh Points, N
The number of mesh points used for a problem involving a
semi-infinite medium begins with some number N at time zero and
increases as the changes in potential approach the greatest depth. After
each time step, the system determines if more points are needed. The
default value for N is 10. This option allows the user to set it to any
number between 5 and 198. If the user wants to begin with 20 mesh
points, the program is executed by entering CHEMFLO N20
. This option does not affect the number of mesh points
used in the case of finite soil systems.
Minimum Number of Mesh Points, M
The mesh size in depth for semi-infinitemedia is doubled if the mass
balance criteria are satisfied and the number of mesh points being used
exceeds a specified minimum M. The default minimum is 30. This
option enables the user to set it to another number between 5 and 198.
If the number 50 is desired, the program is executed by entering
CHEMFLO M50
Several of these options can be specified at the same time. They are simply entered in
sequence with a space separating them. For example, to specify a precision of .05 and a minimum
number of points M of 100, the program is executed by entering CHEMFLO P.05 M100
The order in which the options are specified is not important.
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OPERATING CONVENTIONS
The following conventions are used in this software:
1. Program Interruption: The user can interrupt the execution of the program by pressing the
key. This key may also be pressed to skip screens containing introductory
information at the beginning of the program.
2. Keyboard Inputs: Single-letter entries from the keyboard such as menu selections and
responses to yes/no questions are made by pressing only the desired key. The key
is not needed.
3. Default Values: The software makes use of default values to reduce the amount of typing
required. Default values are displayed in square brackets when inputs are requested. If the
default value is desired, the user may press the key instead of typing the entire
response. If another value is desired, that value may be entered.
4. File Names: File names may be any legal DOS file name. File extensions are not needed
since meaningful extensions are assigned by the software. File names must include a
drive designation and/or path if the file is not on the default disk drive or directory.
Parameter Entry Editor: Data entry for new soils, graphics selections, output table
selections, chemical parameters, and initial conditions for non-uniform systems are made
by means of a special editor. This editor uses function keys and cursor keys to enable the
user to edit all the parameters on the screen. The special keys used and their functions are
listed below.
This key moves the cursor to the right one character within the present
field. If the cursor is located at the end of a field, this key does nothing.
This key moves the cursor to the left within the present field. If the
cursor is located at the beginning of a field, this key does nothing.
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This key moves the cursor up one record. If the cursor is in the first
field on the screen, the cursor moves to the last field on the screen.
This key moves the cursor down one record. If the cursor is in the last
field of the screen, the cursor moves to the first field on the screen.
This key moves the cursor to the first field on the screen.
This key moves the cursor to the last field on the screen.
This key is used to end data entry or editing of a particular field.
Characters to the right of the cursor are dropped. The cursor then
moves to the next field on the screen. If there are no characters to the
left of the cursor, the key does nothing.
This key deletes the character to the immediate left of the cursor. If the
cursor is on the first character in the field, this key does nothing.
This key deletes the character at the cursor location. If the cursor is at
the end of the field, this key does nothing.
This key serves two purposes in editing. When using the
multi-screeneditor for parameter entry, pressing this key causes the
preceding screen to be displayed. If the first screen of the group is
already displayed, pressing this key does nothing. When editing soil
parameters in the soil file, pressing this key causes the system to
display the data for theprevious soil (or the previous record) on the
screen. If the data for the first soil in the file (the first record) is already
on the screen, this key does nothing.
This key serves two purposes in editing. When using the multi-screen
editor for parameter entry, pressing this key causes the next screen to
be displayed. If the last screen of the group is already displayed,
pressing this key does nothing. When editing soil parameters in the soil
file, pressing this key causes the data for the next soil in the file to be
27
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displayed. If no more soils exist in the file, the values in the fields are
filled with decimal points symbolizing no data. The user may then
proceed to enter soil parameters for a new soil and save them in the
disk file.
This key is used to display help information for the field being entered.
This key is used only when editing the soil parameters in the soil file.
It is used to delete the soil on the screen from the data file. The system
asks the user to verify that the soil should be deleted before
proceeding.
This key is used only in the multi-screen editor to save the values
stored on the screens in a user-specified file. These values can be read
at a later time using the key.
This key is used in the multi-screen editor to read data from a file
previously saved using the key.
This key is used when all entries on the screen(s) have been made. It
indicates to the system that data entry on this screen is finished. The
program then proceeds using the values specified. When editing soil
data in the soil file, pressing this key also indicates that the user is
finished entering soil data so the data are stored in the file and control
returns to the main menu.
Pressing the key aborts the present option. Control returns to the
main menu. If the user was editing a file, the data are not stored in the
file.
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ILLUSTRATIONS OF SOFTWARE FEATURES
OPTION W: WATER MOVEMENT: The main menu for this software system is shown
in Figure 2. The desired option is selected by entering the letter corresponding to that option.
Each option in the menu will be illustrated in this manual. In this case, option W was selected.
This enables one to define a soil system and to simulate water movement in the system.
Simulation of One-Dimensional Water and Chemical Movement in Soils
Main Menu
W. Define Water Movement Problem and Solve it
S. Define Water and Solute Movement Problem and Solve it
C. Continue Simulation of Problem Stored on Disk
E. Enter, Modify, or Print Soil Parameters
Q. Quit. Stop Execution of Program
Desired Option? W_
Figure 2. Selecting option W in the main menu to simulate water movement.
To define the problem you must do the following:
1. Define the soil system by selecting the soil of interest, defining the orientation of
the soil system, and specifying the length of the soil system.
2. Define the water conditions in the soil system by specifying the water conditions
which exist at the boundaries of the soil system (that is, the boundary conditions
for water), and by specifying the initial conditions for water or the condition of the
soil water before flow begins.
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3. Specify the simulation parameters. These parameters define the time at which
these flow conditions should end, initial finite difference mesh sizes in time and
depth, the period between desired graphical or tabular output, and the name of a
disk file to be used to save computed results.
4. Specify the type of graphical and tabular output desired.
A multi-screen editor illustrated in Figure 3 is used to define the water problem (steps 1
to 3). One screen is used for each part of the definition process listed above. Parameters included
in the figure are default values built into the software. Additional screens, illustrated later in the
manual may then be used to define the graphical and tabular outputs desired.
Cursor keys are used to move the cursor around the screen to make any changes desired.
The key may be pressed to obtain additional information relative to each input. The
key is used to abort this option and to return to the main menu. You may use the and
keys to move from screen to screen. When all the entries have been made on all three
screens, press the key. The key can be used to save the problem defined in the first
three screens in a disk file (which you specify) for recall and reuse at a later time. The key
can be used to read a problem file saved using the key. The values stored in the file are
displayed on the three screens for use or for further modification.
To illustrate this option, we will simulate water movement in a Cobb sandy clay soil. The
soil is oriented vertically and it is 50 cm deep. Before water is applied, the soil has a uniform
water content of 0.092cm3/cm3. We will simulate water movement due to rainfall on the soil
surface at a rate of 1.0 cm per hour for 8 hours. The water content and matric potential will be
maintained at their initial values at the 50cm depth. We are interested in the amount of water
entering the soil, the depth of wetting, and the rate of water infiltration as functions of time
during the rainfall period.
Figures 4, 5, and 7 show the three screens after the problem stated in thepreceding
paragraph was defined in the software. The required entries are described in the paragraphs
following the figures.
30
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Definition of Soil System (SCR: 1/3)-
Name of the soil : YOLO CLAY
Orientation of flow system : 0.0
Finite or Semi-infinite soil system (F or S).: F
Length of soil system (cm) : 30.00
Fl-Help; ESC-Abort; FlO-End editing; PgUp-Prev screen; PgDn-Next screen;
F8-Save input parameters in file; F9-Read input parameters from file;
Definition of Water System (SCR:2/3)»
Boundary condition for water at the UPPER surface (P,F,R,M): P
Desired matric potential (cm) at the UPPER soil surface....: 0.00
Boundary condition for water at the LOWER surface (P,F,M)..: P
Desired matric potential (cm) at the LOWER surface : -5000.00
Uniform initial matric potential throughout the soil (Y/N).: Y
Matric potential (cm) throughout soil before simulation : -5000.00
Fl-Help; ESC-Abort; FlO-End editing; PgUp-Prev screen; PgDn-Next screen;
F8-Save input parameters in file; F9-Read input parameters from file;
31
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Simulation Parameters (SCR:3/3)—
Maximum time to be simulated (hr) : 8.0
Mesh size in depth (cm) : 1.000
Mesh size in time (hr) : 0.0100
Period between graphic or tabular outputs (hr)..: 1.00
Output file name :
Fl-Help; ESC-Abort; FlO-End editing; PgUp-Prev screen; PgDn-Next screen;
F8-Save input parameters in file; F9-Read input parameters from file;
Figure 3. Three editing screens used to define a water flow problem.
Definition of Soil System (SCR: 1/3)-
Name of the soil : COBB SANDY CLAY
Orientation of flow system : 0.0
Finite or Semi-infinite soil system (F or S).: F
Length of soil system (cm) : 50.00
Fl-Help; ESC-Abort; FlO-End editing; PgUp-Prev screen; PgDn-Next screen;
F8-Save input parameters in file; F9-Read input parameters from file;
Figure 4. Screen for defining the soil system
1. Name of the soil: Here you enter the name of the soil to be simulated. This name
must correspond to a soil already defined in the SOIL.S file (See option E in the
Main Menu for illustrations on how to define soils). You may view a list of the
soils already defined by pressing the key when the cursor is in this line. The
number of the soil in that list may be entered instead of typing in the entire name.
32
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2. Orientation of flow system: As explained in the section on mathematical models,
flow can be simulated in any direction. This entry specifies the angle A between
the z axis and the vertically downward direction. See Figure 1 for more
explanation of the meaning of angle A. Zero entered here indicates that flow is
vertically downward.
3. Finite or Semi-infinite soil system: Specify whether the soil is of finite or
semi-infinite length by entering an F or S, respectively. Note: Semi-infinite soils
can be used only for modeling water movement into soils with uniform initial
conditions. If the initial conditions are not uniform or if both waterand chemical
movement are to be modeled, finite soil systems are required.
Length of soil system: If the soil is of finite length, this entry defines the length in centimeters. If
the soil is semi-infinite in length, this lineis removed from the screen.
Definition of Water System (SCR:2/3)»
Boundary condition for water at the UPPER surface (P,F,R,M): R
Desired rainfall rate (cm/hr) at the UPPER surface : 1.00
Boundary condition for water at the LOWER surface (P,F,M)..: P
Desired matric potential (cm) at the LOWER surface : -2000.00
That matric potential corresponds to water content(cc/cc)..: 0.092
Uniform initial matric potential throughout the soil (Y/N).: Y
Matric potential (cm) throughout soil before simulation : -2000.00
That matric potential corresponds to water content(cc/cc)..: 0.092
Fl-Help; ESC-Abort; FlO-End editing; PgUp-Prev screen; PgDn-Next screen;
F8-Save input parameters in file; F9-Read input parameters from file;
Figure 5. Screen for defining the water boundary and initial conditions
1. Boundary condition for water at the upper soil surface: This entry enables the user
to specify the desired boundary condition for water at the soil surface. Four types
of boundary conditions at the upper soil surface are supported. These have been
33
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defined mathematically in the section describing the mathematical model. They
are described below.
a. Constant Potential: This condition, selected by the letter P, specifies that water is
supplied or removed from this boundary at a constant potential or pressure. The
supply of water is adequate to meet the demand of the soil. Flow is controlled by
the soil properties; it is not limited by the supply. This condition may be used to
simulate movement from a pond. Water is often supplied to laboratory columns
using a constant potential device. This condition may also approximate the upper
condition of a soil at large times after evaporation has begun.
b. Constant Flux: This condition selected by the letter F, specifies that water is being
added or removed from the soil surface at a specific rate. If the flux is positive at
the upper end of the soil (or at the location where the distance coordinate is zero)
water is entering the soil. If the flux is negative there, water is being removed
from the soil. This boundary condition may represent flow systems where the soil
is not limiting the rate of water movement across the boundary. This could occur
in cases of low intensity rainfall or sprinkling, initial stages of evaporation, or
cases of no water flow because of artificial barriers covering the soil. Some
laboratory experiments are conducted with water being supplied by pumps which
deliver the water at a constant rate. This boundary condition would be appropriate
for that situation as well.
c. Constant Rainfall: This boundary condition, selected by the letter R, is a
specialized case of the mixed-type boundary condition designed to simulate water
applied at a constant rate by rainfall or sprinkling. In the early stages of rainfall
infiltration, the capacity of the soil to conduct water may exceed the rainfall rate.
Thus, initially, this is a flux boundary condition with the flux equal to the rainfall
rate. As time passes, the soil may reach a point where the surface becomes
saturated and the infiltration rate is limited by the soil. In this case, water would
either pond on the soil surface or it would run off. This boundary condition
assumes that no ponding occurs. As soon as the soil surface becomes saturated,
the boundary condition changes to a constant potential boundary condition with a
potential of zero.
d. Mixed Type: A mixed-type boundary condition, selected using the letter M, is a
combination of constant flux and constant potential boundary conditions. The
specified constant flux is used initially. It continues as the boundary condition
until the matric potential at the boundary reaches a value specified by the user.
After that time, a constant potential of the user-specified value is maintained at the
surface. This boundary condition can be used to simulate rainfall as described in
the rainfall boundary condition above. It could be used to simulate rainfall where
water was allowed to pondto some depth before running off. It can also be used to
34
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simulate evaporation.In that case, the evaporation rate (a negative flux) is
maintained at the surface until the soil surface reaches a certain negative matric
potential approximating air dryness; that matric potential is then maintained.
2. Desired rainfall rate: Since the rainfall boundary condition was selected for the upper
boundary condition, this line is used to specify the desired rainfall rate. This rate becomes
the flux of water at the inlet until the soil surface becomes saturated. At that time, a
potential of zero is maintained (and the flux decreases with time). If another boundary
condition had been specified, this line would have been changed to prompt the user for
the parameter needed for that condition.
3. Boundary condition for water at the lower surface: Since this is a finite soil, boundary
conditions must be specified at both upper and lower boundaries. The types of boundary
conditions supported here are the same as those at the upper surface except for the rainfall
condition. In this example a constant potential was chosen for this boundary condition.
4. Matric potential at the lower surface: Since a constant potential was specified, this entry
defines the value of that matric potential. The water content corresponding to that
potential for the soil selected is displayed on the following line for your information. If
another boundary condition had been selected, the prompt would have requested a
parameter appropriate for that condition.
5. Uniform initial matric potential throughout the soil: This software can simulate water
movement in finite soil systems for soils with uniform or non-uniform initial conditions.
If the initial condition is uniform, enter a Y here (symbolizing "yes"). If not, enter N. In
this example, the soil had a uniform water content throughout before flow began. Hence,
the uniform option was specified.
6. Matric potential throughout soil before simulation: Since this example involves a uniform
initial condition, this line allows you to enter the initial matric potential in the soil. The
next line then displays the water content corresponding to that matric potential. Pressing
the key displays the information shown in Figure 6. This information can be used to
determine the matric potential to be entered if the water content is known.
If you had specified a non-uniform initial condition, the editor would have enabled you to
enter matric potentials at different depths. This is illustrated later in this manual.
35
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Potential (cm)
0.0
-100.0
-200.0
-300.0
-400.0
-500.0
-1000.0
-2000.0
Water Content(cc/cc)
0.320
0.197
0.162
0.145
0.134
0.127
0.107
0.092
Potent! al(cm)
-3000.0
-4000.0
-5000.0
-6000.0
-8000.0
-10000.0
-12000.0
-14000.0
Water Content(cc/cc)
0.086
0.081
0.079
0.076
0.073
0.071
0.070
0.068
Figure 6. Water content of Cobb sandy clay soil at selected matric potentials as displayed after
is pressed when user is prompted for a matric potential value.
Simulation Parameters (SCR:3/3)~
Maximum time to be simulated (hr) : 8.0
Mesh size in depth (cm) : 1.000
Mesh size in time (hr) : 0.005
Period between graphic or tabular outputs (hr)..: 0.50
Output file name : COBB
Fl-Help; ESC-Abort; FlO-End editing; PgUp-Prev screen; PgDn-Next screen;
F8-Save input parameters in file; F9-Read input parameters from file;
Figure 7. Screen for defining miscellaneous parameters.
1. Maximum time to be simulated: This is the time, in hours, when simulation with these
boundary conditions should end. It may be the end of the time of interest or it may be the
time at which a boundary condition is changed.
2. Mesh size in depth: The solution to the partial differential equation is obtained by means
of finite difference techniques as described in the section on computational methods. This
entry defines the value of the mesh size in depth or Az. In this case, A)z = 1 cm so the
matric potential and water content will be determined every 1 cm through the soil system.
Also, derivatives with respect to distance in the partial differential equation and in the
36
-------
boundary conditions will be approximated by differences between values 1 cm apart. In
general, smaller mesh sizes result in more accurate solutions, but they also require more
computational time.
3. Mesh size in time: This entry is used to specify the mesh size in time or At. Matric
potential values will be determined for each time step or every 0.005 hr in this case.
Derivatives over time will be approximated by differences over that time span. Smaller
time steps generally result in more accurate numerical solutions.
4. Period between graphic or tabular outputs: Usually the times at which theuser wants to
see the solution to the problem are much less frequent than the mesh size in time. This
entry enables the user to specify the period of time between graphical or tabular outputs.
In this case, those outputs will be made for every .50 hr. NOTE: THE DISPLAY
PERIOD MUST BE A WHOLE NUMBER MULTIPLE OF THE MESH SIZE IN TIME.
5. Output file name: The software stores the problem definition, computed results, and other
needed data in disk files for later use in generating graphical and tabular outputs and for
restarting the solution process if necessary. The file name to be used is entered here. No
file extension should be specified since the software appends different extensions for the
different files it needs. The file name may include a legal disk drive or subdirectory. Files
created in this example will be
a. COBB.PRB - This file contains the problem definition needed to restart
thesimulation using option C of the main menu.
b. COBB.DAT - This file contains the calculated solution to the problem for each time
output is specified. It is used to redraw graphs and to restart using option C.
c. COBB.TAB - This file is an ASCII text file containing the tables selected if theuser
directed the tables to a file.
d. COBB.DSP - This is a summary of the problem definition for display on the screen
when D is pressed during simulation. A file is required since this definition may be
lengthy if the boundary conditions are changed several times during the simulation.
These files can become large so put them on a disk with plenty of room. If you are using a
flooov disk machine, store the files on a disk which does not contain the program.
When the flow problem has been completely defined and you press the key, the
hydraulic properties of the selected soil are displayed as illustrated in Figures 8 and 9.
37
-------
Figure 8. Soil water content for the Cobb sandy clay soil as a function of matric
potential.
Figure 9. Hydraulic conductivity for the Cobb sandy clay soil as functions of
matric potential and water content.
The Following Graphs May Be Displayed On The Screen:
Water Graphs:
Water Content vs. Distance
Matric Potential vs. Distance
Flux of Water vs. Distance
Driving Force for Water vs. Distance
Water Content vs. Time at Specified Depth
Matric Potential vs. Time at Specified Depth
Flux of Water vs. Time at Specified Depth
Driving Force vs. Time at Specified Depth
Cumulative Flux of Water Passing Specified Depth vs. Time
Cumulative (Net) Inflow vs. Time
Do you want to select graphs [Y/N] :_Y
Figure 10. List of graphs related to water movement.
Results of the simulation for water movement may be displayed in graphical form. A list of
the possible graphs is given in Figure 10. Two or three of these graphs may be displayed on the
screen at one time. They may be different types of graphs, graphs at different scales, or graphs for
different locations in the soil. The graphics are updated with the current solution as soon as it is
obtained. Since users often want to see more than three graphs of the solution, the software is
designed to draw graphs on virtual screens as well as on the actual screen. A virtual screen is a
portion of memory reserved and used just as memory in the video system. Graphs drawn on
virtual screens are not immediately visible but can be moved to the actual screen as desired. As
time passes, all screens are updated as soon as the solution has been calculated. In this way you
can observe the process as time progresses. Moreover, you can easily switch screens to view the
38
-------
solution in another form. If none of the graphs are satisfactory, additional graphs can be added
during the simulation process. Graphics limits may also be changed if needed. Printed copies of
the graphs on the screen can be obtained on an IBM graphics printeror a compatible printer by
pressing the keys or the key (for smaller printouts).
Below is a description of the types of graphs available. Many of them are illustrated on the
following pages.
1. Graphs of Parameters vs. Distance: In these graphs, a line representing the calculated
parameter as a function of depth is drawn for each time the outputs were specified by
the user. Figures 22 and 23 enable the user to select a subset of these lines to remain
on the screen.
2. Graphs of Parameters vs. Time at a Specified Depth: Each of these choices creates a
graph of the calculated parameter versus time at the depth specified. Each time at
which outputs were selected in Figure 7, an additional line segment is added to the
graph.
4. Cumulative (Net) Inflow vs. Time: This is a graph of the difference between the
cumulative amount of water entering the soil and that amount leaving the soil. Each
time at which outputs were selected in Figure 7, an additional line segment is added
to the graph.
Since the response in Figure 10 was Y, Figure 11 was displayed. In this screen the types of
graphs are listed. The user may choose the graphs of interest and specify the location for the
graph on the screen. Select the graph desired using the editor described in the section entitled
OPERATING CONVENTIONS. Use the cursor keys to move to each graph of interest and then
enter the desired screen location. Pressing the key will result in a map of the screen
showing the possible locations for the current graph (see Figure 1 la). (NOTE: Graphs of water
content, matric potential, water flux, driving force, and conductivity vs distance are larger than
the other graphs and can be placed only at locations A or B. Moreover, if one of these graphs is
at location B, location C cannot be used.)
39
-------
Enter the Position of Graphs to be displayed on SCREEN 1
Water Graphs:
Water Content vs. Distance :A
Matric Potential vs. Distance :
Flux of Water vs. Distance :
Driving Force for Water vs. Distance :
Water Content vs. Time at Specified Depth :
Matric Potential vs. Time at Specified Depth :
Flux of Water vs. Time at Specified Depth :B
Driving Force vs. Time at Specified Depth :
Cumulative Flux of Water Passing Specified Depth vs. Time:
Cumulative (Net) Inflow vs. Time :C
Fl-Help; ESC-Abort; FlO-End editing;
Figure 11. Selection of graphs for the first graphics screen.
Enter the letter corresponding to the desired position.
The same graph can be displayed at more than one
position by entering the desired positions separated
by a space.
Figure 1 la. Help message associated with graphics selection screen.
Having selected three graphs to be displayed on one screen, we must now define the limits
desired for each axis. These are entered using the parameter editor as shown in Figures 12, 13,
and 14. Note that in Figure 13, we specified a depth of zero. This means this graph will show the
flux density at depth zero or the infiltration rate.
40
-------
Limits for Graph of Water Content vs. Distance ( Location A )
Minimum Water Content (cc/cc) : 0.000 Maximum Water Content (cc/cc) : 0.400
Minimum Distance (cm) : 0.00
Maximum Distance (cm) : 50.00
Fl-Help; ESC-Abort; FlO-End editing;
Figure 12. Editing limits for graph of water content vs. distance.
Limits for Graph of Flux vs. Time ( Location B )
Minimum Time (hr) : 0.000
Maximum Time (hr) : 8.000
Minimum Flow Rate Upper (cm/hr) : 0.000
Maximum Flow Rate Upper (cm/hr) : 1.200
Depth (cm) from surface : 0.00
Fl-Help; ESC-Abort; FlO-End editing;
Figure 13. Editing limits and depth for graph of flux density vs. time.
41
-------
Limits for Graph of Net Inflow vs. Time ( Location C )
Minimum Time (hr) : 0.000
Maximum Time (hr) : 8.000
Minimum Net Inflow (cm) ... : 0.000
Maximum Net Inflow (cm) ... : 9.000
Fl-Help; ESC-Abort; FlO-End editing;
Figure 14. Editing limits for graph of cumulative (net) inflow vs time.
Enter the Position of GRAPHS to be displayed on SCREEN 2
Water Graphs:
Water Content vs. Distance :
Matric Potential vs. Distance :
Flux of Water vs. Distance :
Driving Force for Water vs. Distance :
Water Content vs. Time at Specified Depth :AB C
Matric Potential vs. Time at Specified Depth :
Flux of Water vs. Time at Specified Depth :
Driving Force vs. Time at Specified Depth :
Cumulative Flux of Water Passing Specified Depth vs. Time:
Cumulative (Net) Inflow vs. Time :
Fl-Help; ESC-Abort; FlO-End editing;
Figure 15. Selecting graphs for the second graphics screen.
42
-------
To illustrate the use of multiple graphics screens, a second graphics screen was defined as
shown in Figure 15. In this case, three graphs of water content versus time at a specific depth
were selected. The depths chosen were 0, 4, and 16 cm as shown in Figures 16, 17, and 18.
Limits for Graph of Water Content vs. Time at Specified Depth (Location A)
Minimum Time (hr) : 0.000
Maximum Time (hr) : 8.000
Minimum Water Content (cm) : 0.000
Maximum Water Content (cm) : 0.400
Depth in (cm) from surface : 0.00
Fl-Help; ESC-Abort; FlO-End editing;
Figure 16. Editing limits for graph of water content vs. time for depth 0.
Limits for Graph of Water Content vs. Time at Specified Depth (Location B)
Minimum Time (hr) : 0.000
Maximum Time (hr) : 8.000
Minimum Water Content (cm) : 0.000
Maximum Water Content (cm) : 0.400
Depth in (cm) from surface : 4.00
Fl-Help; ESC-Abort; FlO-End editing;
Figure 17. Editing limits for graph of water content vs. time for 4 cm depth.
43
-------
Limits for Graph of Water Content vs. Time at Specified Depth (Location C)
Minimum Time (hr) : 0.000
Maximum Time (hr) : 8.000
Minimum Water Content (cm) : 0.000
Maximum Water Content (cm) : 0.400
Depth in (cm) from surface : 16.00
Fl-Help; ESC-Abort; FlO-End editing;
Figure 18. Editing limits for graph of water content vs. time for 16 cm depth.
Enter the Position of GRAPHS to be displayed on SCREEN 3
Water Graphs:
Water Content vs. Distance :
Matric Potential vs. Distance :
Flux of Water vs. Distance :B
Driving Force for Water vs. Distance :A
Conductivity vs. Distance :
Water Content vs. Time at Specified Depth :
Flux of Water vs. Time at Specified Depth :
Driving Force vs. Time at Specified Depth :
Cumulative Flux of Water Passing Specified Depth vs. Time:
Cumulative (Net) Inflow vs. Time :
Fl-Help; ESC-Abort; FlO-End editing;
Figure 19. Selecting graphs for a third graphics screen.
44
-------
The third graphics screen selected in this example will contain graphs of water flux density
versus distance and the driving force causing water to move versus distance. Note that these are
larger graphs so only two graphs can be drawn on the screen. Limits for the graphs are specified
in Figures 20 and 21. The upper limit for flux density was chosen as 1.2 cm/hr since that is
slightly larger than the rainfall rate.
Limits for Graph of Flux of Water vs. Distance ( Location B )
Minimum Water Flux (cm/hr) .. : 0.000
Maximum Water Flux (cm/hr) .. : 1.200
Minimum Distance (cm) : 0.00
Maximum Distance (cm) : 50.00
Fl-Help; ESC-Abort; FlO-End editing;
Figure 20. Editing limits for graph of flux density vs. distance.
Limits for Graph of Driving Force vs. Distance ( Location A )
Minimum Driving Force : 0.00
Maximum Driving Force : 800.00
Minimum Distance (cm) : 0.00
Maximum Distance (cm) : 50.00
Fl-Help; ESC-Abort; FlO-End editing;
Figure 21. Editing limits for graph of driving force vs. distance.
45
-------
As explained previously, graphs of parameters versus distance result in a new curve being
drawn on the graph every time output is generated. Sometimes this is desirable, but often this
results in an excessive number of lines on the graph. Provision has been made in the software to
enable you to select a subset of these lines to remain on the screen. This is carried out as shown
in Figures 22 and 23. If option A is selected in Figure 22, all lines will remain on the graph. If
option B is selected, all lines are drawn as the calculation is completed for that time, but only
lines corresponding to times at which the boundary condition was changed will remain on the
screen. If option C is selected, Figure 23 is displayed and the user may select specific times for
which the curves will remain on the screen. Curves for other times will be shown temporarily as
that time is simulated, but they will not remain on the screen.
The simulated results will be displayed on the graphs every 0.5 hours as calculations are
completed. That is, a new line is drawn every 0.5 hours for graphs of any parameter vs.
distance. This can lead to an excessive number of lines on the graph. The options below
enable you to select certain times to remain on the screen.
A. All lines drawn remain on graph. As new calculations are made, a new
line is added to the screen.
B. Some lines are erased before new lines are added. Only lines
corresponding to times when a new boundary condition is imposed
remain on the screen.
C. Some lines are erased before new ones are added. Only lines
corresponding to times selected by you will remain on the screen.
Desired Option : C
Figure 22. Selection of desired option for parameter profile graphs.
46
-------
Times for which Parameter Profiles will be Saved on Screens
Time to be Saved on Graph (hr): 1.0000
Time to be Saved on Graph (hr): 2.0000
Time to be Saved on Graph (hr): 4.0000
Time to be Saved on Graph (hr): 6.0000
Time to be Saved on Graph (hr): 8.0000
Time to be Saved on Graph (hr): 0.0000
Time to be Saved on Graph (hr): 0.0000
Time to be Saved on Graph (hr): 0.0000
Time to be Saved on Graph (hr): 0.0000
Time to be Saved on Graph (hr): 0.0000
Time to be Saved on Graph (hr): 0.0000
Time to be Saved on Graph (hr): 0.0000
Time to be Saved on Graph (hr): 0.0000
Time to be Saved on Graph (hr): 0.0000
Fl-Help; ESC-Abort; FlO-End editing;
Figure 23. Specifying times for which parameter profiles will remain on screen.
Display the Following Tabular Results:
Surface Fluxes :Y
Matric Potential vs. Distance :Y
Water Content vs. Distance :Y
Water Flux vs. Distance :Y
Water Driving Force vs. Distance .. :Y
Hydraulic Conductivity vs. Distance : Y
Fl-Help; ESC-Abort; FlO-End editing;
Figure 24. Selecting tabular outputs.
47
-------
Simulated results can be displayed in tabular as well as graphical form. Figure 24 shows
the types of tables available. If tabular output is desired, enter aY by the desired table(s). If no
tables are wanted, all entries should be N. Tables are output each time output was specified in
Figure 7. Tables may be displayed on a printer, saved in an ASCII text file, or displayed on the
screen (provided no graphics options were selected). Selection of the output device is illustrated
in Figure 25.
Output Tables to
F. Disk File
P. Printer
Desired Device ? P
Figure 25. Selection of output device for tables. In this case, the screen is not available since
graphics displays have been selected.
This completes the definition of the problem and the selection of the outputs of interest.
The system now displays the first screen of graphs and begins solving the problem. All graphic
screens are updated and tables are output as soon as the solution is determined for the desired
times. Figures 26, 27, 28,and 29 illustrate the screens for this problem after simulating movement
for 0, 1,2, and 4 hours, respectively. Virtual graphic screens may be viewed at any time by
pressing the or keys.
During simulation, the lower left corner of the screen contains a list of keys which may be
pressed during the simulation. These keys enable you to modify the graphics displays, change
tabular outputs, change boundary conditions, display a summary of the defined problem with
boundary conditions, or terminate the simulation.
Figure 26. Screen 1 at time t = 0.0 hr. The vertical line in the water content vs. depth graph
represents the initial water content of the soil.
Figure 27. Screen 1 at time t = 1.0 hr. Curves are shown for t = 0 and t = 1 hr.
48
-------
Figure 28. Screen 1 at time t = 2.0 hr. Curves are shown for t = 0, 1, and 2 hours.
Figure 29. Screen 1 at time t = 4.0 hr. Water content profiles shown on the graph correspond to
times of 0, 1, 2, and 4 hours as selected in Figure 23.
Figures 30, 31, and 32 show the three graphic screens selected in this example at the end
of the simulation. At this time, you may terminate the simulation, change the boundary condition
and extend the time to be simulated, or view additional graphs. By changing boundary
conditions, you can simulate water redistribution or evaporation after a rainfall. In this way,
complex flow processes can be simulated.
Table 2 illustrates the tabular output generated by the options selected. Tables for times of
0, 1, and 2 hours are shown, although they were produced for every 0.5 hours simulated.
Comments on the simulated water movement: FigureS0 indicates that the infiltration rate
for this soil was 1.0 cm/hr for approximately 2.5 hours. After that time the rate gradually
decreased. During the initial 2.5 hours the infiltration rate was equal to the rainfall rate.That is,
the soil had the ability to take up the water as rapidly as it was applied. The water content at the
soil surface increased (see Figure 31) forthis 2.5 hr and then became constant at the saturated
value of 0.32cm3/cm3. After the soil surface reached saturation, the soil could no longer take up
water at the rate it was supplied and the infiltration rate decreased. This model would thus predict
that runoff (assuming no surface storage) would begin after 2.5 hours of rainfall. At the end of
the 8 hours of simulation, the infiltration rate was somewhat larger than 0.6 cm/hr. This rate still
exceeds the saturated hydraulic conductivity of 0.53 cm/hr. This is possible because the driving
forces throughout the wetted soil system exceed 1, as can be seen in Figure 32 and Table 2. The
total amount of water entering the soil was about 6.4 cm. Rainfall during the 8 hours was 8 cm.
Thus, the model predicts that the runoff was approximately 1.6 cm. Graphs of water content vs.
distance show that the water moves deeper and deeper into the soil as time passes. The leading
edge of the water, commonly called the wetting front, is quite steep. Essentially no water
movement occurs ahead of the wetting front. Driving forces become large at the wetting front
and tend toward unity (for vertical downward flow) on both sides of it.
Figure 30. Screen 1: Water content vs. distance, infiltration rate vs time, and net infiltration vs
time after 8 hours.
Figure 31. Screen 2: Water content versus time at 0, 4, and 16 cm from the top of the soil.
Figure 32. Screen 3: Water flux vs distance and driving force vs. distance at 1, 2, 4, 6, and
hours.
49
-------
Table 2. Tabular results of water simulation in Cobb sandy clay soil.
Soil: COBB SANDY CLAY
Orientation: 0.0 Degrees From Vertical Downward
Initial Condition for Water:
Uniform initial condition
Matric Potential =-2000.0 cm
Water Content = 0.092 cc/cc
Boundary Condition imposed at time 0.000 hr
Water Boundary Condition at Upper Soil Surface:
Rainfall Rate = 1.000 cm/hr
Water Boundary Condition at Distance of 50.00 cm:
Matric Potential = -2000.0 cm
Time: 0.0000 hr
Mass Balance Check: Amount
Water
from water content or cone.
from surface fluxes
Total Amount in soil:
from water content or cone.
from surface fluxes
Flux at Upper Surface :
Flux at Lower Surface :
Cum. Flux at Upper Surface :
Cum. Flux at Lower Surface :
Net Accumulation:
from water content or cone.
from surface fluxes
Mesh size in depth = l.OOOOOOe+000;
Distance Potential Water_
cm cm
0.000 -2000.0
1.000 -2000.0
2.000 -2000.0
3.000 -2000.0
4.000 -2000.0
5.000 -2000.0
6.000 -2000.0
7.000 -2000.0
8.000 -2000.0
9.000 -2000.0
10.000 -2000.0
11.000 -2000.0
Content
cc/cc
0.092
0.092
0.092
0.092
0.092
0.092
0.092
0.092
0.092
0.092
0.092
0.092
O.OOOE+000 cm
O.OOOE+000 cm
4.620E+000 cm
4.620E+000 cm
4.620E+000 cm
0.000000 cm/hr
0.000000 cm/hr
0.000000 cm
0.000000 cm
0.0000 cm
0.0000 cm
0.0000 cm
Mesh size in time = 5.000000e-003
Flux Water Driving Force
cm/hr
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
Conductivity
cm/hr
3.687E-005
3.687E-005
3.687E-005
3.687E-005
3.687E-005
3.687E-005
3.687E-005
3.687E-005
3.687E-005
3.687E-005
3.687E-005
3.687E-005
50
-------
Table 2. Continued
Distance
cm
12.000
13.000
14.000
15.000
16.000
17.000
18.000
19.000
20.000
21.000
22.000
23.000
24.000
25.000
26.000
27.000
28.000
29.000
30.000
31.000
32.000
33.000
34.000
35.000
36.000
37.000
38.000
39.000
40.000
41.000
42.000
43.000
44.000
45.000
46.000
47.000
48.000
49.000
50.000
Potential Water Content
cm
-2000.0
-2000.0
-2000.0
-2000.0
-2000.0
-2000.0
-2000.0
-2000.0
-2000.0
-2000.0
-2000.0
-2000.0
-2000.0
-2000.0
-2000.0
-2000.0
-2000.0
-2000.0
-2000.0
-2000.0
-2000.0
-2000.0
-2000.0
-2000.0
-2000.0
-2000.0
-2000.0
-2000.0
-2000.0
-2000.0
-2000.0
-2000.0
-2000.0
-2000.0
-2000.0
-2000.0
-2000.0
-2000.0
-2000.0
cc/cc
0.092
0.092
0.092
0.092
0.092
0.092
0.092
0.092
0.092
0.092
0.092
0.092
0.092
0.092
0.092
0.092
0.092
0.092
0.092
0.092
0.092
0.092
0.092
0.092
0.092
0.092
0.092
0.092
0.092
0.092
0.092
0.092
0.092
0.092
0.092
0.092
0.092
0.092
0.092
Flux Water Driving Force
cm/hr
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
1.000
.000
.000
.000
.000
.000
.000
.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
Conductivity
cm/hr
3.687E-005
3.687E-005
3.687E-005
3.687E-005
3.687E-005
3.687E-005
3.687E-005
3.687E-005
3.687E-005
3.687E-005
3.687E-005
3.687E-005
3.687E-005
3.687E-005
3.687E-005
3.687E-005
3.687E-005
3.687E-005
3.687E-005
3.687E-005
3.687E-005
3.687E-005
3.687E-005
3.687E-005
3.687E-005
3.687E-005
3.687E-005
3.687E-005
3.687E-005
3.687E-005
3.687E-005
3.687E-005
3.687E-005
3.687E-005
3.687E-005
3.687E-005
3.687E-005
3.687E-005
3.687E-005
Time: 1.0000 hr
Mass Balance Check: Amount
from water content or cone.
from surface fluxes
Water
5.068E-001 cm
5.000E-001 cm
51
-------
Total Amount in soil:
from water content or cone.
from surface fluxes
Flux at Upper Surface :
Flux at Lower Surface :
Cum. Flux at Upper Surface :
Cum. Flux at Lower Surface :
Net Accumulation:
from water content or cone.
from surface fluxes
5.634E+000 cm
5.649E+000 cm
5.620E+000 cm
1.000000 cm/hr
0.000037 cm/hr
1.000000cm
0.000037 cm
1.0145 cm
1.0290 cm
1.0000 cm
Mesh size in depth = l.OOOOOOe+000; Mesh size in time = 5.000000e-003
Distance Potential Water Content
cm cm
0.000 -9.6
1.000 -12.8
2.000 -17.5
3.000 -25.4
4.000 -41.7
5.000 -87.9
6.000 -276.9
7.000 -948.2
8.000 -1611.3
9.000 -1877.7
10.000 -1964.0
11.000 -1989.9
12.000 -1997.3
13.000 -1999.3
14.000 -1999.8
15.000 -2000.0
16.000 -2000.0
17.000 -2000.0
18.000 -2000.0
19.000 -2000.0
20.000 -2000.0
21.000 -2000.0
22.000 -2000.0
23.000 -2000.0
24.000 -2000.0
25.000 -2000.0
26.000 -2000.0
27.000 -2000.0
28.000 -2000.0
29.000 -2000.0
cc/cc
0.304
0.297
0.287
0.272
0.247
0.204
0.148
0.108
0.097
0.094
0.093
0.092
0.092
0.092
0.092
0.092
0.092
0.092
0.092
0.092
0.092
0.092
0.092
0.092
0.092
0.092
0.092
0.092
0.092
0.092
Flux Water Driving Force
cm/hr
1.000000 4.199
1.004772 4.946
0.978909 7.278
0.931423 13.077
0.795005 32.266
0.490325 118.632
0.166742 431.133
0.048265 668.179
0.020426 465.778
0.006868 177.363
0.002135 57.098
0.000653 17.643
0.000210 5.691
0.000083 2.261
0.000049 .324
0.000040 .080
0.000038 .019
0.000037 .004
0.000037 .001
0.000037 .000
0.000037 .000
0.000037 .000
0.000037 .000
0.000037 .000
0.000037 .000
0.000037 .000
0.000037 .000
0.000037 .000
0.000037 .000
0.000037 .000
Conductivity
cm/hr
2.703E-001
2.031E-001
1.345E-001
7.123E-002
2.464E-002
4.133E-003
3.868E-004
7.223E-005
4.385E-005
3.872E-005
3.739E-005
3.702E-005
3.691E-005
3.688E-005
3.688E-005
3.687E-005
3.687E-005
3.687E-005
3.687E-005
3.687E-005
3.687E-005
3.687E-005
3.687E-005
3.687E-005
3.687E-005
3.687E-005
3.687E-005
3.687E-005
3.687E-005
3.687E-005
52
-------
Distance
cm
30.000
31.000
32.000
33.000
34.000
35.000
36.000
37.000
38.000
39.000
40.000
41.000
42.000
43.000
44.000
45.000
46.000
47.000
48.000
49.000
50.000
Potential Water Content
cm
-2000.0
-2000.0
-2000.0
-2000.0
-2000.0
-2000.0
-2000.0
-2000.0
-2000.0
-2000.0
-2000.0
-2000.0
-2000.0
-2000.0
-2000.0
-2000.0
-2000.0
-2000.0
-2000.0
-2000.0
-2000.0
cc/cc
0.092
0.092
0.092
0.092
0.092
0.092
0.092
0.092
0.092
0.092
0.092
0.092
0.092
0.092
0.092
0.092
0.092
0.092
0.092
0.092
0.092
Flux Water Driving Force
cm/hr
0.000037
0.000037
0.000037
0.000037
0.000037
0.000037
0.000037
0.000037
0.000037
0.000037
0.000037
0.000037
0.000037
0.000037
0.000037
0.000037
0.000037
0.000037
0.000037
0.000037
0.000037
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
Conductivity
cm/hr
3.687E-005
3.687E-005
3.687E-005
3.687E-005
3.687E-005
3.687E-005
3.687E-005
3.687E-005
3.687E-005
3.687E-005
3.687E-005
3.687E-005
3.687E-005
3.687E-005
3.687E-005
3.687E-005
3.687E-005
3.687E-005
3.687E-005
3.687E-005
3.687E-005
Time: 2.0000 hr
Mass Balance Check: Amount
from water content or cone.
from surface fluxes
Water
5.051E-001 cm
5.000E-001 cm
Total Amount in soil:
from water content or cone.
from surface fluxes
6.640E+000 cm
6.660E+000 cm
6.620E+000 cm
Flux at Upper Surface :
Flux at Lower Surface :
1.000000 cm/hr
0.000037 cm/hr
Cum. Flux at Upper Surface :
Cum. Flux at Lower Surface :
2.000000 cm
0.000074 cm
Net Accumulation:
from water content or cone.
from surface fluxes
2.0198 cm
2.0397 cm
1.9999 cm
Mesh size in depth = l.OOOOOOe+000; Mesh size in time = 5.000000e-003
53
-------
Distance
cm
1.000
2.000
3.000
4.000
5.000
6.000
7.000
8.000
9.000
10.000
11.000
12.000
13.000
14.000
15.000
16.000
17.000
18.000
19.000
20.000
21.000
22.000
23.000
24.000
25.000
26.000
27.000
28.000
29.000
30.000
31.000
32.000
33.000
34.000
35.000
36.000
37.000
38.000
39.000
40.000
41.000
42.000
43.000
44.000
45.000
46.000
47.000
Potential Water_Content
cm
-3.8
-5.2
-6.9
-8.9
-11.6
-15.3
-21.0
-31.0
-53.7
-124.8
-420.9
-1150.8
-1671.4
-1883.0
-1959.6
-1986.4
-1995.5
-1998.5
-1999.5
-1999.9
-2000.0
-2000.0
-2000.0
-2000.0
-2000.0
-2000.0
-2000.0
-2000.0
-2000.0
-2000.0
-2000.0
-2000.0
-2000.0
-2000.0
-2000.0
-2000.0
-2000.0
-2000.0
-2000.0
-2000.0
-2000.0
-2000.0
-2000.0
-2000.0
-2000.0
-2000.0
-2000.0
cc/cc
0.315
0.313
0.309
0.305
0.300
0.292
0.280
0.262
0.233
0.185
0.132
0.104
0.096
0.094
0.093
0.093
0.092
0.092
0.092
0.092
0.092
0.092
0.092
0.092
0.092
0.092
0.092
0.092
0.092
0.092
0.092
0.092
0.092
0.092
0.092
0.092
0.092
0.092
0.092
0.092
0.092
0.092
0.092
0.092
0.092
0.092
0.092
Flux Water Driving Force
cm/hr
0.999584
0.991081
0.980304
0.966598
0.949017
0.925920
0.892518
0.825099
0.647086
0.342006
0.102238
0.037210
0.015615
0.005607
0.001974
0.000702
0.000262
0.000111
0.000061
0.000045
0.000039
0.000038
0.000037
0.000037
0.000037
0.000037
0.000037
0.000037
0.000037
0.000037
0.000037
0.000037
0.000037
0.000037
0.000037
0.000037
0.000037
0.000037
0.000037
0.000037
0.000037
0.000037
0.000037
0.000037
0.000037
0.000037
0.000037
2.287
2.519
2.855
3.363
4.189
5.682
8.857
17.374
47.908
184.604
513.969
626.237
367.109
145.118
52.689
18.928
7.081
3.022
1.659
1.210
.066
.020
.006
.002
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
Conductivity
cm/hr
4.370E-001
3.934E-001
3.434E-001
2.874E-001
2.266E-001
1.630E-001
1.008E-001
4.749E-002
1.351E-002
1.853E-003
1.989E-004
5.942E-005
4.254E-005
3.864E-005
3.746E-005
3.707E-005
3.694E-005
3.689E-005
3.688E-005
3.688E-005
3.687E-005
3.687E-005
3.687E-005
3.687E-005
3.687E-005
3.687E-005
3.687E-005
3.687E-005
3.687E-005
3.687E-005
3.687E-005
3.687E-005
3.687E-005
3.687E-005
3.687E-005
3.687E-005
3.687E-005
3.687E-005
3.687E-005
3.687E-005
3.687E-005
3.687E-005
3.687E-005
3.687E-005
3.687E-005
3.687E-005
3.687E-005
54
-------
Distance Potential Water_Content Flux_Water Driving_Force Conductivity
cm cm cc/cc cm/hr cm/hr
48.000 -2000.0 0.092 0.000037 1.000 3.687E-005
49.000 -2000.0 0.092 0.000037 1.000 3.687E-005
50.000 -2000.0 0.092 0.000037 1.000 3.687E-005
55
-------
OPTION S: WATER AND CHEMICAL MOVEMENT: This section of the manual will
illustrate using the software to model water and chemical movement. This option requires you to
define a soil system, initial conditions and boundary conditions for water, initial and boundary
conditions for the chemical, additional soil and chemical properties, and the simulation
parameters. Three of these five steps are similar to those used to simulate only water movement.
These have been illustrated and explained previously. This section will concentrate on the
additional items required for chemicals.
Before proceeding with the example, a word of explanation is in order about units of
concentration. Table 1 lists symbols and units for different parameters. The unit of concentration
listed is |ig/cm3. This leads to the units shown in Table 1 for the flux, cumulative flux, and mass
of chemical. You may enter concentrations with other units. The computed concentrations will
then be displayed in those units, even though the unit labels in tables will not change. If the
concentration is not based on a volume of one cubic centimeter, then you must be careful in
interpreting the units of flux, cumulative flux, and mass.
Selecting option S in the Main Menu (Figure 2) results in a group of 5 screens needed to
define the water and chemical flow problem. These screens are illustrated in Figures 33, 34, 35,
and 36. In this example, pure water is applied to a Yolo clay soil by ponding water 1 cm deep at
the soil surface. The soil had an initial concentration of chemical of 10 jig/cm3 throughout. The
soil had initial matric potential of -50 cm throughout. We will observe the change in water
content and concentration of chemical with time and depth as well as the flux and cumulative
flux of water and chemical.
The soil system and initial and boundary conditions for water are specified in Figure 33.
These entries have been explained previously.
56
-------
Definition of Soil System (SCR: 1/5)-
Name of the soil : YOLO CLAY
Orientation of flow system : 0.0
Finite or Semi-infinite soil system (F or S).: F
Length of soil system (cm) : 30.00
Fl-Help; ESC-Abort; FlO-End editing; PgUp-Prev screen; PgDn-Next screen;
F8-Save input parameters in file; F9-Read input parameters from file;
Definition of Water System (SCR:2/5)»
Boundary condition for water at the UPPER surface (P,F,R,M): P
Desired matric potential (cm) at the UPPER soil surface....: 1.00
That matric potential corresponds to water content(cc/cc)..: 0.495
Boundary condition for water at the LOWER surface (P,F,M)..: P
Desired matric potential (cm) at the LOWER surface : -50.00
That matric potential corresponds to water content(cc/cc)..: 0.406
Uniform initial matric potential throughout the soil (Y/N).: Y
Matric potential (cm) throughout soil before simulation : -50.00
That matric potential corresponds to water content(cc/cc)..: 0.406
Fl-Help; ESC-Abort; FlO-End editing; PgUp-Prev screen; PgDn-Next screen;
F8-Save input parameters in file; F9-Read input parameters from file;
Figure 33. Screens for defining the soil and water systems for the chemical transport problem.
57
-------
Definition of Chemical System (SCR:3/5)~
Boundary condition for chemical at the UPPER surface (I,S).: I
Desired concentration of the inflowing solution (|ig/cc) ...: 0.00
Boundary condition for chemical at the LOWER surface (M,S).: M
Uniform chemical concentration throughout the soil (Y/N)...: Y
Chemical concentration before simulation (|ig/cc) : 10.0
Fl-Help; ESC-Abort; FlO-End editing; PgUp-Prev screen; PgDn-Next screen;
F8-Save input parameters in file; F9-Read input parameters from file;
Figure 34. Screen for defining the boundary and initial conditions for the
chemical.
1. Boundary condition for chemical at the upper surface: Two types of boundary conditions
for the chemical are supported in this software. They have been described mathematically
in the Mathematical Models section.
a. Constant Concentration of Inflowing Solution: This condition, selected by the
letter I, is used to specify that the concentration of the chemical in the water
entering the soil is some constant value. The quantity of the chemical entering the
soil is determined by this concentration and the amount of water entering the soil
(as determined from the solution to the water flow problem). If water is leaving
this surface, this boundary condition states that all of the chemical remains behind
in the soil, as would be the case for evaporation at the surface.
b. Constant Concentration in Soil Surface: This condition is used to impose a
constant concentration of chemical in the soil solution at this surface. It is selected
by pressing the letter S. This condition would be rather difficult to impose
experimentally.
2. Desired concentration of the inflowing solution: This line enables you to specify the
concentration of the solution entering the soil system. Since pure water is entering the soil
in this example, the value entered was zero. If the other boundary condition had been
selected on line 1, this entry would have requested the concentration of the soil solution.
58
-------
3. Boundary condition for the chemical at the lower surface: The following boundary
conditions may be imposed at the lower surface:
a Chemical Movement by Mass Flow Only: This boundary condition states that the
chemical moves across this boundary only by moving with the soil solution.
Diffusion does not occur. Thus the amount of chemical moving past the surface
depends upon the volume of water moving across the surface and the
concentration of chemical in that water. If no water movement occurs, no
chemical movement occurs. This boundary condition is selected by pressing the
letter M.
b. Constant Concentration in Soil Surface: This condition is used to impose a
constant concentration of chemical in the soil solution at this surface. It is selected
by pressing the letter S. This condition would be rather difficult to impose
experimentally, but it might be appropriate for simulating upward movement of
water in soil in contact with a constant water table at the lower surface.
4. Uniform chemical concentration throughout: This entry is Y if the concentration of
chemical in the soil solution is uniform at the beginning of the simulation.
5. Chemical concentration before simulation: This entry defines the concentration of
chemical in the soil solution before simulation begins.
59
-------
Soil and Chemical Parameters (SCR:4/5)~
Soil bulk density (g/cc) : 1.4000
WaterSoil partition coefficient (cc/g soil) : 0.0000
Diffusion coefficient of chemical in water (cm2/hr).: 3.00E-002
Dispersivity (cm) : 2.00E+000
First-order degradation constant, liquid (1/hr) : O.OOE+000
First-order degradation constant, solid (1/hr) : O.OOE+000
Zero-order rate constant, liquid (|ig/cc/hr) : O.OOE+000
Fl-Help; ESC-Abort; FlO-End editing; PgUp-Prev screen; PgDn-Next screen;
F8-Save input parameters in file; F9-Read input parameters from file;
Figure 35. Screen for defining additional soil and chemical parameters needed for simulating
chemical movement.
1. Soil bulk density: This is the mass of dry soil per unit volume of soil (including solids
and pores).
2. Water: Soil partition coefficient: This is the proportionality factor between the
concentration of chemical in the solid and liquid phases as shown in equation 14.
3. Diffusion coefficient of chemical in water: This parameter is one component of the
dispersion coefficient as shown in equation 26. It is the diffusion coefficient for the
chemical in bulk water.
4. Dispersivity: This is an empirical index of the magnitude of variations of the pore
velocities in the soil. Soils with a small range of pore sizes have smaller values than those
with a wide range in pore sizes. Values are generally less than 1 cm for laboratory soil
columns and less than 10 cm for field soils (Rao et al., 1987).
5. First-order degradation constant, liquid: This model assumes the chemical degradation
can be described by first-order kinetics. This value is the degradation rate for the
chemical in the liquid phase. If the degradation half-life of the chemical in the liquid
phase is known, this value is simply 0.693/half-life (hours) or 0.0289/half-life(days).
6. First-order degradation constant, solid: This is the degradation constant for the chemical
in the solid phase.
60
-------
7. Zero-order rate constant, liquid: This is value of the rate constant for production or decay
of the chemical by a zero-order process.
The remaining parameters needed to define the problem are shown in Figure 36.They were
explained in the water movement example. At this point the problem is defined. You press the
key and then specify the desired graphical and tabular outputs in a manner similar to that
used in water movement. Figure 37 shows the screen which enables you to specify the desired
graphs. Note that this list of graphs now contains additional graphs involving the chemical.
After specifying the desired graphs, you may select any tables of interest from the screen shown
in Figure 38.
Simulation Parameters (SCR: 5/5)—
Maximum time to be simulated (hr) : 8.00
Mesh size in depth (cm) : 1.000
Mesh size in time (hr) : 0.0100
Period between graphic or tabular outputs (hr)..: 0.50
Output file name : YOLO
Fl-Help; ESC-Abort; FlO-End editing; PgUp-Prev screen; PgDn-Next screen;
F8-Save input parameters in file; F9-Read input parameters from file;
Figure 36. Screen for completing the definition of a transport problem.
61
-------
Enter the Position of Graphs to be displayed on SCREEN 1
Water Graphs:
Water Content vs. Distance :A
Matric Potential vs. Distance :
Flux of Water vs. Distance :
Driving Force for Water vs. Distance :
Conductivity vs. Distance :
Water Content vs. Time at Specified Depth :
Matric Potential vs. Time at Specified Depth :
Flux of Water vs. Time at Specified Depth :
Driving Force vs. Time at Specified Depth :
Cumulative Flux of Water Passing Specified Depth vs. Time:
Cumulative (Net) Inflow vs. Time :
Chemical Graphs
Concentration vs. Distance :B
Flux of Chemical vs. Distance :
Concentration vs. Time at Specified Depth :
Flux of Chemical vs. Time at Specified Depth :
Cum. Flux of Chemical Passing Specified Depth vs.Time... :
Mass of Chemical in Soil vs. Time :
Fl-Help; ESC-Abort; FlO-End editing;
Figure 37. Selecting graphs involving both water and chemical.
62
-------
Display the Following Tabular Results:
Surface Fluxes :Y
Matric Potential vs. Distance :N
Water Content vs. Distance :Y
Water Flux vs. Distance :Y
Water Driving Force vs. Distance .. :N
Hydraulic Conductivity vs. Distance :N
Chemical Concentration vs. Distance : Y
Chemical Flux vs. Distance :Y
Fl-Help; ESC-Abort; FlO-End editing;
Figure 38. Selecting tabular outputs involving water and chemical.
Comments on the simulated water and chemical movement: Figure 39 contains graphs of
water content and chemical concentration in the soil asa function of distance from the inlet.
Curves are shown for each hour simulated. In this case the water content scale begins at
0.40cm3/cm3 instead of zero. Because water was ponded at the surface, the water content at that
point was the saturated value immediately after flow began. This is in contrast with the rainfall
example shown in Figure 30. The vertical line at a concentration of 10 jig/cm3 in the graph on
the right represents the initial concentration of chemical in this soil. As pure water flows into the
soil, this concentration decreases near the surface, but it does not become zero immediately. As
time passes, the concentration at the surface continues to decrease. Figure 40 illustrates the
manner in which water content and concentration change over time at the 5-cm position. The
water content approaches saturation quickly, although the chemical concentration decreases more
slowly. In fact, water content changes occur beyond the 20-cm depth during the 8 hours
simulated, while concentration changes occur only to about 10 cm. This occurs even though the
chemical in this example is not adsorbed on the soil.
Figures 41 and 42 show the flux and cumulative flux of water and chemical as functions
of time at 5 cm. The fluxes of water and chemical are initially very small before water reaches
that depth. They then increase to a maximum value and then decrease as the overall flux of water
into the soil decreases. The cumulative fluxes have approximately the same shape. This graph
indicates that approximately 4.5 jig of chemical (per sq. cm) moved past the 5-cm position in the
8 hours.
63
-------
Figure 39. Water content and chemical concentration as functions of depth at one hour
intervals.
Figure 40. Water content and chemical concentration as functions of time at the 5-cm
position.
Figure 41. Flux of water and chemical as functions of time at the 5-cm depth.
Figure 42. Cumulative flux of water and chemical as functions of time at the 5-cm position.
64
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TABLES
Table 3. Simulated results of water and chemical movement into Yolo clay.
Soil: YOLO CLAY
Orientation: 0.0 Degrees From Vertical Downward
Initial Condition for Water:
Uniform initial condition
Matric Potential =-50.0 cm Water Content = 0.406 cc/cc
Initial Condition for Chemical:
Uniform initial condition
Concentration = 10.000 micrograms/cc
Soil and Chemical Properties :
Soil Bulk Density (g/cc) : 1.400
Water:Soil Partition Coefficient (cc/g soil) : 0.000
Diffusion Coefficient of chemical in water(cm2/hr): 3.000E-002
Dispersivity (cm) : 2.000E+000
First-order degradation constant, liquid (1/hr).. : O.OOOE+000
First-order degradation constant, solid (1/hr)... : O.OOOE+000
Zero-order rate constant, liquid (microgram/cm2/hr): O.OOOE+000
Boundary Condition imposed at time 0.000 hr
Water Boundary Condition at Upper Soil Surface:
Matric Potential =1.0 cm
Water Boundary Condition at Distance of 30.00 cm:
Matric Potential = -50.0 cm
Chemical Boundary Condition at Upper Soil Surface:
Concentration of inflowing solution = 0.000 microgram/cc
Chemical Boundary Condition at Distance of 30.00 cm:
Mass Flow only, no dispersion.
Time: 0.0000 hr
Water Chemical
Mass Balance Check: Amount
from water content or cone. O.OOOE+000 cm O.OOOOE+000 micrograms/cm2
from surface fluxes O.OOOE+000 cm O.OOOOE+000 micrograms/cm2
Total Amount in soil: 1.217E+001 cm 1.2171E+002 micrograms/cm2
from water content or cone. 1.217E+001 cm 1.2171E+002 micrograms/cm2
from surface fluxes 1.217E+001 cm 1.2171E+002 micrograms/cm2
Flux at Upper Surface: 0.000000 cm/hr O.OOOOE+000 micrograms/cmVhr
Flux at Lower Surface: 0.000000 cm/hr O.OOOOE+000 micrograms/cm2/hr
Cum. Flux at Upper Surface : 0.000000 cm O.OOOOE+000 microgram/cm2
Cum. Flux at Lower Surface : 0.000000 cm O.OOOOE+000 microgram/cm2
Net Accumulation: 0.0000 cm O.OOOOE+000 microgram/cm2
65
-------
Table 3. Continued.
from water content or cone.
from surface fluxes
0.0000 cm
0.0000 cm
O.OOOOE+000 micrograms/cmVhr
O.OOOOE+000 micrograms/cm2/hr
Mesh size in depth = l.OOOOOOe+000; Mesh size in time = l.OOOOOOe-002
Distance
cm
0.000
1.000
2.000
3.000
4.000
5.000
6.000
7.000
8.000
9.000
10.000
11.000
12.000
13.000
14.000
15.000
16.000
17.000
18.000
19.000
20.000
21.000
22.000
23.000
24.000
25.000
26.000
27.000
28.000
29.000
30.000
Water_Content
cc/cc
0.406
0.406
0.406
0.406
0.406
0.406
0.406
0.406
0.406
0.406
0.406
0.406
0.406
0.406
0.406
0.406
0.406
0.406
0.406
0.406
0.406
0.406
0.406
0.406
0.406
0.406
0.406
0.406
0.406
0.406
0.406
Flux_Water
cm/hr
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
Concentration
microgram/cm3
10.000
10.000
10.000
10.000
10.000
10.000
10.000
10.000
10.000
10.000
10.000
10.000
10.000
10.000
10.000
10.000
10.000
10.000
10.000
10.000
10.000
10.000
10.000
10.000
10.000
10.000
10.000
10.000
10.000
10.000
10.000
Flux_Chem
microg/cnf/hr
O.OOOOE+000
O.OOOOE+000
O.OOOOE+000
O.OOOOE+000
O.OOOOE+000
O.OOOOE+000
O.OOOOE+000
O.OOOOE+000
O.OOOOE+000
O.OOOOE+000
O.OOOOE+000
O.OOOOE+000
O.OOOOE+000
O.OOOOE+000
O.OOOOE+000
O.OOOOE+000
O.OOOOE+000
O.OOOOE+000
O.OOOOE+000
O.OOOOE+000
O.OOOOE+000
O.OOOOE+000
O.OOOOE+000
O.OOOOE+000
O.OOOOE+000
O.OOOOE+000
O.OOOOE+000
O.OOOOE+000
O.OOOOE+000
O.OOOOE+000
O.OOOOE+000
Time: 1.0000 hr
Mass Balance Check: Amount
from water content or cone.
from surface fluxes
Water
1.199E-001cm
1.254E-001 cm
Chemical
-2.4172E-002 micrograms/cm2
-2.4172E-002 micrograms/cm2
66
-------
Table 3. Continued.
Total Amount in soil:
from water content or cone.
from surface fluxes
Flux at Upper Surface :
Flux at Lower Surface :
Cum. Flux at Upper Surface :
Cum. Flux at Lower Surface :
Net Accumulation:
from water content or cone.
from surface fluxes
Mesh size
Distance
cm
0.000
1.000
2.000
3.000
4.000
5.000
6.000
7.000
8.000
9.000
10.000
11.000
12.000
13.000
14.000
15.000
16.000
17.000
18.000
19.000
20.000
21.000
22.000
23.000
24.000
25.000
26.000
27.000
28.000
29.000
30.000
1.259E+001 cm
1.257E+001 cm
1.261E+001 cm
0.218378 cm/hr
0.004834 cm/hr
0.440957 cm
0.004834 cm
0.4163 cm
0.3965
0.4361
cm
cm
1.2189E+002 micrograms/cm2
1.221 1E+002 micrograms/cm2
1.2167E+002 micrograms/cm2
O.OOOOE+000 micrograms/cmVhr
4.8344E-002 micrograms/cm2/hr
O.OOOOE+000 microgram/cm2
4.8344E-002 microgram/cm2
1.7499E-001 microgram/cm2
3.9832E-001 microgram/cm2
-4.8344E-002 microgram/cm2
in depth = l.OOOOOOe+000; Mesh size in time = l.OOOOOOe-002
Water_Content
cc/cc
0.495
0.494
0.487
0.474
0.457
0.439
0.423
0.413
0.408
0.407
0.406
0.406
0.406
0.406
0.406
0.406
0.406
0.406
0.406
0.406
0.406
0.406
0.406
0.406
0.406
0.406
0.406
0.406
0.406
0.406
0.406
Flux_Water
cm/hr
0.218378
0.219352
0.211011
0.189563
0.152125
0.104680
0.061965
0.032879
0.016707
0.009257
0.006324
0.005297
0.004968
0.004871
0.004844
0.004837
0.004835
0.004834
0.004834
0.004834
0.004834
0.004834
0.004834
0.004834
0.004834
0.004834
0.004834
0.004834
0.004834
0.004834
0.004834
Concentration
microgram/cm3
4.906
7.193
8.758
9.554
9.838
9.925
9.981
10.011
10.012
10.006
10.002
10.001
10.000
10.000
10.000
10.000
10.000
10.000
10.000
10.000
10.000
10.000
10.000
10.000
10.000
10.000
10.000
10.000
10.000
10.000
10.000
Flux_Chem
microg/cnf/hr
O.OOOOE+000
7.2161E-001
1.3436E+000
1.6038E+000
1.4393E+000
1.0237E+000
6.1307E-001
3.2809E-001
1.6735E-001
9.2726E-002
6.3297E-002
5.2989E-002
4.9690E-002
4.8710E-002
4.8438E-002
4.8367E-002
4.8349E-002
4.8345E-002
4.8344E-002
4.8344E-002
4.8344E-002
4.8344E-002
4.8344E-002
4.8344E-002
4.8344E-002
4.8344E-002
4.8344E-002
4.8344E-002
4.8344E-002
4.8344E-002
4.8344E-002
67
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Table 3. Continued.
Time: 8.0000 hr
Mass Balance Check: Amount
Water
Chemical
from water content or cone.
from surface fluxes
Total Amount in soil:
from water content or cone.
from surface fluxes
Flux at Upper Surface :
Flux at Lower Surface :
Cum. Flux at Upper Surface :
Cum. Flux at Lower Surface :
Net Accumulation:
from water content or cone.
from surface fluxes
4.398E-002 cm
4.401E-002cm
1.342E+001 cm
1.340E+001 cm
1.344E+001 cm
0.092186 cm/hr
0.005269 cm/hr
1.308252cm
0.039075 cm
1.2470 cm
1.2248 cm
1.2692 cm
-2.5921E-002 micrograms/cm2
-2.600 1E-002 micrograms/cm2
1.2155E+002 micrograms/cm2
1.2177E+002 micrograms/cm2
1.2132E+002 micrograms/cm2
O.OOOOE+000 micrograms/cnrVhr
5.2694E-002 micrograms/cmVhr
O.OOOOE+000 microgram/cm2
3.9076E-001 microgram/cm2
-1.6754E-001 microgram/cm2
5.5900E-002 microgram/cm2
-3.9098E-001 microgram/cm2
Mesh size in depth = 1 .OOOOOOe+000; Mesh size in time = 1 .OOOOOOe-00 1
Distance Water_Content
cm cc/cc
0.000 0.495
1.000 0.495
2.000 0.495
3.000 0.495
4.000 0.494
5.000 0.492
6.000 0.490
7.000 0.486
8.000 0.483
9.000 0.478
10.000 0.474
11.000 0.468
12.000 0.462
13.000 0.455
14.000 0.448
15.000 0.441
16.000 0.435
17.000 0.429
18.000 0.423
19.000 0.419
20.000 0.415
21.000 0.412
22.000 0.410
23.000 0.409
Flux Water Concentration
cm/hr microgram/cm3
0.092186 2.482
0.092438 3.747
0.092524 5.086
0.092470 6.367
0.092225 7.482
0.091645 8.370
0.090637 9.018
0.089117 9.453
0.087000 9.720
0.084194 9.871
0.080609 9.950
0.076169 9.988
0.070836 10.003
0.064643 10.008
0.057725 10.007
0.050334 10.004
0.042819 10.002
0.035572 10.000
0.028947 9.999
0.023192 10.000
0.018426 10.000
0.014643 10.000
0.011751 10.001
0.009612 10.001
Flux Chem
microg/cnf/hr
O.OOOOE+000
9.8172E-002
2.2052E-001
3.6017E-001
4.9954E-001
6.2196E-001
7.1627E-001
7.7796E-001
8.0813E-001
8.1117E-001
7.9243E-001
7.5659E-001
7.0713E-001
6.4670E-001
5.7788E-001
5.0384E-001
4.2845E-001
3.5579E-001
2.8946E-001
2.3190E-001
1.8425E-001
1.4643E-001
1.1752E-001
9.6125E-002
68
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Table 3. Continued.
Distance Water_Content Flux_Water Concentration Flux_Chem
cm cc/cc cm/hr microgram/cm3 microg/cnf/hr
24.000 0.408 0.008075 10.000 8.0753E-002
25.000 0.407 0.006999 10.000 6.9996E-002
26.000 0.406 0.006267 10.000 6.2671E-002
27.000 0.406 0.005784 10.000 5.7846E-002
28.000 0.406 0.005484 10.000 5.4842E-002
29.000 0.406 0.005320 10.000 5.3196E-002
30.000 0.406 0.005269 10.001 5.2694E-002
69
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Illustration: Non-uniform Initial Conditions
Non-Uniform Initial Conditions: The examples shown in this manual up to this point deal
with problems having uniform initial conditions. This example will illustrate the simulation into
soils with non-uniform initial conditions. The problem is that of a Cobb sandy clay which
contains a known distribution of the chemical aldicarb. The soil is irrigated at 1 cm/hr for 8
hours. Then the surface is covered so no water movement occurs at the soil surface. If the
partition coefficient for aldicarb in this soil is 0.1 cc/g soil and the half-life is 28 days, what will
be the distribution of aldicarb after irrigation and then after 1 week?
Figures 43, 44, and 45 show the screens used to define the problem. These are similar to
the previous examples with the exception of the presence of an editor here for entering tables of
matric potential and concentration as functions of depth. The software uses the values entered to
define the matric potential and concentration at the mesh points used in the problem. Linear
interpolation is used to estimate values for mesh points between depths entered. The value
entered at the minimum depth is used for all mesh point spreceding that depth. The value for the
greatest depth entered is used for all mesh points exceeding that depth.
Initial water content, matric potential, and water content distributions are shown in
Figures 46 and 47. These distributions after irrigation are shown in Figure 48. Final distributions
of water content and concentration are shown in Figure 49.
70
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Definition of Soil System (SCR: 1/5)-
Name of the soil : COBB SANDY CLAY
Orientation of flow system : 0.0
Finite or Semi-infinite soil system (F or S).: F
Length of soil system (cm) : 100.00
Fl-Help; ESC-Abort; FlO-End editing; PgUp-Prev screen; PgDn-Next screen;
F8-Save input parameters in file; F9-Read input parameters from file;
Definition of Water System (SCR:2/5)»
Boundary condition for water at the UPPER surface (P,F,R,M): R
Desired rainfall rate (cm/hr) at the UPPER surface : 1.00
Boundary condition for water at the LOWER surface (P,F,M)..: P
Desired matric potential (cm) at the LOWER surface : -100.00
That matric potential corresponds to water content(cc/cc)..: 0.197
Uniform initial matric potential throughout the soil (Y/N).: N
Depth (cm) Matric Potential
0.0 -10000
5.0 -2000
20.0 -500
50.0 -100
Fl-Help; ESC-Abort; FlO-End editing; PgUp-Prev screen; PgDn-Next screen;
F8-Save input parameters in file; F9-Read input parameters from file;
Figure 43. Definition of soil and water parameters for non-uniform initial conditions
71
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Definition of Chemical System (SCR:3/5)~
Boundary condition for chemical at the UPPER surface (I,S).: I
Desired concentration of the inflowing solution (|ig/cc) ...: 0.00
Boundary condition for chemical at the LOWER surface (M,S).: M
Uniform chemical concentration throughout the soil (Y/N)...: N
Depth (cm) Concentration
5.0 20
10.0 100
20.0 5
30.0 0
Fl-Help; ESC-Abort; FlO-End editing; PgUp-Prev screen; PgDn-Next screen;
F8-Save input parameters in file; F9-Read input parameters from file;
Soil and Chemical Parameters (SCR:4/5)~
Soil bulk density (g/cc) : 1.4000
Water: Soil partition coefficient (cc/g soil) : 0.1000
Diffusion coefficient of chemical in water (cm2/hr).: 3.00E-002
Dispersivity (cm) : 2.00E+000
First-order degradation constant, liquid (1/hr) : 1.03E-003
First-order degradation constant, solid (1/hr) : 1.03E+003
Zero-order rate constant, liquid (|ig/cc/hr) : O.OOE+000
Fl-Help; ESC-Abort; FlO-End editing; PgUp-Prev screen; PgDn-Next screen;
F8-Save input parameters in file; F9-Read input parameters from file;
Figure 44. Definition of chemical parameters for soil with non-uniform initial conditions.
72
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Simulation Parameters (SCR: 5/5)—
Maximum time to be simulated (hr) : 8.0
Mesh size in depth (cm) : 1.000
Mesh size in time (hr) : 0.0050
Period between graphic or tabular outputs (hr)..: 0.500
Output file name : ALDICARB
Fl-Help; ESC-Abort; FlO-End editing; PgUp-Prev screen; PgDn-Next screen;
F8-Save input parameters in file; F9-Read input parameters from file;
Figure 45. Definition of parameters for aldicarb simulation.
Figure 46. Water content and matric potential as functions of depth at time zero
Figure 47. Water content and concentration as functions of depth at time zero.
Figure 48. Water content and concentration as functions of depth at the end of irrigation.
Figure 49. Water content and concentration as functions of depth after 1 week.
73
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Illustration: Continue Simulation Option
Simulation of One-Dimensional Water and Chemical Movement in Soils
Main Menu
W. Define Water Movement Problem and Solve it
S. Define Water and Solute Movement Problem and Solve it
C. Continue Simulation of Problem Stored on Disk
E. Enter, Modify, or Print Soil Parameters
Q. Quit. Stop Execution of Program
Desired Option? C
Figure 50. Selecting option C in the main menu to continuesimulation
OPTION C: CONTINUE SIMULATION OF PROBLEM STORED ON DISK This
option enables you to continue simulation of a problem defined at a previous time.Once you have
proceeded through the definition of the problem to the stage of defining output tables and graphs,
the problem definition and calculated solution are saved on disk using the file name specified on
the screen for Simulation Parameters (Figure 7 or 36). This definition file can be used at a later
date.
After selecting option C, you are prompted for the disk file name. Once that has been
entered, you are prompted to select the output graphs and tables desired. The computer then
proceeds to simulate water and chemical movement from the time at which the calculation was
terminated previously. For example, if you want to simulate movement for 120 hr. and have time
to complete only 40 hr. at one session, the solution can be continued at a later date. This option
can also be used to review data or print tables for a solution computed at an earlier session.
74
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Enter, Modify, or Print Soil Parameters
Simulation of One-Dimensional Water and Chemical Movement in Soils
Main Menu
W. Define Water Movement Problem and Solve it
S. Define Water and Solute Movement Problem and Solve it
C. Continue Simulation of Problem Stored on Disk
E. Enter, Modify, or Print Soil Parameters
Q. Quit. Stop Execution of Program
Desired Option? E_
Figure 51. Selecting option E in the main menu to enter, modify, or print values of the
hydraulic properties of soils.
ENTER. MODIFY. OR PRINT SOIL PARAMETERS: Before water or chemical
movement can be simulated using this software, the hydraulic properties of the soil must be
defined and stored in a disk file. This option enables you to enter this data to define a new soil, to
modify properties of an existing soil, and to display the properties of soils already in the file on a
printer or screen.
Before simulation of water or chemical movement is possible, the water content and
hydraulic conductivity must be specified as functions of matric potential. Tables 4 and 5 list the
mathematical forms of the functions which may be used for water content and conductivity
functions, respectively. You must choose appropriate functions which describe the experimental
data. Once the functional form is selected and the parameter values have been determined,enter
these values as shown in Figure 52. A description of each entry on thescreen follows the figure.
After the data have been entered correctly, press the key to save the data in the file and to
return to the main menu.
75
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Table 4. Water content functions supported by the software.
Identifier Equation
A.
6(*) - 6(n«) . a
Q(h) = 0(s)
(Brutsaert, 1966)
° ~
a + \h\*
for h < 0
for h > 0
B.
(In
0(/z) = 6(s)
(Haverkamp et al, 1977)
for h < -1
for h ^ -1
for h < 0
0(A) = 00) for h > 0
where m - 1 - lib (van Genuchten, 1980)
0(A) = 0(res) + [0(5) - 0(res)] • [a/A]* for h < a
0(A) = 0(5) for h ^ 0
(Brooks and Corey, 1964)
6(h) water content at matric potential h;
6(s) saturated water content;
6(res) residual water content;
76
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Table 5. Hydraulic conductivity functions supported by software.
Identifier Equation
K(h) = K(sat) • for h < 0
A. a + \h\"
K(h) = K(sat) for h > 0
(Haverkamp, 1977)
K(h) - a • exp(b'e(h))
where 6(h) is the water
content of the soil
c.
[1+ (a|A|)"J""
for h < 0
K(h) = K(sat)
for h > 0
where m = 1- lib (van Genuchten, 1980)
K(h) = K(sat)
for A < 0
= K(sat)
where 6(/z) is the water
content of the soil
K(/z) hydraulic conductivity of soil at matric potential h
K(sat) saturated hydraulic conductivity
77
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Parameters Required to Define a Soil (1/4 )
Soil Name : YOLO CLAY
Water Content Function (A, B, C, D) . : B
Conductivity Function (A, B, C, D, E) : A
Saturated Water Content, 8(s), cc/cc. : 0.4950
Residual Water Content, 6(res), cc/cc : 0.1240
Water Content Parameter a : 7.3900E+002
Water Content Parameter b : 4.0000
Saturated Conductivity, K(sat), cm/hr : 4.4280E-002
Conductivity Parameter a : 1.2460E+002
Conductivity Parameter b : 1.7700
Suggested Minimum Potential, cm : -10000.0
Suggested Maximum Potential, cm : 100.0
Suggested Minimum Flux, cm/hr : 0.0000
Suggested Maximum Flux, cm/hr : 1.0000
Suggested Minimum Rainfall Rate,cm/hr : 0.0000
Suggested Maximum Rainfall Rate, cm/hr : 1.0000
Fl-Help; PgDn-Next record; F4-Delete record;
ESC-Abort; PgUp-Previous record; FlO-End editing and save;
Figure 52. Screen used to enter or modify soil hydraulic data.
Parameters required to define a soil include the following:
1. Soil Name: This is an identifier for the soil. It may be up to 35 characters long.
Any printable characters may be included.
2. Water Content Function: This letter identifies the functional form of the water
content function as listed in Table 4.
3. Conductivity Function: This letter identifies the functional form of the
conductivity function as listed in Table 5.
78
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4. Saturated Water Content, 6(s): This is the water content of the soil when all the
pores are filled with water. It must be expressed on a fractional volume basis.
5. Residual Water Content, 6(res): This is limiting value of the water content of the
soil as the matric potential becomes more and more negative.
6. Water Content Parameter a: Each water content equation shown in Table 4
includes parameter a. This is the value of that parameter for the equation selected.
7. Water Content Parameter b: Each water content equation shown in Table 4
includes parameter b. This is the value of that parameter for the equation selected.
8. Saturated Conductivity, K(sat): This is the hydraulic conductivity of the water
saturated soil, expressed in units of cm/hr.
9. Conductivity Parameter a: This is the value of parameter 'a' if it is used in the
conductivity equation selected (Table 5).
10. Conductivity Parameter B: Each conductivity equation shown in Table 5 includes
parameter b. This is the value of that parameter for the equation selected.
11. Suggested limits for potential, flux, and rainfall rates: These values define ranges
of the parameters which are considered reasonable or are well-behaved. They are
displayed as recommended ranges when the "Help" key is pressed when a problem
is being defined. The user is not restricted to entering values within these limits.
After entering these values, you may press the key to define another soil. When
all data entry and modification has been completed, exit the option using the key to save
the information in a file. If the key is pressed the data edited are not stored in the disk file.
79
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Numerical Experiments For Water Movement
1. Infiltration of Water Ponded on the Soil Surface
Objective: To determine the nature of the dynamic infiltration process for water ponded on
the soil surface. To compare the infiltration rate at different times with the
saturated hydraulic conductivity of the soil.
Situation: Water is applied to a Yolo clay soil by flooding the soil to a depth of 2 cm. Water
is continually applied to the soil surface to maintain this height of water. The soil
was somewhat dry throughout before the water was applied. We want to observe
the rate at which water enters the soil and the total amount entering the soil.
Simulation: Simulate water movement into a vertical semi-infinite Yolo soil with an initial
matric potential of-2000 cm. Apply water to the soil at a constant potential of 2
cm. Simulate movement for 12 hours. Display the flux of water at the soil surface
and the cumulative infiltration of water as functions of time.
1. What was the infiltration rate or the flux of water at the soil surface
at 1, 2, 4, 6, 8, 10, and 12 hours? Was the infiltration rate
increasing or decreasing?
2. Look at the data for the Yolo soil in the soil data file. What is the
saturated conductivity for the Yolo clay used in this simulation?
Compare the infiltration rates observed above with the saturated
conductivity. Which is larger? Why? What infiltration rate would
you expect if the wetting process continued for 2 days? Why?
3. How much water entered the soil profile in the first hour? How
much in 2, 4, 6, 8, 10, an 12 hours?
Additional Work:
Repeat the above exercises for different soils. Compare the infiltration
rates and the saturated hydraulic conductivities. Are the results consistent
with those above?
-------
2. Infiltration of Water From Rainfall or Sprinkler Irrigation
Objective: To determine the nature of the dynamic infiltration process for rainfall or sprinkler
irrigation. To compare the infiltration rate at different times with the saturated
hydraulic conductivity of the soil. To determine the total amount of infiltration,
the total amount of runoff, and the time at which runoff occurs.
Situation: A farmer recently irrigated his field so that the soil was relatively wet.
Unexpectedly, a rainstorm occurred. The storm lasted for 6 hours. The rainfall rate
was 0.6 cm/hr. The field was a Cobb sandy clay soil. How much of the rain water
entered the soil? Did any runoff occur? If so, how much? When did runoff begin?
Simulation: Simulate water movement into a vertical semi-infinite Cobb sandy clay soil with
an initial matric potential of-100 cm. Apply water to the soil at a rainfall rate of
0.6 cm/hr. Simulate movement for 6 hours. Display the flux of water at the soil
surface and the cumulative infiltration of water as functions of time.
1. Describe the curve for the infiltration rate as a function of time. It
is initially constant. What is the value of the infiltration rate during
this constant phase? Compare this rate to the rainfall rate.
2. Eventually the infiltration rate decreases with time. At this time the
soil is no longer able to transport water from its surface as fast as it
is applied. This is the beginning of the runoff phase. At what time
does runoff begin?
3. How much water entered the soil surface by the end of the 6 hour
period? How much water was applied as rainfall during this
period? How much runoff occurred? (The amount of runoff is the
difference between the amount applied and the amount entering the
soil. This calculation assumes that there is no surface storage of
water.)
4. Compare the rainfall rate to the saturated hydraulic conductivity
for the soil. Compare the final infiltration rate to the saturated
conductivity of the soil.
81
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3. Water Content and Matric Potential Distributions During Infiltration
Objective: To observe water content and matric potential distributions during infiltration by
means of graphs of water content and matric potential as functions of time at
selected locations as well as water content and matric potential profiles at selected
times. To compare the distributions for infiltration due to ponding with those due
to infiltration of rainfall.
Situation: The settings are similar to those described in the preceding exercises. However, in
this case there is an interest in the behavior of the water within the soil profile, not
just the rate at which it enters the soil.
Simulation: Simulate water movement into a vertical, semi-infinite Yolo soil with an initial
matric potential of-2000 cm. Apply water to the soil at a constant potential of 2
cm for 12 hours as done in exercise 1. Repeat the simulation for the same soil
with the same initial condition but with water applied as rainfall at an intensity of
0.5 cm/hr.
1. On one screen,display graphs of water content versus depth and
matric potential versus depth.These graphs can be viewed as "snap
shots" of the water content and matric potential at an instant in
time.
a. Locate the line on each graph representing the water
content and matric potential at time zero. It should be a
vertical line since the matric potential and water content are
constant initially.
b. Observe each new line added to the graphs as time
increases. Note that the soil water content and matric
potential change only to a certain depth. Below that depth,
the parameters retain their initial value. This indicates that
water movement has not penetrated to that depth at the time
indicated. Record the depth of wetting for each hour. Does
the wetting depth increase uniformly with time or does it
appear to slow down? Why?
c. Observe the water content at the soil surface (distance = 0).
What is its value? Does the value change with time when
the water is applied by ponding? Does it change when
water is applied as rainfall?
82
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d. Compare the shape of the water content profiles with those
of the matric potential profiles. Remember that these
curves are related to each other by means of the water
release or water characteristic curve.
2. On a second screen display graphs of water content versus time at
depths of 0, 5, and 10 cm. These curves illustrate the way the
water content changes with time at each location.
a. Observe the curves for the three depths. What similarities
and differences do you observe?
b. In general, the water content at a specific location remains
at its initial value until water reaches that depth. It then
increases. At what time does the water content begin to
increase at 0, 5, and 10 cm? Does it take longer for the
water to move from 5 cm to 10 cm than it took for water to
move from 0 to 5 cm?
c. Compare the slope of the water content vs. time graphs for
the three depths. Which depth changes most rapidly?
Which changes least rapidly?
d. Compare the times at which water content changes occur
and the slopes of the curves for water applied by ponding
with those values for water applied as rainfall. What
differences do you observe? Why?
Additional Work: Determine the time at which runoff began for the simulation with water
applied as rainfall. What was the value of the water content at a depth of
zero at that time? What was the value of the matric potential at that time?
Formulate an hypothesis about the relationship between these parameters
and test that hypothesis.
83
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4. Comparison of Horizontal and Vertical Water Movement in Unsaturated Soils
Objective: To compare the water movement in horizontal and vertical soil systems. To assess
the significance of the force of gravity in unsaturated water movement.
Situation: Water is applied to a Yolo clay soil by means of furrow irrigation.The field was
irrigated for 10 hours. The farmer noticed that the soil surface between the
furrows became wet rather quickly. The farmer wanted to compare the distance
the water moved horizontally with the distance it moved vertically downward.
Simulation: Simulate water movement into a vertical semi-infinite soil with an initial matric
potential of -2000 cm. Apply water to the soil at a constant potential of 1 cm.
Simulate movement for 8 hours. Observe the depth of water movement each hour
using graphs of water content vs. distance. Also observe the flux of water at the
soil surface and the cumulative infiltration of water as functions of time. Repeat
the simulation for a horizontal soil with the same initial and boundary conditions.
Compare the results
1. How far did the water move in each direction? (Choose a water
content in the middle of the range and determine the depth to
which that water content penetrated.)
2. Compare the flux of water at the soil surface (the infiltration rate)
for the two cases.
3. Compare the cumulative infiltration in both cases.
4. Compare the driving forces for the two systems.
5. Why does water move horizontally nearly as fast as vertically?
Additional Work:
Repeat the above exercises for soils which are initially wetter. For
example, choose initial matric potentials of-100 and -50 cm and repeat the
experiments. Are the results consistent with those above?
Repeat the simulations for a course sand and compare your results to those
of the clay soil.
These simulations compare vertically downward with horizontal water
movement. You might want to simulate water movement and compare
results for selected cases of upward flow (against the force of gravity).
You can do this by selecting an orientation of 180 degrees.
84
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5. Redistribution of Soil Water following Infiltration
Objective: To observe movement of water within a soil profile after infiltration has taken
place but in the absence of evaporation.
Situation: A scientist flooded a plot of Cobb sandy clay to a depth of 5 cm for 6 hours. At
that time, the water was drained from the soil surface and the surface was covered
with plastic and insulated to prevent evaporation. If the soil had an initial matric
potential of -1000 cm at all depths, what will be the distribution of water at the
time infiltration stopped? How will this distribution of water change during the
next 5 days while the plot is covered?
Simulation: Simulate water infiltration into a vertical semi-infinite Cobb soil with an initial
matric potential of-1000 cm. Water was applied by flooding the soil surface to a
depth of 5 cm for 6 hours. At that time, the surface was covered so no infiltration
or evaporation took place. This is simulated by specifying a flux of zero at the soil
surface. This zero flux boundary condition should continue until the simulated
time reaches 120 hours. (Note: During the redistribution, you might want to store
results in the disk file only every hour.) Using graphs of water content profiles,
matric potential profiles, and water content vs. time, answer the following
questions:
1. Describe the water content profiles during the redistribution
process. In what ways do they differ from profiles observed during
infiltration?
2. What was the depth of wetting when infiltration stopped? What
was the depth of wetting at 12, 24, 48, 72, 96, and 120 hours?
3. What changes in water content and matric potential occurred in the
soil near the surface?
4. Does movement continue beyond 2 days? When will movement
stop?
5. Why does the rate of water movement decrease as redistribution
time increases?
Additional Work
Conduct additional experiments to determine if the observations made
above can be generalized for other soils, wetting times, and initial
conditions.
85
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6. Redistribution and Evaporation of Soil Water following Infiltration
Objective: To observe the simultaneous downward redistribution and upward evaporation of
water within a soil profile after infiltration.
Situation: A field of Cobb sandy clay was flooded to a depth of 5 cm for 6 hours. At that
time, the water was drained from the soil surface. If the soil had an initial matric
potential of -1000 cm at all depths, what was the distribution of water at the time
infiltration stopped? How will this distribution of water change during the next 5
days.
Simulation: Simulate water infiltration into a vertical semi-infinite Cobb soil with an initial
matric potential of-1000 cm. Water is applied by flooding the soil surface to a
depth of 5 cm for 6 hours. At that time, evaporation and redistribution will take
place. The potential evaporation rate is 0.05 cm/hr. This is simulated by
specifying a mixed type boundary condition in which the flux is -0.05 cm/hr until
the soil surface reaches a matric potential of-5000 cm. At times greater than this,
the matric potential is maintained at this potential. This mixed type boundary
condition should continue until 120 hrs. have been simulated. (Note: During the
redistribution, you might want to store results in the disk file only every hour.)
Using graphs of water content profiles, matric potential profiles, and water content
vs. time, answer the following questions:
1. Describe the water content profiles during the evaporation and
redistribution process. In what ways do they differ from profiles
observed during infiltration? How does the evaporation process
change the curves?
2. What was the depth of wetting when infiltration stopped? What
was the depth of wetting at 12, 24, 48, 72, 96, and 120 hours?
3. What changes in water content and matric potential occurred in the
soil near the surface?
4. What is the evaporation rate from the soil surface? Does it change
with time? Explain. (The evaporation rate is the flux of water at a
depth of zero. This number will be negative since it is upward, out
of the soil.)
5. What is the total amount of water lost to evaporation during the
120 hours?
6. Why does the rate of water movement decrease as time increases?
86
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Additional Work Design and carry out additional experiments to determine the influence of
the initial evaporation rate upon the duration of the "constant rate" phase
of the evaporation process and upon the total amount of water lost to
evaporation during the 120 hour period.
Conduct additional experiments to determine if the observations made
above can be generalized for other soils, wetting times, and initial
conditions.
87
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7. Influence of Rainfall Rate upon Infiltration and Depth Wetting
Objective: To determine the influence of rainfall rate upon the infiltration rate, time to
runoff, and depth of wetting.
Situation: A farmer has the option of applying water by sprinkler irrigation at different rates.
He would like to know if the rate of application affects the way the soil wets and
the amount of water entering the soil. He wants to try irrigating the Cobb sandy
clay at 0.25, 0.5,1.0, and 2.0 cm/hr. In each case he will apply 4 cm of water. The
soil before irrigation has a matric potential of-1000 cm.
Simulation: Simulate water infiltration into the vertical Cobb soil for rainfall rates of 0.25
cm/hr for 16 hr. Observe the infiltration rate, depth of wetting, and total
infiltration. Calculate the amount of runoff, if any. Repeat the simulation for a
rainfall rate of 0.5 cm/hr for 8 hr,1.0 cm/hr for 4 hr, and 2 cm/hr for 2 hr. Answer
the following questions:
1. What was the total amount of water entering the soil at each rate?
2.
What was the amount of runoff?
Additional Work:
3. Did the rainfall rate affect the form of the wetting process and the
depth of wetting in the soil? If so, how?
4. Should the farmer be concerned about the rate of irrigation? Why?
Allow water to redistribute from the end of the irrigation until the time
equals 16 hrs. Now compare the shapes of the water content profiles and
the depth of wetting.
Repeat the experiment for other soils.
88
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8. Influence of Initial Water Content upon Water Movement
Objective: To observe the influence of initial soil wetness upon infiltration, runoff, and depth
of wetting for a fixed rainfall rate.
Situation: A person wanting to assess the runoff potential of a certain field, applied water to
it by sprinkling at an intensity of 1 cm/hr for 8 hours. Runoff began at 6 hours. He
concluded that runoff would not occur unless storms exceeded 6 hr in duration.
Another person stated that the time to runoff would depend upon the initial
wetness of the soil. You have been asked to simulate infiltration for different
initial water contents to inform them of the importance of initial water content
upon wetting. Since they are asking for your services, they also want comparisons
of the total amount infiltrating the soil in 8 hours and the depth of wetting.
Simulation Simulate water movement into 4 vertical columns of Cobb sandy clay with initial
matric potentials of-5000 cm, -1000 cm, -100 cm, and -20 cm., respectively.
Apply water at a rate of 1.5 cm/hr for 8 hr. Use graphs of water content profiles,
infiltration rates, and cumulative infiltration to answer the questions.
1. Compare the infiltration rates each hour for the different soil
systems. How does the infiltration rate depend upon the initial soil
wetness? Explain why this change occurs.
2. Compare the cumulative infiltration amounts during the entire
application.
3. Does the time to the beginning of runoff depend upon the initial
soil wetness? How much does it change for these soils?
4. Compare the final infiltration rates for the different initial
conditions. How do they compare with the saturated hydraulic
conductivity of the soil?
5. What is the depth of wetting for each case? Do the water content
profiles change?
6. Does the time to runoff depend upon the initial wetness? Does this
answer depend upon the soil? Does it depend upon the rainfall
rate? Explain your answer.
89
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9. Steady-State Water Movement in Finite Unsaturated Soils
Objective To determine the rate of water movement through an unsaturated soil when the
system is at steady state. To determine the distribution of matric potential, water
content, driving force, conductivity, and flux throughout the soil system. Note:
The soil is said to be at steady-state when water properties of the soil do not
change with time. That is, at steady-state, thematric potential, water content,
driving force, conductivity, and flux at a particular location do not change with
time.
Situation: A bare Cobb soil has a water table at 50 cm. It has not rained for a long time, but
water is evaporating from the surface. The surface has become air-dry with a
matric potential of-20000 cm. What is the steady-state rate of water movement
through the soil?
Simulation Simulate water movement into a 50-cm vertical Cobb sandy clay. The boundary
condition at the top should be a constant matric potential of-20000 cm. The
boundary condition at the water table is a constant potential of zero. Using the
option for non-uniform initial conditions, enter a series of matric potentials which
you think will be close to the distribution at steady-state. Simulate movement for
200 hours. Observe graphs of water content and matric potential vs. distance as
well as other parameters of interest. You may want to print tables of the calculated
quantities, also. Continue the simulation until the parameters are the same for
several hours. Then answer the following questions:
1. What is the flux of water at the top of the soil? What is the flux at
the bottom? How does it vary through the soil?
2. Describe the final matric potential and water content distributions
in the soil. Are they what you expected?
3. Describe the hydraulic conductivity and driving force distributions.
Why does the hydraulic conductivity increase with depth?
4. Why does the matric potential change slowly near the water table
and then more rapidly near the top?
Additional Work: It is possible to have an unsaturated soil at steady state with a uniform
water content throughout and a non-zero flux. What will be the orientation
and boundary conditions of such a soil?
90
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Numerical Experiments For Water and Chemical Movement
1. Chemical Movement during Infiltration Due to Rainfall
Objective: To observe the movement of a chemical applied with irrigation water.
Situation: A farmer decided to apply nitrate nitrogen to his field with his irrigation water. He
irrigated for 6 hours at 1 cm/hr with a solution of 20|ig/cm3 nitrate. The soil
contained no nitrate nitrogen before irrigation. What will be the distribution of the
chemical immediately after irrigation?
Simulation: Simulate movement into a Cobb sandy clay soil with an initial matric potential of
-500 cm and a length of 50 cm. The lower boundary condition for water is a
constant potential of-500 cm. The upper boundary condition is a constant rainfall
rate of 1 cm/hr. The upper boundary condition for chemical is that the inflowing
solution has a concentration of 20|ig/cm3. The chemical leaves the bottom by
mass flow only. The Cobb soil has a bulk density of 1.4 g/cm3. The partition
coefficient, degradationrate constants, and zero-order rate constants are all zero.
Simulate movement for 6 hours. Then consider the following questions:
1. Compare the shape of the water content vs. distance graph with the
concentration vs.depth. What similarities do you observe? What
are the differences? Does one seem to be ahead of the other?
Additional Work:
2. Compare graphs of the flux of chemical at selected depths with the
flux of water at those depths.
Imagine that an unexpected storm came up after the irrigation. During the
12 hour storm, rain fell at a rate of .5 cm/hr. The concentration of the
chemical in the rainfall was zero.
1. What was the distribution of chemical after the rain storm.
Compare the water content and concentration distributions.
2.
How far has the chemical moved into the soil?
91
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2. Influence of Initial Soil Wetness upon Depth of Chemical Movement
Objective: To determine the influence of the initial water content of a soilupon the depth of
movement of surface applied chemicals.
Situation: An alert environmental consultant recognizes the importance of initial soil water
content upon the depth of wetting. He is now concerned about the depth of
penetration of a chemical applied with the infiltrating water.
Simulation: A column of Cobb soil, 50 cm long, is oriented vertically. Water is applied at the
top at a constant potential of 1 cm. Make a series of simulations for initial matric
potential values of-1000, -500, -100, and -50 cm. In each case, the potential at the
lower boundary should be the same as the initial matric potential. The
concentration of the inflowing solution should is 10 jig/cm3. The chemical leaves
the lower surface by mass flow only. The partition coefficient and rate constants
are zero. Simulate movement until the water content at 40 cm begins to change.
Discuss the following using graphs of water content vs. distance and
concentration vs. distance.
1. Construct a table showing the depth which has a concentration of
5|ig/cm3 at times when the wetting front is at 10, 20, and 30 cm.
Initial Matric Potential(cm)
-1000 -500 -100 -50
Initial Water Content
Depth of Chemical for:
Wet front of 10cm
Wet front of 20 cm
Wet front of 3 Ocm
Additional Work:
2. Discuss the influence of the initial water content of the soil upon
the depth of penetration of the chemical? What explanation can
you give for this behavior?
Repeat the experiment for other soils. Are the depths of penetration similar
to those for Cobb? Can you make the same conclusions there that you
made for Cobb?
92
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3. Influence of Adsorption on Chemical Movement
Objective: To determine the impact of different amounts of adsorption of chemicals upon the
movement during infiltration.
Situation: The farmer described in exercise 1 is considering applying other chemicals to his
soil. These soils are adsorbed on the soil solids. How will this affect the
movement of the chemicals?
Simulation: Define the flow problem as in the case of exercise 1 with one exception. In this
case, specify a partition coefficient of 0.5 cc/g for one experiment and 5 cc/g for a
second experiment.
1. Compare the shape of the water content vs. distance graph with the
concentration vs.depth. What similarities do you observe? What
are the differences? Does one seem to be ahead of the other?
2. Compare the graphs of concentration vs. time at the soil surface for
the different partition coefficients with those for a partition
coefficient of zero. Explain the differences.
93
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4. Chemical Movement Without Water Movement
Objective: To observe the movement of a chemical due to diffusion only.
Situation: A Yolo soil has a uniform water content of 0.4 cm3/cm3. The soil is sealed and
oriented horizontally so no water movement occurs. A concentration of 100
jig/cm3 of a chemical is maintained at one end. How will the chemical move in
this soil?
Simulation: Simulate water and chemical movement into a horizontal Yolo clay with an initial
water content of 0.40 cm3/cm3 and a length of 20 cm.The initial concentration of
chemical is zero throughout. The concentration in the soil solution at one end is
zero and at the other end is 100 jig/cm3. The water content at each end of the soil
is maintained at 0.40 cm3/cm3. The partition coefficient and rate constants are
zero. The diffusion coefficient is 10 cm2/hr. Simulate movement for 16 hours.
1. Describe the concentration profile after 1, 2, 4, 8, and 16 hrs.
How are the concentration profiles similar to the profiles in
exercise 1? How do they differ?
2. What similarities and differences do you see between the
concentration and water content profiles found in the water
movement exercises?
Additional Work:
Repeat the above exercise with diffusion coefficients of 2 and 50 cm2/hr.
What impact does this have on the shape and position of the curves?
94
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5. Degradation and Production of Chemicals
Objective: To observe the effect of first order and zero order terms upon the concentration of
chemical in the soil.
Simulation: Define the soil system to be 20 cm long and oriented horizontally. The initial
matric potential should be -10 cm. A constant potential of-10 cm is imposed at
each end of the soil. The initial concentration of chemical in the system is 100
jig/cm3. The inflowing solution has a concentration of 0. Outflow is by mass flow
only. The partition coefficient is zero.
1. Will water move in this soil system? If so, in what direction?
Explain your answer.
2. Simulate movement as needed to complete the table below.
3. The degradation process is considered a "first-order" process. What
differences do you observe in the manner in which the
concentration changes for this process when compared with a
zero-order process?
4. The last column in the table represents a system in which the
chemical is degrading by a first-order process and being is
produced by a zero-order process. What impact does the
production have on the shape of the curves? What will be the
concentration at 100 hr? 1000 hr? Explain.
Data Table:
Experiment
#1 #2 #3 #4
Degradation Rate, liquid(l/hr) 0.1386 0.0693 0.0 0.0693
Degradation Rate, solid(l/hr) 0.1386 0.0693 0.0 0.0693
Zero-order Rate Const(|ig/cc/hr) 0.0 0.0 -4.0 5.0
Concentration at 1 hr
Concentration at 2 hr
Concentration at 3 hr
Concentration at 4 hr
Concentration at 5 hr
Concentration at 10 hr
Concentration at 15 hr
Concentration at 20 hr
95
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REFERENCES CITED
1. Brooks, R.H., and A.T. Corey. 1964. Hydraulic properties of porous media. Hydrology
Paper No. 3. Colorado State University, Fort Collins, Colorado. 27 pp.
2. Brutsaert, W. 1966. Probability laws for pore-size distributions. Soil Science 101:85-92.
3. Haverkamp, R., M. Vauclin, J. Touma, P. J. Wierenga, and G. Vachaud. 1977. A
comparison of numerical simulation models for one-dimensional infiltration. Soil Science
Society of America Journal 41:285-294.
4. Jury, W.A. 1986. Chemical movement through soil. In Vadose Zone Modeling of Organic
Pollutants. Stephen C. Hern and Susan M. Melancon, Ed. Lewis Publishers, Inc., Chelsea,
MI, USA. p 135-159.
5. Millington, R. J., and J.M. Quirk. 1961. Permeability of porous solids. Trans. Faraday
Soc. 57:1200-1207.
6. Nofziger, D.L. 1985. Interactive simulation of one-dimensional water movement in soils:
user's guide. University of Florida, Institute of Food and Agricultural Sciences, Cir. 675.
56pp.
7. Rao, P.S.C, Ron E. Jessup, and James M. Davidson. 1987. Mass flow and dispersion. In
Environmental Chemistry of Herbicides. Vol. 1, R. Grover, Ed., CRC Press, p 21-43.
8. Richards, L. A. 1931. Capillary conduction of liquids through porous mediums. Physics
1:318-333.
9. Van Genuchten, M. Th. 1978. Mass Transport in Saturated-Unsaturated Media:
One-Dimensional Solutions. Princeton University, Research Report 78-WR-l 1. 118pp.
10. Van Genuchten, M. Th. 1980. A closed-form equation for predicting the hydraulic
conductivity of unsaturated soils. Soil Science Society of America Journal 44: 892-898.
96
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