• TABLE OF CONTENTS
HIDE
 Front Cover
 Title Page
 Table of Contents
 Introduction
 Hardware and software requirem...
 Operating conventions
 Getting started
 Illustrations of software
 Description of model
 Computational methods
 Limitations of model
 References
 Appendix
 Back Cover






Group Title: Computer series
Title: Interactive simulation of one-dimensional water movement in soils
CITATION THUMBNAILS PAGE IMAGE ZOOMABLE
Full Citation
STANDARD VIEW MARC VIEW
Permanent Link: http://ufdc.ufl.edu/UF00095250/00002
 Material Information
Title: Interactive simulation of one-dimensional water movement in soils user's guide
Physical Description: Book
Language: English
Creator: Nofziger, D. L.
Publisher: Florida Cooperative Extension Service, Institute of Food and Agricultural Sciences, University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 1985
Copyright Date: 1985
 Subjects
Subject: Water in agriculture   ( lcsh )
Soil percolation -- Computer simulation   ( lcsh )
Groundwater flow -- Computer simulation   ( lcsh )
Seepage -- Computer simulation   ( lcsh )
Genre: bibliography   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
non-fiction   ( marcgt )
 Notes
Statement of Responsibility: by D.L. Nofziger.
Bibliography: Bibliography: p. 54.
General Note: "November 1985."
General Note: Florida Cooperative Extension Service, computer series circular 675
 Record Information
Bibliographic ID: UF00095250
Volume ID: VID00002
Source Institution: University of Florida
Holding Location: University of Florida
Rights Management: All rights reserved by the source institution and holding location.
Resource Identifier: oclc - 15205022

Table of Contents
    Front Cover
        Front Cover 1
        Front Cover 2
    Title Page
        Title Page 1
        Title Page 2
    Table of Contents
        Page 1
        Page 2
    Introduction
        Page 3
    Hardware and software requirements
        Page 4
    Operating conventions
        Page 5
    Getting started
        Page 6
    Illustrations of software
        Page 7
        Page 8
        Page 9
        Page 10
        Page 11
        Page 12
        Page 13
        Page 14
        Page 15
        Page 16
        Page 17
        Page 18
        Page 19
        Page 20
        Page 21
        Page 22
        Page 23
        Page 24
        Page 25
        Page 26
        Page 27
        Page 28
        Page 29
        Page 30
        Page 31
        Page 32
        Page 33
        Page 34
        Page 35
        Page 36
        Page 37
        Page 38
        Page 39
        Page 40
        Page 41
        Page 42
        Page 43
        Page 44
        Page 45
        Page 46
        Page 47
        Page 48
        Page 49
    Description of model
        Page 50
        Page 51
    Computational methods
        Page 52
    Limitations of model
        Page 53
    References
        Page 54
    Appendix
        Page 55
        Page 56
    Back Cover
        Page 57
        Page 58
Full Text
10(

C.2.
November 1985

Interacti
Water


Floppy disc included with this
item has been shelved separately.
Consult LUIS or ask circulation
staff for assistance.


ve Simulation of One-Dimensional
Movement in Soils: User's Guide

D. L. Nofziger


COMPUTER SERIES


Software in Soil Science I


mn .6r.id C-.ativa Extension Service / Institute of Food and Agricultural Sciences / University of Florida / John T. Woaste, Dean
101
F636c
675
guide


Circular 675












INTERACTIVE SIMULATION

OF

ONE-DIMENSIONAL

WATER MOVEMENT IN SOILS:

USER'S GUIDE




by

D. L. Nofziger

Visiting Associate Professor
Soil Science Department
University of Florida
Gainesville,FL 32611


Department of Agronomy
Oklahoma State University
Stillwater, OK 74078










CONTENTS




1. Introduction ....................................................... 3

2. Hardware and Software Requirements ................................ 4

3. Operating Conventions.............................................. 5

4. Getting Started.................................................... 6

5. Illustrations of Software
Introductory Information........................................ 7
Option D: Define a New Problem and Solve It .................... 9
Interaction With Computer While Solution Is Being Calculated.... 35
Option C: Continue Simulation of Problem Stored on Disk......... 38
Option E: Enter, Modify, or Print Soil Parameters .............. 39

6. Description of Model............................................... 50

7. Computational Methods............................................. 52

8. Limitations of Model.............................................. 53

9. References Cited......................................... ......... 54

10. Appendix.................................................... .. .... 55





Copyright 1985
by
Institute of Food and Agricultural Sciences
University of Florida








INTERACTIVE SIMULATION OF ONE-DIMENSIONAL WATER MOVEMENT
IN SOILS: USER'S GUIDE

by

D. L. Nofziger




INTRODUCTION

The movement of water into and through soils is an important process in nature.
This dynamic process is important as it influences the amount of water entering the
soil, evaporating from the soil surface, moving through the soil to the ground water
below, and being stored in the soil profile for plant use. Water movement is also
important because of its strong influence on the movement of fertilizers,
pesticides, and other chemicals in the soil and on runoff and resulting soil
erosion. The process of water movement in soils is dependent upon the soil
hydraulic properties, the extent of the soil system, the condition of the soil at
the time flow begins, the manner in which water is applied to and removed from the
soil, and the duration of the flow process. These factors generally influence the
process in a rather complex manner. Therefore it is difficult to ascertain the
influence of a particular change in one factor in the flow system upon the entire
system. Although many of these questions can be answered experimentally, the amount
of time, expense, and sophisticated equipment required is generally prohibitive.
However, soil scientists have developed mathematical models of the flow process and
have invested a large amount of effort in testing and verifying these models. This
software has taken one model of water flow from that research and has made it into
an interactive system which enables the user to simulate water movement into soils
and to observe the results in graphical or tabular form. Repeated simulations of
the flow process for different soils and/or different conditions of flow can provide
insight into the complex process.

The model used in this software is the one-dimensional non-linear partial
differential equation known as the Richards equation (Richards, 1931). The soil is
homogeneous and can be oriented in any direction. A finite difference technique is
used to solve the equation. This permits the user to interrupt the flow process at
any time to change the boundary conditions as needed to model complex flow
processes.

The model can accommodate finite or semi-infinite soil systems. (A semi-infinite
soil is one that extends without limit in one direction). The user may specify one
of the following boundary conditions at the soil surfaces:

1. Constant Potential: In this case, the water potential at the surface is
specified. The supply of water is unlimited. This is useful in simulating
infiltration of water under ponded conditions.








2. Constant Flux Density: In this case, the volume of water entering the soil
surface per unit cross sectional area per unit time is specified. This is
useful for simulating flow in soils where water movement is controlled by the
application rate- or the removal rate. This may be the case in the early
stages of infiltration from rainfall or sprinkler irrigation, during
redistribution of water without evaporation, and in the early stages of
evaporation.

3. Rainfall: This boundary condition is an approximation to the boundary
condition representing rainfall or sprinkler irrigation. The user specifies
the rainfall rate. This becomes the flux density of water applied to the soil
surface as long as the surface soil is not saturated. When the surface
becomes saturated and the matric potential is zero, the boundary condition
changes to one of a constant potential of zero. (That is, water is not
allowed to pond on the soil surface.)

4. Mixed Type: This case is a combination of the flux and potential boundary
conditions and is a generalization of the rainfall boundary condition
described above. The initial flux density of water at the soil surface is
specified. This flux is maintained until the water potential at the surface
reaches a user-specified value. At that time the boundary condition changes
to a potential boundary condition. This is useful for simulating infiltration
due to irrigation or rainfall where water is allowed to accumulate on the soil
surface before runoff occurs. It is also useful to simulate evaporation when
the initial rate of water loss is controlled by the environment until the
surface soil becomes relatively dry. Here the specified flux is that for
evaporation. The specified potential is that of the relatively dry soil.

The software permits the user to define the hydraulic properties and to simulate
flow in additional soils of interest. For each soil, the user must know the water
content and the hydraulic conductivity as functions of the matric potential.

HARDWARE AND SOFTWARE REQUIREMENTS

The software operates on an IBM PC or XT (or a comparable) computer with one disk
drive, 192k bytes of random access memory, an 8087 coprocessor, an IBM comparable
color/graphics card, and a comparable monitor. A printer is desirable for printed
copies of tables and graphs. PC-DOS or MS-DOS 2.0 is required. The GRAPHICS.COM
file from your DOS diskette must be executed to obtain copies of the graphics on the
printer. If the computer has more than 192k bytes of random access memory, a RAM
disk emulator can significantly increase the speed of the software.









OPERATING CONVENTIONS


The following conventions are used throughout this software:

1. Program Interruption: The user can interrupt the program and return to the
main menu by pressing the escape key.


2. Keyboard Inputs: Single letter entries such as
to yes/no questions are made by pressing only I
key is not required. All other inputs require
depressed.


menu selections and responses
the desired key. The
that the key be


3. Default Values: The software makes use of default values to reduce the amount
of typing required. These values are displayed in square brackets when inputs
are requested. If the default value is the desired input, the user can press
only the key. If another value is desired, that value may be
entered.


4. File Names:
not needed.
be assigned


File names can be any legal MS-DOS file name. File extensions are
Meaningful file extensions for the different types of files will
by the software.


5. Cursor Control Keys: Parameters used in the program can be edited at several
places using a full screen editor. The arrow keys in the numeric keypad can
be used to position the cursor as desired for editing. Characters can be
deleted by pressing the or keys. When finished editing data
on the screen, the key should be pressed.

6. Parameter Limits: Numeric data entered into the computer is compared with
specified limits for each parameter. If the value entered is out of the
accepted range, a message is displayed for the user. This message includes
the accepted range of values. The range of values is surrounded by square
brackets if the range includes the end points specified. It is surrounded by
parentheses if it does not include the end points. For example:

[0 to 100] means the parameter must be greater than or equal to 0
and less than or equal to 100.

(0 to 100) means the parameter must be greater than 0 and less than
100.

(0 to 100] means the parameter must be greater than 0 and less than
or equal to 100.

[0 to ??] means the parameter must be greater than or equal to 0.
No upper limit exists.









GETTING STARTED

Making a Working Diskette: The software is distributed on a single diskette. The
first step is to make a working diskette from the original. The following steps can
be used to make a working diskette:

1. FORMAT a diskette with the /S option.

2. COPY the file GRAPHICS.COM from your DOS diskette to the new diskette.

3. COPY the entire software distribution diskette to the new diskette. This is
your working diskette.

4. Place the distribution diskette in a safe place.

Details on the use of the FORMAT and COPY commands are given in your DOS manual.

Program Execution: The program is supplied as an executable file called WATERFLO.
The working diskette is assumed to be in the default disk drive. Before executing
WATERFLO, the GRAPHICS.COM file must be executed. This can be done manually by
entering

GRAPHICS .

Then, WATERFLO is executed by entering

WATERFLO .

A batch file is provided to execute both of these commands. This is done by
entering

WATER .

Some default values used in this software can be modified at the time the program is
loaded. These are described in the Appendix.

The following pages illustrate the use of various program options. Information
entered by the user is underlined. Comments have been inserted to explain the
operational details of the software.










INTRODUCTORY INFORMATION


Screen 1. Purpose of the Software.


Screen 2. Special Acknowledgments.


Simulation of One-Dimensional Water Movement in Soils

by

D. L. Nofziger
Department of Agronomy
Oklahoma State University


Copyright 1985
by
Institute of Food and Agricultural Sciences
University of Florida


This program was written to solve the partial differential equation
developed by L. A. Richards(1931) describing water movement in
unsaturated soils and to display solutions in graphical form.

Press Space Bar to Continue:


ACKNOWLEDGEMENTS

The author expresses appreciation to Mr. Ron Jessup, Dr. P. S. C. Rao and
Dr. A. G. Hornsby for their helpful suggestions during the development of
this software. Appreciation is also expressed to Oklahoma State University
and the University of Florida for supporting this work.


Press Space Bar to Continue:








DISCLAIMER

The University of Florida (UF), Institute of Food and Agricultural
Sciences (IFAS), and Florida Cooperative Extension Service (FCES) shall
have no liability or responsibility to cooperator or any other person
or entity with respect to any liability, loss, or damage caused
or alleged to be caused directly or indirectly by programs released by
IFAS for sale or cooperative use including but not limited to any
interruption of service, loss of business, or anticipatory profits or
consequential damages resulting from use or operation. And in no event
shall FCES be liable for loss of profits, indirect, special, or
consequential damages arising out of any breach of the agreement or
obligations of this contract.


CONDITION OF RELEASE OR SALE

All computer software distributed by IFAS or FCES are on a 'AS IS'
basis without warranty. Distribution or resale without written
permission of the department of origin is not permitted.


Press Space Bar to Continue:


Screen 3. Disclaimer and Conditions of Sale.









OPTION D: DEFINE A NEW PROBLEM AND SOLVE IT


Simulation of One-Dimensional Water Movement in Soils

Main Menu

D. Define a New 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? D


Screen 4. Selecting Option D in Main Menu to Define a Problem and Solve It.

Option D is used to define a new problem and to solve it. Defining the problem
involves the following steps:

1. Select the soil to be used.

2. Define the orientation of the soil system. That is, specify whether the flow
is vertical, horizontal, or at some other angle.

3. Define the extent of the soil system. This software can deal with finite and
with semi-infinite soil systems.

4. Define the initial condition of the soil. That is, define its condition
before flow begins.

5. Define the boundary condition at one soil surface. This specifies the way
water is applied to the soil or removed from it.

6. If the soil system is finite, define the boundary condition at the second soil
surface.

7. Specify the time at which flow with these boundary conditions should end.








The soil is selected by entering the number associated with the soil on screen D-l.

Flow can be Calculated for the Following Soils:

1. YOLO CLAY
2. PORT SILTY CLAY
3. COBB SANDY LOAM
4. BEIT NETOFA CLAY


Enter the Number of the Soil Desired : 1


Screen D-1. List of Soils Which Can Be Selected.

After selecting the soil of interest, the user is given the option of seeing more
information about the soil. The kind of information displayed is shown in Figures 1
and 2. It consists of a graph and table of the water content as a function of matric
potential and graphs of conductivity versus matric potential and water content.
When these figures are displayed, printed copies can be obtained by simultaneously
pressing the and keys if the computer is connected to a comparable
dot matrix printer.

Data for these four soils are included in the distribution disk. The user may add
new soils using option E in the Main Menu.















1 19 188 1988 18888
NEGATIVE KATRIC POTENTIAL, CON


Natric Potential
8
-28
-40
-60


-600
-888
-1889
-2989
-4088
-6009
-8888
-10088


Matep Content
cc/cc
0.495
8.459
8.421
8.393
0,8.372
0.355
8.304
8.259
8.238
8.224
0.215
0.191
0.174
8.166
8.162
0.159


UoluMetpic Mater Content as a Function
for the VOLO CLAY Soil.


of Natric Potential


Press Space Bar to Continue:


Figure 1. Soil information for Yolo soil.








.1 -1 --A t-
.91
.681

.001



.8I 8881- 1 I l
1 18 18 1888 1988
NEGATIVE mARIC POTENTIAL, cm


.81 /"

.091

.8881


.888881
.88880808,1 ., i
8.88 0.29 8.48 8.68
mATER CONTENT, cc/cc


I-


Hydraulic Conductivity (cN/hp) as a Function of Natric Potential and
of Uoluwetic Hatep Content for the VOLO CLAY Soil.


Press Space Bar to Continue:
Figure 2. Soil information for Yolo soil.










The orientation of the soil system is specified by the angle the system makes with a
vertical line. In this example, flow is vertical and downward. Thus the angle
specified was zero as shown below.

Orientation of Flow System

This model can simulate flow in any direction. The direction is specified
by the angle (in degrees) between the column and the vertical downward
direction. Some possible orientations and the corresponding angles
are shown below.

Angle Orientation
0 Vertical: Semi-infinite downward
90 Horizontal: Semi-infinite to the right
180 Vertical: Semi-infinite upward
270 Horizontal: Semi-infinite to the left
45 Inclined at an angle of 45 degrees
counter-clockwise from vertical:
Semi-infinite downward to the right

Desired Orientation [Default is 0.0 degrees] 0


Screen D-2. Specifying the Orientation of the Soil System.

The user must now specify the extent of the soil system. This is done by selecting
option S or F shown below.



This Model Can Be Used For Two Types of Soil Systems:

S. A soil which is so long that the water content and
potential at one end never change from their initial
values. This is often called a SEMI-INFINITE soil system.

F. A soil with a finite length and boundary conditions
specifying the matric potential or flux at both ends.

Enter the Desired Soil System (S, or F): F

Length of Soil System (cm)? 20


Screen D-3. Specifying the Extent of the Soil System.







The next step in the definition of the problem is to specify the initial soil
condition. This is the condition of the soil before flow begins. The initial
condition is specified in terms of matric potential. A table of water content vs.
matric potential is displayed for the user's information. This is illustrated in
screen D-4.


Thismodel assumes the soil has uniform hydraulic properties
at all depths. To define the flow system, the initial matric
potential (and hence tpe soil wetness) must be defined.


Here is a table of matric
for YOLO CLAY.

Matric Potential
cm
0.0
-100.0
-200.0
-300.0
-400.0
-500.0
-1000.0
-2000.0
-3000.0
-4000.0
-5000.0
-6000.0
-8000.0
-10000.0
-12000.0
-14000.0


potentials and corresponding water contents


Water Content
cc/cc
0.495
0.355
0.304
0.277
0.259
0.247
0.215
0.191
0.181
0.174
0.170
0.166
0.162
0.159
0.156
0.154


What is the Initial Matric Potential? -1000
That Potential Corresponds to a Water Content of 0.215 cc/cc
Is that Satisfactory (Y,N)? Y


Screen D-4. Specifying the Initial Condition of Soil.

The next step is to specify the boundary condition at the upper soil surface. This
specifies the manner in which water is supplied to the soil or removed from it.
This process is illustrated in the following screen for one boundary condition.









The Following Conditions Can Be Imposed On the Upper Soil Surface:

BOUNDARY CONDITION RECOMMENDED RANGE

P. Constant Potential (cm) -10000 to 100
F. Constant Flux (cm/hr) -0.1 to 1.0
R. Constant Rainfall Rate (cm/hr) 0.0 to 1.0
M. Mixed Type:
Constant Flux Imposed Until Potential
At Boundary Reaches a User Defined
Value. This Potential Is Then Maintained.

Desired Boundary Condition? P

Enter the Desired Potential (cm):0

That Potential Corresponds to a Water Content of 0.495 cc/cc
\ Is this Boundary Condition Satisfactory (Y,N)? Y J
Screen D-5. Specifying Boundary Condition at Upper Soil Surface.

The boundary condition is selected by pressing the letter corresponding to it. The
recommended range is strictly for guiding the user. It does not restrict the user
to values within those limits. See the Description of Model section for more
information about the boundary conditions. Note: The user may change boundary
conditions at any time and continue the simulation with new boundary conditions.

If the soil system is finite, the user must specify the boundary condition at the
other end. This is illustrated in screen D-6.

The Following Conditions Can Be Imposed On the Lower Soil Surface:

BOUNDARY CONDITION RECOMMENDED RANGE

P. Constant Potential (cm) -10000 to 100

F. Constant Flux (cm/hr) -0.1 to 1.0

M. Mixed Type:
Constant Flux Imposed Until Potential
At Boundary Reaches a User Defined
Value. This Potential Is Then Maintained.

Desired Boundary Condition? F

Enter the Desired Flux (cm/hr): 0
Is this Boundary Condition Satisfactory (Y,N)? Y

Screen D-6. Specifying the Lower Boundary Condition.








The final step in defining the flow problem is
flow with these boundary conditions should end.
hours.


that of defining the time at which
In this example that time is 4


At What Time (hours) Should the Flow With These Boundary
Conditions End? 4


Screen D-7. Defining Maximum Time to be Simulated with the Present Boundary
Conditions.

Although the flow problem is defined, several more user inputs are required
generate the output graphs and tables desired. The user is also given the option
specifying the mesh sizes used in the finite difference solution process.


Initial Calculations Will Be Made Every 0.5
and Every 0.002000 Hours in Time

Simulated Results Will Be Stored On Disk at
Graphical and Tabular Form Every 0.200000

Are These Parameters Satisfactory (Y,N)? Y


500000 cm in Depth


id Displayed In
ir.


Screen D-8. Selecting Finite Difference Parameters.

The defined flow problem and its solution are saved in three disk files. The files
have the same name but different extensions. The software provides the needed
extensions. The following screen illustrates the way the user is asked for the file
name. In this case the user entered c:yolo. The three files will be placed on disk
drive C. File YOLO.PRB will contain the definition of the problem. File YOLO.DAT
will contain the solution at selected times. File YOLO.TAB will contain text files
of tables if selected by the user. Note: If the specified file exists on the disk,
its contents will be replaced by the new data.



The Computed Values Must Be Stored In Disk Files. The Files Have
Different Extensions Provided By the Program.


Enter Name of File to be Used : c:yolo

File C:YOLO.PRB does not exist.
Do you want to create it (Y,N)? Y

Screen D-9. Entering File Name.


J










The Following Types of Graphical Results Can Be Displayed:

A. Water Content vs. Distance From Upper Surface
Flow Rate at Upper Soil Surface vs Time
Cumulative (Net) Inflow vs. Time

B. Matric Potential vs Distance From Upper Surface
Flow Rate at Upper Soil Surface vs Time
Cumulative (Net) Inflow vs. Time

C. Water4 Content vs Distance From Upper Surface
Matric Potential vs Distance From Upper Surface

D. Flow Rate at Upper Soil Surface vs Time
Flow Rate at Lower Soil Surface vs Time
Cumulative (Net) Inflow vs. Time

N. None of the Above

Desired Option : A


Screen D-10. Selecting Graphical Output Desired.

The four types of graphical output are listed above. In this example, option A was
selected. The following two screens illustrate how the user can enter special
limits for the graphs. If no special limits are desired or when the desired changes
have been made, the user presses the key.


Minimum Water Content (cc/cc) : 0.000000
Maximum Water Content (cc/cc) : 0.500000
Minimum Distance (cc/cc) ) : 0.000000
Maximum Distance (cm) : 20.000000


Use the cursor control keys to position cursor as needed.
Then make the desired changes.

Press the key when finished making changes.


Screen D-ll. Editing Limits for Graph of Water Content vs Distance.









Minimum Time (hr) : 0.000000
Maximum Time (hr) : 4.000000
Maximum Inflow Rate (cm/hr) : 1.080000
Minimum Inflow Rate (cm/hr) : 0.000000
Maximum Net Inflow (cm) : 1.750000
Minimum Net Inflow (cm) 0.000000


Use the cursor control keys to position cursor as needed.
Then make the desired changes.

Press the key when finished making changes.


Screen D-12. Editing Limits for Graphs of Inflow Rate and Net Inflow vs Time.

Graphs of water content versus depth and matric potential versus distance are drawn
each time output was requested in Screen D-8. Sometimes the user may want to see all
of these curves to see how the quantity of interest changed with time. In other
situations, these curves add confusion and clutter. The options shown in the
following screen allow the user to select the times to be displayed. These times
can be changed during the simulation by selecting the graphics option and redefining
the times of interest.



Graphs of Water Content vs Distance Will Be Drawn Every 0.20 Hours.

The Following Options Permit You to Alter the Graphic Displays:

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


Screen D-13. Selecting Times for Which Water Content Profiles Will
Remain on Screen.


In this case the user selected option C. That is,
for those corresponding to the times entered by the
using the editor as shown in the following screens.


all lines will be erased except
user. Those times are entered











Time
Time
Time
Time
Time
Time
Time
Time
Time
Time
Time
Time
Time
Time
Time


Saved
Saved
Saved
Saved
Saved
Saved
Saved
Saved
Saved
Saved
Saved
Saved
Saved
Saved
Saved


Graph
Graph
Graph
Graph
Graph
Graph
Graph
Graph
Graph
Graph
Graph
Graph
Graph
Graph
Graph


(hr)
(hr)
(hr)
(hr)
(hr)
(hr)
(hr)
(hr)
(hr)
(hr)
(hr)
(hr)
(hr)
(hr)
(hr)


Use the cursor control keys to
Then make the desired changes.


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


position cursor as needed.


Press the key when finished making changes.


Screen D-14. Editing Times for Which Water Content Profiles Will be Saved.


Since no times have yet been entered for this soil, they are all set to
In this case, the user wanted to see curves each hour. The user changed
to that shown below and then pressed the key.


Note: Times specified here must
specified in Screen D-8. (In this
these times are satisfactory.) A
always included.


zero here.
the screen


match a time at which graphics are updated as
example, updates are obtained every 0.2 hr so
maximum of 15 times may be specified. Time 0.0 is









Time
Time
Time
Time
Time
Time
Time
Time
Time
Time
Time
Time
Time
Time
Time


Saved
Saved
Saved
Saved
Saved
Saved
Saved
Saved
Saved
Saved
Saved
Saved
Saved
Saved
Saved


Graph
Graph
Graph
Graph
Graph
Graph
Graph
Graph
Graph
Graph
Graph
Graph
Graph
Graph
Graph


(hr)
(hr)
(hr)
(hr)
(hr)
(hr)
(hr)
(hr)
(hr)
(hr)
(hr)
(hr)
(hr)
(hr)
(hr)


Use the cursor control keys to
Then make the desired changes.


0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000
0.000000


position cursor as needed.


Press the key when finished making changes.


Screen D-15. Editing Times for Which Water Content Profiles Will


be Saved.


Figure 3 illustrates the graph selected above.
graphs for options B, C, and D, respectively.


Figures 4, 5, and 6 illustrate









1 4.B

A 8.a
C
1 12.8

N 16.8


IIHE 4.60 hie
SOIL: VOLO CLAY
ORIENTATION: 8.8 Degrees
INITIAL CONDITION: Potential : -18B cN
BOUNDARY CONDITION at time : 8.88 hie
Potential : 8 cN at Upper Surface
Flux : 8.88 cm/hr at 28-cn Position


8.72

8.36


8.
1.75
1.48


I 1.65
N
F 0.78
L
0 9.35
8
0.1


GB


1.88 2.88 3.81
TINE, he


I I


1.a8 2.88 3.88
TINE, he


Figure 3. Graphics option A. Water content profiles are for 0, 1, 2, 3, and 4 hours.


Uppei SuIa'ce


I ~' '*I *..


4.88


4.80


88B






NATRIC POTENTIAL, cn F
-188 -58 8 L
o.6: ----i 0




N
C
E 12.6

n U6.8 T
I
TINE 4.88 hp F
SOIL: VOLO CLAY L
ORIENTATION: 8.0 Degrees 0
INITIAL CONDITION: Potential : -10 cm U
BOUNDARY CONDITION at tiNe : .00. hp
Potential : 0 cN at Upper Surface
Flux : 0 .08 cm/h at 28-cN Position


1.08-

0.72

0. 3~

9.00 -
0.00


1.75
1.46
1.65
6.76
8.35
8.88
0.I


1.88 2.08 3.88
TINE, hr


1.08 2.60 3.68
TINE, hr


Figure 4. Graphics option B. Matric potential profiles are for 0, 1, 2, 3 and 4 hours.


4.88


4.08


H6





UATU CONTENT,
5.959.2~
A B I.-L--.4--. UI U


4.0

8.0

12.5


20.0


SOL: VOLO CLAY
ORIENTATION: 0.0 Demes
INITIAL CONDITION: Potential : -1000 cO
mOUNDAR CONDITION at time : 0.00 hb'
Potential : I cO at Upper Surface
Flux: .8 cN/hr at 2F0-C Position


TINE 4.00 hp


Figure 5. Graphics option C. Profiles are for 0, 1, 2, 3, and 4 hours.


cc/co


I I 1


B.50


1






1.88 F1 i-- F
Lower Surface L
0
8.68 N

8.28 A

--.20 i -,i-
8.98 1.88 2.00 3.88 4.08
TIME, N
-E
TINE 4.08 hr

F
FUNCTION L
Display Deined ProbleN 0
Select Gpaph N
Select Table
Specitfy Hew Boundarg Condition
Quit. Stop Simulation


1.88

8.60

9.28

-9.28
9.
1.75
1.48
1.95
8.78
,8.35


9.99
9,09


1.88 2.99 3.90
TINE, hr


Figure 6. Graphics option D. Flow rates are in cm/hr. Net inflow has units of cm.


Upper Suoface










Finally, the user must specify the tabular output desired as shown below. These can
be output to the printer, a file, or the screen (if no graphics are being
displayed). File output is ASCII text which can be displayed, printed, edited, or
incorporated into other documents. Note: These files can get quite large, so
adequate disk space should be available. Options A and B require approximately 350
and 2000 bytes of disk space for each time.



The Following Forms of Tabular Results Can Be Displayed:

A. Inflow Rate and Cumulative (Net) Inflow vs Time

B. Inflow Rate and Cumulative (Net) Inflow vs Time
and
Matric Potential and Water Content vs Distance
From Upper Surface

N. None of the Above

Desired Option: B

.Output Tables to
F. Disk File
P. Printer
Desired Device ? P


Screen D-16. Selecting Tabular Output and Output Device.

Examples of the tabular output are shown in Tables 1 and 2 for options A and B,
respectively. Each table begins with a summary of the defined problem. When
boundary conditions are changed, an updated definition is displayed. For each time
at which outputs are generated, the table includes the time, cumulative inflow by
integration of water content changes, cumulative inflow by integration of surface
fluxes, and the average of these two values. In addition the flux densities at the
ends are listed. Finally the mesh size in time and depth are shown. In addition to
this information, Table 2 for option B includes a table of the water content and
matric potential at each mesh point.

Note: In this example, the mesh size in time was .02 for time 0.0 to 0.4 hr. From
that time to .6 hr the mesh size was .04. This was increased because the mass
balance criteria was met. In this case, the mass balance precision was set at .01
which is the default value. If we compare the cumulative inflows at 0.2 and 0.4 hr,
we see that integration of the change in water content indicates that .1433 cm of
water entered the soil during that .2 hr period. Integration of the surface fluxes
indicated that .1426 cm entered. The difference between these values was .0007
which is less than .01 .1426, so the mesh size in time was increased.









Table 1. Partial Listing of Table from Option A.


Soil: YOLO CLAY
Orientation: 0.0 Degrees From Vertical Downward
Initial Condition:
Matric Potential =-1000.0 cm. Water Content =0.215 cc/cc


Boundary Condition
Boundary Condition
Boundary Condition


at Upper Soil Surface:
at Distance of 20.00 cm:
imposed at time 0.000 hr


Matric Potential = 0.0 cm
Flux Density = 0.000 cm/hr


Time: 0.0000 hr
Cumulative Inflow: 0.0000 cm
Cumulative Inflow by Integration of Water Content:
Cumulative Inflow by Integration of Surface Fluxes:


Inflow Rate at Upper Surface:
Outflow Rate at Lower Surface:
Mesh size in depth =5.000000E-1;


0.000000 cm/hr
0.000000 cm/hr
Mesh size in time =2.000000E-3


Time: 0.2000 hr
Cumulative Inflow: 0.3621 cm
Cumulative Inflow by Integration of Water Content:
Cumulative Inflow by Integration of Surface Fluxes:


Inflow Rate at Upper Surface:
Outflow Rate at Lower Surface:
Mesh size in depth =5.000000E-1;


0.856702 cm/hr
0.000000 cm/hr
Mesh size in time =2.000000E-3


Time: 0.4000 hr
Cumulative Inflow: 0.5050 cm
Cumulative Inflow by Integration of Water Content:
Cumulative Inflow by Integration of Surface Fluxes:


Inflow Rate at Upper Surface:
Outflow Rate at Lower Surface:
Mesh size in depth =5.000000E-1;


0.612833 cm/hr
0.000000 cm/hr
Mesh size in time =2.000000E-3


Time: 0.6000 hr
Cumulative Inflow: 0.6156 cm
Cumulative Inflow by Integration of Water Content:
Cumulative Inflow by Integration of Surface Fluxes:


0.6710 cm
0.5602 cm


Inflow Rate at Upper Surface: 0.503084 cm/hr
Outflow Rate at Lower Surface: 0.000000 cm/hr
Mesh size in depth =5.000000E-l; Mesh size in time =4.000000E-3


0.0000 cm
0.0000 cm


0.4168 cm
0.3074 cm


0.5601 cm
0.4500 cm










Table 1 continued.


Time: 0.8000 hr
Cumulative Inflow: 0.7093 cm
Cumulative Inflow by Integration of Water Content:
Cumulative Inflow by Integration of Surface Fluxes:


Inflow Rate at Upper Surface:
Outflow Rate at Lower Surface:
Mesh size in depth =5.000000E-1;


0.437149 cm/hr
0.000000 cm/hr
Mesh size in time =8.000000E-3


Time: 1.0000 hr
Cumulative Inflow: 0.7922 cm
Cumulative Inflow by Integration of Water Content:
Cumulative Inflow by Integration of Surface Fluxes:


Inflow Rate at Upper Surface:
Outflow Rate at Lower Surface:
Mesh size in depth =5.000000E-1;


0.393410 cm/hr
0.000000 cm/hr
Mesh size in time =8.000000E-3


Time: 1.2000 hr
Cumulative Inflow: 0.8677 cm
Cumulative Inflow by Integration of Water Content:
Cumulative Inflow by Integration of Surface Fluxes:


Inflow Rate at Upper Surface:
Outflow Rate at Lower Surface:
Mesh size in depth =5.000000E-1;


0.361177 cm/hr
0.000000 cm/hr
Mesh size in time =8.000000E-3


Time: 1.4000 hr
Cumulative Inflow: 0.9374 cm
Cumulative Inflow by Integration of Water Content:
Cumulative Inflow by Integration of Surface Fluxes:


Inflow Rate at Upper Surface:
Outflow Rate at Lower Surface:
Mesh size in depth =5.000000E-1;


Time: 1.6000 hr
Cumulative Inflow: 1.0025 cm
Cumulative Inflow by Integration of
Cumulative Inflow by Integration of


0.335020 cm/hr
0.000000 cm/hr
Mesh size in time =1.538461E-2


Water Content:
Surface Fluxes:


1.0597 cm
0.9452 cm


0.7651 cm
0.6534 cm


0.8485 cm
0.7360 cm


0.9242 cm
0.8112 cm


0.9943 cm
0.8805 cm









Table 1 continued.


Inflow Rate at Upper Surface:
Outflow Rate at Lower Surface:
Mesh size in depth =5.000000E-1;


0.314750 cm/hr
0.000000 cm/hr
Mesh size in time =1.538461E-2


Time: 1.8000 hr
Cumulative Inflow: 1.0639 cm
Cumulative Inflow by Integration of Water Content:
Cumulative Inflow by Integration of Surface Fluxes:


Inflow Rate at Upper Surface: 0.298060 cm/hr
Outflow Rate at Lower Surface: 0.000000 cm/hr
Mesh size in depth =5.000000E-1; Mesh size in time


Time: 2.0000 hr
Cumulative Inflow: 1.1222 cm
Cumulative Inflow by Integration of Water Content:
Cumulative Inflow by Integration of Surface Fluxes:


Inflow Rate at Upper Surface:
Outflow Rate at Lower Surface:
Mesh size in depth =5.000000E-1;


=1.538461E-2


1.1802 cm
1.0641 cm


0.282928 cm/hr
0.000000 cm/hr
Mesh size in time =2.857142E-2


1.1214 cm
1.0063 cm










Table 2. Partial Listing of Table from Option B.


Soil: YOLO CLAY
Orientation: 0.0 Degrees From Vertical Downward
Initial Condition:
Matric Potential =-1000.0 cm. Water Content =0.215 cc/cc


at Upper Soil Surface:
at Distance of 20.00 cm:
imposed at time 0.000 hr


Matric Potential = 0.0 cm
Flux Density = 0.000 cm/hr


Time: 0.0000 hr
Cumulative Inflow: 0.0000 cm
Cumulative Inflow by Integration of Water Content:
Cumulative Inflow by Integration of Surface Fluxes:


Inflow Rate
Outflow Rate
Mesh size in


at Upper Surface: 0.000000 cm/hr
at Lower Surface: 0.000000 cm/hr
depth =5.000000E-1; Mesh size in time =2.000000E-3


Distance Potential


cm
0.000
1.000
2.000
3.P00
4.000
5.000
6.000
7.000
8.000
9.000
10000
11.000
12.000
13.000
14.000
15.000
16.000
17.000
18.000
19.000
20.000


cm
0.000
-1000.000
-1000.000
-1000.000
-1000.000
-1000.000
-1000.000
-1000.000
-1000.000
-1000.000
-1000.000
-1000.000
-1000.000
-1000.000
-1000.000
-1000.000
-1000.000
-1000.000
-1000.000
-1000.000
-1000.000


Water Content
cc/cc
0.495
0.215
0.215
0.215
0.215
0.215
0.215
0.215
0.215
0.215
0.215
0.215
0.215
0.215
0.215
0.215
0.215
0.215
0.215
0.215
0.215


Distance Potential


cm
0.500
1.500
2.500
3.500
4.500
5.500
6.500
7.500
8.500
9.500
10.500
11.500
12.500
13.500
14.500
15.500
16.500
17.500
18.500
19.500


cm
-1000.000
-1000.000
-1000.000
-1000.000
-1000.000
-1000.000
-1000.000
-1000.000
-1000.000
-1000.000
-1000.000
-1000.000
-1000.000
-1000.000
-1000.000
-1000.000
-1000.000
-1000.000
-1000.000
-1000.000


Water Content
cc/cc
0.215
0.215
0.215
0.215
0.215
0.215
0.215
0.215
0.215
0.215
0.215
0.215
0.215
0.215
0.215
0.215
0.215
0.215
0.215
0.215


Boundary
Boundary
Boundary


Condition
Condition
Condition


0.0000 cm
0.0000 cm









Table 2 continued.


Time: 0.2000 hr
Cumulative Inflow: 0.3621 cm
Cumulative Inflow by Integration of Water Content:
Cumulative Inflow by Integration of Surface Fluxes:


Inflow Rate
Outflow Rate
Mesh size in


at Upper
at Lower
depth =5


Surface: 0.856702 cm/hr
Surface: 0.000000 cm/hr
.OOOOOOE-1; Mesh size in time =2.000000E-3


Potential
cm
0.000
-33.081
-313.929
-976.206
-999.871
-1000.000
-1000.000
-1000.000
-1000.000
-1000.000
-1000.000
-1000.000
-1000.000
-1000.000
-1000.000
-1000.000
-1000.000
-1000.000
-1000.000
-999.987
-999.644


Water Content
cc/cc
0.495
0.432
0.274
0.216
0.215
0.215
0.215
0.215
0.215
0.215
0.215
0.215
0.215
0.215
0.215
0.215
0.215
0.215
0.215
0.215
0.215


Distance Potential


cm
0.500
1.500
2.500
3.500
4.500
5.500
6.500
7.500
8.500
9.500
10.500
11.500
12.500
13.500
14.500
15.500
16.500
17.500
18.500
19.500


cm
-11.392
-96.232
-782.014
-998.124
-999.992
-1000.000
-1000.000
-1000.000
-1000.000
-1000.000
-1000.000
-1000.000
-1000.000
-1000.000
-1000.000
-1000.000
-1000.000
-1000.000
-999.998
-999.921


Water Content
cc/cc
0.478
0.358
0.225
0.215
0.215
0.215
0.215
0.215
0.215
0.215
0.215
0.215
0.215
0.215
0.215
0.215
0.215
0.215
0.215
0.215


0.4168 cm
0.3074 cm


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










Table 2 continued.


Time: 0.4000 hr
Cumulative Inflow: 0.5050 cm
Cumulative Inflow by Integration of Water Content:
Cumulative Inflow by Integration of Surface Fluxes:


Inflow Rate
Outflow Rate
Mesh size ir
4
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


at Upper Surface:
at Lower Surface:
depth =5.000000E-1;


Potential
cm
0.000
-17.874
-91.342
-586.114
-986.272
-999.824
-999.998
-1000.000
-1000.000
-1000.000
-1000.000
-1000.000
-1000.000
-1000.000
-1000.000
-1000.000
-1000.000
-1000.000
-999.997
-999.944
-999.451


0.612833
0.000000
Mesh


Water Content
cc/cc
0.495
0.463
0.361
0.239
0.215
0.215
0.215
0.215
0.215
0.215
0.215
0.215
0.215
0.215
0.215
0.215
0.215
0.215
0.215
0.215
0.215


cm/hr
cm/hr
size in time =2.000000E-3


Distance
cm
0.500
1.500
2.500
3.500
4.500
5.500
6.500
7.500
8.500
9.500
10.500
11.500
12.500
13.500
14.500
15.500
16.500
17.500
18.500
19.500


Potential
cm
-7.233
-38.859
-239.185
-903.345
-998.363
-999.983
-1000.000
-1000.000
-1000.000
-1000.000
-1000.000
-1000.000
-1000.000
-1000.000
-1000.000
-1000.000
-1000.000
-1000.000
-999.987
-999.803


Water Content
cc/cc
0.487
0.423
0.291
0.219
0.215
0.215
0.215
0.215
0.215
0.215
0.215
0.215
0.215
0.215
0.215
0.215
0.215
0.215
0.215
0.215


0.5601 cm
0.4500 cm









Table 2 continued.


Time: 0.6000 hr
Cumulative Inflow: 0.6156 cm
Cumulative Inflow by Integration of Water Content:
Cumulative Inflow by Integration of Surface Fluxes:


Inflow Rate
Outflow Rate
Mesh size in


at Upper Surface: 0.503084 cm/hr
at Lower Surface: 0.000000 cm/hr
depth =5.000000E-1; Mesh size in time =4.000000E-3


Distance Potential


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


cm
0.000
-13.041
-49.345
-250.378
-862.735
-995.689
-999.915
-999.999
-1000.000
-1000.000
-1000.000
-1000.000
-1000.000
-1000.000
-1000.000
-1000.000
-1000.000
-999.999
-999.990
-999.886
-999.310


Water Content
cc/cc
0.495
0.474
0.407
0.288
0.221
0.215
0.215
0.215
0.215
0.215
0.215
0.215
0.215
0.215
0.215
0.215
0.215
0.215
0.215
0.215
0.215


Distance Potential


cm
0.500
1.500
2.500
3.500
4.500
5.500
6.500
7.500
8.500
9.500
10.500
11.500
12.500
13.500
14.500
15.500
16.500
17.500
18.500
19.500


cm
-5.628
-25.162
-106.377
-554.891
-973.312
-999.371
-999.989
-1000.000
-1000.000
-1000.000
-1000.000
-1000.000
-1000.000
-1000.000
-1000.000
-1000.000
-1000.000
-999.998
-999.964
-999.694


Water Content
cc/cc
0.491
0.448
0.350
0.242
0.216
0.215
0.215
0.215
0.215
0.215
0.215
0.215
0.215
0.215
0.215
0.215
0.215
0.215
0.215
0.215


0.6710 cm
0.5602 cm









Table 2 continued.


Time: 0.8000 hr
Cumulative Inflow: 0.7093 cm
Cumulative Inflow by Integration of Water Content:
Cumulative Inflow by Integration of Surface Fluxes:


Inflow Rate
Outflow Rate
Mesh size in


at Upper
at Lower
depth =5.


Surface: 0.437149 cm/hr
Surface: 0.000000 cm/hr
OOOOOOE-1; Mesh size in time =8.OOOOOOE-3


Distance Potential


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


cm
0.000
-10.589
-34.066
-132.575
-586.382
-967.501
-998.858
-999.971
-999.999
-1000.000
-1000.000
-1000.000
-1000.000
-1000.000
-1000.000
-1000.000
-1000.000
-999.998
-999.977
-999.822
-999.194


Water Content
cc/cc
0.495
0.480
0.431
0.333
0.239
0.216
0.215
0.215
0.215
0.215
0.215
0.215
0.215
0.215
0.215
0.215
0.215
0.215
0.215
0.215
0.215


Distance Potential


cm
0.500
1.500
2.500
3.500
4.500
5.500
6.500
7.500
8.500
9.500
10.500
11.500
12.500
13.500
14.500
15.500
16.500
17.500
18.500
19.500


cm
-4.728
-19.197
-64.097
-291.559
-860.075
-993.613
-999.810
-999.996
-1000.000
-1000.000
-1000.000
-1000.000
-1000.000
-1000.000
-1000.000
-1000.000
-1000.000
-999.993
-999.932
-999.595


Water Content
cc/cc
0.492
0.460
0.388
0.278
0.221
0.215
0.215
0.215
0.215
0.215
0.215
0.215
0.215
0.215
0.215
0.215
0.215
0.215
0.215
0.215


0.7651 cm
0.6534 cm










Table 2 continued.

Time: 1.0000 hr
Cumulative Inflow: 0.7922 cm
Cumulative Inflow by Integration of Water Content:
Cumulative Inflow by Integration of Surface Fluxes:


Inflow Rate at Upper Surface:
Outflow Rate at Lower Surface:
Mesh size in depth =5.000000E-1;


0.393410 cm/hr
0.000000 cm/hr
Mesh size in time =8.000000E-3


Distance Potential


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


cm
0.000
-9.111
-26.558
-84.572
-352.680
-876.459
-992.963
-999.725
-999.992
-1000.000
-1000.000
-1000.000
-1000.000
-1000.000
-1000.000
-1000.000
-1000.000
-999.995
-999.959
-999.758
-999.093


Water Content
cc/cc
0.495
0.483
0.445
0.367
0.267
0.220
0.215
0.215
0.215
0.215
0.215
0.215
0.215
0.215
0'.215
0.215
0.215
0.215
0.215
0.215
0.215


Distance Potential


cm
0.500
1.500
2.500
3.500
4.500
5.500
6.500
7.500
8.500
9.500
10.500
11.500
12.500
13.500
14.500
15.500
16.500
17.500
18.500
19.500


cm
-4.153
-15.907
-45.674
-170.319
-642.673
-968.354
-998.562
-999.951
-999.999
-1000.000
-1000.000
-1000.000
-1000.000
-1000.000
-1000.000
-1000.000
-999.999
-999.985
-999.894
-999.505


Water Content
cc/cc
0.493
0.468
0.412
0.315
0.234
0.216
0.215
0.215
0.215
0.215
0.215
0.215
0.215
0.215
0.215
0.215
0.215
0.215
0.215
0.215


0.8485 cm
0.7360 cm









INTERACTION WITH COMPUTER WHILE SOLUTION IS BEING CALCULATED


These types of flow problems generally require 2 to 10 minutes to complete.
Graphical and tabular outputs occur approximately every 5 to 60 seconds. The
software is written to permit the user to select different graphics, select
different tables, specify new boundary conditions, or terminate the simulation while
the solution is being calculated. Thus a user could begin using option A in the
graphics options and later change to another option. This process is described
below.

If you compare Figures 3, 4, and 5 with Figure 6, you may note that the summary of
the flow problem is given in the first 3 figures where a brief Help Menu is given in
Figure 6. That menu is also shown below.


KEY FUNCTION
D Display Defined Problem
G Select Graph
T Select Table
B Specify New Boundary Condition
Q Quit, Stop Simulation

While the computation is in progress, the information about the defined problem is
displayed as in Figure 1. The software monitors the keyboard from time to time to
see if the user wants to interrupt the computation. If a key listed in the above
menu is pressed by the user, a message is displayed and the computer serves that
interrupt as soon as possible. If a key is pressed which is not listed above, this
menu is displayed for the user's information. Computations then continue until
another key is pressed. The operation resulting from each key in this menu is
described below.

D. This key replaces the Help Menu shown above with the summary of
the defined problem.

G. This option clears the screen and displays the menu for graphics
options (screen D-10). The user then must select the desired option.
The data for the solved problem are then read from disk and drawn
for the selected option. The computer then continues to solve the
flow problem.

T. This option saves an image of the screen in memory. It then clears
the screen and displays the menu for selecting tables (screen D-16).
The user then selects the desired table and output device.
The graphics screen is then replaced and the solution process
continues. The selected table will be output each time the graphics
and data file are updated.

B. This option allows the user to specify new boundary conditions and
to change the time at which the simulation will end. The computer
saves an image of the screen in memory. It then clears the screen
and permits the user to change the boundary conditions and
termination time as shown in screens D-5, D-6, and D-7. (The user









cannot change the size of the soil system). The screen is then
restored and the solution process resumes with the new boundary
conditions.

Q. This option permits the user to terminate the simulation. After
the user verifies that the solution should be terminated, the
the computer returns control to the main menu.

The capability of interrupting the solution process adds a great deal of flexibility
to the software. For example, these options were used to change the boundary
condition at the surface of the yolo clay to one of zero flux and to continue the
simulation to 24 hours. Results are shown in Figure 7. The water content profiles
shown are for 0, 4, 8, 12, 16, 20, and 24 hours.





















SOIL: YOLO CIAV
ORIENTATION: 0.9 Dewees
INITIAL CONDITION: Potential : -1900 cN
BOUNDARY CONDITION at time : 4.80 he
Flux : 0.00 cn/h at ippe Sutace
Flux: 0.00 c/hp at 20-CN Position


l^ .---,--.----,-o
Upper Suotace
0.60



-0.20 -
0.00 6.88 12.9 18.08
TINE, h,
Mt a l


1.40
1.05
8.79
8.35

0.1


08


6.00 12.88
TINE, hp


24.90


Figure 7. Graphics option A. Water content profiles are for 0, 4, 8, 12, 16,
20, and 24 hours.


.






I I


18.00 24.00


t









OPTION C: CONTINUE SIMULATION OF PROBLEM STORED ON DISK


Simulation of One-Dimensional Water Movement in Soils

Main Menu

D. Define a New 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


Screen 4. Selecting Option C in Main Menu to Continue Simulation of a
Problem Started at Another Time and Stored in a Disk File.

Option C enables the user to continue simulation of a problem defined previously.
It is useful if a simulation must be terminated by the user before the maximum time
of interest has been reached. This option saves the time involved in defining the
problem and the computational time already used. To use this option, the user must
specify the name of the file used when the problem was defined. This is illustrated
below.




Enter Name of File to be Used: c:yolo


Screen C-1. Entering Name of File Containing Problem Defined Previously.

Note: The file name does not include an extension, but it may include a disk drive.

At this point the computer reads the specified file containing the defined problem.
It then asks the user for output options (screens D-9 and following). The solution
process then continues.










OPTION E: ENTER, MODIFY, OR PRINT SOIL PARAMETERS


Simulation of One-Dimensional Water Movement in Soils

Main Menu

D. Define a New 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


Screen 4. Selecting Option E in Main Menu for Entering, Modifying, or
Displaying Soil Parameters.


The hydraulic conductivity and water
matric potential before a simulation
five conductivity functions can be
parameters used to define the water ci
must be entered into a file before f
used to aid the user should also be ei


content must be specified as functions of
can be made. Three water content functions and
used. These are shown in Tables 3 and 4. The
content and conductivity functions for each soil
low can be simulated. Several other parameters
entered.


The following pages illustrate the way these soil parameters are entered, modified,
and printed using option E in this Main Menu.











Table 3. Water Content Functions Supported by Software.


WC(res) + {A*[WC(sat)-WC(res)]}/{A + [-h]B}


and WC(h) = WC(sat)


B. WC(h) = WC(res) + {A*(WC(sat)-WC(res)]}/{A + [in(-h)]B}


WC(h) = WC(sat)


C. WC(h) = WC(res) + {WC(sat)-WC(res)}/{l + [A*(-h)]B}m


WC(h) = WC(sat)


for h < 0

for h >= 0.


for h < -1

for h >= 1.


for h < 0

for h >= 0


where m = 1 1/B.


In these equations, WC(h) represents the water content at matric potential h;
WC(res) represents the residual water content, and WC(sat) represents the water
content at saturation. All water contents are expressed on a fractional volume
basis. Equations A and B are from Haverkamp et.al.(1977). Equation C is from van
Genuchten (1980).


A. WC(h) =











Table 4. Hydraulic Conductivity Functions Supported by Software.


A. K(h) =


K(sat) A/{A + [-h] }


for h < 0

for h >= 0.


and K(h) = K(sat)


B. K(h) = A exp(B WC(h))

where WC(h) is given by a water content function above.


C. K(h) =


K(sat) *{1 (A*(-h])B-I [1 + (A*[-h])B ]- }2
{1 + (A*[-h])B }m/2


for h < 0


and K(h) = K(sat)

where m = 1 1/B.


D. K(h) = K(sat) exp(B*h)


for h >= 0


for h < 0

for h >= 0.


and K(h) = K(sat)


E. K(h) = A [WC(h)]B
where WC(h) is given by a water content function above.


For each function, K(h) represents the conductivity at a matric potential h, and
K(sat) represents the saturated conductivity. Equation A was taken from
Haverkamp(1977), and equation C is from van Genuchten(1980).




































Screen E-1. Introduction Listing Parameters Required to


Define a Soil.


This is a list of the 15 parameters required for each soil. The soil name is made
up of up to 35 printable characters. The water content and conductivity functions
in items 2 through 9 refer to the functions in Tables 3 and 4. Items 10 through 15
are suggested limits for the potential, flux, and rainfall boundary conditions.
These limits are displayed as realistic values for the user's information only.
Users may specify values outside of these limits if they desire.

Note: 1. Water contents are specified as the fraction of the total soil volume
occupied by water.
2. Hydraulic conductivities have units of cm/hr.

The user may choose any of the supported water content and conductivity functions
which describe the data for the soil of interest. Parameters may be estimated by
graphical or least-squares techniques. Van Genuchten (1980) provides a useful
discussion of parameter estimation for his equation.


Enter, Modify, or Print Soil Data:

This simulation of water movement in soils requires the following
information about the soil:

0. Soil Name
1. Water Content Function (A, B, or C)
2. Conductivity Function (A, B, C, D, E)
3. Saturated Water Content, cc/cc
4. Residual Water Content, cc/cc
5. Water Content Parameter A
6. Water Content Parameter B
7. Saturated Conductivity, cm/hr
8. Conductivity Parameter A
9. Conductivity Parameter B
10. Suggested Minimun Potential, cm
11. Suggested Maximum Potential, cm
12. Suggested Minimum Flux, cm/hr
13. Suggested Maximum Flux, cm/hr
14. Suggested Minimum Rainfall Rate,cm/hr
15. Suggested Maximum Rainfall Rate,cm/hr

NOTE: The soil properties are assumed to be uniform over depth.

Push Space Bar to Continue:









Entering Soil Data

In this screen, the user specifies the file in which the data will be stored. This
will usually be the default SOIL.S file. This was selected in this example by
pressing the key.

Enter Name of File to be Used [Default is SOIL.S]:

OPTIONS:
E. Enter new information
M. Modify existing data
P. Print data in file

Desired Option: E
'\ -


Screen E-2. Selecting Soil File and Option


E to Enter New Information.


Option E allows the user to enter data for a new soil as illustrated below.


the word END to stop data entry

Soil Name
Water Content Function (A, B, or C)


Conductivity Function (A, B, C,
Saturated Water Content, cc/cc
Residual Water Content, cc/cc
Water Content Parameter A
Water Content Parameter B
Saturated Conductivity, cm/hr
Conductivity Parameter A
Conductivity Parameter B
Suggested Minimum Potential, cm
Suggested Maximum Potential, cm
Suggested Minimum Flux, cm/hr
Suggested Maximum Flux, cm/hr
Suggested Minimum Rainfall Rate
Suggested Maximum Rainfall Rate


D, E):




:


,cm/hr:
,cm/hr:


yolo clay
b
a
.495
.124
739
5
T.428e-2
124.6
1.77
1-o000
100
-0.1
1
0
1


Screen E-E-1. Entering Data for a New Soil.


This illustrates the way data for yolo clay were
completed, the data were stored in the disk file.
following screen.


entered. When the last entry was
The computer then displayed the


Enter
















Screen E-E-2. Terminating Data Entry.

Here the user entered the word end to terminate data entry. This results in a
return to the main menu.









Modifying Soil Data

The following screens illustrate the manner in which data in a file can be
modified. In this example, Water Content Parameter B entered above should have been
4 instead of 5. This was corrected using option E in the main menu and then option M
as shown below.

Enter Name of File to be Used [Default is SOIL.S]:

OPTIONS:
E. Enter new information
M. Modify existing data
P. Print data in file

Desired Option: M


Screen E-2. Selecting Soil File and Option M to Modify


Soil Name
Water Content Function (A, B, or C)
Conductivity Function (A, B, C, D, E)
Saturated Water Content, cc/cc
Residual Water Content, cc/cc
Water Content Parameter A
Water Content Parameter B
Saturated Conductivity, cm/hr
Conductivity Parameter A
Conductivity Parameter B
Suggested Minimun Potential, cm
Suggested Maximum Potential, cm
Suggested Minimum Flux, cm/hr
Suggested Maximum Flux, cm/hr
Suggested Minimum Rainfall Rate,cm/hr :
Suggested Maximum Rainfall Rate,cm/hr :

Use the cursor control keys to position
Then make the desired changes.


Existing Information.


YOLO CLAY
B
A
0.495000
0.124000
739.000000
5.000000
4.428000E-2
124.599998
1.770000
-10000.000000
100.000000
-0.100000
1.000000
0.000000
1.000000

cursor as needed.


Press the key when finished making changes.

Enter function key to delete record from file.
Press the key when finished editing the entire file.


Screen E-M-1. Editing Data in File.


information was written on the screen, the cursor was located
CLAY. The user used the down-arrow key to move the cursor to
The correct number of 4 and the key were pressed. The


under the Y
the 5 to be
screen then


When this
of YOLO
changed.












Soil Name
Water Content Function (A, B, or C)
Conductivity Function (A, B, C, D, E)
Saturated Water Content, cc/cc
Residual Water Content, cc/cc
Water Content Parameter A
Water Content Parameter B
Saturated Conductivity, cm/hr
Conductivity Parameter A
Conductivity Parameter B
Suggested Minimun Potential, cm
Suggested Maximum Potential, cm
Suggested Minimum Flux, cm/hr
Suggested Maximum Flux, cm/hr
Suggested Minimum Rainfall Rate,cm/hr :
Suggested Maximum Rainfall Rate,cm/hr :

Use the cursor control keys to position
Then make the desired changes.


YOLO CLAY
B
A
0.495000
0.124000
739.000000


4.428000E-2
124.599998
1.770000
-10000.000000
100.000000
-0.100000
1.000000
0.000000
1.000000


cursor as needed.


Press the key when finished making changes.

Enter function key to delete record from file.
Press the key when finished editing the entire file.


Screen E-M-1. Editing Data in File.

Since no more data needed to be corrected, the user pressed the key.
corrected data were written on disk. When data for all soils were corrected,
user pressed the key to return to the main menu.


was


The
the








Printing Soil Data


Enter Name of File to be Used [Default is SOIL.S]:

OPTIONS:
E. Enter new information
M. Modify existing data
P. Print data in file

Desired Option: P


Screen E-2. Selecting Soil File and Option P to Print Data.





C Print Data on Printer (Y,N) ? Y

Screen E-P-1. Selecting Printer as Output Device.

The information printed is shown in Table 5.









Table 5. Contents of File Defining Soil Properties


File : SOIL.S


Soil Name
Water Content Function (A, B, or C)
Conductivity Function (A, B, C, D, E)
Saturated Water Content, cc/cc
Residual Water Content, cc/cc
Water Content Parameter A
Water Content Parameter B
Saturated Conductivity, cm/hr
Conductivity Parameter A
Conductivity Parameter B
Suggested Minimum Potential, cm
Suggested Maximum Potential, cm
Suggested Minimum Flux, cm/hr
Suggested Maximum Flux, cm/hr
Suggested Minimum Rainfall Rate,cm/hr
Suggested Maximum Rainfall Rate,cm/hr


Soil Name
Water Content Function (A, B, or C)
Conductivity Function (A, B, C, D, E)
Saturated Water Content, cc/cc
Residual Water Content, cc/cc
Water Content Parameter A
Water Content Parameter B
Saturated Conductivity, cm/hr
Conductivity Parameter A
Conductivity Parameter B
Suggested Minimum Potential, cm
Suggested Maximum Potential, cm
Suggested Minimum Flux, cm/hr
Suggested Maximum Flux, cm/hr
Suggested Minimum Rainfall Rate,cm/hr
Suggested Maximum Rainfall Rate,cm/hr


:YOLO CLAY
:B
:A
:0.495000
:0.124000
:739.000000
:4.000000
:4.428000E-2
:124.599998
:1.770000
:-10000.000000
:100.000000
:-0.100000
:1.000000
:0.000000
:1.000000

:PORT SILTY CLAY
:C
:B
:0.350000
:0.160000
:1.400000E-2
:1.250000
:1.250000E-2
:1.820000E-25
:150.300003
:-10000.000000
:100.0000
:-0.100000
:1.000000
:0.000000
:1.000000









Table 5 continued


Soil Name
Water Content Function (A, B, or C)
Conductivity Function (A, B, C, D, E)
Saturated Water Content, cc/cc
Residual Water Content, cc/cc
Water Content Parameter A
Water Content Parameter B
Saturated Conductivity, cm/hr
Conductivity Parameter A
Conductivity Parameter B
Suggested Minimum Potential, cm
Suggested Maximum Potential, cm
Suggested Minimum Flux, cm/hr
Suggested Maximum Flux, cm/hr
Suggested Minimum Rainfall Rate,cm/hr
Suggested Maximum Rainfall Rate,cm/hr

Soil Name
Water Content Function (A, B, or C)
Conductivity Function (A, B, C, D, E)
Saturated Water Content, cc/cc
Residual Water Content, cc/cc
Water Content Parameter A
Water Content Parameter B
Saturated Conductivity, cm/hr
Conductivity Parameter A
Conductivity Parameter B
Suggested Minimum Potential, cm
Suggested Maximum Potential, cm
Suggested Minimum Flux, cm/hr
Suggested Maximum Flux, cm/hr
Suggested Minimum Rainfall Rate,cm/hr
Suggested Maximum Rainfall Rate,cm/hr


:COBB SANDY LOAM
:C
:B
:0.320000
:5.000000E-2
:3.700000E-2
:1.429999
:0.520000
:7.539999E-7
:42.099991
:-1000.000000
:100.0000
:-0.100000
:3.000000
:0.000000
:3.000000

:BEIT NETOFA CLAY
:C
:C
:0.446000
:0.000000
:1.520000E-3
:1.170000
:3.416700E-3
:1.520000E-3
:1.170000
:-1000.000000
:100.000000
:-0.100000
:1.000000
:0.000000
:1.000000







DESCRIPTION OF MODEL


The partial differential equation used here to describe one-dimensional vertical

water movement is that of L. A. Richards(1931):


C(h) = 3 -[K(h)(s cos(a))]
at 3s


where h = h(s,t) is the matric potential; s is the distance in 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

function; and C(h) is the specific water capacity (i.e. C(h) = d@/dh where e is the

volumetric water content).


The model can be used for finite or semi-infinite soil systems. In the finite case,

the initial condition is

h(s,t) = h initial for t = 0 and 0 < s < L


where L is the length of the soil system. In the semi-infinite case, the initial

condition is

h(s,t) = initial for t = 0 and 0 < s


At time t=0, and any later time, one of the following boundary conditions can be

imposed at the upper boundary (s = 0).


BC#1. Constant Potential h : h(0,t) = h'
0 0
BC#2. Constant Flux Density qo: -K(h)[3h/as cos(a)] = q0 for s = 0

BC#3. Mixed Type:

-K(h)[Dh/as cos(a)] = qo for s = 0; t <= tO

h(0,t) = h0 for s = 0; t > t0









where h and q0 represent the specified potential and flux at the soil surface,

respectively, and to is the time at which the soil at s = 0 reaches a potential ho

(i.e. h(0, t ) = h ). The rainfall boundary condition is simply BC#3 with qo equal

to the rainfall rate and h0 equal to zero. The flux is positive for water entering

the soil system at s = 0 and negative for water leaving the soil at s = 0.


For the finite soil system, at time t=0 (and any later time), one

boundary conditions can be imposed at the lower boundary (s = L).

BC#4. Constant Potential hL: h(L,t) = hL

BC#5. Constant Flux Density qL: -K(h)(0h/3s cos(a)) = qL

BC#3. Mixed Type:


-K(h)[ah/is cos(a)] = qL

h(0,t) = hL


for s = L;

for s = L;


of the following




for s = L


t <= tL
t > tL


where hL and qL represent the specified potential and flux at s = L, respectively,

and tL is the time at which the soil at s = L reaches a potential hL (i.e. h(L, tL)

= hL). The flux is positive for water leaving the soil system at s = L and negative

for water entering at s = L.


The soil hydraulic properties are defined by defining the e(h) and K(h) functions.

The 9(h) functions and K(h) functions supported in this software are shown in Tables

3 and 4.










COMPUTATIONAL METHODS


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


C(i,j)h(ilj+l)-h(i) K(i+/2,j)(h(i+l+l)h(i+l) cos(a))


_K(il-1/2,j)(h(ii+l)-h(i-li+1) cos(a))]


where h(i,j) = h(iAs, jAt),

C(i,j) = C(h(i,j)),

K(i+1/2,j) = [K(h(i,j))+K(h(i+l,j)]/2,

K(i-1/2,j) = (K(h(i-l,j)) + K(h(i,j))]/2,

and At and is are the mesh sizes in time and depth, respectively.

The finite difference equation above is used for all interior mesh points of the
soil system. Special forms of this equation are used to represent the boundary
conditions selected. This results 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 define a
tridiagonal matrix which is relatively easily solved for up to 200 equations in the
microcomputer. All floating point calculations are performed in double precision
(about 16 decimal digits).

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 appendix for details.










LIMITATIONS OF MODEL


The limitations of this model to describe movement in soils include the limitations
of the basic flow equation, the limited flexibility imposed on the initial and
boundary conditions and on the e(h) and K(h) functions, and the limitations of the
finite difference approximation to the problem. The fact that the model is for flow
in one dimension for homogeneous soils means that it will not precisely describe
flow in heterogeneous soils where flow is likely three dimensional. Any limitations
due to the types of initial and boundary conditions and due to the functions used to
describe the hydraulic properties should be apparent to the user. Additional
functions can be supported relatively easily. Complex initial conditions could be
supported but at a cost of greater effort for the user.

Limitations due to the finite difference approach include some error in mass
balance. That is, the quantity of water entering or leaving the soil surfaces in a
period of time may not be the same if determined from surface fluxes and from
changes in water content. This is especially true for small times and for abrupt
changes in boundary conditions. If large mass balance errors exist, the calculated
water content and potential distributions must be questioned. The cumulative
inflows determined from water contents and from surface fluxes are shown in the
tabular outputs. Large mass balance errors are indicated on the screen as well.
Mass balance is often improved by decreasing the mesh sizes.

Another limitation is exhibited when one attempts to simulate the 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 does not occur
for initial matric potentials less than -2 cm nor for non-uniform 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.

Computational speed may be a limitation. This problem was greatly reduced by the
use of the 8087 processor. Many problems can be defined, solved, and displayed in 5
to 10 minutes. Users with more time consuming problems may prefer to let the
machine run and to view the results later from the disk file (option C can be used
for this).

Due to the wide range of flow problems which may be specified and the highly
non-linear form of the partial differential equation, THE USER SHOULD ALWAYS BE '
ALERT FOR ABNORMALITIES IN THE SOLUTION. If results look suspicious (as indicated
by poor mass balance or unexpected water content and water potential profiles),
compare the results with those for additional simulations with mesh sizes having
smaller at/As ratios. If the solution is important to you, simulate the flow with
another model using a different solution method and compare the results.









REFERENCES CITED


1. 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.

2. Richards, L. A. 1931. Capillary conduction of liquids through porous mediums.
Physics 1:318-333.

3. 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.










APPENDIX


Options Specified at Execution

Several parameters used in the model can be defined at the time the program is
executed. These include


F This option causes the model to use only a fixed mesh size in time
and depth. It is executed by entering

WATERFLO F .

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 .01. The user can set it to .05, for
example, by entering

WATERFLO P.05 .

U This option is used to set the upper limit for the mesh size in
time. The default value of this is 0.1 hr. That is, the mesh size
in time At cannot exceed 0.1 hr. The user can set this upper limit
to 1.0 hour by entering

WATERFLO Ul.0O .

N The number of mesh points used for a problem involving a semi-
infinite medium begins with some number N and increases as
the changes in potential approach the deepest 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

WATERFLO N20 .

This option does not affect the number of mesh points used in
the case of finite soil systems.









M The mesh size in depth for semi-infinite media 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

WATERFLO M50 .


Several of these options can be specified at
in sequence with a space separating them.
.05 and a minimum number of points M of 100,


the same time. They are simply entered
For example, to specify a precision of
the program is executed by entering


WATERFLO P.05 M100 .

The order in which the options are specified is not important.
















































































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