step · 2021. 1. 27. · step: bulletin 85-3 issn 0096-6088 1linear parameter estimation program...
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Agricultural Experiment Station )lytechnic Institute and State University
·'.STEP:
Bulletin 85-3
ISSN 0096-6088
1linear Parameter Estimation Program ··aluating Soil Hydra
1
ulic Properties Jne-Step· Outflow Experiments ~ . J. C. Parker, and M. Th. van Genuchten
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James R. Nichols, Dean and Director College of Agriculture and Life Sciences Virginia Agricultural Experiment Station Virginia Polytechnic Institute and State University Blacksburg, Virginia 24061
The Virginia Agricultural and Mechanical College came into being in 1872 upon acceptance by the Commonwealth of the provisions of the Morrill Act of 1862 "to promote the liberal and practical education of the industrial classes in the several pursuits and professions of life." Research and investigations were first authorized at Virginia's land-grant college when the Virginia Agricultural Experiment Station was established by the Virginia General Assembly in 1886.
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ONESTEP: A Nonlinear Parameter Estimation
Program for Evaluating Soil Hydraulic
Properties from One-Step Outflow Experiments
J. B. Kool and J. C. Parker
Department of Agronomy
Virginia Polytechnic Institute and State University
Blacksburg, Virginia 24061
and
M . Th. van Genuchten
U. S . Salinity Laboratory
Riverside, California 92501
Virginia Agricultural Experiment Station
Bulletin 85-3
V!RGINIA POLYTECHNIC INSTITUTE AND STATE. U..NlV~•TY ueRARES
March 1985
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( . ..
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TABLE OF CONTENTS
Abstract . . . . .
Acknowledgements
Introduction .
Di re ct sol utiori of flow prob I em
Solution of inverse problem
Program description
Example problem . . .
Cone I us ions and future extensions
References .
Appendix A.
Appendix B.
Appendix C.
Appendix D.
Appendix E.
Input instructions for ON ESTEP.
Glossary of variables in ONESTEP.
Input file for example problem .
Output file for example problem.
Program listing ........ .
iii
.V
vi
. 1
.3
9
11
13
17
19
21
23
28
29 31
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LIST OF FIGURES
Figure 1. Nodal arrangement of the flow system.
Figure 2. Cross-sectional view of Tempe
pressure cell. Pneumatic pressure
is applied through A. Outflow is
collected and measured in burette B.
Air is removed from beneath the porous
plate through the small diameter tube
tube D via peristaltic action on
tube C .
Figure 3. Observed ( O ) and predicted moisture
characteristic for silt loam soil
Figure 4 . Hydraulic diffusivity calculated with
method of Passioura ( O ) and predicted
curve
iv
. 5
14
15
16
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ABSTRACT
J. B. Kool, J. C. Parker, and M. Th. van Genuchten. 1985.
ONESTEP: A nonlinear parameter estimation program for evaluating
soil hydraulic properties from one-step outflow experiments. Bulletin
85-3. Virginia Agricultural Experiment Station, Blacksburg.
This report contains a description of the parameter estimation
program ONESTEP. The program, written in FORTRAN IV, will
estimate up to five unknown parameters in the van Gen uchten soi I
hydraulic property model from measurements of cumulative outflow
with time during one-step outflow experiments. The outflow data can
be optionally supplemented with measurements of equilibrium moisture
contents and pressure heads. The[ program combines a nonlinear
optimization routine with a Galerkin finite element model for the one-
dimensional flow equation. Results obtained for a silt loam soil are
shown. Input instructions for the program, example input and
output files, and a program listing are given in appendices.
v
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ACKNOWLEDGME ns
The authors would like to express their appreciation to the
Virginia Department of Health and the Virginia Soil and Water
Conservation Commission for funding under which this research was
carried out.
vi
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INTRODUCTION
In recent years, interest has 6 risen in the feasibility of us ing
parameter estimation methods to determine soil hydraulic properties
from transient flow measurements. This approach can be summarized
as follows:
1. Hydraulic properties are assumed to be described by a
given model that contai h s a small number of unknown
parameters.
2 . Some flow-controlled attribute is measured at a number of
times during transient flow.
3. The same flow process is simulated numerically using initial
guesses for the unknown parameters.
4. Step 3 is repeated with adjusted parameter values at every
step until an optimum match between observed and
simulated response is obtained .
5. Back-substitution of fi na I parameter va I ues into the
assumed model yields the soil hydraulic properties .
Different authors (Zachman et al, 1981, 1982; Hornung, 1983;
Dane and Hruska, 1983) have considered a variety of experimental
procedures for obtaining input data for the estimation problem. Kool
et al. (1985) have presented a parameter estimation procedure which
uses measurements of cumulative outflow against time from
undisturbed soil cores, subjected to an instantaneous increase in
pneumatic pressure. Experimentally, the procedure is identical to
the familiar one-step method for qetermining soil water diffusivity.
The procedure is experimentally simple, quickly executed, and
applicable to soils of widely varying hydraulic properties.
Theoretical results dealing with solution uniqueness and sensitivity to
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2
error, as
presented
This
FORTRAN
well as actual results for a number of natural soils, are
elsewhere (Kool et al., 1985; Parker et al., 1985).
report describes the program ON ESTEP, written in
IV, that solves the parameter estimation problem. Input
instructions, example input and output files, and a program listing
are given in appendices.
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DIRECT SOLUTION OF FLOW PROBLEM
The hydraulic system being considered consists of two layers --
a soil core and a porous plate. For vertical flow in the assumed
nondeformable medium a solution tc Richard's equation is required
which .may be written in the head formulation as:
C(h) ~~ = ;x [K(h)(ah/ax-1] (1)
and subject to initial and boundary conditions:
ah/ax =
h = h - ha L
t = 0, 0 ~ x ~ L
t > 0, x 0
t > 0, x = L
(2a)
(2b)
(2c)
where x is distance taken positive downward with x=O located at the
top of the soil core and x=L at the bottom of the porous plate, t is
time, K is hydraulic conductivity, C = d8/dh is the water capacity
with 8 the volumetric water content and h the pressure head, h0
( x)
is the initial pressure head distribution, hL is the regulated pressure
head at the bottom of the porous plate and ha = tip/ pg is the
pneumatic head where tip is the gauge gas pressure applied to the
core, g is gravitational acceleration, and p is the density of water.
The notation employed regards the pressure potential h as the
component of total potential attributable to matric and hydrostatic
components but excluding pneumatic contributions. On the
assumption that gas pressure increments cause pneumatic potentials,
ha, to instantaneously propagate through the porous medium, ha is
effectively translated to the lower boundary condition.
3
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4
Properties of the porous plate are independent of h with C=O
and K=K . For the soil, e(h) is assumed to be descr ibed by van p Genuchten ' s (1978a) expression
J (1 + !ah i nrm h
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5
boundary problem is solved by means of simple forward difference
scheme that uses the same spatial discretization of the flow domain as
applied to the finite element solutio h (Figure 1). From the specified
initial condition (2a), it is first determined if part or all of the soil
column is unsaturated. If the entire column is initially unsaturated,
initial condition (2a) is simply passed on to the finite element routine
to begin flow simulation . The criterion for determining whether the
soil at node x . is unsaturated is: I
h (x.) $ h 0 I e (6)
where he is some value of the pressure head close to zero, which was
a rbitra ri ly fixed at:
(7)
On the other hand, if all or p art of the soil is saturated, the
solution proceeds in the following manner. Let x. be the nodal I
coordinate(x) node 0 •
2 • • • •
i+1 • soil • • • •
L' • • } pcrous olat~ • L NN •
Figure 1. Nodal arrangement of the flow system.
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6
coordinate at which the boundary between unsaturated and saturated
zones is located, i.e. the soil is unsaturated at O
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7
By employing this scheme for the first stage of outflow from
saturated cores, marked reductions in computational time were
obtained for the problems that we have investigated, with negligible
concomitant loss in accuracy.
After al I elements become unsaturated, program control is passed
to the finite element routine. Equations ( 1), (2b), and (2c) are then
solved with the modified initial condition:
h(x,t0
) =he
M-1 to = r tit .
j=i J
( 13)
Cumulative outflow at time t during the finite element simulation is
obtained as:
Q(t;l =A f~ [B(x,t) - B(x,0)] dx ( 14)
Note that the equilibrium pressure head distribution hf(x)=h(x,t=00 )
and therefore 8(hf) may be obtained directly from the lower boundary
condition (2c). The corresponding equilibrium outflow can thus be
obtained immediately without the ne~d to solve ( 1) for large times.
The finite element routine uses a variable weighted finite
difference model to approximate ~ime derivatives (van Genuchten,
1978b, eq. 14), where the temporal weighting coefficient w may vary
between 0 and 1. Stability requires that 0.5 5 w 51. Choosing w =
0. 5 corresponds to a second-order correct time-centered model.
When w=l is used, a first-order correct, backward difference scheme
res u Its. Coefficients K and C in ( 6) a re a I ways evaluated at the
half-time level, independent of the time weighting scheme used. Due
to the strong nonlinearity of (1), an iterative procedure is used to
obtain the new pressure head distribution ht+tit' at the end of tit.
The general iteration scheme is:
h k + (1 )hk-1 £ t+tit -e: t+tit ( 15)
where e: is a weighting coefficient (0 5 e:5 1) and k denotes iteration
number. Iteration continues u nti I a specified degree of
correspondence is obtained between pressure head distributions
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8
before and after a certain iteration step. As in the original code,
convergence is determined by the program variables TOL 1 and TOL2.
In most cases choosing E:=l will lead to fastest convergence. In some
cases, however, notably when s imu la ting flow th rough coarse
materials, the above scheme with E:=l fails to converge rapidly due to
oscillation in successive iterations. These oscillations are most
pronounced when a time-centered (w=O. 5) scheme is used and often
may be effectively removed by switching to a backward difference
scheme (w=l). In severe cases, oscillations can be further damped
by using E:=0.5 in (15). Time step size is controlled by the number
of iterations required for convergence. When the iteration fails to
converge in a given number of steps (controlled by variable
NITMAX), the time step is halved and the iteration started anew.
Slow convergence may greatly increase computer costs, due to both
the greater computational effort required per time step and to the
increased number of (smaller) time steps. To avoid exces.sive
computer costs, the number of times the iterative procedure fails to
converge within NI TMAX timesteps is counted (variable NOCON) and
execution is interrupted when NOCON exceeds a specified limit
(controlled by variable NOMAX).
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SOLUTION OF INVERSE PROBLEM
Values of the unknown
properties in
function:
(3)-(5) are
parameters defining the soil hydraulic
desired which min 1m1ze the objective
N A 2 E(b) E [w.{Q(tt)-Q(b,t.)}]
i =l l l
M " 2 +E[v.{e(h.)-e(b,h.)}] j= l J J J
( 16)
where Q(ti) is the measured cumulative outflow at times ti (i=l, .. . N),
Q(b , ti) represents the numerica jly calculated cumulative outflow
computed for the tria I pa ramete 1 vector b, 8 ( h .) is the water
content corresponding to pressure head hj for equili~rium desorption, 8( b , hj) is the predicted water content for trial parameter vector bas
calculated from (3) , and w. and v . are weight ing factors. The I J
second term in the objective function allows available data from
equilibr ium desorption experiments to be included in the optimization
process. As shown by Parker et al. (1985), this inclusion will
reduce the likelihood of nonuniqueness problems dur ing the inversion
process The differences 8( hj)-8(b , hj) are automatically pre-weighted
by the factor :
( 17)
which gives 8( hj)-values approximately the same weight as the
Q ( ti)-observat ions. Unless otherwise specified in the program input,
weighting coefficients wi are fixed at unity, and coeffic ients vj are
set equal to a .
Parameters are adjusted until the optimum set of va lues , b 0 , for
which E( b) has a minimum, is obtained . Assuming that the problem
has a unique solution, that is that E( b) has only one (global)
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10
minimum, then backsubstitution of the parameter values b 0 into
(3)-(5) yields the soil hydraulic properties .
The optimization algorithm used to evaluate b0 is based on
Marquardt ' s maximum neighborhood method (~larquardt, 1963) which
is an opt imum combination of the method of steepest descent and the
Gauss-Newton Taylor series method. The computer code for
imp lementing this method was adapted from Meeter (1964). For
highly nonlinear problems this method is efficient and quite robust.
The value of any of the five parameters 8s' Sr ' Ks , ex, and n
may be either optimized or kept constant during optimization. Since
8 and K can be measured relatively easily , it is recommended that s s measured values be used for these two parameters . Limiting the
number of parameters to be optimized wi 11 reduce problems of non-
u n iqueness and wi 11 al so reduce computational effort. The
optimization algorithm evaluates the partial derivatives aE/aj for each fitted parameter j at every iteration of the optimization routine, thus
requiring for each iteration at least J + 1 solutions of the flow prob I em,
where J is the number of fitted parameters.
Both upper and lower limits may be specified for the parameters
to be optimized. When no limits are specified, unconstrained
optimization is used. Note that both upper and lower limits must be
specified fo r constrained optimization. For the three parameter model
(a, n, 8 r), it was found in practice to be unnecessary to specify
limits for ex. The van Genuchten model ( eqs. 3-5) requires n~l.
Using a lower limit of 1. 1 for n will avoid numerical problems that
may occur when n is very close to 1. Finally, it is recommended to
specify an upper limit for Sr to insure 8r
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PROGRAM DESCRIPTION
The FORTRAN IV program ONESTEP couples nonlinear
regression analysis and a numerical solution of the direct flow
problem. ONESTEP consists of a main program (MAIN) and seven
subprograms (MATINV, FLOW, STAGEl, TOTALM, BANSOL, MATEO,
SPR). The main program first reads data from an input file
(unit=5) which is echoed back to an output file (unit=6). Input
instructions and a glossary of impo 1rtant program variables are given
in Appendices A and B, respectively.
Input data consist of a rlumber of program parameters,
dimensions of soil core and porous plate, and initial values for the
five soil parameters (ex, n, 8 , 8 and K ) . Each of the parameters r s s can be either held constant or optimized (controlled by the value of
INDEX for each parameter). Input data also specify the initial
pressure head distribution and nodal spacings. Material properties
are node-centered so the boundary between plate and soil must be
located between two nodes with different material indices. Observed
Qi and ti data (FO(I) and HO(I), respectively) are read in along
with the weighting factors, WT(I), if nonuniform weighting is
desired. If equilibrium h-8 data are included in the optimization,
they a re stored in the same arrays FO (I) and HO (I), respectively,
following the Q (t) data. The variable I TYPE disti ngu is hes whether
data are Q(t) data (ITYPE=O) or 8(h) data (ITYPE=l) . If WT(I)
values are omitted, weighting factors default to WT(l)=l for all
observations. With respect to eqs. (16) and (17), WT corresponds to
w. for Q(t) data and to v ./a for 8(h) data. I J
Most of the parameter estimation routine is carried out in MA IN
which also outputs results when the optimization is completed, either
because the parameters have converged (controlled by variable
STOPCR) or because the maximym number of iterations of the
optimization routine is reached (controlled by variable MIT).
Subroutine MATI NV performs the matrix inversion for the optimization
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routine, whereas subroutine FLOW controls the solution of the flow-
equation. Subroutine ST AG El checks whether the soi I is in itia I ly
saturated or unsaturated, and in the former case solves for the first
stage of the outflow process. Subroutine MATEO performs the finite
element simulation, and performs the necessary calculations for
assembly of the global matrix equation, which is subsequently solved
in subroutine BANSOL to obtain the updated values of the pressure
heads and their gradients. Subroutine TOTALM calculates the
amount of water present in the sample at desired times by spatia I ly
i nteg rating the nodal moi st.u re contents. The function SP R generates
the different soil hydraulic functions [8(h), K(h), C(h), and h(8)]
according to (3)-(5).
Versions of the program are currently operating on an IBM 3084
mainframe, Prime 750 minicomputer and I BM PC microcomputer.
Minimum hardware requirements to run the program on an IBM PC are
70 K of random access memory, disk drive and an 8087 math
coprocessor. Machine readable copies of source and compiled code
are available from the first author on request.
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EXAMPLE PROBLEM
As an example of the parameter estimat ion program, res u Its a re
given for a silt loam soil. An undisturbed core sample (3 . 95 cm
long, 5. 4 cm diameter) was ta ken from the field and eq u i Ii brated at
zero tension in a Tempe pressure cell (Figure 2). For comparison
with the transient met ho~, the moisture retention characteristic 8 ( h)
was first determined by stepwise increases of pneumatic pressure on
the sample up to a pressure of 98 kPa (ha = 10 m) with water loss
measured at every step. Moisture contents for h=-30 and -150 m
were measured on disturbed samples of the same soil. After
resaturating, the pneumatic pressure was increased instantaneously to
ha=lO m and cumulative outflow was recorded with time . To maintain
a constant head lower boundary condition during the one-step outflow
test, the posit ion of the measuring burette was adjusted every time a
reading was made. Entrapped air beneath the porous plate was
f lushed through tube D by applying a peristaltic action on the lower
tube C (see Figure 2). Upon cor pletion of the one-step test the
porous plate was removed and the soil resaturated. Saturated
hydraulic conductivities of the soil and porous plate were measured
by falling head tests using leaching solutions of 0.01 M CaCl 2 .
The three un known parameters a., n and e r were est imated from
the observed cumulative outflow versus time data and also the
measured 8 at h=-150 m. Input and output files for this problem are
given 1n Appendices C and D, respectively . Note that in our
example all lengths are given in centimeters and times in hours ; in
general any consistent set of units may be used . Figure 3 compares
the 8 ( h )-curve obtained by parameter est imat ion with the
experimental 8(h)-data. In Figure 4, the predicted diffusivity curve
is plotted with D(S) values that were determined independently from
one-step outflow measurements by t Ke method of Pass iou ra ( 1976) .
Running this example problem required 45 seconds of CPU time
on an I BM 3084 mainframe. The same problem on an I BM PC ( with
8087) took about 60 minutes .
13
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14
a-ring
Figure 2 .
A
~---soil core
~-------,...,.....-----..........- ~~1-- o- ring porous plate
B
Cross - sectional view of Tempe pressure cell . Pneumatic
pressure is applied through A. Outflow is collected and
measured in burette B. Air is removed from beneath
porous plate through the small diameter D via peristaltic
action on tu be C.
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15
103
102
-..§ 0 a: w 101 I
w a:: ::J tf)
lJ) 10° [!] w a: Q..
10- 1
10-2 +-~--~~------~------~~--~~
Figure 3.
0.1 0.2 0.3 0.4 e &n3 m-3)
Observed (0) and predicted moisture characteristic for
silt loam soil.
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16
Figure 4 .
10-10...-~~~~--,r--~~~~-.-~~~~----i
0.1 0.3 0.4
Hydraulic diffusivity cal cu lated with method of Passiou ra
(D) and predicted curve .
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CONCLUSIONS AND FUTURE EXTENSIO NS
Inversion of the unsaturated flow equation a !lows the water
retention characteristic and hydraulic conductivity to be determined
simultaneously from transient flow measurements . The one-step
outflow method is a convenient procedure to obtain the necessary
data from laboratory soil cores. Outflow versus time measurements,
complemented with the measured 15 bar moisture content of the soi I,
in practice yield sufficient information to obtain a unique solution for
the inverse prob I em. A requirement is that initial parameter
estimates are sufficiently close to their final values. Reasonable
initial estimates can be made on the basis of the texture of the
sample. The FORTRAN IV program described in th is bulletin
specifically estimates the parameters in the van Genuchten model for
hydraul ic properties from outflow and / or equi librium moisture content
vs. pressure head data. Future work will involve the use of other
input data for the inversion procedure. Measurements during
infiltration into the soil can be used to obtain the wetting hydraulic
properties of th~ soil. Used in conjunction with the outflow test,
this may provide a convenient procedure for evaluat ing hysteresis .
Al so, extension of the method to use field measured i nfi It ration and
drainage data wi 11 be studied. I Si nee most studies of soi I-water
cha racteri sties a re ultimately directed towards f ield-sea le flow
processes, in-situ measurements are more relevant than data obtained
from generally small soil cores, the collect ion of which will
unavoidably introduce some disturbance of the soil .
17
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18
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1.
REFERENCES
Dane, J. H. and S. Hruska. 1983. In-situ determination of
soil hydraulic properties during drainage.
J. 47:619-624.
Soil Sci. Soc. Am.
2. Hornung, U. 1983. Identification of nonlinear soil physical
parameters from an in ut-output experiment. In: P. Deufl ha rd
and E. Hairer, eds. Progress in scientific computing.
Birkhauser, Boston.
3. Kool, J. B., J. C. Parker and M. Th. van Genuchten. 1985.
Determining soil hydraulic properties from one-step outflow
experiments by parameter estimation. I. Theory and numerical
studies. Soil Sci. Soc. Am. J. (submitted).
4. Marquardt, D. W. 1963. An algorithm for least-squares
estimation of nonlinear parameters. J. Soc. Ind. Appl. Math.
11 : 43 1 - 44 1 .
5. Meeter, D. A. 1964. Norn-linear least-squares (Gaushaus).
Univ. Wisc. Computing Center. Program revised 1966.
6. Mualem, Y. 1976. A new model for predicting the hydraulic
conductivity of unsaturated porous media. Water Resour. Res.
12 : 513- 522 .
7. Parker, J.C., J . B. Kool and M. Th. van Genuchten. 1985.
Determining soil hydraulic properties from one-step outflow
experiments by parameter estimation. 11. Experimental studies
Soil Sci. Soc '. Am. J. (submitted).
8. Passioura, J. B. 1976. Determining soil water diffusivities
from one-step outflow experiments. Au st. J. Soi I Res. 15: 1 -8.
9. van Genuchten, M. Th. 1978b. Calculating the unsaturated
hydraulic conductivity with a new closed-form analytical model.
Res. Rep . 78-WR-08. Dept. of Civil Engine~ring, Princeton
University, Princeton, New Jersey.
19
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20
10. van Genuchten, M. Th. 1978b. Numerical solutions of the
one-dimensional saturated-unsaturated flow equation. Res.
Rep. 78-WR-09, Dept. of Civil Engineering, Princeton, New
Jersey.
11. van Genuchten, M. Th. 1980. A closed-form equation for
predicting the hydraulic conductivity of unsaturated soils . Soil
Sci. Soc . Am. J. 44:892-898.
12. Zachmann, D. W., P. C. Duchateau , and A. Klute. 1981.
The calibration of the Richards flow equation for a draining
column by parameter identification. Soil Sci. Soc. Am . J .
45: 1012-1015.
13. Zachmann, D . W., P . C. Duchateau , and A. Klute. 1982.
Si mu ltaneou s approximation of water capacity and soi I hyd rau I ic
conductivity by parameter identification. Soil Sci . 134: 157-163.
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Card
2
3
4
5
6
7
8
APPENDIX A: Input instructions for ON ESTEP
Columns Format
1-5
1-80
1-80
1-5 6-10
11-20 21-30 31-40 41-50 51-60
1-10 11-20 21-30 31-40 41-45 46-50 51-55
56-60
1-10
11-20 21-30 31-40
15
20A4
20A4
15 15 ElO .O FlO.O F10.0 FlO.O F10 .0
FlO .O FlO. 0 FlO .O FlO .O 15
15 15 15
FlO .O FlO .O FlO. 0 FlO .O
Variable
NCASES
TITLE
TITLE
NN
LNS
DNUL
PNl
AIRP
EPSl
EPS2
SLL PLL DIAM
CPLT
NOBB
MDATA
MODE
MIT
B ( 1)
B (2)
8 (3)
8 (4)
21
Comments
Number of cases considered. The remaining cards are read in for each case.
Title
Title
Blank card
Number of nodes
Number of nodes in soi I
In itia I time step
Pressure head lower boundary
Pneumatic head
Temporal weighting coefficient
Iteration weighting coefficient
Length of soil core
Thickness of por-ous plate
Diameter of soil core
Conductiv ity of porous plate
Number of observations
Mode for i nput data
Mode for output
Max imum iterations of optimi-
zat ion rout ine
Blank card
Init ial value of a
Initial value of n
I nit i a I v a I u e of 8 r
Initial v alue of 8 s
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22
9
10
11
41-50
1-10
11 - 20
21-30
31-40
41 - 50
1-10
11-20
21-30
31-40
41-50
1-10
11-20
21-30
31-40
41-50
12 1 1-5
6-10
11-20
21-30
13+NN 2 1-10
11-20
21-30
31-40
FlO. 0
110
110
110
110
110
FlO.O
FlO.O
FlO.O
FlO.O
FlO.O
FlO.O
FlO.O
FlO.O
FlO.O
FlO.O
1-5
15
FlO.O
FlO.O
FlO.O
FlO.O
FlO.O
15
B (5) Initial value of Ks
INDEX(l) Index for each
INDEX(2) coefficient
INDEX(3)
INDEX(4)
INDEX (5)
BMIN(l)
BMIN(2)
BMIN(3)
BMIN(4)
BMIN(5)
BMAX(l)
BMAX(2)
BMAX(3)
BMAX(4)
BMAX(S)
K
MAT
X(K)
P(2K-l)
HO( I)
FO( I)
Minimum value for
each coefficient
Maximum value for
each coefficient
Nodal number
Material index, l=soil;2=plate
Nodal coordinate
Initial pressure head
Time (ITYPE=O) or pressure-
head (ITYPE=l)
Outflow ( ITYPE=O) or mois-
ture content (I TY PE=l)
WT (I) Weighting factor; omit for
default weighting
ITYPE(I) Data type: ITYPE=O for Q(t),
ITYPE=l for 8(h)
1 This ca rd specifies the geometry and the initial conditions of the flow system, and is repeated for each of the NN nodes.
2 This card contains the observed Q(t) and/or 8(h)-data and is repeated NOBB times.
-
APPENDIX B: List of most significant variables in ON ESTEP
Units are given in brackets (L=length T=time) , and name of the
subprogram in which the variable is used is given in parentheses.
Variable
ALPHA
AEP
AIRP
AREA
B(5)
BI ( 10)
BMAX(5)
BMIN(5)
Definition
Parameter ex [L- 1] (SPR)
Air-entry value of h [L] (STAGEl).
Pneumatic head [ L].
Cross-sectional area of soil core [L].
Array containing initial values of parameters
(MAIN); B(l)=cx, 8(2)=n, B(3)=8r, B(4)=8s,
B(5)=K5
.
Array containing names of parameters (MAIN).
Array containing maximum permissible parameter
values. See note on BMIN .
Array containing minimum permissible parameter
values. If BMIN and BMAX are omitted for any
parameter, their values will not be subject to any
constraints.
BN(l5), TH(15), TB(l5) Arrays containing present parameter values.
CONDS Hydraulic conductivity [LT- 1] (SPR).
CPLT Hydraulic conductivity of porous plate [LT- 1].
23
-
24
DELT
DELCH
DELMAX
DELMIN
DIAM
DNUL
EPSl
EPS2
FC(25)
F0(25)
H0(25)
I NDEX(5)
!STEP
!TYPE
LNS
Timestep [T] (FLOW).
Relative increase of DEL T between two consecutive
time steps (FLOW).
Maximum value for DEL T [T] (FLOW).
Minimum value for DEL T [T] (FLOW).
Diameter of soil core [L] (MAIN).
Initial time step [T] (FLOW) .
Temporal weighting coefficient, Q::;EPSl::;l (FLOW)
EPSl=O, 0.5 and 1 corresponds to forward, central
and backward difference model respectively .
Iteration weighting coefficient.
Array containing simulated results (FLOW).
Array containing observed results (FLOW).
Array containing observation times [T] or pressure
heads [ L] .
Index for each parameter . If INDEX(l)=O, the par-
ameter 8(1) is known and kept constant; if
INDEX(l)=l , B(I) represents only a initial guess and
the best-fit value for the parameter is determined by
optimization.
Time step counter (FLOW).
Flag for input data. ITYPE=O: Q(t) data, ITYPE=l:
9(h) data.
Number of nodes located in soil .
-
MAT
MAX TRY
MOAT A
MIT
MODE
NN
NCASES
NIT
NITMAX
NITT
NOCON
25
Material index; MAT=l: soil, MAT=2: porous plate.
Maximum number of function evaluations within an
iteration of the optimization routine to find new par-
ameter values that decrease SSQ. Currently set to
20 in MAIN.
Mode for outflow data. MOAT A=l: transient outflow
data only; MDA T A=2: last Q ( t) entry represents
equilibrium outflow (t is dummy value).
Maximum number of iterations for optimization rout-
ine. (MAIN)
Mode for optimization routine. MODE=O: flow equation
is solved only for initial parameter values. MODE=l:
optimization process continues until parameter values
converge or the number of iterations reaches MIT;
all intermediate parameter values are printed.
MODE=2: as MODE=l, except parameter values are
only printed at end of every iteration. MODE=3: as
MODE=2 but 8(h) and K(h) according to final param-
eter values are also printed. MODE=9: error condi-
tion, program continues with next case.
Total number of nodes used in finite element solu-
tion. (FLOW)
Number of cases considered (MAIN).
Iteration number within time step (FLOW).
Maximum for NIT (FLOW).
Iteration number for optimization routine (MA IN) .
Counter for number of times NIT exceeds NI TMAX
(FLOW).
-
26
OB
NOMAX
NP
NSTEPS
P(NN2)
PE(NN2)
PNl
PLL
QOUT
RELSAT
SLL
Number of observations.
Maximum for NOCON (FLOW)
Number of parameters to be optimized
Maximum for ISTEP (FLOW).
Array containing values of h and ah/ax at previous
time step (FLOW).
Array containing latest values of h and ah/ax
(FLOW).
Lower boundary condition during outflow process [L]
(FLOW).
Thickness of porous plate (STAG El).
Cumulative outflow during first stage (STAGEl).
Relative saturation ( 8/8 s) at which the soi I is
assumed to be unsaturated (STAG El).
Length of soil core [L] (STAGEl).
SPR(MAT,BN,N,PR) Function to calculate the soil hydraulic
properties . MAT: material index, MAT=l: soil,
MAT=2: porous plate. NB: array containing param-
eter values. N: Index. N=l: 8(h) is calculated,
N=2: K(h) is calculated. N=3: C(h) is calculated,
STOPCR
N=4: h(8) is calculated.
when N=4).
PR: value of h (or 8
Stop criterion for parameter optimization. Optimiza-
tion stops when relative change in each parameter
becomes less than STOPCR (MAIN).
-
SUMT
T(60)
TE(60)
TOL 1, TOL2
TMINIT
TMIN
WCR
wcs
WT(25)
X(30)
27
Cumulative time [T] (FLOW).
Array containing intermediate values of h and ah/ax
(FLOW)
Array containing values of h and ah/ax at previous
iteration (FLOW).
Absolute and relative convergence criteria for itera-
tive solution process (FLOW).
Initial amount of water in soil [L 3 ] (FLOW).
Current amount o~ water in soil [L 3 ] (FLOW).
Parameter er (SPR).
Parameter 8 (SPR) . s
Array containing weights assigned to every observa-
tion.
Array containing nodal coordinates [L].
-
APPENDIX C. INPUT FILE FOR EXAMPLE PROBLEM
1 SIL l LAM ll/011/1311 MrlllOD II INPUI DATA (PARKEH FT AL, 19811)
13 10 3.95
0.0250 1
1 1 2 I 3 1 11 1 5 I (> I I 1 H 1 9 1
10 1 11 ?. 12 2 13 ?. o. () 17 (). 03 :1 O.O'j() 0. 1(j7 0. 500 1 . 033 2. 150 'j . 111 7
99'). 9 -1 5000. ()
1 . I -05 0. 57
1. 50 1
1.1 10.0
o.n (). 5 1.0 1. 5 2 . () ? . '.J :\.()
:l.'..> O 3. 7 '..> 3.'.J() 11. no 11. 2) 11 . '.>2
1. 80 3 . /() 11.110 7.80
lU. 20 11 .110 12 .135 13. 59 1'.J. 62 0. 157
?.5? 5.110
0.200
0.300 -?. . () -1. 5 -1. (J -0. 5
(),()
(). 5 1 .Cl 1. 5 1. 1') 1 . 90 2.00 2.25 2.52
28
1000.0 0.003
1.ll 10
0.3138 5 .ll()()
1. 0 2 ?
0 ()
15
-
APPENDIX D. OUTPUT FILE FOR EXAMPLE PROBLEM
****************************K*K****************H*******K***K******K********KH** * *
K
* * SI LT LO/l.M 8/011/811 * : METHOD 11 INPUT DAT/I. (P/l.Rl
-
30
8 5.417 13.590 0 1.0 9 999.900 15.620 0 1. 0
10-15000.000 0. 157 1 1. 0 ITERATION NO SSQ ALPHI\ N WCR
0 14.3551178 0.0250 1.5000 0.2000 1 8.6202688 0.0395 1. 5927 0. 1829 2 5. 13811296 0.0586 1.5318 o. 1871 3 IL 3154287 0.0495 1.5358 0.1828 4 4.0541239 0.0530 1.5177 o. 1823 5 3.81~510112 0.0511 1. 5077 0. 1806 6 3.6868916 0.0504 1.4988 o. 1792 7 3. 5398378 0.0494 1.4891 o. 1780 8 3.4026499 0.0484 1.4813 o. 1767 9 3.2833033 o. 01179 1 .11737 0. 1756
10 3.1732512 0.01112 1.4667 o. 111111 11 3.0758791 0 :)471 1.lJ610 0.1732
RSQUl\RE FOR REGRESSION OF PREDICTED VS OBSERVEU =0 . 99930
CORRELATION Ml\TRIX
1 1 1.0000 2 0.6918 3 0.574Q
2
1. 0000 0.9510
3
1.0000
NON-LINEAR LEAST-SQUl\R[S l\Nl\LYSIS: rlNAL RESULTS
VARIAl3LE ALPllA N WCR
VALUE 0. 01~705 1.116097 0.17321
S.E.COEFF. 0.0125 o. 1035 0 . 0166
95% CONFIDENCE LIMITS LOWER UPPER 0.02 0.0767 1. 22 1. 7058 0.13 0 .21 211
--------013SfRVED & FITTED OUTFLOH --------Hr.SI-
NO TIME (HR) 013S r I TTED DUAL 1 0.017 1.800 2.077 -0. 2Tl 2 0.033 3.700 3. 8117 -0. 147 3 0.050 ll. 800 11. 8118 -0.048 4 0. 167 7.800 7. 59ll 0.206 5 0.500 10.200 9 . 97'.J 0.225 6 1. 033 11. llOO' 11. l11Q -0.010 7 2.750 12.850 13. 078 -0.228 8 5.lt 17 13.590 111. 01t1 -0.1124 9 999.900 15.620 16. 1111 -0.521
10-15000.000 0. 157 0.164 -0.027
FINAL CONDITIONS ================
PRESSURE 11 [ /\0 MOISTURE CON1FN1 NOOE OE Prn FUNCTION GRAD I ENI rUNCI ION GRAD I EN r
1 0.00 -1002.000 1 .000 0.210 0.000 2 0.50 -1001.500 1. 000 0.210 0.000 3 1. 00 -1001. 000 1. 000 0.210 0.000 ,, 1. 50 -1000.500 1. 000 0.210 o.uuo 5 2.00 -1000. 000 1. 000 0.210 0.000 6 2.50 -999.500 1. 000 0.210 0.000 7 3.00 -999.000 1. 000 0.210 0.000 8 3.50 -998.500 1 .000 0.210 0.000 9 3.75 -998.250 1. 000 0.210 0.000
10 3.90 -998.100 1. 000 0.210 0.000
INITIAL AMOUNT OF MOISTURE IN SAMPLE 35.099 CM3 FINAL 18. 910
-
c c c c c c c c c c c
c c
c c
c c
c c
APPENDIX E. PROGRAM LISTING
****************************************************************M* * * * [V/\I U/\ TI ON or so IL llYOR/\UL I c PRO PE.HT I [S rrwM * ONESTEP OUTFLOW DAT/\ BY PARAMETER ESTIMATION *
* * *
* J.B. l
-
32
c
NU1 -= NV/\R+1 NlJ?- NVAR*? Nl' -= 0 lJO fl l =- NlJl,NU? 11 -= l-NVAH H3( I ) = B( I 1) IF(INDEX(ll).EQ.0) GO TO 8 NP- NP+l 1
-
c C ----- BEGIN OF ITERATION -----
c
311 NITf= NITT+l NET=O GA= O. l*GA 00 38 J = 1, NP l[MP= Tll( ,J) TH(J) = l.Ul*Tll(J) O(J) = O. CALL FLOW(Tll,OELZ(1,J),NITT,NOCON,MDATA,MODE) I f(MOO[. EQ.1)WRITE(6,1038) (TH( I), 1= 1,NP) lf(MODE.EQ.9) GO TO 144 00 36 1= 1,NUBB OEl.Z( l,.J) =Wf( I )*(OELZ( l,J)-fC( I)) l F( I .GI. NOl3) DELZ( I ,J ) = DELZ( I , ,J )*DEFWf
36 Q(J) = Q(J)+DELZ( l,J)*R( I) Q(J) = 100.*Q(J)/TH(J)
C ----- Sl[[PEST DESCENT -----
c
38 Tll( .J ) -= TLMI' DO t111 1= 1,NP 00 112 ,J =- 1, I SUM=- 0. 00 11() K-=- 1, NOBB
40 SUM= SUM+DELZ(K, I )*DELZ(K,J) D( I ,.J) -= IOUOO.*SUM/(HI( I )*Tll(,J))
4?. D(J, I ) = D( 1,J)
C ----- 0 = MOM[NT MATRIX 411 E( I ) = SQRT( D( I, l)) 50 DO 52 I = 1 , NP
DO 52 J = 1,NP '}2 A( I ,J ) c:: O( 1,J )/( [(I )*E(J))
c C -----/\IS lllE SCALE.D MOMENf MATRIX-----
rm ')11 I :-: 1. NP C( I) ' Q( I)/[( I) Cll I (I ) :-o C( I)
511 /\(1,1) - /\(1,l)~GA C/\I L MAflNV(/\,NP,C)
c c ----- c;r Is fllE CORIU:CT I ON VEClOR -----
SI ff' -: 1. 0
c
56 N[l · NI T+l DO '.> 8 1- 1, NP l B( I ) ·· C( I) l+ Slf P/[( I )+Tit( I) ll(BMIN(l).[Q.flMAX(I)) GO 10 58 I r ( 113 ( I ) . L r . OM I N ( I ) ) 113 ( I ) :- (3M I N ( I ) I F ( 1 R ( I ) . G I . 11M/\X ( I ) ) l B ( I ) = 13MAX ( I ) C( I) = ( rlJ( I )-111{ I) )*E( I )/STEP
58 CON I I NU[ 60 DO 62 1=1,NP
IF ( fll ( I ) * 113 ( I ) ) 66, 66, 62 62 CON I I NU E
SUM!1o-:: O.U C/\I. I. I LOH( I B, r C, NI TT, NOCON, MDI\ l /\,MOOE) I r ( MO()[ . [CL 1 ) WR I T [ ( 6 ' 1 0 3 8 ) ( rn ( I ) , I = 1 , N p ) I F ( MODF. [Q . 9) GO TO 11111 DO 611 ' " 1, Norm R( I ) =WI{ I)"' ( 10( I )-re( I)) II (I . GI .NOU)R( I ) ~ R( I )l+OEFWf
611 SUMU- SUMU-+R( I )*R( I) 66 SllMl = 0.0
SllM2=0.fl SUM3 "-0.0 DO 68 1- l, NP SllMl = SllMl+C( I )*CHI( I) SUM2 = SlJM?+C( I ) *C( I)
68 SUM3 =- SlJM1+Cll I ( I )*Cll I ( I ) ARG .- SUM1/SQHT(St1M2*SUM3) ANGLE~ 57. 2 9578*ATAN2(SQRT(1.-ARG*/\RG),ARG)
33
134 135 136 137 138 139 1 llO 1111 1'12 1113 141~
145 1116 1111 1118 1'19 150 151 152 153 1511 155 156 157 158 159 160 161 162 163 1611 165 166 16 7 168 169 170 1 7 1 172 173 1 ,,~ 1 f '.) 176 177 118 179 180 181 rn 2 183 1811 18'} 186 187 188 189 190 191 192 193 1911 1')5 196 197 1913 199 ?00 2 01 2 0 2 203 2 011 2 05
-
34
c ---------- 206 00 72 I == 1 , NP 20 7 Ir( Tll( I )*TB( I) )74, 71-t, 72 ?OB
72 CONllNUE 209 IF(N[T.GE.MAXTRY) GO TO 79 2 10 lf(SlJMB/SSQ-1.0)80,80,7/t 211
74 IF(ANGLr- :rn.0)76, 76, 78 2 12 16 s H r- s 1 E r /? . o 2 1 3
GO I 0 '..>6 21'1 78 GA~ lO.~GA 2 15
GO TO 50 216 79 WRl1E(6,1086) 217
GO TO 96 218 c 2 19 C ----- PRINT COEFflCIENTS AFTER [ACH ITERATION ----- ?20
80 CONJ INUl 221 DO 82 l = l,NP 222
82 111( I) = fB( I) ?23 WRITE(6, 10112) NITT,SUMB, (HI( I), 1= 1,NP) 2211
c 225 90 DO 92 1= 1,NP 226
I F(ABS(C( I )*SfEP/E( I))/( 1.0E-20+ABS(TH( I)) )-STOPCl1) 92,92,911 227 92 CONTINUE 228
GO 10 96 229 94 SSQ~ SUMU 230
I r ( N I 1 T • l T . M I r ) GO T 0 3 ,, 2 3 1 c 232 c ----- fNO or lfERATION LOOP 233
96 CONllNlJE 2311 CALL MATINV(D,NP,C) 235
c 236 C ----- WRITE RSQUARE, CORRELATION MAfRIX ----- 237
SUMOc=- 0.0 238 StJMC=O. O 239 SllM02= 0. 0 2110 SUMC2=0. 0 2 11 1 SUMOC= O.O 242 00 98 1= 1,NOl3B 2113 SUMO= SUMO+FO( I) 21111 SUMC= SUMCHC( I ) 2115 SUM02= StJM02+rO( I )*FO( I) 2"6 SUMC2= SllMC2+rC( I )*FC( I) 2117
98 SUMOC=SUMOC+FO( I )*FC( I) 248 RSq= ( SlJMOC-SUMO*SUMC/NOBB )**2/ ( ( SUM02-SUMO*SllMO/NOBB) *( SUMC2-SUMC* 2119
1 SUMC/NOBl3) ) 250 WRITE(6, 1050) RSQ 251 DO 100 I = 1, NI' 252
100 E( I ) = SQRT( D( I, I)) 253 WRlfE(6,lOl16) (1,1 = 1,NP) 2511 00 1011 1= 1,NP 255 DO 102 J := l, I 256
102 A( .J, I ) -= D(,J, I)/( E( I )*E(J)) 257 104WRITE(6,1048) 1,(A(J, I ),J = l, I) 258
c 259 C ----- CALCULATE 95% CONFIDENCE INTERVAL ----- 260
Z= l./FLOAT(NOBB-NP) 261 SDEV= SQRT(Z*SUMB) 262 WRITE(6, 1052) 263 TVAR= 1. %+Z*( 2. 3 779+Z*( 2. 7135+Z*( 3. 187936+2. l166666*Z**?.))) 2611 DO 108 1= 1, NP 265 SECOEF= E( I )*SDEV 266 TSEC= fVAR*SFCOlF 267 TMCOl= lH( I )-TSEC 268 TPCOE= Tll( I )+TSEC 269 K=2*1 270 J = K-1 271
108 WRITE(6,1058) Bl(,J),Bl(K),TH(l),SECOEF,TMCOE,TPCOE 272 c 273 C ----- PREPARE FINAL OUTPUT ----- 2 flt
110 WRITE(6,1066) TYPE(1),TYPE(2) 275 DO 118 I = 1, NOUB 276 R(l) = FO(l)-fC(I) 277
118 WRITE(6, 1068) ~,HO( I), FO( I), FC( I ),R( I) 278
-
35
c ?..79 C ------FINAL PRESSURE HEAD AND MOISTURE CONTENT DISTRIBUTION----- 280
122 lMIN= 0. 28 1 WR 11 [ ( 6, I 080) 252 NL~ I NS-1 283 DO 130 L= 1,NF. ?8l1 l ~ ?*L-1 285 11 = 1+1 286 12 7 1+~ 287 137. I ~3 288 El =X(L+l)-X(L) 289 P13 -= . 7llfl/1107*P( I )+.2592593*P( 12)+.071107111*E.L*( 2.*P ( 11)-P(13)) 290 P23 -= .2592593*P( I)+. 7Ll07ll07*P( 12)+.07110711l*[L-M( P( 11)-2 .*1'(1 3)) 29 1 Zl = Sf'R(l,113,1,P(I)) 29?. Z2= SPR( 1, 113, 3, P( I) )*P( 11) 293 Z3=SPR(1,TB,1,P13) 2911 Zl~ = Sf'R( 1, ll3, 1, P23) 295 Z5 -= SPR(1,TB,1,P(l2)) 296 WRITE(6,1060) L,X(L),P(l),P(l1),Z1,Z2 297
130 1MIN :-.: TMIN+Ll.*(0.5*(Zl+Z5)+Z3+Zl1)/3. 298 1 MI N= l MI N*AREA 299 Z2 -= SPR( 1, ru,3,P( 12))*P( 13) 300 WRI lE( 6, 1fl60) LNS,X( LNS), P( 12), P( 13) ,Z5,Z2 301 lMINI T= TMINll-Tll( ll1)*AREA*PLL 30?. WR I H ( 6 , 1 0 8 2 ) 1 M I N I T, 1 M I N 3 0 3 lf(MODF...LE.2) GO TO 1l1l1 3011
c 305 C ----- WRllE SOIL HYDRAULIC PROPERTIES ----- 306
WRITE(6, 1069) 307 PRESS-: 1. 18850 308 SNl =c ll.O 309 RKLN~ l.O 310 SALPllA= tn( 6) 311 SN= ll3(7) 312 SWCR= lB(8) 313 SWCS =TB(9) 3111 SCONDS= Tl3(10) 315 WRITE{6, 1072) SNl,SWCS,RKLN,SCONDS 316 DO 1l10 I = 1, 75 3 11 lf(RKLN.Ll.(-16.)) GO TO 1l12 318 PRESS= 1. 18850*PRESS 319 SM= l.-1./SN 320 SNl = SM*SN 321 RWC=- 1. / ( 1. +(SAL Pit/\* PRESS) **SN) **SM 322 WC= SWCR+( SWCS-SWCR)*RWC 323 TE.RM= 1.-RWC*(SALPHA*PRESS)**SN1 32'-l lf((TEHM.LT.5.E-05).0R.(RWC.LT.0.06)) TERM = SM"RWC**(l./SM) 325 RK= SQRl(RWC)*TE.RM*rERM 326 TERM= SALPllA*SN 1 *( SWCS-SWCR) *RWC*RWC**( 1. /SM)* ( SALPltA*PRESS) ** 327
l(SN-1.) 328 AK= SCONOS*RK 329 DIFfUS= AK/TERM 330 l'RLN= ALOGlO(PRESS) 331 AKLN=AIOG10(AK) 332 RKLN =-= Al.OC10(RK) 333 IJ I f I. N =fl I. OG 1 0 ( DI Fr US ) 3 31~
1110 WRI TE(6, 1071l) PRESS,PRLN,WC,RK,RKLN,AK,AKLN,DIFFUS,DlfLN 335 142 CONTINUE 336 1111~ CONTINUE 337
c 338 C ----- FND OF PROBLEM ----- 339
1000 fORMA I ( I 5) 3110 1002 roRMfll ( 1111, lOX, 82( 111* )/ 11X, 111*, BOX, 111*/ 11X, lH*, 811X, 111*) 3111 1004 r ORM/\ I ( 20flll) 3112 1006 FORMAT( 11X, 1H*,20M, 1H*) 3'-13 1008 FORMAT( 1IX,1H*,80X, Hl*/1lX,82(111*)) 34Lt 10111 FORM/\T(/215,E10.1,4F10.0) 3115 1016 FORM/\ T( 11FHJ.0, 1115/) 3116 1018 fORMAT(//11X, 'PROGRAM PARAMETERS'/11X, 18( 11t= )/11X, 3117
+'NUMB R OF NODES •••.••..•••.•.••.•••. (NN) . ••... •....•.... 1 ,13/llX, 3118 +'NOOE AT SOIL-PLATE BOUNDARY •.•...•.. (LNS) .•........•• . •. 1 ,13/llX, 3119 +'INITIAL TIME STEP ...•.....••.....••. (ONUL) •...•.....•. 1 ,E9.2/11X, 350 +'PRESSURE ltEAD LOWER BOUNDARY ••.•••.. ( PNl) ...••.....•.. ', F8. 3/1 lX, 351
-
36
+'PNEUMATIC PRESSURE ....••............ (AIRP) ..........•. ',F8.3/11X, 352 +'fE.MPORAL WEIGHTING COEFF ...••....... (EPS1) ............ ',F7.2/11X, 353 +'ITERATION WEIGHTING COEFr •..•......• (EPS2) ....•....•.. ',F7.2/11X, 3511 +'MAX. ITCRATIONS ••.••........•....... (MIT) ............... ',13/llX, 355 +'DATA MODE •....••••••..••....••....•• (MDAfA) .......••.... I, 13/11X, 356 +'No. or OBSERVATIONS ....•...••..•.... (NOIJB) .......•....•. ', 13) 357
1020 roRMAf(5t10.0) 358 1021 FORM/\T(2f10.0, 15, f10.0) 359 1022 FORMAT(5110) 360 1026 tORMAT(//11X,'SOIL AND PLATE PROPERTIES'/11X,25(11t= )/11X, 361
+'SOIL COLUMN LENGTH ..•......•...•.... (SLL) ............. ',F8.3/11X, 362 +'COLUMN DIAMETER •••...•••••....••...• (DIAM) ........•... ' ,f8.3/11X, 363 +'llllCKNESS or PL/\1E. .•........••..•.. (PLL) ....•........ ',F8.3/11X, 3611 +'PL/\lE CONDUCTIVITY •..•••.••...•..... (CONDS(2)) .....• ',E9.4/11X, 365 +'SAlUR/\TEO MOISTURE CONTENT ...•...... (WCS) ............. ',r8.3/11X, 366 +'RESIDUAL MOISTURE CONTENf ........... (WCR) ...........•. ',FB.3/11X, 367 +'FIRST cour1c1ENT ................•.. (ALPHA) ..•.•...... ' ,rB.3/11X, 36B +'SECOND c0Err1c1ENT ..............••.. (NJ ......•........ ' ,FB.3/11x, 369 +'SAfUR/\TED CONDUCTIVITY SOIL ...•••.•. (CONDS(l)) .•.•.. ',E9.4) 370
1021~ FORM/\T(//11X,' INITIAL CONDITIONS'/11X, 18( 11t= )/11X, 'NODE' ,2X, 'DEPTH 371 l 1 ,2X,'PRESSURE ltEAD',5X,'MOISTllRE CONfENf') 372
1028 FORMAT(215,2F10.0) 373 1030FORMAf(//5X,8(111~),'ERROR ENCOUNTERED WHILE READING INITIAL CONDIT 374
110NS, CHECK NODE',IL1,1X 'EXECUTION lERM!NAfE0',9(111*)) 375 1032 roRMAr u 111 x, •OBSERVED 1 , 2A4/ 11 x, 16( lit= l / 14x, 'OBS•, 5X, '1ms ··, 5x, 2A11 376
1,11x, 'TYPE' ,11x, 'WEIGHT') 377 1036 FORMl\f(11X,15,2F10.3,5X,13,F10.1) 378 1038 FORMAT(ll?X,5(F8.4,3X)) 379 101!0FORMAT(1H1, 10X,' ITERATION NO' ,6X, 'SSQ' ,5X,5(6X,A4,A2)) 3BO 10112 fORMAT(15X,12,5X,F12.7,8X,5(f8.11 3X)) 381 10116 FORMAT(// I lX, I CORRE LAT ION MATR 1x 1/11X,1B( HI= )/111X, 10( l1X, 12, 5X)) 3B2 1048 roRM/\T(11X,13,10(2X,r7.4,2X)) 3B3 1050 FORMAT(//11X, 'RSQUARE FOR REGRESSION OF PRrOICTEO VS OBSERVED = ', 3B4
1F7.5) 385 1052 ronMAl(//11X,'NON-LINE/\R LEAST-SQUARES ANALYSIS: rlN/\L RESULlS'/ 386
lllX,118( 1H :-: )/53X, '9'.J% CONFIDENCE LIMI rs• /11X, 'VARIABLE' ,BX, 'VALUE'. 387 ?lX, 'S.E.COErr. ',11x, 'LOWER' ,BX, 'UPPER') 31rn
1058 FORM/\ f( UX, All, /\2, llX, FlO. 5, 5X, F9.1t, 5X, r6. 2, llX, F9.11, 5X, F9. II) 389 1 060 roHMA T( 1 ox • 1 11 • 1 x. F7 . 2. 2 r 1 1 • 3 , 3 x, 2 r 9 . 3 ) 3 9 o 1062 roRMAl(lOX,ll1,1X,F7.2,f11.3,8X,F9.11) 391 1066 IOHMATl//HlX,8(111-),'0BSEHVEO & FITTED ',2All,13(111-)/45X,'RESl-'/1 39?.
lOX, 'NO ,3X, 'TIM[ (HR)' ,11x, '011s' ,11x, 'FITTED' ,11x, 1 1Jll/\L 1 ) 393 1068 roRMAT( lOX, 12, FlO. 3, lX, 3F9. 3) 3911 1069 roRM/\l(IH1,10X,'PRESSURE',11X, 1 LOG P',6X,'WC',7X,'REL K',5X,'LOG RI< 395
1',6X,'AllS K',ltX,'LOG KA',5X,'DIFFUS',5X,'LOG O') 39(> 1070 roRM/\ r( HJX. E 10. 3, r8. 3, r 10. 11, 3 ( E 1 3. 3, rn . 3) ) 391 1072 roRM/\ l ( 1ox.r10. 3, BX, F 10. 11, E 13. 3, BX, E 1 3. 3) 398 1080 roRM/\T ( // 1 lX, Ir I NAL CONDI r IONS' I I lX, 16( IH'" )/ 25X, I PRESSURE HEAD'. 12 399
1x, 'Mo1s11mr coNJ[Nf' 111x, 'NODE' ,2x, 'D · r1H' ,3x, 'ruN
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37
lr(/\Ml\X) 30 , 30, 111 11 2 11 111 INDX(IC,l) = IR /125
Ir( IR. EQ. IC) GO TO 18 1126 DO 1(1 L-= 1,NP 11?.7 f' -:-- 1\( I H, I.) /128 /\( IR,L) =I\( IC:,I) 11?9
16 /\( IC,L) :: p 1130 r ~- n( 1 R) 1131 B(IR) = ll(IC) '13? B ( IC) -= P 113 3 I ::: I+ 1 11311 INUX(l,2) = 1C 113'..i
18 P= l .//\(IC, IC) 1136 /\ ( IC, IC) :· 1 . ll t13 1 DO 20 L= 1, N r 113n
20 A(IC,L) = /\(IC,L)*P 1139 B( IC) = B( IC)*P 11110 DO ?II K= l,NP 11111 If ( K. [.Q. IC) GO TO 211 11112 P=A(K,IC) 11113 /\( K, IC) :..: Q. O 111111 DO 22 1_ -- 1,Nr 11115
22 A(K,L) -::1\(K,L)-A( IC,L)*P 4116 13( K) = B( K)-!3( IC)*P 1147
211 CON I I NUL l111n GO TO 11 1~119
26 IC= INOX ( I, ?) 1150 IR= INDX ( IC, 1) 1151 D028K= l,NP 11'..)2 P=I\( K, IR) 1153 I\( K, IR ) -o- 1\( K, IC) 11511
28 l\(K,IC) = P 1155 1-= 1-1 1156
30 IHI) 26,32,26 1157 32 RE 1 lJRN !158
[N() 1159 SUl3HOlJ r I NE FLOW( E3N, re, NI TT, NOCON, MDATA, MOOE) '160 DI Mrns I ON r( 60), FC( 25). p IN( 60). PE( 60), l E( 60), BN( 15) "61 COMMON/MA/X( 30), P( 60), I SPH( 30), NN , AREA, LNS, PLL, SLL, PNl, 110( 25), DNlJ 1162
1 L, NOB, NOB2, l MIN IT, EPSl, EPS2, INDEX( 5), NVAR 1163 COMMON/ST 1 I I OBS. SMT 1, I STP 1, Ir LAG, oLDT 11611 DAT/\ Nl1Ml\X/10/,TOL1/1.00/,TOL2/0.005/,NSTEPS/300/,0ELMl\X/0.5/ 1165 OATA NOMAX/45/ 466
c 1167 C ----- UPD/\TE PARAMETER ARRAY ---- 1168
K-= O L169 NUl = NVAR+l 1170 NU2::-: NV/\R*2 1171 DO? l = NU1,NU2 472 IF( INDEX( 1-NVAR).EQ.O) GO TO 2 473 K= K+ 1 1111~ BN( I ) =BN( K) L175
2 CONTINUE 476 C ----- O[FINE INITIAL CONDITIONS & ~l\LCULAlE OUTFLOW /177 C OU~ I NG SATURATED STAGE-------- l17H
EPSM= l.-EPS2 '179 ISTP1 =1 '180 1013S= 1 1181 QOUT=O. 482 I FL/\G=O 483 SMT 1 =O 1184 NN2= 2*NN 485 IF(NITT.GT.O) GO TO 5 486 DO I~ 1= 1,NN2 1187 PIN(l) = P(I) 1188
4 CONl INUE 489 NOBl = NOB-1 1190 IF(MDATA.LE.1) NOBl = NOB 491
5 DO 6 1= 1,NN2 1192 P( I )=PI N( I) 1193
6 CONT I NU [ 11911 P(NN?-l) = PNl 495
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38
c C ----- SOIVE FOR FIRST STAGE OF OUTrLOW -----
CALL SfAGt:l(BN,FC,QOUT) 00 8 1-= 1, NN2 PE( I ) =~ I'( I )
8 CONllNU~ c c ------ D[T[RMIN[ AMOUNT or WATER IN SAMPLE -----
CALL IOlALM(P,BN,TMIN)
c c
9 c
10
12
1 3 c c
11~
15 c
16
17
18
19
20
22
24
c c c
28
30
c
TMINll =lMIN+QOUT DrL T:: ONUL 0(1 .M I N== O. 005*DNUL OIN - O[LT SUM I =SM 1 1 +OELT ISTEP= ISlPl
----- DYNAMIC PART OF MODEL -----Nl =NN?-1 Nf T- O Ir( MOOE. EQ. 0 )WR I TE( 6, 1002) NIT I DEL TI I ST[P I SUMT. (P E( I) I I= 1. NN 2 ) DO 12 1== 1,NN2 T{ I )= PF.( I) CO N I I NUF NIT =Nlltl Cl\Ll Ml\ I [Q ( BN I [PS 1, P[, OF.LT) I r ( N I T. GT. 1 ) GO TO 1 4 DO 1 3 I= 1, NN2 1 E( I )=P[( I)
----- CHECK ITERATIVE PROCESS DO 15 l - 1,NN2,2 10L-= 10Ll+TOL2*A13S(T( I)) IF(l\IJS(Pf{l)-T(l)).GT . TOL) GO TO 16 CONTI NU[ IF{MOOE.EQ.O)WRITE(G, 1002) NIT,DELT, ISTEP,SIJMT, (PE( I), 1=1,NN2) IF(DELT.LT.DELMIN) GO TO 19 GO 10 28 IF(NI r.GE . NI fMAX) GO TO 18 !JO 17 1=1,NN2 ff.MJ>:-EPS2'"1'E.( I )+EPSM*lE( I) H( I )=P[( I) PE( I )-= lLMP CONTINUE GO 10 10 NOCON=NOCON+l DELT=0.5*DELT IF(DELT.GE.DELMIN.AND.NOCON.LE.NOMAX) GO TO 22 tr(NOCON.GT.NOMAX) WRITE(6,1007) IF(OELl.Ll.DELMIN) WRITE(6,1008) DELT,DELMIN,SUMl,NITT
WR I TE( 6, 1009) DO 20 1=- 1,NN .1 =2*1-1 WR I TE ( 6 I 1010) I Ix ( I ) • p ( J ) , p ( J + 1 ) I PE ( J ) I PE ( J + 1 ) CONTINUE MODE=9 REl URN SUMT=SUMT-OELT DO 211 I= 1 , NN2 Pf( I )=O. 5*( P( I )+PE( I)) GO TO 9
---- CALCULATE CUM. OUTFLOW IF IFLAG=l ------
IF( IFLl\G.EQ.O) GO TO 34 DELF=( SUMl-110( IOBS) )/DELT DO 30 1= 1,NN2 T( I )=Pf ( I )-DELF*( PE( I )-P( I)) CONTINUE CALL 10TALM(T,13N,TMIN) FC( 1013S) =TMINIT-TMIN 1013S= IOl3S+1 IFl.AG=O
11 ~>6 1191 1198 1199 50lJ 501 502 503 5011 505 506 507 508 509 51() 511 512 513 51'1 515 516 ) 1 7 518 519 '.120 521 '.)?.2 5?3 521~
525 526 527 528 529 530 531 532 533 5311 535 536 537 538 539 540 541 5112 5113 51111 51~5 5116 5111 5ll8 549 550 551 552 553 554 555 556 557 558 559 560 561 562 563 5611 565 566 567 568
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C ----- PREPARE FOR NEXT TIME STEP -----
c c
c c
c c
c
34 IF( IOOS.GT.NOOl.OR. ISTEP.GE.NSTEPS) GO TO 40 DELCll=-1. 0 If (NIT. u : . 2) DELCll= 1 • 25 lf(Nlf.GE.6) DCLCll=0.80 DELCll= AMINl(OELCH,DELMAX/D[LT) DELT=UfLT*D[LCH DO 36 J=1,NN2 PEl = PE(J)-P(J) P(J ) = P[(J) PE(J) = P(J)+DELCH*PE1
36 CONf INllE SUMf =- StJMf+Dr:Lr IF(SUMT.GE.110( 1013S)) IFLAG= 1 ISTEP=IST[P+1 GO TO 9
--------------------40 IF( ISIEP.GE.NSTEPS) WR I TE( 6, 10111 )NSTEPS, SUMf, NI TT
IF( MDATA. LE. 1) GO TO 42
---- COMPlJH [QUI LIBRIUM OU Tr LOW If MDAfA= 2 ----XZfRO= PLL+SLL-PNl 1)0 41 1= 1, NN ,J =2*1-1 J 1=- .J+I PE(J) -= X( I )-XZERO PE(,J 1) = 1. 0
41 CONllNU[ CALL IOTALM(PE,BN,TMIN) rC( IOOS) = lMINI r-TMIN
112 DO 11t1 I = 1, NN2 P( I) = PF ( I)
I~ II CONTINUE
------ CALCULATE lllElA(ll) IF N0132 > 0 -----1r1Non2.r:q . o) GO ro 60 Nl =NOB+l N2 -: NOFJ+NOO? DO 116 1- Nl, N? fC( I ) -= SPR( 1,13N, 1,110( I))
116 CONTINllF 60 REl URN
c ----------
c
1001 roRMAI( 11X,lt[10.3) 1002 roRMAl(/11X,'PEll) DURING ITEHf\llON (Nll = ',13, 1 DLLl -=- 1 ,[10.?,' ISf
1[ P= I ' 111. I SlJM I = , [ 10. 3' I ) I I ( lOX, 10 I 11 . 3) ) 1uo3 r ORMf\I ( 1 1 x. 2 r 10. 5 ) 1007 fORMAl(//11X, 1 TROUl3LE CONV[RGING, START AGAIN Willi DlrfER[NT INlll
11\L VAl.UF s I) 1008 roRMAl(//llX,8(111*),'DELT = ',r11.11,', IS LESS TllAN D[LMIN ( = ',Ell.
111, 1 ), EX[ClJllON TERMINATED AT TIME = ',[11.11,' (Nll =- )',15) 1009 FORMAT(//1X,' LAST CALClJLATEO VAl.lJES'/11X,22\11P•)/11X,'NODE',5X,'D
IEPIH' ,9X, 'P( I ) 1 ,6X, 'GR/\DIENf' .9X, 'Pf( I ) 1 ,6X, GR/\UIE.NI"') 10 10 fOHMA I ( 11 X, 111, F 10. 2, 2 ( 3X, 2 F 12 . 4) ) 10111 IOHM/\1(/11X,'NO. or SfEPS F.XCE[DS',11~.· AT llM~. - ',Fl0.3,' Dl!HING
1 1 r LHA 1 1 ON' • 111 ) 1016 FORMAT"( llX, 15,F10.3,2(2X,FI0.3))
[N()
SUl3ROUTIN[ STAGEl(BN,FC,QOUT)
c PURPOSE: SIMlJL/\TE flRST (S/\llJRATED) STAG[ or rtow c
DIMr.NSION BN( 15), rC(25) COMMON/ A/\A/X( 30), P( 60), I SPR( 30), NN, AH£.A, LNS, PLL, SLL , PN 1, 110( 25 ) COMMON/S l l /I 0135, SIJMT, IS TEP, I FLAG, OLD r OAT/\ RELSAl/0.99/ LPLUS= LNS+l UNSAf ~ RI LS/\l*BN(9) /\fP- SPR( 1,mi,11,UNS/\T)
10 DEIWC~ FJN(9)-UNSAT 00 ?O 1-=- 1, LNS
39
569 570 571 572 573 5111 575 576 577 578 579 580 581 582 583 58ll 585 586 587 588 589 590 591 592 593 5911 595 596 597 59fl 599 600 601 602 603 6011 605 606 60 7 608 609 610 611 612 613 6111 61'.i 616 617 618 619 620 621 622 623 6 211 625 626 627 628 629 6 311 631 63 2 633 6311 635 636 637 638 639 6llfJ 6111
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c
c
40
J = ?* 1-1 lf(P( .J) . Gf ./\[P) GO 10 21
20 CON I I NIJf. 1)[111 - l'(LNS)-PNl GO TO 3 7
? 1 I r( I . GI . 1 ) GO TO 22 orut= P( 1 )-PNl-X(NN) EL=X(2 )- X( 1) GR/\D- BN( 1'.:> ) *DF.LH/(BN( 10)*PLL+l3 N( 15 )*SI L) l =- 2 GO 10 2 11
22 IMIN= l-1 Df.Lll =- /\EP+X( IMIN)-PN1-X(NN) E.L= X( I )-X( IM IN) TS -= SLL-X ( I ) +0.5*EL GR/\D-:: 13N( 15 )!10FLH/(ON( 10)*PLL+RN( 15)*TS)
24 Ol.DT = SUM r QOLD= QOll r QOUf = QOUf+ OELWC*ARE.A*EL oru ·- ou WC*CL/(ON( 10)*Gn/\D) SlJMl -= SIJMf+DEL I lf"( SUMf.GC.110( 1005)) IFl./\G= l Ir (I I l/\G . fQ.O) CO 10 26 re( IOB S) -= ( SllM f-110( IOOS) )/O[Ll*QOLO+(llO( IOll S) -01 01 )/DlLl*QOUT IOf\S::: IOBS+ l I FL/\G -= O
26 1-= 1+1 ISIE.P= l.::;1[1'+ 1 Ir ( I • c; r. l NS) GO TO 311 GO I 0 ??.
34 DO 36 1-:: 1,LNS J =?* l-1 P( .J )= Al P
36 P(J+l) = l.U 37 DO 38 l = l.PLUS,NN
J =- ?.* 1-1 P(J) -:- -D [l. ll*( X ( I )-SLL)/PLL + P(LNS)
38 P(J+l ) - -D ELl l/PLL l12 CO NTINU E
R[ ru1rn [ND
c -------------------c
c
SUOROUTINE lOTALM(P,BN,TMIN) DIM[NSION P(60),BN(15) COMMON//\A/\/X(30),EMTY(60), ISPR(30),NN,/\RE/\
C PURPOSE: TO CALCULATE THE /\MOUNT OF WATER IN SAMPLE c
TMIN= O. NE= NN-1 00 10 L-= 1 , NE MA I = IS PR ( l. ) MATl -:: I SPR( L+l) 1= 2*L-1 11 = 1+1 12= 1+2 13= 1+3 [L-X(L+l)-X(L) P13 = . 7ll07ll07*P( I )+.2592593*P( 12)+.0740711l*EL!1(2 . *P( I 1)-P(13)) P23 = . 711()711Q7*P( I 2 )+. 2592593*P( I)+. 071107!11 *EL*( P( I 1 )-2. *P( 13)) Z 1 = S PR (MAT, ON, 1 , P ( I ) ) Z3 -: 0. 7ll071107*SPR(M/\f,ON, 1, P13)+0.2592593*SPR(M/\Tl,BN, 1, P13) Zll =O. 2592593*SPR( MAT, BN, 1, P23) +O. 71~07407*SPR( MA Tl, BN, 1, P23) Z 5 = SP R ( Ml\ I 1 , l3 N , 1 , P ( I 2 ) ) TMIN= TMIN+/\REA*EL*(0.5*(Zl+Z5)+Z3+Z4)/3.
10 CONflNUE RETURN END SUBROUTIN E B/\NSOL(NEQ)
6112 6113 (,1111 6115 6"6 6117 6118 6119 650 651 652 653 6511 655 656 651 658 659 660 66 1 662 66 .1 66 11 6(15 666 66 7 668 669 670 611 672 6 73 614 6 7'j 676 677 67fl 679 680 681 682 6fl3 6811 685 686 687 688 689 690 691 692 693 6911 695 696 697 698 699 700 101 702 703 1011 705 706 701 708 709 710 711 712 713
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41
c 7111 C PURPOSE: TO SOLVE TllE GLOl3/\L M/\TRIX EQU/\TION 715 c 716
COMMON /CCC/ S( 60, 4), r( 60) 711 Nl = NCQ-1 718 DO 11 I == 1 , N 1 11 9 J = l-1 720 M-: M I Nil( 11, Nf.Q -J) 7? 1 P=- S(l,1) 722 no 11 L, ? ,M 123 C=S(l,L)/P 7211 f f - J+I 725
, Jj :- (J 726 DO 2 K- I , M l? I J J - .J J + 1 7 2 8
2 S( 11,.JJ ) : S( I I ,JJ )-C*S( I, K) 729 11 S ( I , L ) - C / 3 0
DO 6 I =- 1 , N 1 7 3 1 J-1-1 732 M=MINO(l1,NEQ-J) 733 C=- F ( I ) 7 311 f(l) =C/S(l,1) 735 DO 6 l =-? ,M 736 11 =.J+I 737
6 r( 11 ) = r( 11 )-S( I, L)*C "/38 r(NEln = r(NEQ)/S(NFQ, 1) 1]9 DO 8 1= 1,N1 7110 11 -= NEQ-I 7111
.J = I I - 1 7112 M-= MINO(ll,NEQ-J) 7113 IJO 8 l
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42
11 r( L 1 ) = ( EPSM*P( L 1 )+1. )*CONDl c C ----- ELEMlNT LOOP; CONSTRUCT GLOOAL MATRIX -----
DO 12 L::- 1, NE LL= 2·*L-2 Ll = l.L+l L2= LL+2 L3 = LL+3 L'1 = LL+l1 U =X( L+l )-X( L)
c C ----- CALCULATE llEHMITIAN BASIS FUNCTIONS-----
fE(2, 1) = .1181895*EL
c
fE(2,2) -= .1?.5*CL f[(2,3) = .0246676*EL OX(2, 1) = .1993777*EL DX(2,2) = -. 125*EL DX(2,3) = -.1279491*EL DO 6 K=- 1, 3 r c ( 11, K ) = - r E ( 2, 11- K)
6 DX(4,K) =DX(2,4-K)
C ----- CALCULATE MATERIAt PROPERTIES AT LOOAlTO POINTS -----W 1 = FE ( 1 , 1 ) * T ( L 1 ) +FE ( 2, 1 ) * T ( L2 ) +F E ( 3 • 1 ) * r( L3 ) +r E ( 11 , 1 ) * l ( Lii ) W2= rE.( 1, 2 )*1 ( L 1)+FE(2, 2 )*1 ( L2 )+FE( 3, 2 )*T( I 3) +rC( 11, 2 )*T( Lii) W 3 = F [( I , 3 ) * I ( L1 ) +r [ ( 2, 3 ) * T ( L2 ) +r E ( 3 , 3 ) * T ( L3 ) +F E ( 11 , 3 ) * T ( Lii ) MATl = ISPR(L)
c
MAT2= I SPR( L+ I) G2= .08G1869 Gl - 1.0027021 CONDI :: (Gl*SPR(MATl,UN,2,Wl )+G2*Sl'R(MAT2,BN,2,W1) )/EL COND2= . 7111111*(SPR(MAT1,0N,2,W2)+SPR(MAT2,BN,2,W2))/EL COND3 = (G2*Sl'R(MAT1,BN,2,W3)+Gl*SPR(MAT2,0N,2,W3))/E.L EL1 = .25*CL/DELT CAPl = (Gl*SPR(MAfl,BN,3,Wl )+G?*SPR(MAT2,0N,3,W1) )*[L 1 CAP2 = .7111111*(SPR(MAT1,BN,3,W2)+SPR(MA12,BN,3,W2))*EL1 CAP3 = (G?.*SPR(MAT1,BN,3,W3)+Gl*SPR(MA12,AN,3,W3))*EL1
C ----- ADD f.l.CMENT CONTR113UTIONS TO GLOOAL MAlRIX -----K=O
c
DO 10 I =-- 1 .11 I l = l L+ I DO 10 ,J -= 1,11 Wl :-: DX( J, 1)*OX(I,1)*CONOl+DX(J,2 )*DX( I, 2 )*CON02+DX( .J, 3 )*OX( I, 3 )*
1COND3 W?= f[( J, 1 ) *FE( I, 1) *CAP 1+fE(J,2) *FE( I, 2) *CAP2+FE( J. 3 )*FE ( I, 3) *CAP3 JJ =J+l-1 K-= K+l S( 11,J.J) = S( I 1,JJ)+Wl*EPSl+W2
10 SRtK) -=Wl*f PSM+W2
C ----- C:ONSTRUCl RIIS VECTOR ----
c
fL1 =. ?14?85 l*EL*( GON01+1. 75*CON02+CON03) f(Ll ) - r(l 1)+SR(1 )*P(Ll )+SR(2)*P(l2)+SR(3)*P(U)+SR(ll)*P(lll)-EL1 f( L? ) :-:. I ( L2 )+SR(?. )*P( L 1)+SR(5 )*P( l2 )+SR( 6 )* P( L3 )+SR( 7 )*P( LI~)+
1 (. 0996889"CON01-. 0625*COND2-. 06397116""COND3) *LL*El I ( L3 ) -=- r ( 1.3) +SR ( 3) *P( L 1 ) +SR ( 6) *P( L2) +SR ( 8) * P( L3) +SR ( 9) * P (Lit) +[Ll
1?. F (Lit) -= f ( 1_11) +SR( It) *P( L1 ) +SR( 7) * P( L2) +SR( 9) * P( L3) +SR( 10) * P( Lit)+ 1( .0996889*COND3-.0625*COND2-.0639746*CON01)*fL*[l
C ----- INCLUDE OOUNDARY CONDITIONS S( 2, 1) = 1. Wl =AM IN 1( 0. 5, 100 . / ( X( 2 )-X( 1 ) ) )
C W2= 1 . F(2) = ( 1.-Wl )*PE(2)+W1 F( 1) = F(1)-S(1,2)*F(2) F(3) = F(3)-S(2,2)*F(2) F ( 11 ) = r (It ) - S ( 2, 3 ) * F ( ?. ) S( 1, 2) -= 0. 5(2,2) =0. S(2,3) =0.
78() 787 788 789 790 791 792 793 7911 795 796 797 798 799 800 1301 802 803 8011 805 806 807 808 809 810 811 812 813 81'1 815 816 81 l 8 Hl 1319 820 821 822 823 8211 825 826 827 8213 829 830 831 832 833 8311 835 836 837 838 839 8110 8111 8112 8113 81111 8115 1346 8117 8'113 8119 850 851 852 853 8511 855 856
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c
211 CON f I NUf r(Nl ) = I (NN?)-S(N1,2)*P(N1) F(N2) = r(N2)-S(N2,2)*P(N1) F(N3)-F(N3)-S(N3,3)*P(N1) S( Nl, 1 ) = S( NN2, 1) S(N2,2) =-= S(N2,3) S(N3,3) := S(N3,ll)
30 CONTINllf
c ----- SOLVE roR UNKNOWNS CALL BANSOL(NEQ)
c c ----------
c c
DO 3'1 I :-: 1 , N2 311 Pr ( I ) - r ( I)
PE(NN 2 ) = F(N1) RL rtJHN END FUNG 1 I ON SPR( MAT, ON, N, PR)
C PURPOSE: TO CALCULATE lllE SO I L-HYIDRAULI C f'ROPERl I ES c
DIMENSION RN(15) DATA CONOM/1.E-08/,SS/1.E-07/ K=MATl
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44
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Virginia's Agricultural Experiment Stations
1 -- Blacksburg Virginia Tech Main Station
2 -- Steeles Tavern Shenandoah Valley Research Station Beef, Sheep, Fruit, Forages, Insects
3 -- Orange Piedmont Research Station Small Grains, Corn, Alfalfa, Crops
4 -- Winchester Winchester Fruit Research Laboratory Fruit, Insect Control
5 -- Middleburg Virginia Forage Research Station Forages, Beef
6 -- Warsaw Eastern Virginia Research Station Field Crops
7 -- Suffolk Tidewater Research and Continuing Education Center Peanuts, Swine, Soybeans, Corn, Small Grains
8 -- Blackstone Southern Piedmont Research and Continuing Education Center Tobacco, Horticulture Crops, Turfgrass, Small Grains, Forages
9 -- Critz Reynolds Homestead Research Center Forestry, Wildlife
10 -- Glade Spring Southwest Virginia Research· Station Burley Tobacco, Beef, Sheep
11 -- Hampton Seafood Processing Research
and Extension Unit Seafood
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I• ,·"---
image36865image36866image36867image36868image36869image36870image36871image36872image36873image36874image36875image36876image36877image36878image36879image36880image36881image36882image36883image36884image36885image36886image36887image36888image36889image36890image36891image36892image36893image36894image36895image36896image36897image36898image36899image36900image36901image36902image36903image36904image36905image36906image36907image36908image36909image36910image36911image36912image36913image36914image36915image36916image36917image36918image36919image36920