V-/EPA
United States
Environmental Protection
Agency
Robert S Kerr Environmental Research
Laboratory
Ada OK 74820
Research and Development
EPA-600/S2-81-058 June 1981
Project Summary
Areal Predictions of Water and
Solute Flux in the
Unsaturated Zone
Arthur W Warnck and Azizolah Amoozegar-Fard
This investigation was undertaken
to develop procedures for evaluating
distribution of water and salt fluxes
over land areas. Relevant applications
include numerical simulations and
sampling in fields of large areal extent.
The primary focus is on irrigated lands
including effects of salinization and
crops on the ground and surface
waters. The study was in three parts:
1) observations of distributions for a
variety of soil physical parametersand
inference on sampling; 2) simulations
of water and salt fluxes for nondeter-
ministic systems; and 3) a sensitivity
analysis for drainage. The major em-
phasis was placed on Part 2.
Simulations of water and salt fluxes
were made using the "crude" Monte
Carlo technique. For infiltration, "Phil-
ip's" equation was utilized in a scaled
form by solving one time. Individual
simulations were made algebraically
without repeating the laborious steps
of resolving the unsaturated moisture
flow equation each time. Similarly,
results for the nonlinear drainage case
were solved based on only one finite
difference determination. The Monte
Carlo simulation was carried out by
simple interpolation from the one
nonlinear solution. Unfortunately, no
great short-cut was found for cyclic or
seasonal irrigation regimes, although
some interesting results based on
linearized solutions were found for
high frequency water applications.
Salt distributions were calculated
for cases of equal irrigation amounts
over time but with intake rate varying
over space. Deterministic calculations
based on the mean velocity and appar-
ent diffusion coefficient gave errone-
ous results compared to the "average"
values over the field for both salt
profiles or fluxes. The true "average"
by depth for a given time is much more
dispersed, with more salts reaching
very deep depths and also with more
salts remaining close to the surface
when pulses of salt are added. Simi-
larly, the mass emission of salts aver-
aged over a field for a given depth
appear earlier in time and taper off
more gradually for a pulse input than
deterministic calculations based on
mean velocities would indicate.
This Project Summary was devel-
oped by EPA's Roberts. Kerr Environ-
mental Research Laboratory, Ada,
OK. to announce key findings of the
research project that is fully docu-
mented in a separate report of the
same title (see Project Report ordering
information at back}.
Introduction
This two-year study dealt with areal
predictions of water and solute fluxes
within the soil profile The project was
designed to develop methods to account
quantitatively for the inherent variability
of soils over a region — such as an
irrigated field or larger. Two very impor-
tant observations should be made in
terms of trends of current research and
awareness since the inception of this
project: (1) there has been a tremendous
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increase of interest in variability of soil
properties; and (2) there has been an
equally impressive increase of interest
among hydrologists and soil scientists
with regard to geostatistical techniques
which were largely ignored until recently.
Soil scientists (and farmers) have
always recognized that soils are hetero-
geneous. The approach to the problem
has necessarily been almost universally
deterministic in nature. The procedure
has generally been to sample, average
the samples, and use the results to
make calculations. For example, if a
mass flux of salts is needed, the land
area is multiplied by the "average"
profile results to get total emissions.
That such an approach may not give the
right answer is stated in elementary
works on stochastic processes (e.g.
Hammersly and Handscomb, 1964, p.
13) and is demonstrated in the case of
mean water flux by Warricketal.(1977b)
and in results from this project. In some
cases, a choice other than the arithmetic
mean may be appropriate; in other
cases, no "average" value may be
satisfactory to obtain an overall response
or integrated estimate. Efforts to ade-
quately assess confidence of results
have been generally lacking.
The techniques within this projectare
somewhat intermediate between the
deterministic and the geostatistical
methods. Ramifications of spatial varia-
bility are pursued in terms of water and
salt fluxes, primarily by Monte Carlo
simulations. It is hoped that sampling
and confidence intervals can be obtained
more efficiently in the future, by taking
advantage of what is known of the
spatial structure and by using geostatis-
tical techniques (Journel and Huijbregts,
1978).
These problems of area distribution
and predictions encompass all aspects
of earth sciences. An immediate and
obvious connection between soil physi-
cal properties and soil maps exists and
suggests mutual benefits for close
cooperation between classifiers and the
soil physicists. Not only is this true for
soil physical measurement, but also for
other soil properties, e.g., fertility level,
chemical activity and distributions of
biomass and microbes.
Conclusions
Observed variations of soil parameters
in the literature were reasonably con-
sistent when more than one source was
found. Generally these parameters can
be grouped into three classes:
1. Low variability — (Coefficient of
variation less than 20%)
Bulk density
Water content at a zero tension
2. Medium variability — (Coefficient of
variation 20-75%)
Textures (sand, silt or clay)
Field water content
Water content at specified tension
between 0.1-15 bars
3. High variability — (Coefficient of
variation greater than 100%)
Saturated hydraulic conductivity
Unsaturated hydraulic conductivity
Apparent diffusion coefficient
Pore water velocity
Electrical conductivity of extract
Scaling coefficients.
Sample numbers may be estimated
assuming independence and that the
central limit theorem applies, by
N = t02sVd2
where N is the number of samples, ta is
the "Student's t" with n-1 degrees of
freedom at a probability level of a, s is
the standard deviation of the mean, and
d is a specified limit. Table 1 shows an
analysis of the number of samples
required to estimate the mean values of
selected soil properties within 10 per
cent at the 0.05 significance level.
Scaling techniques offer distinc
advantages in terms of economy o
calculation and in synthesizing large
volumes of data. Figure 1 demonstrate!
the results of scaling the hydraulic hea<
values for 840 data points. The scalinc
(based on the assumption that the
internal geometry for similar medij
differs only by the characteristics size
process coalesces the data points into i
curvilinear function as shown in Figure
1, A & B. In this particular data set the
sum of squares of the scaled data was
reduced by 80 percent over the same
form of equation for the non-scale(
data.
Solute movement is a function of soi
water flux and apparent diffusion coef
ficient. Use of the deterministic value o
these parameters can result in erroneous
estimates of solute concentration ant
movement when the pore-water velocit'
and apparent diffusion are highly vari
able. Figures 2A and 2B showthe solute
concentrations with depth after five
days using a deterministic approacf
compared to the mean values for step
Table 1. Summary of Approximate Number of Samples Required to Estimate
Mean Values Within 10% at 0.05 Significant Level (After
GUMAA. 1978)
Soil Depth, cm
Parameters
Low Variation
Bulk density
Medium Variation
In situ field
capacity
In situ available
water capacity
15 bars
% clay
% silt
% sand
High Variation
Ksat
Field
1
2
3
1
2
3
1
2
3
1
2
3
1
2
3
1
2
3
1
2
3
1
2
30
1
1
1
10
12
10
21
55
47
20
25
23
25
28
20
20
16
8
15
19
1
110
119
60
1
1
1
28
23
9
43
36
31
55
78
19
49
91
18
57
61
20
28
16
1
150
49
90
1
1
1
24
61
15
35
110
33
33
68
31
33
104
24
66
88
47
13
21
3
362
155
120
1
1
1
47
49
10
55
78
30
57
57
35
51
36
36
122
83
28
27
23
2
635
102
150
1
1
1
2
75
2.4
45
116
45
47
125
30
47
110
36
71
104
40
43
47
3
155
560
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7.0
OS
0.6
0.4
02
\
All 6 Soil Depths
840 Data Points
t
•
o
SS = / Ox706
h = 800((I-S)-2.19(I-S*)+1,01(I-S3)
—0.385(/-S4)]S~1
a o.o
1
-700 -200 -300
Head /?r,i(cm)
-400
-500
SS = 2.0x705
h = -6020[(I-S)-2.14(I-S2)+2.04(I-S3)
—0.694(/-S4)]S~1
-700
-200 -300
Scaled Head ^,
-400
-500
cigure
Soil water characteristics data for six depths of Panoche soil:
(A) unsealed and (B) scaled.
200
400
Figure 2.
Mean Value
Deterministic
B
Salt concentration with
depth for a "step input"
(A) and a "pulse input"
IB) after 5 days
and pulse inputs. The true means were
evaluated using the Monte Carlo simu-
lations in which an average of 2000 salt
profiles is calculated for each case. For
both step and pulse inputs, the solute
concentration at larger depth is greater
for the mean values than the determi-
nistic solution. The depth at which c/c0
= 0.5 is about 220 cm for the determi-
nistic and 110 cm for the mean value for
step input, a consequence of averaging
in some of the high velocity sites. For the
pulse input, the maximum concentration
for the mean value is closer to the soil
surface although it is less than the
deterministic value. In fact, there is no
single value of pore-water velocity that
could give the shape of the true mean
for this example.
Recommendations
The variability in data of soil param-
eters should always be included in
addition to mean values when reporting
environmental data. Information regard-
ing the frequency distribution and/or
the spatial distributions of the data
should be included.
Sensitivity analysis should be con-
ducted to evaluate the behavior of de-
pendent variables in relation to changes
in the independent variable. Relative
sensitivity is more meaningful when the
range of variability is masked by the
numerical magnitude of the parameter.
Techniques such as geostatistics
should be examined in soil science to
provide basic descriptions of soil physi-
cal properties and for integrating over
large land areas.
References
Gumaa, G.S. 1978. SpatialVariabilityof
In situ Available Water. Ph.D. Dis-
sertation, University of Arizona.
> US GOVERNMENT PRINTING OFFICE 1981-757-012/7148
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140 pages. (No. 78-24, 365, Xerox
University Microfilms, Ann Arbor,
Ml 48106).
Hammersly, J.M. and D.C. Handscomb.
1964. Monte Carlo Methods.
Metheum and Co., London.
Journel, A.G. and CJ. Huijbregts. 1978.
Mining Geostatistics. Academic
Press, New York. 600 pages.
Warrick, A.W., G.J. Mullen, and D.R.
Nielsen. 1977b. Predictions of the
Soil Water Flux Based Upon Field-
Measured Soil-Water Properties.
Soil Sci. Soc. Amer. J. 41:14-19.
Arthur W. Warrick and Azizolah Amoozegar-Fard are with the Department of
Soils, Water, and Engineering, University of Arizona, Tucson, AZ.
Arthur Hornsby is the EPA Project Officer (see below).
The complete report, entitled "Area! Predictions of Water and Solute Flux in the
UnsaturatedZone, "(Order No. PB 8 J -191 124; Cost: $9.50, subject to change)
will be available only from.
National Technical Information Service
5285 Port Royal Road
Springfield, VA 22161
Telephone- 703-487-4650
The EPA Project Officer can be contacted at:
Robert S. Kerr Environmental Research Laboratory
U.S. Environmental Protection Agency
P. O Box 1198
Ada, OK 74820
United States
Environmental Protection
Agency
Center for Environmental Research
Information
Cincinnati OH 45268
Postage and
Fees Paid
Environmental
Protection
'Agency
EPA 335
Official Business
Penalty for Private Use $300
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