Published online March 8, 2006

Field-Scale Water Flow Simulations Using Ensembles of Pedotransfer Functionsfor Soil Water Retention
A. K. Guber, Ya. A. Pachepsky,* M. Th. van Genuchten, W. J. Rawls, J. Simunek, D. Jacques,
T. J. Nicholson, and R. E. Cady
three large soil hydraulic property databases, and used
a powerful tool—neural networks—to develop a water
retention PTF for each of the databases. They subsequently tested the functions against data from the othertwo databases, and found that while the RMSE of watercontent estimates was only 0.06 m3 m23 for the development database, it was as large as 0.12 m3 m23 for thetesting databases. Similar results were obtained in othercomparisons of pedotransfer predictions and measured
soil hydraulic properties (Tietje and Tapkenhinrichs,
1993; Wösten et al., 2001). There are indications thatsimilarities in geographical settings may cause similarities in PTFs (Pachepsky et al., 1999), but such observations are scarce and it is not clear how general they are.
The existence and use of multiple models that are developed and tested in one region but perform relatively
poorly in other regions is fairly common in meteorology(Molteni et al., 1996). Justifying the selection of a single
model has become an unsolvable problem. The multimodel ensemble prediction method was developed during the last decade to address this dilemma (Houtemaker
et al., 1996; Palmer et al., 2004). The basic idea of themethod is straightforward since it involves the use of
several models and simply averaging prediction fromthose models. The argument is that at present no underlying theoretical formalism exists from which a probability distribution of model uncertainty can be estimated,and hence that a pragmatic approach is need. One suchapproach relies on the fact that different research groups
have developed climate models somewhat independently. An ensemble comprising such quasiindependent
models is referred to as a multimodel ensemble (Palmer
et al., 2004). Ensemble forecasts offer a way of filtering thepredictable from the unpredictable through averaging—features that are consistent among ensemble members arethen preserved, while those that are inconsistent are reduced in amplitude. Perhaps more important, the ensemble itself, as a sample from possible forecast outcomes, canbe used to estimate the forecast uncertainty and the likely
structure of forecast errors (Hamill et al., 2004).
Multimodel ensemble methods are now slowly also
being used in subsurface hydrology. Ye et al. (2004) suggested averaging of spatial variability models in unsaturated fractured tuff for situations when standard
information criteria provide an ambiguous ranking of
the models, such that it is not justified to select one ofthem while discarding all others. Several general approaches to multimodel predictions now also exist (e.g.,
Burnham and Anderson, 1998).
The objective of this work was to estimate applicability of an ensemble of PTFs for simulation of field water

Reproduced from Vadose Zone Journal. Published by Soil Science Society of America. All copyrights reserved.

ABSTRACT
Using pedotransfer functions (PTF) to estimate soil hydraulic properties may be necessary in soil water flow simulations for large-scale
projects or in pilot studies. The accuracy of a PTF outside of its development dataset is generally unknown. The existence of multiple models
that are developed and tested in one region, but may perform relatively
poorly in other regions, is also common in meteorology, where multimodel ensemble prediction techniques have been developed (i.e., thoseusing an averaged prediction from several models) to address this problem. The objective of this work was to estimate the applicability of an
ensemble of PTFs for water regime simulations. Measured soil watercontents and pressure heads of 60 points at five depths in a 6-m transect ofa layered loamy soil were collected during an extremely wet year in
Belgium. Soil water fluxes were measured with passive capillary lysimeters at two depths. Water retention was measured in the laboratory on
samples taken at 60 locations at three depths. Contents of soil textural
fractions, organic matter content, and bulk density were averaged acrossthe transect and used as input in the ensemble of 22 published PTFs
developed from large datasets in different regions. The HYDRUS-1D
software was used to simulate water content time series with (i) each of
the PTFs from the ensemble and (ii) the laboratory-measured water
retention data of each of the 60 locations. Simulations with the PTF ensemble had, on average, two times smaller errors those from using laboratory data. A possible explanation for this is that the PTF estimation
gave substantially better approximations of field water retention thanthe laboratory data. The ensemble prediction appears to be a promisingsource of soil hydraulic properties to simulate soil water dynamics.

S

IMULATIONS of soil water flow are often performed

with parameters estimated using PTFs, which
are empirical relationships between the soil hydraulicproperties and more easily obtainable basic soil properties available, for example, from soil surveys. The useof PTFs is necessary when the simulations have to bedone for large-scale projects or for pilot studies.
Applying PTFs always introduces substantial uncertainty because the accuracy of a PTF outside of its development dataset is unknown. Schaap and Leij (1998)
demonstrated the dependence of pedotransfer predictions on the development database. They worked with

A.K. Guber and J. Simunek, Dep. of Earth and Environmental
Sciences, Univ. of California, Riverside, CA 92521. Ya.A. Pachepsky,
USDA-ARS, Environmental Microbial Safety Lab., BARC-East, 173
Powder Mill Rd., Beltsville, MD 20705. M.Th. van Genuchten, USDAARS, George E. Brown, Jr. Salinity Lab., Riverside, CA. W.J. Rawls,
USDA-ARS Hydrology and Remote Sensing Lab., Beltsville, MD. D.
Jacques, SCK-CEN, Belgium. T.J. Nicholson and R.E. Cady, USNRC,
ONRR, Washington, DC. Received 14 Sept. 2005. *Corresponding
author (ypachepsky@anri.barc.usda.gov).
Published in Vadose Zone Journal 5:234–247 (2006).
Special Section: From Field- to Landscape-Scale Vadose Zone Processes
doi:10.2136/vzj2005.0111ª Soil Science Society of America
677 S. Segoe Rd., Madison, WI 53711 USA

Abbreviations: PTF, pedotransfer function.

234

235

www.vadosezonejournal.org

regime. We will compare PTF-estimated results with measured soil water retention data from a well-instrumented
field site in Belgium.

Reproduced from Vadose Zone Journal. Published by Soil Science Society of America. All copyrights reserved.

MATERIALS AND METHODS
Soil Water Flow Experiment
The experimental field was located in a meadow near
Bekkevoort, Belgium, at the bottom of a 4% slope. The soil
was classified as Eutric Regosol (FAO, 1998). Typically the top
1 m includes three soil horizons: an Ap horizon between 0 and
25 cm, a C1 horizon between 25 and 55 cm, and a C2 horizon
between 55 and 100 cm. A trench, 1.2 m deep and 8 m long,
was excavated at the field site. Soil texture was measured
with the pipette method following pretreatment with Nahexametaphosphate. Textural classes were loam at the 15-, 35-,
and 55-cm sampling depths, and silty loam at the 75- and 95-cm
depths (Table 1). The grass cover was removed from the experimental area. A plastic sheet covered the side of the trench
where equipment was installed. Volumetric water contents
were measured with TDR. Sixty TDR probes (two rods, 25 cm
long, 0.5-cm rod diameter, 2.5-cm rod spacing) were installed
along the trench at 12 locations with 50-cm spacing at five
depths (15, 35, 55, 75, and 95 cm deep). The TDR measurements were done with a Tektronix 1502B cable tester(Beaverton, OR). The automated system of Heimovaara andBouten (1990) was used to control, retrieve, store, and analyze
measurements of the travel time of an electromagnetic wave
along the TDR rods. One measurement cycle for all two-rod
TDR probes took approximately 35 min, while the time difference between two measurements for the same probe was
2 h. Triplets of passive capillary samplers (PCAPS) were installed at the 15- and 55-cm depths at a distance of about 5 mfrom the trench to measure soil water fluxes once every two
to 3 d. Pressure heads were measured with tensiometers.
Tensiometric porous cups (6-mm diameter, 25 mm long) were
installed at a horizontal distance of 10 cm from each of the
60 TDR probes. The porous caps were connected with waterfilled tubes to pressure transducers. Measurements of the pressure transducers were controlled and stored using a Campbell(Logan, UT) CR10X datalogger and AM416 multiplexers.
Rainfall was measured and recorded continuously near the
trench over the catch area of 200 cm2 (Fig. 1).
The trench was filled after all devices were installed. A thinlayer of gravel (1–2 cm) was evenly distributed on the study
area to (i) decrease the erosive effect of rain impact on thebare soil surface, (ii) minimize evaporation from the soil surface, and (iii) decrease the growth of weeds on the experimental plot. Weeds were regularly removed from the site
during the summer. Field measurements started on 11 Mar.
1998 (Day 0) and concluded on 31 Mar. 1999 (Day 384). Additional details about the site and the experiment are given by
Jacques (2000) and Jacques et al. (2001).

Table 1. Average values of soil properties at the monitoring depths.
Diameters of soil textural fractions
Depth
cm
15
35
55
75
95

No. ofsamples
7
8
5
3
4

.50
mm
58.6
56.7
57.3
49.6
43.8

50–20
mm
19.3
18.9
17.6
21.2
30.03

20–10
mm
6.4
7.8
6.6
7.9
7.4

10–2
mm
4.5
3.2
3.7
4.4
4.5

Fig. 1. Precipitation during the period of measurements.

A separate study of the soil hydraulic properties was performed along a 30-m trench in the same soil at an adjacent site
(Mallants et al., 1996). Undisturbed 5-cm-long and 5.1-cmdiameter cores were taken from three horizons: from the Ap
horizon at 10 cm depth, C1 at 50 cm and C2 at 90 cm withalternating lateral sampling distances of 0.1 and 0.9 m. Valuesof van Genuchten parameters were estimated from the water
retention data obtained with a sand-box apparatus for capillary pressures of 1, 5, 10, 50, and 100 cm, and with a pressure
cell for pressures of 200, 630, 2500, and 15 000 cm. The van
Genuchten water retention equation (van Genuchten, 1980)u 2 ur1¼
us 2 ur [1 1 (ah)n ]m[1]

was fitted to the data from each sample. In Eq. [1], u is thevolumetric water content, h is the capillary pressure (the absolute value of the matric potential), us is the saturated watercontent, ur is the residual water content, and a, m, and n areempirical shape-defining parameters. Statistics of the van
Genuchten parameters along the trench are shown in Table 2.
Values of the saturated hydraulic conductivity Ks were measured for each sample using a constant head permeameter(Klute, 1965).

Ensemble of Pedotransfer Functions
The literature was searched for PTFs to estimate soil water
retention and soil hydraulic conductivity from soil data availTable 2. Statistics of van Genuchten water retention parameters
and the saturated hydraulic conductivity along the 30-m trench(Mallants et al., 1996).
ur

us†
3

cm cm
Min.

0.0

Avg.
Max.
CV, %

0.040
0.083
57.8

Min.

0.0

,2
mm

Bulk
density

Organic
C

Avg.
Max.
CV, %

0.012
0.075
156.4

11.1
13.3
14.8
17.4
14

g cm23
1.42
1.54
1.53
1.53
1.53

%
2.2
0.8
0.4
0.3
0.6

Min.
Avg.
Max.
CV, %

0.0
0.044
0.100
54.9

23

a
21

cm
Ap horizon
0.348
0.0012n†Ks†–

cm d21

1.378

1.4

0.420
0.00700.484
0.0142
7.2
45
C1 horizon
0.330
0.0012

1.754
3.568
22

245.5
5254.8
599

1.263

1.8

0.360
0.01270.424
0.02905.1
47
C2 horizon
0.378
0.00140.430
0.00380.502
0.0079
7.6
53

1.386
2.355
11

95.1
3161.0
322

1.405
1.788
2.656
17

1.7
449.5
5059.7897† CV was calculated using loge-transformed data.

236

VADOSE ZONE J., VOL. 5, FEBRUARY 2006

Table 3. Median and spread of the saturated hydraulic conductivity Ks (cm d21) for 12 USDA textural classes (after Rawls
et al., 1998).
Soils withhigh porosity

Soils withlow porosity

Reproduced from Vadose Zone Journal. Published by Soil Science Society of America. All copyrights reserved.

USDA
Avg.
Avg.
textural class Ks50% Ks75%–Ks25% porosity Ks50% Ks75%–Ks25% porosity
Sand
Fine sandLoamy sandLoamy finesand
Sandy loam
Fine sandy
loam
Loam
Silt loam
Sandy clay
loam
Clay loam
Silty clay
loam
Clay

cm3cm23
0.44
218.4
0.49
240.0
0.45
98.4
0.46
28.8

369.6
364.8
110.4
261.6

cm3cm23
0.39
0.39
0.37
0.37

31.2
19.7

74.03
32.6

0.37
0.36

0.47
0.49
0.44

14.9
8.2
6.7

32.9
21.4
23.8

0.39
0.39
0.37

26.1
19.5

0.48
0.5

1.7
11.8

8.6
28.1

0.4
0.43

12.2

0.48

4.3

15.9

0.4

436.8
338.4
295.2
148.8

408.0
283.2
266.4
206.4

134.4
52.8

240
62.4

0.47
0.45

9.4
34.6
18.5

63.4
70.8
116.4

10.1
8.9
4.8

able at the site. We intended to use PTFs developed from large(.200 samples) databases. To estimate soil water retention, we
selected 22 PTFs developed in different regions. The PTFs arelisted in the Appendix A.1 Six of the PTFs estimated parameters of the Brooks–Corey equation (Brooks and Corey, 1964): lhb
u 2 ur, h . hb5hf 2 ur1,h # hb5

us, ur, a, and n were evaluated by fitting Eq. [1] to the water
retention points assuming m 5 1 2 1/n. We also used theRosetta software (Schaap, 2004) to generate van Genuchten
parameters from texture and bulk density.
We could find only two PTFs to estimate soil hydraulicconductivity that were developed and/or tested with large
databases (Rawls et al., 1998; Wösten et al., 1999). Since theensemble prediction method did not seem feasible with only
two PTFs, we used the PTF developed by Rawls et al. (1998),
which gave estimates of the median and the difference between values corresponding to 25 and 75% probability levels(Table 3). This PTF hence could be used in principle to generate random values of the saturated hydraulic conductivity.

Multimodel Ensemble Prediction of Soil Water Flow
The HYDRUS-1D software (Simunek et al., 1998) was used
for the simulations. This software gives options to run simulations either with the van Genuchten water retention Eq. [1]or with the Brooks–Corey Eq. [2]. This option was selected
depending on the pedotransfer function. The unsaturated hydraulic conductivity was calculated with the model of van
Genuchten–Mualem (1980):
1/m m 2K(h) 5 Ks S0:5
e [1 2 (1 2 Se ) ] Se 5

and five other equations estimated parameters of the van
Genuchten Eq. [1]. In Eq. [2], f is the porosity, hb is bubblingpressure, l is pore size distribution index. Ten more PTFs
estimated the water contents at several fixed capillary pressures. The van Genuchten parameters us, ur, a, and n of Eq. [1]were evaluated by fitting to the water retention points obtained from those PTF equations. The value of parameter m
was calculated as m 5 1 2 1/n. The residual water content ur
was set to 0.001 cm3 cm23, and the saturated water content us
was set equal to the porosity for PTFs that evaluated values ofwater content at two capillary pressures (330 and 15000 cm).
Two PTFs (Vereecken et al., 1989; Varallyay et al., 1982) evaluated van Genuchten parameters in Eq. [1] assuming m 5 1.
To use these PTFs for the water flow simulations, water contents were calculated at capillary pressures used by thoseauthors to derive their PTFs. The van Genuchten parameters
1
A FORTRAN code to estimate water retention with PTFs of thiswork is available on request from the corresponding author.

[3]

or with the model of Brooks and Corey (1964):
1 2:5
K(h) 5 Ks S2/le

[2]u 2 urus 2 ur[4]

The multimodel ensemble prediction of soil water flow was
performed by generating parameters with each of 22 PTFs fora separate simulation run. Water retention was estimated fromthe PTFs for individual layers (i.e., 0–25, 25–45, 45–65, 65–85,
and 85–150 cm; Table 1).
Another 60 simulations of soil water dynamics weremade using parameters of the van Genuchten Eq. [1] andGenuchten–Mualem Eq. [3] obtained from the laboratorywater retention measurements. Each simulation corresponded
to the soil profile at one of the 60 locations. Median values of
Ks distributions from Table 3 were used for the loam and silt
loam texture classes at depth ranges 0 to 65 and 65 to 105 cm,
respectively, for simulations with both PTF-estimated andlaboratory-measured water retention data.
All simulations of the soil water regime were done for the
precipitation data shown in Fig. 1. Five periods without precipitation were selected to evaluate values of evaporation. Vertical soil water fluxes were calculated for each period using themass conservation equation and Darcy–Buckingham Law.
Estimated daily evaporation results are shown in Fig. 2. The
variability in evaporation between periods was less than thevariability within periods. A Kruskal–Wallis rank sum test

Fig. 2. Estimated daily evaporation rates for dry periods during the experiment.

237

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www.vadosezonejournal.org

did not indicate a difference ( p 5 0.924) in mean daily evaporation values between periods, while an ANOVA test did notselect the period as an influential factor at the 0.05 probability level. The evaporation rate at a probability level of 50%
was 0.86 mm d21. This value was included in the surface
boundary condition. A free drainage condition was used at thelower boundary, assumed to be at a depth of 150 cm. Valuesof the water content at measurement depths of 15, 35, 55, 75,
and 95 cm were used as the initial condition across the 0- to25-, 25- to 45-, 45- to 65-, 65- to 85-, and 85- to 150-cm soil
layers, respectively.
Simulated soil water contents and soil water fluxes werecompared with measured values at the trench scale. Averagemeasured across-trench soil water contents were estimated atfive measurement depths, with corrections for missing data as
described in (Pachepsky et al., 2005a, 2005b). Simulated water
fluxes at depths of 15 and 55 cm were compared with fluxes
measured with passive capillary lysimeters. Simulated water
fluxes at the depth of 105 cm were compared with flux values
estimated at this depth from daily mass balance computations
assuming that water contents measured at depths of 15, 35, 55,

75, and 95 cm are representative across 0- to 25-, 25- to 45-, 45to 65-, 65- to 85-, and 85- to 150-cm soil layers, respectively.

RESULTS
Soil Water Contents
Simulated water contents are compared with measured
values in Fig. 3 and Fig. 4. Using the laboratory-measured
water retention did lead to the relatively low accuracy(Fig. 3) with the simulated initial distributions of pressure
heads deviating apparently far from the actual ones, while
the first period of simulations was characterized by a
substantial loss of water through the bottom of the profile.
The simulations consistently underestimated measured
soil water contents. The average difference between average simulated and average measured water contents
varied with depth from 20.085 to 20.149 cm3 cm23. The
minimum average error was obtained for a depth of 15 cm,
and maximum error at 55 cm. The RMSE was 0.086 cm3

Fig. 3. Average field-measured water content data at several depths (symbols) and simulated results obtained with the laboratory water retention
data (lines). Solid line is the median value; dotted lines are the 95% tolerance interval.

Reproduced from Vadose Zone Journal. Published by Soil Science Society of America. All copyrights reserved.

238

VADOSE ZONE J., VOL. 5, FEBRUARY 2006

Fig. 4. Average field-measured water content data at several depths (symbols) and simulated results obtained with the pedotransfer function
ensemble (lines). Solid line is the median value; dotted lines are the 95% tolerance interval.

cm23 at the 15-cm depth and varied between 0.12 and0.15 cm3 cm23 at larger depths.
Results of water content simulations with the ensembleof PTFs (Fig. 4) were qualitatively similar to those obtained with the laboratory water retention data (Fig. 3).
However, the accuracy of PTF simulations was generally
better than those using the laboratory data. The average
difference between the simulated and measured watercontents was 20.068 cm3 cm23. Measured water contents
were mostly within the 95% tolerance interval of simulated values. The median simulated water contents wereless than field-measured values, much like for the simulations using the laboratory-measured water retention data.
The range in the average error of the predicted watercontents was less compared with the simulations using thelaboratory-measured water retention data. The values
error was in the range from 20.062 to 20.076 cm3 cm23.
The minimum average error was obtained at depths of
15 and 95 cm, while maximum error occurred at depth of

55 cm. The RMSE was between 0.062 and 0.072 cm3 cm23.
No relationship between the errors of simulation andvalues of measured water content were found either
for the laboratory-measured or PFT ensemble estimatedwater retention data.
The uncertainty in simulated water contents varied withdepth. The maximum width of the 95% tolerance interval
was found at a depth of 15 cm using the laboratory water
retention data and at a depth of 55 cm for the ensemblepredicted water retention estimates. The narrowest
tolerance interval occurred at a depth of 55 cm using
laboratory water retention data and at a depth of 95 cm
using the ensemble-predicted water retention information. In general, the uncertainty in simulated water contents was higher with the laboratory data, which resulted
in tolerance intervals that were 1.14 to 1.79 times wider
than the ensemble-predicted water retention estimates.
A comparison of the statistical distributions of the
RMSEs obtained in simulations with the laboratory data

239

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www.vadosezonejournal.org

Fig. 5. Probability distributions of the RMSEs for soil water contents
simulations using water retention data measured in the laboratory(s) and estimated with the pedotransfer function ensemble (,).

and with the PTFs supported the finding that the watercontent simulations with ensemble estimated water retention data was substantially better than using the laboratory data (Fig. 5). The graphs of the two probability
distribution functions are parallel to each other, with thedifference between them being about 0.062 cm3 cm23.

Comparison of Measured and EnsembleEstimated Water Retention
To find a possible explanation of the better simulation
results with the PTF ensemble as compared with the“ensemble” of 60 soil columns using the laboratorywater retention data, we compared both the laboratory
and PTF-estimated water retention results with water
retention data measured in the field. Results of thiscomparison are shown in Fig. 6. The ensemble estimation provided a better match with the field water retention data as compared with laboratory data. Boundariesof the 95% tolerance intervals for the ensemble estimates provided an envelope encompassing the fieldmeasurements (Fig. 6). A relatively few experimental
field water retention points were outside the toleranceinterval of the PTF ensemble. At the same time, how-ever, a substantial number of experimental field water
retention points were outside the tolerance interval of
the laboratory water retention data at a depth of 15 cm,
and especially at a depth of 95 cm. In general, the fieldwater retention data were closer to the middle sectionof the 95% tolerance interval of the PTF ensembleestimated water contents than to the middle section of
the 95% tolerance interval of the laboratory data.
The uncertainty in ensemble-estimated water retention estimates was comparable to that in the laboratory estimates. The average ratio of the width of thetolerance intervals computed with the laboratory andensemble-estimated water contents was 0.79. This ratio
varied from 0.24 to 3.19, depending on the sampling
depth and capillary pressure. Maximum differences inthe tolerance interval widths between the ensemble andlaboratory data were observed in the range of capillarypressure between 200 and 800 cm and for capillarypressure ,10 cm. (Fig. 6). Laboratory measurements
showed the ability of the soil to lose substantial amountsof water with changes in the capillary pressure from 100
to 1000 cm, especially at the 15- and 95-cm depths. The
PTF ensemble predicted a more gradual loss of water
during this drying process. The PTF ensemble also gavea much wider range of estimates of the water contents
around the wilting point (»15000 cm) as compared withthe laboratory data.

Performance of Individual Pedotransfer Functions
Data on the accuracy of the simulations with individual PTFs are shown in Table 4. The differences between RMSEs in the water contents were substantial. A
PTF ranking in terms of their RMSE values shows thatthe best results were obtained with PTFs derived fromthe all-USA database (Gupta and Larson, 1979) and theall-European database (Wösten et al., 1999).

Effect of Saturated Hydraulic
Conductivity Estimation
Results of the simulations shown in Fig. 3 and 4 may
be affected by the value of the saturated hydraulic conductivity. To assess this effect, we assumed lognormal

Fig. 6. Field-measured and estimated soil water retention curves along the trench. Dots are field measurements, dashed lines the 95% toleranceinterval of the laboratory water retention data, and solid lines the 95% tolerance interval of pedotransfer function ensemble-estimated water
retention curve.

240

VADOSE ZONE J., VOL. 5, FEBRUARY 2006

Table 4. Root-mean-square errors of water contents in simulations with individual pedotransfer functions.

1

1

1

1

1

1
1

1

1
1

1
1
1

1
1

1

DISCUSSION

1

1

1

1

1
1

1
1

1

1
1

1
1
1

1
1

PTF predictors

Pedotransfer
function

Reproduced from Vadose Zone Journal. Published by Soil Science Society of America. All copyrights reserved.

1

windows of 1, 2, 4, 8, 16, and 32 d. Some of our results
are shown in Fig. 9. The error in the daily flux increased
as the time window decreased. A well-defined scaling
dependence of the error existed in the daily flux on thewindow size. The exponent was approximately 20.75 at
the 15- and 105-cm depths, but was smaller at the 55-cm
depth. However, the measurements at this depth (55 cm)
showed a substantial scatter, while the average was neverreproduced well (Fig. 9). The scaling hence may notdepend on depth.

RMSE Rank† Clay Silt Sand BD OM Itop‡

Baumer, 1992
Bruand et al., 1994
Campbell andShiosawa, 1992
Canarache, 1993
Gupta andLarson, 1979
Hall et al., 1977
Mayr and Jarvis, 1999
Oosterveld andChang, 1980
Peterson et al., 1968
Rajkai andVarallyay, 1992
Rawls et al., 1983
Rawls andBrakensiek, 1985
Rawls et al., 1982
Rosetta
Saxton et al., 1986
Tomasella andHodnett, 1998
Varallyay et al., 1982
Vereecken et al., 1989
Williams et al., 1992
Williams et al., 1992
Wösten et al., 1999
Wösten et al., 1999

cm3cm23
0.044
0.072
0.102

6
11
18

1
1
1

0.083
0.024

14
1

1
1

0.030
0.087
0.111

3
15
20

1
1
1

0.032
0.129

4
21

1
1

0.068
0.133

10
22

1
1

0.076
0.109
0.095
0.042

13
19
17
5

1
1
1
1

0.066
0.055
0.094
0.073
0.049
0.029

9
8
16
12
7
2

1
1
1
1
1
1

1

1

1
1

1
1
1
1
1

1
1

1
1
1

1
1

1

1
1

† PTF ranked according the RMSE values; smallest rank corresponds tothe smallest RMSE.
‡ Variable equal zero for subsoil and one for topsoil.

distribution of the Ks values in Table 3 and performed
Monte Carlo simulations of soil water flow with Ks
randomly sampled from this lognormal distribution, andusing fixed laboratory water retention data taken at the
50% probability. Figure 7 demonstrates that the effect of
Ks on the simulation results can indeed be profound.
The 95% tolerance interval of the simulated watercontents was on average from 1.27 to 1.53 times wider
when the water retention was varied as compared withsimulations with variable Ks. The difference was more
pronounced at depths of 15 and 35 cm. In 75% of cases,
simulations with a variable Ks produced water content
RMSE values that were smaller than for simulations
with variable water retention data.

Soil Water Fluxes
The accuracy of soil water flux predictions using boththe PTFs and the laboratory water retention data wasevaluated over three wetting-drying periods (Days 112–
143, 144–232, and 233–275) that are visible in both theprecipitation data (Fig. 1) and in the measured soil watercontent time series (Fig. 3 and 4). The accuracy was
satisfactory (Fig. 8) for simulations with both the laboratory and PTF ensemble-estimated water retention data.

Effect of the Time Scale
To evaluate the ability of PTF models to estimate thesoil water fluxes for shorter periods of time, we computed simulated and measured daily averages using time

The accuracy of the water content simulations washigher when the ensemble of PTFs was used as comparedwith simulations with the laboratory-measured retention
data (Fig. 3 and 4). This may be attributed to a better
representation of water retention with the PTF ensemble
as compared with the laboratory measurements (Fig. 6).
This probably occurred because water retention was generally higher in the field than in the laboratory, while theensemble predicted higher water retention. Such differences were previously also observed within a large dataset (Pachepsky et al., 2001) and were found to increase
with an increase in clay content. The differences were
attributed to the difference in measurement scales between the field and laboratory, and a scale dependence inthe soil bulk density. The largest differences in our study
were observed for the C2 horizon at the 90- to 95-cm
depth, where the clay content was the largest comparedwith other horizons. The ensemble prediction also produced a smaller initial loss of water from the profile
due to the mismatch between simulated and actual capillary pressures.
The PTF ensemble provided more robust simulations.
The tolerance interval of water contents simulated with
the PTF ensemble prediction was found to be substantially smaller than with the laboratory water retention
data (Fig. 3 and 4), in spite of the larger uncertainty inwater retention estimated using the ensemble of PTFs,
as compared with the laboratory data. No close relationship was found between the uncertainty in water retention and uncertainty in the simulated water contents. For
example, the variability in laboratory water retention
was similar at depths of 15 and 95 cm within the range ofcapillary pressures observed in the field. However, thevariability in simulated water contents was two times
smaller at the 95-cm depth than at 15 cm. At the sametime, a similar variability in simulated water contents
was found at depths of 15 and 55 cm, although thelaboratory water retention data were about two times
more variable at 15 cm than at 55 cm. We note that thevariability in ensemble-predicted water retention was
higher than the variability in laboratory-measured water
retention. However, the difference in widths of the tolerance intervals was less than one would expect, mostly
because the small-scale variability in water retention was
relatively high (Fig. 6). Such variability at the core scale is
not uncommon, and therefore a comparable variability
in the ensemble water retention and the small-scalewater retention data could be expected at other sites.

Reproduced from Vadose Zone Journal. Published by Soil Science Society of America. All copyrights reserved.

www.vadosezonejournal.org

241

Fig. 7. Average field-measured water content data at several depths (symbols) and simulated results obtained with the random Ks and the laboratorywater retention data having a 50% probability (lines). Solid line is the median value; dotted lines are the 95% tolerance interval.

Using the PTF ensemble is, in essence, the utilizationof generic information available before the site study.
Data in Fig. 6 show that such information inherently
has considerable variability. The differences in accuracyof simulations with individual PTF (Table 4) are large
and illustrate difficulties in selecting a single PTF for a
specific site. Although the all-USA PTF of Gupta andLarson (1979) is ranked relatively high, other all-USA
PTFs have relatively low ranks. The PTF developed for
Belgian soils (Vereecken et al., 1989) was ranked eighthand provided only moderate accuracy with the Belgian
dataset in this work compared with the all-European
PTFs of Wösten et al. (1999), which had a rank of 2.
Analysis of the data in Table 4 and the original publications did not allow us to explain why some PTFs
performed better than others in our particular case.
We note that the variability in field water retention
data was quite high in our study. Natural spatial variations in soil structure, soil water retention hysteresis, anda nonequilibrium state of the soil water system areamong possible reasons for this. Neither the available
PTFs nor typical draining measurements can account forfield hysteresis and nonequilibrium in water retention.
These possibilities, among other reasons, may cause errors in the soil water content simulations.
An ensemble of saturated hydraulic conductivity PTFs
was not tested in this study. Far less literature exists on
estimating Ks as compared with water retention (see,e.g., review by Pachepsky and Rawls, 2004). The effectof varying Ks within a realistic range was substantial (Fig.
7); this implies a need to emphasize measurement of thehydraulic conductivity in field campaigns to characterize
the soil hydraulic properties.
The differences in accuracy of the various water content simulations did not manifest themselves in the simulated soil water fluxes (Fig. 8). The accuracy was
similar at both large (Fig. 8) and small (Fig. 9) temporalscales. No statistically significant correlation was foundbetween fluxes at small temporal scales simulated with
the PTFs ensemble and the laboratory water retentionReproduced from Vadose Zone Journal. Published by Soil Science Society of America. All copyrights reserved.

242

VADOSE ZONE J., VOL. 5, FEBRUARY 2006

Fig. 8. Measured and simulated cumulative soil water fluxes for three wetting–drying periods (Days 112–143, 144–232, and 233–275). s, simulatedwith laboratory-measured water retention; ,, simulated with the pedotransfer function ensemble. Error bars show standard deviations.

data (results not shown). The similarity in flux simulation errors shown in Fig. 9 did not stem from the similarity in fluxes. A possible reason for the error scaling in
Fig. 9 could be a smoothing effect of a wick-imposed
suction on the measured flux dynamics. Oscillations insoil water fluxes are probably better captured by simulations as compared with flow collected using passive
capillary lysimeters.
Although predictions with a single PTF depend on the
database used for the PTF development, an ensemble
prediction will be less dependent on the individual PTFs
if the number of individual PTFs is sufficient enough torepresent natural variability in soil water retention. Predictions in meteorology often evaluate the uncertainty
in multimodel predictions using both different models
and the variability in predictions from each of thosemodels. This approach, however, may have a limited applicability to the case of PTFs since the published information on the most PTFs is not sufficient to estimate theuncertainty envelope of the predictions. The technology
for this has been introduced only recently (Schaap andLeij, 1998), while most of the large-database PTFs weredeveloped much earlier.
Simulations with the PTF ensemble were averaged
without assigning any weights to the results from simulations with individual PTFs. Such weights can be assigned in applications where time series of the soil watercontent are measured, and where the accuracy of simulations with individual PTFs is known. Such assignmentof weights has been used for multimodel predictions inmeteorology (Hamill et al., 2005). This approach allows
one to decrease the effect of an outlier (i.e., of a PTF thatgives results completely inapplicable to the site in question). Another way to decrease the effect of outliers is to
use the median predictions from the ensemble simulations instead of average values. The median and average
predictions from the PTF ensemble simulations werevery close in our study (results not shown).
The PTF ensemble was assembled somewhat arbitrarily in this work. Developing guidelines to compose
such ensembles requires further research. For example,
if a regional PTF is used in an ensemble with PTFs

Fig. 9. Dependencies of average daily flux estimation error on time window over which fluxes were averaged. s, simulated with laboratorymeasured water retention data; ,, simulated with the pedotransfer function ensemble.

243

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www.vadosezonejournal.org

developed from a large database that included data fromthe same region, then those data may be weighted moreheavily since they influence the ensemble results at least
twice. Besides, large databases usually contain data thatare obtained by a variety of methods. Perhaps this leads
to a cancellation of errors compared with a PTF set derived using one specific method that may have a consistent bias when predicting specific soil water processes.
More experiments with PTF ensembles are needed todecide on preferable attributes that have to be different
between the ensemble elements (e.g., region, soil types,
or landscape types).
As the ensemble prediction methodology is relatively
young, the terms ensemble predictions and multimodel
predictions are still often used with different meanings.
While some researchers apply these terms to combining
results from conceptually different models, others use
them for averaging results from conceptually equivalentmodels developed on subsets of the large datasets andthen averaging the results. For example, the method of“bagging” results of regression trees, which combines
results from neural networks developed on subsets of
the large dataset, is also referred to as an ensemble
method (e.g., Opitz and Maclin, 1999). Even averaging
of Monte Carlo simulations results is sometimes referred as an ensemble prediction. In general, ensemble
modeling finds applications in disciplines where the object complexity is high, measurements are difficult, andwhere many conceptually different models hence may
provide the same level of accuracy when developed andtested on different datasets or on different subsets of thesame database. The fact that ensemble predictions are
more accurate than individual models is something thatis now supported by more and more empirical evidence.
Overall, the uncertainty in the ensemble-estimatedwater retention estimates (as quantified by the widthof the 95% tolerance interval of the water content at a
specific pressure head) was comparable with the uncertainty in the laboratory water retention data. The PTF
ensemble estimation gave substantially better approximations of field water retention compared with the laboratory data. Simulations of the soil water regime were
performed using the HYDRUS-1D software with thelaboratory-measured water retention at 60 locationsof the trench and with the ensemble of PTF-estimatedwater retention data. Simulations with the PTFs ensemble produced, on average, two times smaller errors
compared with laboratory data. The accuracy of simulating cumulative soil water fluxes did not differ between
simulations with the laboratory-measured data and the
PTF ensemble water retention estimates. We conclude
that the ensemble prediction methodology is a promising approach for estimating hydraulic properties within
an uncertainty context.
APPENDIX
Pedotransfer Functions to Estimate Soil
Water Retention
In the equations below, the symbols w and u denote gravimetric (g g21) and volumetric (cm3 cm23) water contents, re-Table A1. Coefficients in the PTF of Rawls et al. (1982) u 5 a 1b(% sand) 1 c(% silt) 1 d(% clay) 1 e(% OM) to predict
volumetric soil water content at specific capillary pressure.
Pressure head
kPa
210
220
233
260
2100
2200
2400
2700
21000
21500

a

b

c

d

e

0.41180.31210.25760.20650.03490.02810.02380.02160.02050.026020.0030
20.0024
20.0020
20.0016
0
0
0
0
0
0

0
0
0
0
0.00140.00110.00080.00060.000500.00230.00320.00360.00400.00550.00540.00520.00500.00490.00500.03170.03140.02990.02750.02510.02000.01900.01670.01540.0158

spectively; the subscripts 330 and 15 000 indicate the capillarypressures (cm). Clay and sand denote percentages of textural
fractions according the USDA textural classification. OM isthe organic matter content (%), OC is the organic C content(%), rb is the bulk density (g cm23), and the other symbols aredefined as they appear.

Equations for Estimating the Soil Water Content
at Fixed Capillary Pressures
Rawls et al. (1982) used the U.S. Cooperative Soil Survey
Database to develop 12 regression equations to relate the soil
water contents at 10 capillary pressures to sand, clay, and organic matter contents (Table A1). A similar set of equations
was later developed to use knowledge of the bulk density alongwith the sand, clay and organic matter contents (Rawls et al.,
1982; Table A2).
Baumer (1992) used the U.S. National Soil Survey databaseto predict the gravimetric water content at capillary pressuresof 15 000 cm and 330 cm with the equations:w15000 5 0:01rb (0:71 1 0:45OM 1 0:336 clay
1 0:117clay(CA3=2 ) 1 0:004claySAR)[A1]

w330 5 0:01rb (15:84 1 0:746OM 1 2:2025CA2
2 0:137sand 1 0:743w15000 ) if clay . 10%[A2]

w330 5 0:01rb (15:84 1 0:746OM 1 0:02CA2 clay2
2 0:137sand 1 0:743w15000 ) if clay # 10%[A3]

Table A2. Coefficients in the PTF of Rawls et al. (1983) u 5 a 1b(% sand) 1 c(% clay) 1 d(% OM) 1 erb to predict thevolumetric soil water content u (cm3cm23) at specific capillarypressure from soil texture, organic matter content and soil bulk
density (g cm23).
Pressure head
cm
2200
2330
2600
21000
22000
24000
27000
210000215000

a

b

c

d

e

0.41800.3486
0.28190.23520.18370.14260.11550.10050.085420.002120.0018
20.001420.001220.0009
20.0007
20.0005
20.0004
20.0004

0.00350.00390.00420.00430.00440.00450.00450.00450.00440.02320.02280.02160.02020.01810.01600.01430.01330.012220.0859
20.0738
20.061220.051720.0407
20.0315
20.0253
20.0218
20.0182

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VADOSE ZONE J., VOL. 5, FEBRUARY 2006

where CA is the clay activity (i.e., the ratio of the cationexchange capacity of the mineral fraction to the clay content,
molc kg21), and SAR is the sodium adsorption ratio.
Bruand et al. (1994) estimated the volumetric water content
at capillary pressures of 15 000 and 330 cm as

Reproduced from Vadose Zone Journal. Published by Soil Science Society of America. All copyrights reserved.

u15000 5 (0:008 1 0:00367clay)/(0:471 1 0:00411clay)[A4]
u330 5 (0:043 1 0:004clay)/(0:471 1 0:00411clay) [A5]Canarache (1993) applied regression analysis to the Romaniannational database to obtain the predictive equations:u15000 5 0:01rb (0:2805clay 1 0:0009615clay2 )[A6]u330 5 0:01rb (2:65 1 1:105clay 2 0:01896clay2
1 0:0001678clay3 1 15:12rb 2 6:745r2b
2 0:1975clayrb )hb 5 exp(5:340 1 0:185clay 2 2:484 f 2 0:002clay2
2 0:044sandf 1 0:001sand2 f2 2 0:009clay2 f2
2 0:00001sand2 clay 1 0:009clay2 sand2 0:0007sand2 f 1 0:000005clay2 sand 2 0:500f2 clay)[A18]
l 5 exp(20:784 1 0:018sand 2 1:062f 2 0:00005sand2
2 0:003clay2 1 1:111f2 2 0:031sandf
1 0:0003sand2 f2 2 0:006clay2 f2
2 0:000002sand2 clay 1 0:008clay2 f2 0:007f2 clay)[A19]
ur 5 20:018 1 0:0009sand 1 0:005clay 1 0:029f[A7]

Gupta and Larson (1979) used a subset of the U.S. National
Cooperative Survey database to derive predictive equations forthe volumetric water content at capillary pressures of 15 000 and
330 cm as follows:

2 0:0002clay2 2 0:001sandf 2 0:0002clay2 f2
1 0:0003clay2 f 2 0:002f2 clay

Campbell and Shiozawa (1992) set the value of the residual
water content in Eq. [2] equal to zero to transform the Brooks–
Corey model to:

u330 5 0:003075sand 1 0:005886silt 1 0:008039clay
1 0:002208OM 2 0:1434rb

h 5 hb (u/us )2b[A8]

u15000 5 0:000059sand 1 0:001142silt 1 0:005766clay
1 0:00228OM 1 0:02671rb

hes 5 20:05d21/2
gHall et al. (1977) analyzed a subset of British Soil Survey data
and derived the equations

u15000 5 0:01(1:48 1 0:84clay  0:0055clay2 )u330 5 0:01(11:83 1 0:96clay 2 0:008clay2 )2u15000 5 0:01(1:74 1 0:76clay 2 0:005clay )

[A12]
[A13]

Rajkai and Várallyay (1992) analyzed the Hungarian national
database to obtain:

u330 5 0:01[38:62 2 0:00479sand 2 0:0019(sand/silt)2 ][A14]
u15000 5 0:01(1:39 1 0:36clay 1 0:22OM2 )b ¼ 220hes 1 0:2sg[A15]

In our study we used clay content instead of the unavailable fine
fraction content in Eq. [A15].
Tomasella and Hodnett (1998) studied Brazilian soils andderived the equations:

u330 5 0:01(4:046 1 0:426silt 1 0:404clay)[A16]

u15000 5 0:01(0:91 1 0:150silt 1 0:396clay)[A17]

Equations to Estimate Brooks–Corey Parameters
Rawls and Brakensiek (1985) developed the following
equations to estimate the Brooks–Corey parameters in Eq. [1]:[A22]

where the value of hes corresponds to the air entry pressure at astandard bulk density, rb of 1.3 g cm23. The proposedadjustment for bulk density is[A11]Petersen et al. (1968) worked with the Pennsylvania soil
database. Their equations are:

[A21]

The parameters in (A21), estimated from two data sets for
British soils, were found to be[A9]u330 5 0:01(20:81 1 0:45clay 1 0:13silt 2 5:95rb )
[A10]

[A20]

hb 5 hes (rb /1:3)0:67b[A23]

The geometric mean diameter dg and geometric standard
deviation are given by

dg 5 exp(20:025 2 0:0363silt 2 0:0688clay)
sg 5 exp(0:133silt 1 0:477clay 2 ln2 dg )1/2

[A24]

Saxton et al. (1986) also set the value of the residual watercontent in Eq. [2] equal to zero and transformed the equation
toh 5 AuB

[A25]

where
A 5 100exp(24:396 2 0:0715clay 2 0:000488sand2
2 0:00004285sand2 clay)[A26]

B 5 23:1402 0:00222clay2 2 0:00003484sand2 clay
[A27]
Oosterveld and Chang (1980) used a Canadian database andtransformed Eq. [2] with ur 5 0 to the formu 5 0:01rb (35:367 1 0:644clay 2 0:251sand
2 0:045D)h20:190[A28]

where D is the mean depth of the sample in centimeters.

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www.vadosezonejournal.org

Williams et al. (1992) transformed Eq. [1] with ur 5 0 to thelogarithmic formu 5 A 1 Blnh

[A29]

Reproduced from Vadose Zone Journal. Published by Soil Science Society of America. All copyrights reserved.

and applied it to an Australian database. Different pedotransfer equations were developed in their work for different typesof available data of basic properties. The equations

A5 2:571 0:238ln(clay) 2 0:000192sand2 2 0:0137sandus 5 0:2345971971 1 0:0046614221sand
1 0:0088163314silt 1 0:0064338641clay
2 0:3028160229rb 1 1:79762 3 102 sand2
2 3:134631 3 102 silt2[A40]

Equations to Estimate van Genuchten Parameters[A30]

Wösten et al. (1999) analyzed the all-Europe database andderived the following PTFs to estimate van Genuchten
parameters in Eq. [1]:[A31]

us 5 0:7919 1 0:001691clay 2 0:29619rb

were suggested when data on the organic matter areavailable, and the equations

2 0:000001491silt2 1 0:0000821OM2

2 0:0926lnOM 1 0:0412OM
B 5 20:403 1 0:0871ln(clay) 2 0:00077sandA 5 1:839 1 0:257ln(clay) 1 0:3812 2 0:0001sand2
[A32]

2

[A33]

for cases when no information about the organic matter
content was available.
Mayr and Jarvis (1999) set ur 5 0 and porosity f equal to thesaturated water us in the Brooks–Corey equation andcombined this equation for the dry range of soil water
retention curve
21/bu 5 us (h/a)[A34]u , uiwith a parabolic equation for the wet range:[A35]

u $ uiThe water content ui and the equivalent capillary pressure hi at
the matching point are given by:2bus
1 1 2b

[A36]

and



2b
hi 5 a
1 1 2b

[A41]

10:646OM 1 15:29rb 2 0:192topsoil 2 4:671r2b
2 0:000781clay2 2 0:00687OM2 1 0:0449/OM
1 0:0663ln(silt) 1 0:1482ln(OM) 2 0:04546rb silt[A42]
2 0:4852rb OM 1 0:00673topsoil clay]n 5 1:0 1 exp[225:23 2 0:02195clay 1 0:0074silt
2 0:1940OM 1 45:5rb 2 7:24r2b 1 0:0003658clay2
1 0:002885OM2 2 12:81/rb 2 0:1524/silt
2 0:01958/OM 2 0:2876ln(silt) 2 0:0709ln(OM)

us h2 (1 2 ui /us )u 5 us 2
a2 (ui /us )22bui 5

2 0:001183rb OM 2 0:0001664topsoil silta 5 exp[214:96 1 0:03135clay 1 0:0351silt

B 5 20:303 1 0:093ln(rb ) 1 0:0565ln(clay)
2 0:00003sand

1 0:02427/clay 1 0:01113/silt 1 0:01472ln(silt)
2 0:0000733OMclay 2 0:000619rb clay

2b
[A37]

Pedotransfer functions developed by Mayr and Jarvis (1999)
from a Scandinavian dataset were:log(a) 5 24:9840297533 1 0:0509226283sand
1 0:1575152771silt 1 0:1240901644rb
2 0:1640033143OC 2 0:0021767278silt

us 5 0:81 2 0:283rb 1 0:001clay[A44]

ur 5 0:015 1 0:005clay 1 0:014OC[A45]

FAO textural class

1 0:0000143822silt3 1 0:0008040715clay2

ur

us

a

n

Topsoils[A38]

log(1/b) 5 20:8466880654 2 0:0046806123sand
1 0:0092463819silt 2 0:4542769707rb
2 0:0497915563OC 1 0:0003294687sand2
3

where topsoil is an ordinal variable having the value of 1 or of
0. Parameter m in Eq. [1] was computed as 1 2 1/n .
Wösten et al. (1999) also estimated average van Genuchten
parameters (Table A3) for the FAO textural classes that are
depicted in Fig. A1.
Vereecken et al. (1989) used a Belgian dataset to develop thefollowing PTFs for the van Genuchten equation with m 5 1:

Table A3. Tabulated van Genuchten parameters by FAO texturalclasses (Wösten et al., 1999).

2

1 0:0044067117OC2

2 44:6ln(rb ) 2 0:02264rb clay 1 0:0896rb OM
1 0:00718topsoil clay
[A43]

2

1 0:000001689056sand 1 0:0011225373OC[A39]

CoarseMediumMedium fineFine
Very fine

0.025
0.010
0.010
0.010
0.010

0.403
0.439
0.430
0.520
0.614
Subsoils

0.03830.03140.00830.03670.02651.37741.1804
1.25391.1012
1.1033CoarseMediumMedium fineFine
Very fine

0.025
0.010
0.010
0.010
0.010

0.366
0.392
0.412
0.481
0.538

0.04300.02490.00820.01980.01681.5206
1.16891.21791.08611.0730Reproduced from Vadose Zone Journal. Published by Soil Science Society of America. All copyrights reserved.

246

VADOSE ZONE J., VOL. 5, FEBRUARY 2006

Fig. A1. Textural classification system according to the FAO Soil Map
of Europe (1998). The FAO classes are: C (coarse), M (medium),MF (medium fine), F(fine), VF (very fine).

a 5 exp(22:486 1 0:025sand 2 0:351clay
2 2:617rb 2 0:023clay)[A46]

n 5 exp(0:053 2 0:009sand 2 0:013clay
1 0:00015sand2 )[A47]

Finally, Varallyay et al. (1982) applied the van Genuchten
equation with m 5 1 and ur 5 0 to the Hungarian national
database and found the following regression equations for A
horizons:

us 5 0:01(256:4rb 1 0:205clay 1 123:79)
n 5 0:336rb 2 0:

[A49]

a51020:04701r clay 2 1:513r 1 0
b

[A48]

b

[A50]

and for C horizons:

us 5 0:01(246:8rb 1 115:39)[A51]

n 5 0:00439rb clay 1 0:625[A52]

a 5 1020:03268r clay 2 0:865r r 2 0:301

[A53]

b

b b

ACKNOWLEDGMENTS
This work was partly supported by Interagency Agreement
RES-02-008 “Model Abstraction Techniques for Soil Water
Flow and Transport” and also by the SAHRA Science Technology Center as part of NSF grant EAR-9876800.

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