DIVISION S-6-SOIL AND WATER MANAGEMENT
AND CONSERVATION
Using Texture and Other Soil Properties to Predict
the Unsaturated Soil Hydraulic Functions
J. H. M. WOSTEN AND M. TH. VAN GENUCHTEN*

ABSTRACTThe unsaturated hydraulic properties of soils are important but
difficult to measure. Rather than measuring the hydraulic properties
directly, we followed a different approach by fitting analyticalexpressions for the soil water retention and hydraulic conductivity
functions to experimental data for a wide range of soils in the Netherlands. Analysis of the data shows the flexibility of the analyticalexpressions and also gives insight into how the different model parameters affect the calculated unsaturated hydraulic functions.
Regression analyses are used to relate the estimated model parameters to more easily measured soil properties, such as bulk densityand percentages silt, clay and organic matter. After calibration, therelations are used to predict the hydraulic functions of soils for which
only the more easily measured soil properties are available. Accuracy of the predictions is analyzed in terms of functional criteria
which are relevant to practical management problems. The predictive regression models are useful for estimating the unsaturated soil
hydraulic properties of large areas of land, but need improvement
for application to specific sites.

OIL HYDRAULIC BEHAVIOR is characterized by theSsoil water retention curve which defines the volumetric water content (6) as a function of the soil waterpressure head (h\ and the hydraulic conductivity curve
which relates the hydraulic conductivity (K) to watercontent or pressure head. These curves are crucial ingredients for predicting water flow and solute transport in the vadose zone, and for evaluating alternativesoil-water-crop management practices.
Even though new field or laboratory techniques formeasuring the unsaturated soil hydraulic functions
have been developed (e.g. Bouma, 1983; Klute, 1986),
the methods have remained relatively cumbersome
and costly, especially for the hydraulic conductivity.
The measurement problem is complicated by resultsof studies (e.g., Nielsen et al., 1973; Russo and Bresler,
1981) which show that soils exhibit significant temporal and spatial variabilities in their hydraulic properties. This variability implies that numerous samples
may be needed to properly characterize a given field.
To partially circumvent the measurement problem,
several investigators have proposed theoretical poresize distribution models that predict the hydraulicconductivity from more easily measured soil water retention data (Millington and Quirk, 1959; Mualem,

J.H.M. Wosten, Netherlands Soil Survey Inst., P.O. Box 98, 6700
AB Wageningen, The Netherlands; and M.Th. van Genuchten, U.S.
Salinity Lab., USDA-ARS, 4500 Glenwood Dr., Riverside, CA 92501.
Joint contribution from the Netherlands Soil Survey Institute andthe U.S. Salinity Lab., USDA-ARS. Received 27 Nov. 1987. *Corresponding author.
Published in Soil Sci. Soc. Am. J. 52:1762-1770 (1988).

1762

1976). Others have approximated the hydraulic properties from soil textural, bulk density or other soil data
(Bloemen, 1980; Rawls et al., 1982; Haverkamp andParlange, 1986).
One of the proposed unsaturated hydraulic models
is described by van Genuchten (1980) who combined
an empirical S-shaped curve for the soil water retention function with the pore-size distribution theory of
Mualem (1976) to derive a closed-form analyticalexpression for the unsaturated hydraulic conductivity.
Except for the saturated hydraulic conductivity, Ks,
the resulting conductivity function contains parameters that can be estimated from measured soil water
retention data. An advantage of this model, like previous ones by Brooks and Corey (1964) and others, isthat the hydraulic properties are expressed in the formof analytical (nontabular) functions, a feature that facilitates their efficient inclusion into numerical simulation models and also enables the rapid comparisonof the hydraulic properties of different soils. Van Genuchten's unsaturated hydraulic functions have beenshown in several recent studies (e.g., Stephens andRehfeldt, 1985; van Genuchten and Nielsen, 1985;
Hopmans and Dane, 1986) to give good descriptionsof observed retention and/or conductivity data for alarge number of soils. Hopmans and Overmars (1986)
recently also demonstrated the applicability of thosefunctions in a hydrological research project.
The above studies rely on available soil water retention data for predicting the unsaturated hydraulicconductivity. Sometimes, as is the case in this study,
directly measured unsaturated hydraulic conductivity
data may also be available. To make use of all available data, we will apply in this paper nonlinear leastsquares parameter estimation techniques to fit van
Genuchten's functions simultaneously to observed
water retention and hydraulic conductivity data froma large number of soils in the Netherlands. Once estimated, the optimized model parameters will be used
in a multiple regression analysis to investigate relationships between the fitted parameters and such moreeasily measured basic soil properties as bulk density,
soil texture, and organic matter content. The regression model, in turn, is used to predict the hydraulicfunctions of three soils using only their basic soil properties. Rather than focusing on a statistical analysis of
the fitted hydraulic functions, we will compare thepredicted and the measured hydraulic functions interms of functional criteria (Wosten et al., 1986) which
relate directly to practical applications (e.g., travel timefrom the soil surface to the groundwater table).
Specific purposes of this study are hence (i) to fit
the analytical functions of van Genuchten (1980) to alarge set of measured soil water retention and hy-

WOSTEN & VAN GENUCHTEN: PREDICTING UNSATURATED SOIL HYDRAULIC FUNCTIONS

draulic conductivity data, (ii) to explore the possibilityof predicting the hydraulic functions from basic soil
properties, and (iii) to compare measured and predicted hydraulic functions on the basis of functional
criteria which are relevant to soil-water management

practices.
MATERIALS AND METHODS
Soil water retention and hydraulic conductivity curves were
measured for a large number of soils in the Netherlands.
The soils were classified according to soil texture (as usedby the Netherlands Soil Survey Inst.), and type of horizon,
being either topsoil (A horizon) or subsoil (B and C horizons). This classification resulted in 20 different soil groups(Table 1) comprising a total of 197 individual curves. Tabulated forms of the geometrically averaged curves for the 20
soil groups are given elsewhere (Wosten et al., 1987a). Because of wide ranges in soil texture, the individual curves
within each group are quite variable. As a set, the curves
form a unique data base covering a broad spectrum of soils
in the Netherlands.
Hydraulic conductivities were estimated using a combination of the following five methods:
1. The column method (e.g., Bouma, 1982) for the vertical saturated hydraulic conductivity, Ks.
2. The crust-test (an updated version of the method described by Bouma et al., 1983) for unsaturated conductivities when the pressure head, h, is between 0 and-50cm.
3. The sorptivity method (Dirksen, 1979) for conductivities of coarse-textured soils when h ^ —50 cm.
4. The hot-air method (Arya et al., 1975) for conductivities of medium- and fine-textured soils when h «£ — 50
cm.

1763

5. The evaporation method (Boels et al., 1978) for hydraulic conductivities when h is between 0 and — 800
cm.
Soil water retention curves were obtained by slow evaporation of wet, undisturbed samples in the laboratory asreported by Boels et al. (1978) and Bouma et al. (1983). In
this method, pressure heads are periodically measured withtransducer-tensiometers while at the same time subsamples
are taken to determine water contents, thus yielding points
relating to h and 8. Water contents corresponding with pressure heads lower than —800 cm were obtained by conventional methods using air pressure (Richards, 1965). For relatively fine-textured soils, a staining technique was applied
to record the effects of horizontal cracks on the upward fluxof water from the water table to the rootzone (Bouma, 1984).
DATA ANALYSIS
The volumetric soil water content, 0, as a function of pressure head, h, is described with the following empirical equation of van Genuchten (1980)(er < ewhere the subscripts r and 5 refer to residual and saturated
values, and where a, n and m are parameters which determine the shape of the curve. The residual water content, 6n
refers to the water content where the gradient d6/dh becomeszero (h ~» — °°). In practice, 6, is the water content at somelarge negative value of the soil water pressure head. The
dimensionless parameter n determines the rate at Which the
S-shaped retention curve turns toward the ordinate for large
negative values of h, thus reflecting the steepness of the curve,
while a (cm~') equals approximately the inverse of the pres-

Table 1. Number of individual curves, ranges in measured soil properties, and average values for the optimized parameters a, n and I
for 20 soil groups.
Soil

Numberof curvessat

2-50 pClay< 2 ioOrganic
matterBulk
density

M50f

3

g/cm

Coarse-textured soils (105 samples)
TopsoilBl
B2
B3
B4
Subsoil
01
02
03
04
Topsoil
B7
B8
B9
Subsoil
08
09
010

5
11
9
5

4-7
11-17
19-29
37-49

49
7
14
5

1-9
10-16
21-32
37-47

140-170130-170130-165
130-160

0.01690.02030.02900.0157

1.83
1.52
1.44
1.58

0.826
-0.432-0.1520.225

0.1-2
1.4-1.8
150-180
0.3-2
1.5-1.7
150-175
0.2-2
1.4-1.8130-170
1.4-1.7
0.3-1
130-165
Medium-textured soils (43 samples)

0.05510.02010.02780.0154

2.43
2.05
1.75
1.82

0.310

1-4

3-10
4-13
2-5

1.4-1.6
1.3-1.5
1.1-1.5
1.1-1.5

0.666
0.229
0.153

5
10
3

10-12
12-16
18-22

2-6
2-3
2-8

1.2-1.7
1.3-1.6
1.3-1.6

0.03470.06240.0536

1.27
1.25
1.15

-0.543

7

9-11
12-16
18-22

0.4-1
0.3-1
0.1-1

1.5-1.6
1.4-1.7
1.3-1.5

0.03160.04240.0400

1.32

-1.14
-2.43
-3.26

1.1-1.5
1.1-1.7
0.9-1.3

0.133

1.12
1.12

1.4-1.6
1.0-1.5
1.0-1.4

0.05100.06020.0740

12
6

1.28
1.21

-3.30
-4.59

Fine-textured soils (49 samples)
Topsoil
BIO
Bll
B12
Subsoil

8
5
5

26-34
35-50
51-77

Oil
012
013

7
12
12

28-33
37-47
52-77

t Median sand particle size.

2-5
4-15
2-5

0.9-2
0.1-2
0.1-2

t Not included in the regression analysis.

0.138
0.141

1.08

-8.36
-7.66
-8.30

1.13
1.14
1.08

-5.50
-6.37
-9.38

1764

SOIL SCI. SOC. AM. J., VOL. 52, 1988

sure head at the inflection point where dd/dh has its maximum value.
Assuming m = 1 — l/n, van Genuchten combined Eq. [1]with the following theoretical pore-size distribution model
which was derived by Mualem (1976)

where / is an unknown parameter, x is a dummy variable,
and S is relative saturation (0 < S < 1):o, - er).

[3]

Combining Eq. [1] and [2] leads to (van Genuchten, 1980)
K(S) = KSS' [1 - (l-S1"")'"]2
or in terms of the soil water pressure head

K(h) = Ks-

[4]

[5]

[1 + ahfl
Equations [1] and [5] are the analytical functions describing the 6(h) and K(h) relationships, respectively. Although /is presumably a soil specific parameter, Mualem (1976) concluded from an analysis of 45 soil hydraulic data sets that /should be on the average about 0.5. In this study / is not
fixed but considered to be one of the experimental unknowns.
Figure 1 shows how the parameters n, a, 8r and / affectthe shapes of the calculated soil water retention (Eq. [1]) andunsaturated hydraulic conductivity (Eq. [5]) functions. Unless noted otherwise, all curves were obtained with 6r = 0. 10,
es = 0.50, a = 0.005 (cm-'), n = 2.5 and / = 0.5. Figure
Ic shows that the parameter 8r affects only the shape of theretention curve while leaving the relative conductivity (Kr= K/KS) function unaffected. The parameter /, on the other
hand, only affects the hydraulic conductivity and leaves theretention curve unchanged (Fig. Id). These properties; follow
immediately from Eq. [1] and [5]. Figure 1 clearly 'demonstrates the flexibility of the analytical functions hi. generating
different shapes of the soil water retention and hydraulicconductivity curves. We note that, except for the parameter/, similar plots of the hydraulic functions, with different scales
and from different perspectives, have been presented anddiscussed also by Stephens and Rehfeldt (1985) and Hopmans and Overmars (1986). Van Genuchten and Nielsen(1985) in addition discussed the computationally more complicated case when the parameters m and n in Eq. [1] areindependent.
A nonlinear least-squares optimization program (SOHYP) was previously constructed (van Genuchten, 1978) toestimate the parameters 8n a and n from observed soil water
retention data. The SOHYP code was modified to yield the
RETC code (van Genuchten, 1986; unpublished) which allows some or all unknown coefficients (6n 6S, a, n, I and/orKs) in Eq. [1] and [5] to be estimated simultaneously frommeasured soil water retention and hydraulic conductivity
data. As before, the least squares parameter estimation process is based on Marquardt's maximum neighborhood
method (Marquardt, 1963). The objective function, O(b),minimized in RETC is of the general form

i-M+ 1

Kb - \D.(KtJ>)]}2

where 6* and K* are the measured water contents and hydraulic conductivities, respectively, d,(b) and Kj(b) are thepredicted responses for a given parameter vector [b] of un-

known coefficients, w, are weighting coefficients for the individual observations (set to unity in this study), M is thenumber of observed retention data and ./Vis the total numberof observed retention and conductivity data. The parameters W , and W2 are also weighting coefficients. Parameter
W2 is calculated internally in the program as follows

+ 1

** m

which gives the water content data approximately the same
weight as the ln(K) data. Parameter W\ is an independent
input parameter which adds extra flexibility in assigning moreor less weight to the water content data as compared to thewater conductivity data. Because hydraulic conductivities
often show more scatter than retention data, it is sometimes
beneficial to assign a relatively small value to W:. In ourstudy a value of 1.0 was assigned to W{, except for the sandy
soils which required a much smaller value of 0. 1 to ensure
visibly better fits of the typically steep part of the retention
curve at the inflection point.
In the most general case, the parameter vector {b} willcontain all coefficients, i.e.: {b} = [Bn 0S, a, n, /, Ks}. The
parameters ds and Ks in this study were fixed at their independently measured values, thus reducing the number of
unknowns to four. The parameter Br was initially also considered to be an unknown. Since only a few soil water retention and hydraulic conductivity data points were available in the dry range, we restricted our analysis to pressure
heads in the range from 0 to — 5000 cm. Because of thislimited range in pressure heads, 0r was estimated to be zero,or close to zero, for a majority of the data sets. Following
the example of Greminger et al. (1985), we consequently
fixed 8r at zero for all soils, and then reanalyzed the datawith only three unknown parameters: {b} = [a, n, /).
After the parameter estimation step, multiple regression
techniques were used to investigate the dependency of theestimated model parameters on more easily measured basic
soil properties. Model parameters for the coarse-textured soils

were found to be correlated to the quantitative variables
percent silt, percent organic matter, bulk density and median sand particle size (M50), and also to the qualitative
variable "topsoil or subsoil." For medium- and fine-textured
soils, the regressed variables were percent clay, percent organic matter, bulk density and again topsoil or subsoil. Linear, reciprocal and exponential relationships of these basic
soil properties were used in the regression analysis, while
also possible interactions among the soil properties themselves were investigated. Thus, the resulting regression model
consisted of various basic soil properties, and their interactions, which contributed significantly to the optimized soil
hydraulic parameters. Once established, the regression
models were used to predict the unknown hydraulic parameters of three typical fine-, coarse- and medium-textured soils
using their basic soil properties only.
Finally, predicted and measured hydraulic functions of
the three soils will be compared on the basis of functional
criteria which have immediate relevance to managementtype applications Wosten et al. (1986) introduced for thispurpose three functional criteria:
1 . Travel time, Tn of water from the soil surface down toa water table at depth L, assumed to be 1 m. The travel
time is approximated by T = 6L/qd, where qd the average daily vertical downward_ flux for Dutch winterconditions (0.14 cm d~'), and 0_is the profile-averaged
water content corresponding to qd as derived from thecalculated or measured K(h\ff) curve.
2. Depth of water table, Lc, which can sustain a given
upward flux of water to the soil surface or to the bottom of the root zone. As shown by Gardner (1958),
this depth may be obtained by integrating Darcy's law

1765

WOSTEN & VAN GENUCHTEN: PREDICTING UNSATURATED SOIL HYDRAULIC FUNCTIONS

Kr
h(Cm)

-500-

n=4.53.5

1,5

2.5

10°-: —_ __-t^
I\^^:sSs

1a

\
\\ \
\\ \
\
\
\\ \
\\ \
\
\\ \
\

-400-

-300-

•

10-'-

•
1 3

^^ \
'SA

°~

:

X
1

-100-

0-

,

i

OJOO

0.10

0.20

X
^\

10-2-

\

-200-

X

\S.
^
\N^
\\^\"
\\"
\

i5

\

\.

10-°- ——————— ,——————— ,——————— r ——————— ,——————— ,

0.30

0,40

0

0.50

-100

-200

-300

-400

-500

h(cm)
Kr

"1!T\
1b

10-'-

10'=-:

•

-400-

-300-

-200-

\

in\\\ \ \
\
\\\
\\\ \

c(=0.035V\rjj025XQ.015

'

v

\\
\ \ \\\\\ \ \ \^

io-«-

\

Q 005

\

\\
\ \ \\

-500-

\

\v\
\ ^\ '=
\\ \
\ \

10-3r

h(cm)

11
111
\\

\\\

1O-6-

\

io-«-

v.

\

^^ oats\^^\p.005^^ 0.025

10-'^

-100-

0\ \
"--^^^

^^

OJ335

"
^
0-, ——————— ,——————— ,—————

o.oo

0.10 a2o

ojo

OAO

0£o

0

-100

-200

-300

-400

-500

h(cm)

Fig. 1. Effect of the parameters n, a, 9, and / on the calculated soil water retention, 9(h), and relative hydraulic conductivity, Kj(h), curves(Fig. la, b, c, d, respectively). Continued on next page.
to give

L-r
Lci

Jo 1+5

7m dh

[ $1

where hc is the imposed soil water pressure head (taken
as — 500 cm) at the bottom of the root zone, and qu is
the steady-state upward water flux density (assumed tobe 0.2 cm d~').

1766

SOIL SCI. SOC. AM. J., VOL. 52, 1988

3. Downward flux of water, qa, corresponding to a minimum soil air content, 6a (taken here to be 5%) whichis required (FAO, 1985) to maintain adequate aerationin the root zone for maximum root activity and crop
growth. The qa follows immediately from 3 the K(h$)
function at a water content which is 0.05 cm cm~ 3 lessthan the saturated value.

We refer to Wosten et al. (1986) for additional discussionsof the above functional criteria. Analysis of those criteria as
calculated with the measured and predicted hydraulic functions yields practical information about the accuracy of thepredictions.

Kr
10°-

h(crr

9r=0.0

\
-400-

-200-

0.1

0.2

0.3

\
\

\ \
\
\ \
\ \ \ \
\ \ \ \
\\\\
\\\\

-100-

^v

X
^\^

\

^

00JOO

:"~"^\

1c

0.10

0.20

OJO

0.40

-

0.50

()

-100

-200

-300

-400

-500

9 (cmVcm3)

h(cm)

Kr
10°-=

h(cm

\

-500-

1-

\

:

^^^^^•^•^\\~~^~——

10-' -

N^X^

\

:
\

X^x

,0--

\

-300-

\^

-200-

-100-

\

\

10-' -\"~^~ ——~ -2.0

\x

-4OO-

-s

vVsi

\

0- ———————— I———————— i————————i————————i———————1
0.00
0.10
0.20
0.30
OAO
OSO

10'B-

D

-100

-200

-300

-400

-500

h(cm)

Figure

9s

6r

n

1a

0.5

ai

0.005

1.5,2.5,3.5,4.5

0.5

1b

0.5

0.1

0.005,0.015,0.025,0.035

2.5

0.5

1c

0.5

0,0.1,0.2,0^

0.005

25

05

Id

0.5

0.1

0.005

2.5

0.5, -2.0, 2.0nFig. 1. Continued.

t

WOSTEN & VAN GENUCHTEN: PREDICTING UNSATURATED SOIL HYDRAULIC FUNCTIONSRESULTS AND DISCUSSION
Table 1 summarizes results of the simultaneous fitof Eq. [1] and [5] to the measured soil water retention
and hydraulic conductivity data. Note that the data
sets are divided into three soil textural groups (coarse,
medium, fine) and also according to "topsoil versus
subsoil." The table gives for each group of soil horizons the average2 value of the estimated parameters «,n and /. The R (R is the correlation coefficient) between measured and fitted data ranged from 0.94 to
0.99 for all individual curves.
Figure 2 shows good agreement between measured
and fitted curves for three typical soils selected fromthe three soil textural groups. The three soils were classified as a sandy, siliceous, mesic, Typic Haplaquod(01); a fine loamy, mixed, mesic, Typic Fluvaquent(B8); and a fine clayey, mixed, mesic, Typic Fluvaquent (013), respectively (Soil Survey Staff, 1975). The
R2-values between measured and calculated data were0.97, 0.99 and 0.99, respectively.
Gupta and Larson (1979), Poelman and van Egmond (1979) and Rawls et al. (1982) previously presented several regression equations for predicting watercontents at a limited number of pressure head values
from readily available basic soil properties. Saxton etal. (1986) just recently derived three functions for thesoil water retention curve covering the full range ofpressure heads from saturation to- h = — 15 000 cm.
Hence, they avoided the need to interpolate between(or extrapolate) tabular water contents and pressure
head data. Saxton et al. (1986) found good agreement
between their water retention functions and those calculated with equations of Rawls et al. (1982) A similar
prediction of the hydraulic conductivity curve was lesssuccessful, however. Our study deviates from the above
approaches in that the fitted parameters n, a and / areused for both the soil water retention and the hydraulic conductivity curves.
Multiple regression of each of the model parameterswith the basic soil properties yielded six different
regression equations. The parameter / for the2 coarsetextured soils was found to be uncorrelated (R = 0.07)
with the basic soil properties. Therefore, the averagevalue of 0.22 for / was used for all coarse-textured soils
irrespective of texture, bulk density or median sandparticle size. The 95% confidence limits of/were —0.16
and 0.60, which indicates that the average value of0.22 for these coarse-textured soils is in agreement with
Mualem's (1976) finding that / could be fixed at 0.5.
For the medium- and fine-textured soils / was clearly
related to percent
silt, bulk density, and topsoil or subsoil, with R2 = 0.68 and / for the individual curves
ranging from —16.0 to 2.2. Fixing / at 0.5 in thesecases did not result in acceptable fits of the experimental data (see also Fig. Id).
The regression models for the parameters a and nrevealed .Revalues which ranged from 0.42 to 0.76,
which is much lower than the values of 0.99 reported
by Saxton et al. (1986). This discrepancy is of course
partly due to the fact that our model parameters pertain simultaneously to the water retention and hydraulic conductivity curves over a broad range ofpressure heads. Still, the relatively low .Revalues indicate a need to improve the regression models. One
possible way to achieve this is to use a much larger

1767

hydraulic data set involving a broader array of soils
than used here. Alternative approaches to relate thehydraulic data to basic soil properties may also beneeded. Possible approaches are indicated by Williams et al. (1983) who also included soil structure andclay mineralogy in their analysis, and by Haverkamp
and Parlange (1986) who used the cumulative particlesize distribution instead of specific particle size classes
such as percent sand, silt or clay.
The regression models established in this study wereused to predict the unsaturated soil hydraulic functions from soil texture and other properties in conjunction with the measured values of Bs and K^ Figure
2 shows the measured and predicted curves for threesoils: 01, B8 and 013. The 90% confidence intervals
for the predicted curves were calculated from the standard deviations of the differences between measured
and predicted values of 8 and logATat 12 values for h.
This was done for all soil hydraulic functions of boththe coarse-textured soil group and the medium- andfine-textured soil group. Because these differences werenormally distributed, and because of the relatively large
number of hydraulic functions in the two soil groups,
the confidence limits could be approximated by taking
the predicted values plus and minus 1.65 times therespective standard deviations. The calculated confidence intervals are relatively wide, indicating that predictions made with the regression models of this study
will show considerable dispersion.
Table 2 compares the values of the three functional
criteria (Tn Lc, and qa) as calculated from the measured and predicted hydraulic functions. The hydraulic functions hence are compared in terms of specific management problems and the desired accuracyof the answers for these problems. For example, predicting the travel time Tr for the three soils with anaccuracy of ± 8 wk (2 months) is often good enoughfor most management problems on relatively detailed
scales (e.g., for scales of 1:10 000 or greater; Breeuwsma
et al., 1986). Depth to water table (Lc) and downward
flux density (qa) appear also accurate enough for mostmanagement problems on detailed scales in the caseof coarse-textured soils. However, their accuracy formedium- and fine-textured soils may permit only answers on a more general scale (e.g., for scales of
1:50 000 or smaller; van der Sluijs and De Gruijter,1985). This finding is consistent with the results ofFig. 2 which showed better agreement between measured and predicted hydraulic properties for coarsetextured soils as compared to medium- and fine-textured soils. Our contention that evaluation of theregression results should be based on their intended
Table 2. Functional criteria as calculated from the measured andpredicted hydraulic properties of three typical coarse-, mediumand fine-textured soils.

Travel time, Tr (day)Depth to water table,Lc, (cm)

Downward flux density, qa (cm d" 1 )Coarsetextured soil

Mediumtextured soil

Finetextured soil

Measured

Predieted

Measured

Predieted

Measured

Predieted

143

121

300

257

407

421

145

120

138

65

22

12

30

23

0.5

0.002

0.010

0.2

1768

SOIL SCI. SOC. AM. J., VOL. 52, 1988

use is consistent with the conclusion of de long (1982)
that water retention parameters of soil textural groups
as derived by Clapp and Hornberger (1978) are usefulfor modeling large areas of soils but fail to accurately
approximate soil water characteristics of specific sites.

In this respect we note a soil survey mapping study
by Wosten et al. (1987b) who showed that the scaleof application of a given model should depend on theaccuracy by which answers must be known, and on
the mapping costs involved.
K(cm/day)Coarse-texured soil: 01
silt
(%)
8.0
organic manor (%)
0.5
bulk density(g/cm3)
1.52
M50
(Mm)
140

2a

10-"-

10-'°
0.00

0.10

0.20

0.30

0,40

0.50

-10°

0.60
3

8 (cmVcm )K(cm/day)Medium-textured soil: B8
clay
(%)
12.8
organic matter (%)
3.5
bulk density(g/cm3)
1.39

2b

10°-

10-*-

h(cm)

10"

-102:

10-

-10°0,00

0.10

0.20

0.30

0.40

030

0.60

-10°

-10'

-10=

-103
h(cm

'

Fig. 2 Measured, fitted and predicted soil water retention, 6(h), and hydraulic conductivity, K(h), curves for three typical coarse-, mediumand fine-textured soils. Continued on next page.

WOSTEN & VAN GENUCHTEN: PREDICTING UNSATURATED SOIL HYDRAULIC FUNCTIONSSUMMARY AND CONCLUSIONS
The analytical hydraulic functions of van Genuchten (1980) were fitted simultaneously to observed
soil water retention and hydraulic conductivity data
for a wide variety of soils in the Netherlands. The
parameter Br was fixed at zero without significantly
affecting the accuracy of the results. Soil water retention data was weighted more than hydraulic conductivity data (W{ in Eq. [6] was set at 0.1) to provide
acceptable fits of the retention curves for the coarsetextured soils. The hydraulic properties of these soils
were not dependent upon the parameter /, yielding a
constant value of 0.22 (± 0.38) which agreed well with
Mualem's (1976) average value of 0.5. The conductivity and retention data for the medium- and finetextured soils were weighted equally, leading to /-values which varied between —16.0 to 2.2 as a functionof soil texture and other factors. The optimization
procedure resulted in reasonably accurate analytical
approximations for the hydraulic properties, thus
avoiding the cumbersome and computationally inefficient handling of tabulated data in mathematicalmodels of unsaturated flow.
An approach that relates the estimated parameters
to easily measured soil properties is described. Onceestablished, the resulting expressions allow predictionof the hydraulic functions of unsaturated soils forwhich only soil texture and other data (organic matter
content, bulk density) have been measured. Predicted
hydraulic properties were compared in terms of functional criteria which relate directly to practical management applications. We believe that any judgement
about the accuracy of the predicted hydraulic func-

tions should be based on the desired accuracy of thosecriteria.
Results indicate that the predictive regression
models established in this study can be used to derivesoil hydraulic functions for large areas of land whenworking on scales of 1:50 000 or smaller. The models
need improvement for site-specific applications at
scales of 1:10 000 or larger, however. The use of otherdata bases, or the inclusion of different soil texturalproperties such as the cumulative particle-size distribution (Haverkamp and Parlange, 1986) needs to beconsidered.
ACKNOWLEDGMENT
Soil hydraulic data used in this study included data madeavailable by the Inst. of Land and Water Management Research, Wageningen. Their permission to use those data isappreciated.
APPENDIX-SYMBOLS USED[b] = unknown parameter vector
O = least-squares objective function given by Eq. [6]h = soil water pressure head (cm of water)hc = imposed soil surface boundary condition for thepressure head (cm of water)
K = unsaturated hydraulic conductivity (cm d~')Kr = relative hydraulic conductivity
Ks = saturated hydraulic conductivity (cm d~')/ = parameter in Eq. [2]
L = water table depth (cm)Lc = critical water table depth (cm)m = parameter in Eq. [1]: m = 1 — l/«
M = number of soil water retention data in leastsquares fit
LegendK(cm/day)Fine-textured soil:013

measured

clay
(%)
56.8
organic matter (%)
1.7
bulk density(g/cm3)1.09— ——90% confidence interval

2c10-' -

h(cm)

10-' -

-10*-

10"-

10-"

-10'-:

-

-10°

0.10

0.20

0.30

fittedpredicted

10° -

0.00

0,40

0,50

1769

0.60

8(cm 3 /cm 3 )Fig 2. Continued.

-10°

-10'

1770

SOIL SCI. SOC. AM. J., VOL. 52, 1988

M50 = median sand particle size Gtm)
n = parameter in Eq. [1]AT = total number of data in least-squares fit
qa = water flux density at given air content (cm d^ 1 )qd = downward water flux density (cm d~')qu = upward water flux density (cm d~')S = reduced water content
Tr = travel time in the unsaturated zone
Wj = weighting coefficients in Eq. [6]Wt = Weighting coefficient in optimization process
W2 = Weighting coefficient denned by Eq. [7]a = parameter in Eq. [1] (cm~'). 3
0 = volumetric water content (cm cm"3)8 = profile-averaged water content
6a = volumetric air content of soil
8r = residual water content (cm3 cm~3)
6S = saturated water content (cm3 cm~3).