Journal of Hydrology 251 (2001) 163±176

www.elsevier.com/locate/jhydrol

rosetta: a computer program for estimating soil hydraulicparameters with hierarchical pedotransfer functions
Marcel G. Schaap*, Feike J. Leij, Martinus Th. van Genuchten
George E. Brown Jr. Salinity Laboratory, USDA-ARS, 450 W. Big Springs Road, Riverside, CA 92507-4617, USA

Abstract
Soil hydraulic properties are necessary for many studies of water and solute transport but often cannot be measured becauseof practical and/or ®nancial constraints. We describe a computer program, rosetta, which implements ®ve hierarchicalpedotransfer functions (PTFs) for the estimation of water retention, and the saturated and unsaturated hydraulic conductivity.
The hierarchy in PTFs allows the estimation of van Genuchten water retention parameters and the saturated hydraulicconductivity using limited (textural classes only) to more extended (texture, bulk density, and one or two water retention
points) input data. rosetta is based on neural network analyses combined with the bootstrap method, thus allowing the
program to provide uncertainty estimates of the predicted hydraulic parameters. The general performance of rosetta wascharacterized with coef®cients of determination, and root mean square errors (RMSEs). The RMSE values decreased from
0.078 to 0.044 cm 3 cm 23 for water retention when more predictors were used. The RMSE for the saturated conductivity
similarly decreased from 0.739 to 0.647 (dimensionless log10 units). The RMSE values for unsaturated conductivity ranged
between 0.79 and 1.06, depending on whether measured or estimated retention parameters were used as predictors. Calculated
mean errors showed that the PTFs underestimated water retention and the unsaturated hydraulic conductivity at relatively highsuctions. rosetta's uncertainty estimates can be used as an indication of model reliability when no hydraulic data are available.
The rosetta program comes with a graphical user interface that allows user-friendly access to the PTFs, and can be downloaded from the US Salinity Laboratory website: http://www.ussl.ars.usda.gov/. q 2001 Elsevier Science B.V. All rights
reserved.
Keywords: Soils; Hydraulic conductivity; Retention; Neural networks; Computer programs

1. Introduction
A broad array of methods currently exists to determine soil hydraulic properties in the ®eld or in thelaboratory (cf. Klute, 1986; Leij and van Genuchten,1999). While measurements permit the most exact
determination of soil hydraulic properties, they often
require a substantial investment in both time and* Corresponding author. Tel.: 11-909-369-4844; fax: 11-909342-4964.
E-mail address: mschaap@ussl.ars.usda.gov (M.G. Schaap).

money. Moreover, many vadose zone studies areconcerned with large areas of land that may exhibit
substantial spatial variability in the soil hydraulicproperties. It is virtually impossible to performenough measurements to be meaningful in suchcases, thus indicating a need for inexpensive andrapid ways to determine soil hydraulic properties.
Many indirect methods for determining soil
hydraulic properties have been developed in the past(cf. Rawls et al., 1991; van Genuchten and Leij, 1992;
Leij and van Genuchten, 1999). Most of these methods can be classi®ed as pedotransfer functions (PTFs,

0022-1694/01/$ - see front matter q 2001 Elsevier Science B.V. All rights reserved.
PII: S 0022-169 4(01)00466-8

164

M.G. Schaap et al. / Journal of Hydrology 251 (2001) 163±176

after Bouma and van Lanen, 1987) because theytranslate existing surrogate data (e.g. particle-size
distributions, bulk density and organic matter content)
into soil hydraulic data. All PTFs have a strong degreeof empiricism in that they contain model parametersthat were calibrated on existing soil hydraulic databases. A PTF can be as simple as a lookup table thatgives hydraulic parameters according to textural class(e.g. Carsel and Parrish, 1988; WoÈsten et al., 1995) or
include linear or nonlinear regression equations (e.g.
Rawls and Brakensiek, 1985; Minasny et al., 1999).
PTFs with a more physical foundation exist, such as
the pore-size distribution models by Burdine (1953)
and Mualem (1976), which offer a method to calculate
unsaturated hydraulic conductivity from water retention data. Models by Haverkamp and Parlange (1986)
and Arya and Paris (1981) use the shape similarity
between the particle- and pore-size distributions toestimate water retention. Tyler and Wheatcraft(1989) combined the Arya model with fractals mathematics, while Arya et al. (1999a,b) recently extended
the similarity approach to estimate water retention andunsaturated hydraulic conductivity.
Practical applications of most PTFs are often
hampered by their very speci®c data requirements.
Some authors established PTFs that provided thebest results for their data set, which sometimes
produced models that require many input variables(cf. Rawls et al., 1991) or detailed particle-size distributions (Arya and Paris, 1981; Haverkamp andParlange, 1986). However, users of PTFs are
frequently confronted with situations where one orseveral input variables needed for a PTF are not available. Another problem is that PTFs provide estimations with a modest level of accuracy. It would
therefore be useful if PTFs could accept input datawith varying degrees of detail and if PTF predictions
could include reliability measures.
Recently, neural network analysis was used toestablish empirical PTFs (Pachepsky et al., 1996;
Schaap and Bouten, 1996; Minasny et al., 1999;
Pachepsky et al., 1999). An advantage of neuralnetworks, as compared to traditional PTFs, is thatneural networks require no a priori model concept.
The optimal, possibly nonlinear, relations that link
input data (particle-size data, bulk density, etc.) tooutput data (hydraulic parameters) are obtained andimplemented in an iterative calibration procedure. As

a result, neural network models typically extract the
maximum amount of information from the data.
Schaap et al. (1998) used neural network analyses toestimate van Genuchten (1980) water retention parameters and saturated hydraulic conductivity. To facilitate the practical use of the PTFs, they designed ahierachical structure to allow input of limited andmore extended sets of predictors. The combination
with the bootstrap method (Efron and Tibshirani,1993) provided the reliability for the PTF estimations(Schaap and Leij, 1998).
Yet, while neural network-based PTFs may provide
relatively accurate estimates, they contain a large
number of coef®cients that do not permit easy interpretation or publication in explicit form. To facilitate
application of the PTFs, we have developed thecomputer program rosetta that implements someof the models published by Schaap et al. (1998);
Schaap and Leij (1998) and Schaap and Leij (2000).
The objectives of this paper are (i) to present therosetta program in terms of hydraulic parameters,
calibration data sets, selection of predictors, and characterization of model performance, and (ii) to discuss
the uncertainty of estimated hydraulic parameters as afunction of suction and texture.
2. Materials and methods
Much of this section has been published before in
Schaap et al. (1998), Schaap and Leij (1998), andSchaap and Leij (2000). However, we describe themost important methodology here to provide thereader a concise documentation about the backgroundof rosetta. This section will also present methodology that was not used in previous publications.
2.1. Hydraulic parametersrosetta is able to estimate van Genuchten (1980)
water retention parameters and saturated hydraulicconductivity (Ks), as well as unsaturated hydraulicconductivity parameters based on Mualem's (1976)
pore-size model. The retention function is given byu h  ur 1

us 2 ur
1 1 ahn 121=n1where u h is the measured volumetric water content(cm 3 cm 23) at the suction h (cm, taken positive forM.G. Schaap et al. / Journal of Hydrology 251 (2001) 163±176

165

Fig. 1. Textural distribution of the samples for water retention (a), for the subset for saturated hydraulic conductivity (b), for the subset forunsaturated hydraulic conductivity (c). Fig. 1d depicts the textural classes. S: sand, lS: loamy sand, sL: sandy loam, scL: sandy clay loam, sC:
sandy clay, L: loam, siL: silty loam, Si: silt, sicL: silty clay loam, siC: silty clay, cL: clay loam, C: clay.

increasing suctions). The parameters u r and u s areresidual and saturated water contents, respectively,(cm 3 cm 23); a (.0, in cm 21) is related to the inverseof the air entry suction, and n (.1) is a measure of thepore-size distribution (van Genuchten, 1980).
Combination of Eq. (1) with Mualem's (1976)
pore-size model yields the following closed-form
expression for unsaturated hydraulic conductivity(van Genuchten, 1980)
K Se   K0 SLe {1 2 1 2 Sen= n21 121=n }22where the effective saturation, Se, is computed asSe u h 2 ur
us 2 ur3

K0 is a ®tted matching point at saturation (cm day 21)
while L (±) is an empirical parameter that is normallyassumed to be 0.5 (Mualem, 1976). Eq. (2) can also be

expressed in terms of h with the help of Eq. (1). Schaapand Leij (2000) found that ®tted K0 values were often
about one order of magnitude lower than Ks, while®tted L were often negative, having an optimal valueof 21. Although these ®ndings suggest an increased
level of empiricism in the Mualem model, they provide
a far better description of unsaturated hydraulicconductivity data than the common practice of using
K0  Ks and L  0:5 (see also Hoffmann-Riem et al.,
1999; Kosugi, 1999). However, we should note that theuse of K0 , Ks leads to an untenable situation nearSe  1 or h  0 cm because the hydraulic conductivity
should be equal to Ks while Eq. (2) provides K0. Schaapand Leij (2000) argue that Eq. (2) with ®tted K0 should
be applied only at suctions of at least a few centimetre.
The considerations above therefore require seven parameters (u r, u s, a , n, Ks, K0 and L) to describe water
retention, the saturated and unsaturated hydraulicconductivity.

166

M.G. Schaap et al. / Journal of Hydrology 251 (2001) 163±1762.2. Data set
In order to make the PTFs as widely applicable aspossible, we obtained a large number of soil hydraulicdata and corresponding predictive soil properties fromthree databases (Schaap and Leij, 1998). The data set
thus assembled contained 2134 soil samples for water
retention with a total of 20 574 u h points. Most of
the samples were derived from soils in temperate to
subtropical climates of North America and Europe.
Saturated hydraulic conductivity values were available for a subset of 1306 soil samples, while unsaturated hydraulic conductivity was known for 235 soil
samples with a total of 4117 K h points. The latter
subset was solely derived from the database
UNSODA (Leij et al., 1996; Nemes et al., 2001)
with the requirement that at least ®ve K h data points
were available; samples with chaotic data or withsuction and conductivity ranges less than one orderof magnitude were omitted. Fig. 1a±c gives the
textural distributions of the datasets for water retention, Ks and unsaturated hydraulic conductivity. Fig.
1d provides the abbreviations of the USDA texturalclasses.
The parameters in Eqs. (1) and (2) were ®tted towater retention and unsaturated hydraulic conductivity data with the simplex or amoeba algorithm (Nelder
and Mead, 1965; Press et al., 1988). The objectivefunction for water retention was
Ow p Nw
Xi1

ui 2 u 0i 24where u i and u 0i are the measured and estimated watercontents, respectively. Nw is the number of measured
water retention points for each sample and p is theparameter vector (u r,u s,a ,n). For the optimization of
unsaturated hydraulic conductivity parameters, we
minimized
Ok p NKX
i1

log10 Ki  2 log10 K 0i 2

5

where Ki and K 0i are the measured and estimatedhydraulic conductivity, respectively, NK is the numberof measured K h data points and p  K0 ; L: Logarithmic values of Ki were used in Eq. (5) to avoid bias
towards high conductivities in the `wet' range. We
used log-transformed values of a , n, Ks and K0 to

account for their approximately lognormal distributions.
2.3. Model calibration
Because different numbers of samples were available for water retention, the saturated and unsaturated
hydraulic conductivity, we developed separate PTFs
for each of these characteristics. For the estimation of
the water retention parameters (u r,u s,a ,n) and Ks, wefollowed a hierarchical approach with limited or more
extended sets of predictors (Schaap et al., 1998). The®rst model (H1) is a class PTF, consisting of a lookup
table that provides parameter averages for each
USDA textural class. The second model (H2) uses
sand, silt, and clay as input, and in contrast to H1,
provides hydraulic parameters that vary continuouslywith texture. The third model (H3) includes bulk
density as a predictor while the fourth model (H4)also uses water content at 330 cm suction h 
33 kPa: The last model (H5) includes a water content
at 15 bar suction h  1500 kPa in addition to the
input variables of the fourth model. The choice ofsuctions in models H4 and H5 was determined bytheir availability in the NRCS database (Soil Survey
Staff, 1995).
Schaap and Leij (2000) showed that the hierarchical approach was not possible for unsaturated hydraulic conductivity because K0 and L were poorly related
to texture and bulk density. However, the same study
showed that K0 and L could be estimated from ®tted
water retention parameters (u r,u s,a and n). This PTF(model C2) thus requires such data to be available. To
accommodate situations where this is not the case, weinvestigated how well we can estimate K0 and L using
estimated retention parameters obtained from models
H1 to H5. These models are denoted as C2-H1±C2H5 and allow K0 and L to be estimated in a pseudohierarchical manner.
While model H1 is a simple table with average
hydraulic parameters for each textural class, allother models involve a combination of neuralnetworks and the bootstrap method. The neuralnetworks for water retention parameters and Ks were
calibrated using the following objective function
Onn cnn  

Np
Ns X
X
i1 j1hi;j 2 h 0i;j 2

6

M.G. Schaap et al. / Journal of Hydrology 251 (2001) 163±176

where cnn represents the coef®cient matrices of thearti®cial neural network; Ns is the number of calibration samples. The number of parameters, Np, equals 4
for the water retention models and 1 for Ks model,
while h and h 0 are the ®tted and estimated parameters, respectively. For the neural network models
for unsaturated conductivity, an objective function
similar to Eq. (5) was used. In this case, conductivities
were computed by evaluating Eq. (2) at the watercontents for which measurements were available(Schaap and Leij, 2000).
Models H2±H5 and model C2 were combinedwith the bootstrap method (Efron and Tibshirani,1993) for two reasons. First, it allowed an uncertainty estimate to be assigned to each model
prediction. For example, for a texture of 60%
sand, 30% silt, and 10% clay, model H2 predicts
a saturated hydraulic conductivity of 1.56 log cm day 21 plus or minus a standard deviation of
0.11 log cm day 21. For a coarser texture of 80%
sand, 15% silt and 5% clay, the estimates are
1:99 ^ 0:079 log cm day 21, making this prediction
more reliable than the previous one. The uncertainty estimates are useful because they quantify
the reliability of model estimates Ð even when
no independent hydraulic measurements are available. The second reason for using the bootstrap
method was the possibility to carry out calibrationand testing of the individual neural networks oncomplementary subsets of the data. This was
possible because the bootstrap randomly selects
data with replacement causing 1 2  N 2 1=NN
samples (about 63%) to be selected into each calibration data set. This selection procedure leaves
out 37% of the data, which can subsequently be
used to test the neural network model. The repetition of calibration-testing procedure for the alternative selections of data ensured a minimal bias
towards noise and artifacts in the data.
PTFs H2±H5 and C2 each consist of 60 (water
retention) or 100 (saturated and unsaturated conductivity) neural network models. Because they are basedon different alternative data selections, each neuralnetwork inside a PTF provides slightly different estimates. rosetta reports the average of the 60 or 100
estimates as the prediction of a PTF. The standard
deviation characterizes the uncertainty of theprediction.

167

2.4. Characterization of model performance
While testing on a completely independent data set
is desirable, we chose to test rosetta on the calibration data set because a data set of similar size andcharacteristics was not available. Further, Schaapand Leij (1998) demonstrated that the performanceof a PTF depends on the data sets on which a PTF
is calibrated and tested. Usage of an independent data
set for testing might introduce artifacts speci®c to thatdataset and make characterization of rosetta's properties ambiguous. Finally, the bootstrap procedureensured robust models that provided similar results
for calibration and validation (see Section 2.3 andSchaap and Leij, 1998).
Three error measures were used to characterizerosetta. To test the match between predicted and®tted parameters we computed the coef®cient ofdetermination (R 2). The root mean square error(RMSE) between measured and estimated watercontents, saturated and unsaturated hydraulic conductivities was computed asv
uN
u1 X
RMSE  t7
z 0 2 zi 2
N i1 iIn addition, we computed the mean error (ME) to
quantify systematic errors with
ME 

N
1 X
z 0 2 zi N i1 i8The symbols z and z 0 denote measured or estimated u h; log Ks ; or log K h values;N is thenumber of measurements for which the RMSE
and ME values were calculated. The values for
RMSE and ME will be given with the subscripts
w, s, and u to denote water retention, saturated,
and unsaturated hydraulic conductivity, respectively. Estimated water retention or unsaturated
hydraulic conductivity values were calculated byevaluating the hydraulic functions at the suctionsof the measurements. Because logarithmic values
were used for Ks and K h; the corresponding
RMSE and ME values are dimensionless; theunits of RMSEw and MEw are in cm 3 cm 23. In
this study, we computed the RMSE and ME
values over all available data (i.e. Nw  20 574
for retention, Ns  1306 for Ks, and Nu  4117

168

M.G. Schaap et al. / Journal of Hydrology 251 (2001) 163±176

Table 1R 2 and RMSE values for the ®ve hierarchical models that predict water retention parameters and saturated hydraulic conductivity. SSC:
percentages sand, silt and clay; BD: bulk density; u 33, u 1500: water contents at 330 and 15 000 cm suction. The RMSEw for the direct ®t to water
retention data is also shown
Model

Input

Water retention

Saturated conductivity

R2

H1
H2
H3
H4
H5
Direct ®t to data

Textural class
SSC
SSCBD
SSCBD u 33
SSCBD u 33u 15 000

RMSEw (cm 3 cm 23)

R 2 log Ks

RMSEs (MEs) (±)

ur

us

log a

log n

0.066
0.086
0.094
0.121
0.387

0.143
0.178
0.581
0.605
0.600

0.203
0.238
0.265
0.417
0.577

0.452
0.473
0.495
0.599
0.760

0.078
0.076
0.068
0.047
0.044

0.427
0.461
0.535
0.640
0.647

0.739 (20.001)
0.717 (20.001)
0.666 (0.000)
0.586 (20.004)
0.581 (20.002)

±

±

±

±

0.012

±

±

for K h). To investigate how the RMSE and ME
values vary with suction, we also computed thesevalues for 10 suction classes between 0, 3.2, 10,32, 100, 320, 1000, 3200, 10 000, 32 000, and
10 000 cm.
We like to note that the R 2, RMSE and ME
values differ from Schaap et al. (1998), Schaapand Leij (1998) and Schaap and Leij (2000).
Previously, we averaged R 2 and RMSE values
computed for each of the 60 or 100 neuralnetworks inside each PTF (see Section 2.3). Thisapproach was necessary to evaluate the merits ofusing different sets of predictors. The program
rosetta, however, reports averages and standard
deviations of 60 or 100 sets of estimated hydraulicparameters, as generated by the neural networks
inside models H2±H5. To better re¯ect the errorsthat result from practical use of Roseta, it isnecessary to compute the R 2, RMSE, and ME
statistics based on the averages of the estimatedhydraulic parameters, rather than providing average error values. To this end, we ran rosetta forthe entire data set, without considering independent calibration and validation sets. In addition,
we do not reduce the degrees of freedom in thecomputation of RMSE and ME. Previously, such a
correction was necessary to compare the RMSE of
PTFs with the RMSE of a direct ®t of Eq. (1) or (2)to the data. However, a correction for the degrees of
freedom is not necessary when the PTFs are applied.

Fig. 2. RMSEw (lines, left axis) of the direct ®t to water retention data (F) and the ®ve hierarchical models (H1±H5). The number of retention
points for each suction class is also shown (bars, right axis).

M.G. Schaap et al. / Journal of Hydrology 251 (2001) 163±176

Fig. 3. MEw of the direct ®t to water retention data (F) and the ®vehierarchical models (H1±H5). A negative value indicates an underestimation of water contents.

3. Results
3.1. Model characteristics
An overview of the performance of the hierarchicalmodels for estimation of water retention parametersand Ks is given in Table 1. Not surprisingly, the results
show that correlations between ®tted and estimatedparameters increase and RMSE values decrease
when more predictors are used (H1±H5). Residual
water content is dif®cult to estimate with all models,
while saturated water content is dif®cult to estimate
Table 2R 2 and RMSEk values for estimated unsaturated hydraulic conductivity for the MVG model with K0  Ks L  0:5; and for model C2
where K0 and L were estimated from ®tted (C2-Fit) or estimated(models C2-H1±C2-H5) retention parameters. The RMSEk for the
direct ®t to hydraulic conductivity data is also shown
Model

R2

RMSEK

K0

L

MVG K0  Ks ; L  0:5

±

±

1.40

C2-Fit
C2-H1
C2-H2
C2-H3
C2-H4
C2-H5

0.605
0.070
0.073
0.093
0.187
0.271

0.548
0.001
0.007
0.012
0.019
0.327

0.79
1.06
1.02
1.05
1.01
0.90

Direct ®t to data

±

±

0.41

169

without information about bulk density. The correlation for a increases considerably when one or two
retention points are added to the predictors (H4 andH5). The n parameter and Ks generally have the highest correlations showing a gradual increase in R 2 frommodel H1 to H5.
Fig. 2 shows the RMSEw of models H1±H5 for 10
suction classes as well as the number of water retention points in each class (bars). The RMSEw of thedirect ®t of Eq. (1) to the data (F) provides the minimum possible error because no PTF can estimate
water retention better than this ®t. Models H1 andH2 show a very similar pattern in errors across theentire suction range. This would indicate that there is
not much to be gained by using sand, silt or clay
percentages as predictors (H2) instead of texturalclasses (H1). However, model H2 provides continuously varying prections, whereas model H1 exhibits
discrete jumps at texture class boundaries. Model H3shows a considerable improvement near saturation
and a better performance until h  3200 cm (i.e.
log h  3:5). Including a water content at 330 cm(H4) lowers RMSEw between 10 and 10 000 cm,
whereas addition of a water content at 15 bar provides
a further improvement beyond 100 cm. Because there
were only 28 data points with suctions . 32 000 cm
the increase in RMSEw for this suction range may be
due to statistical effects.
Fig. 3 shows a similar picture for MEw; negative
numbers denote underestimation by the models.
Clearly, the direct ®t to the data (F) closely adheres
the line of MEw  0; indicating that Eq. (1)adequately describes retention data over the entire
suction range. All models underestimate water retention near saturation (h , 3:2 cm suction orlog h , 0:5) and overestimate water contents between
3.2 and 10 cm suction; all models underestimate water
retention beyond 32 cm. Models H1±H3 all behave
similarly, while models H4 and H5 make smaller
systematic errors for h . 100 cm suction. The
systematic errors are probably due to the fact thatthe neural networks were optimized in terms of Eq.
(6) but evaluated according to Eq. (8). Additionally,
the nonlinearity of Eq. (1) probably causes a nonnormal distribution of errors. MEs for Ks are essentially equal to zero (Table 1).
Results for three methods to estimate unsaturated
hydraulic conductivity appear in Table 2. The ®rst

170

M.G. Schaap et al. / Journal of Hydrology 251 (2001) 163±176

Fig. 4. RMSEu (lines, left axis) for the direct ®t to conductivity data (F), for model C2 using ®tted retention parameters (denoted as C2-Fit),model C2 using estimated retention parameters from the hierarchical approach (C2-H1±C2-H5). The MVG model with K0  Ks and L  0:5 isshown as MVG. The number of conductivity points per suction class is also shown (bars, right axis).

method is the traditional Mualem±van Genuchten(MVG) model (Eq. (2)) with K0  Ks and L  0:5:
The second method (C2-Fit) is model C2 of Schaapand Leij (2000) that estimates K0 and L from ®tted
retention parameters. This model presumes the availability of ®tted retention data. The third method alsouses model C2 but with estimated retention parameters derived from models H1 to H5 as input(denoted as C2-H1±C2-H5).
The MVG model clearly provides the poorest estimations of K h with an average RMSEu of 1.40 (i.e.

Fig. 5. MEu for the direct ®t to conductivity data (F), for model C2
using ®tted retention parameters (C2-Fit), model C2 using estimatedretention parameters from the hierarchical approach (C2-H1±C2H5). The MVG model with K0  Ks and L  0.5 is shown as MVG.

1.4 order of magnitude). Schaap and Leij (2000)
showed that its estimation was especially poor for
clayey soils RMSEu  1:70: model C2-Fit has an
RMSEu that is almost half an order of magnitude
lower (0.79), while it also has a more uniform performance over all textural classes (see Table 3 in Schaapand Leij, 2000). As models C2-H1±C2-H5 rely on
estimated input data, they do not perform as well as
model C2-Fit; however, they are better than the MVG
model. For example, model C2-H5 has an RMSEu
value that is only slightly higher than that of C2-Fit(0.90 vs. 0.79). Note, however, that the correlations
for K0 and L of models C2-H1±C2-H4 are extremely
poor and only slightly better for model C2-H5.
Fig. 4 shows the RMSEu for 10 suction classes as wellas the number of conductivity measurements in eachclass (bars). The direct ®t of Eq. (2) to the data (F)indicates the minimum attainable error for all models
with a ¯exible K0 and L. We note that the direct ®t has arelatively large error near saturation. As expected,
model C2-Fit has the best overall performance. Model
C2-H5 has a very similar performance between h  10
and 3200 cm (1 , log h , 3:5; while models C2-H1±
C2-H4 have similar performances in the range betweenh  10 and 1000 cm. The MVG model has the worst
overall performance, except for near saturation where it
performs better than all other models because its matching point is Ks and not K0. The RMSEu of all models
strongly increases beyond 3200 cm where few data
points are available.

M.G. Schaap et al. / Journal of Hydrology 251 (2001) 163±176

171

Fig. 6. Distributions of estimated parameter values a; c; e; g; i; k; m and associated uncertainties b; d; f ; h; j; l; n for model H3 and a bulk
density of 1.3 g cm 23. Each graph provides the parameter; s denotes the standard deviation of a parameter. See text for explanation.

Fig. 5 shows the ME for the 10 suction groups;
negative values indicate an underestimation of unsaturated hydraulic conductivity. The MVG model
overestimates conductivity until h  3000 cm; after
which it underestimates conductivity. Models C2-Fit
and C2-H1±C2-H5 are all based on ®tted K0 and L,
and therefore, they show similar problems of underestimating conductivity between 0 and 32 cm. Again,model C2-Fit has the best performance, followed bymodel C2-H5. The MEs are near zero between 32 and1000 cm, but the error rapidly becomes more negative
beyond 1000 cm. This effect could be due to thesparse data in this suction range. It is also possiblethat the problem is the inaccurate estimation of L,
which controls the slope of the conductivity curveunder dry conditions (Schaap and Leij, 2000).

3.2. Uncertainty estimates
The R 2, RMSE, and ME values can only be estimated when measured hydraulic data are available.
When PTFs are applied, such data are typically athand, thus leaving the user uncertain about the reliability of the PTF. Because we used the bootstrap
method for the calibration of the models in rosetta,
it is possible to estimate standard deviations of thepredicted parameters. Although the standard deviation
is different from the previously discussed errors, itallows a unique model and input data-speci®c assessments of the reliability of the parameter estimates.
Fig. 6a±n provides predictions by models H3 andC2-H3 for the seven hydraulic parameters and theirstandard deviations (s ) as a function of texture and a

172

M.G. Schaap et al. / Journal of Hydrology 251 (2001) 163±176

most likely different for other bulk densities andfor the other models in rosetta.
4. Discussion

Fig. 7. Water retention data for 47 loam samples (totaling 412
points) with a bulk density range between 1.3 and 1.4 g cm 23.
The curve represents the estimation with model H3.

bulk density of 1.3 g cm 23. The parameter values
show trends that concur with empirical knowledge.
For example, values for a , n and Ks decrease
when textures become ®ner, while at the sametime u r becomes larger. The standard deviations
generally show a pattern that re¯ects the distribution of data in Fig. 1a±c. The uncertainty
increases when less data points are available,
such as the silt and clay regions of the textural
triangle. Likewise, uncertainties increase when themodels are used beyond the calibration range ofother predictors in models H1±H5 (results notshown). Fig. 8a±n depict a speci®c example andshould not be used as a general indication of parameter values or uncertainty estimates. Results are

Even with the best predictive models, i.e. H5 forretention and C2-Fit for unsaturated conductivity, thecorrelations between estimated and ®tted or measured
hydraulic parameters were modest at best (cf. Tables 1
and 2). The differences between RMSE and ME
values of estimation and direct ®ts (Figs. 2±5) further
suggest that the models in this study could be
improved upon. However, the direct ®ts only givethe theoretically minimum attainable errors for PTFs
because Eqs. (1) and (2) were ®tted to individual characteristics. Therefore, the ®t ignores any effects thatcause variation among hydraulic properties, such as
variability in physical soil properties or systematicdifferences among measurement methodologies. In
contrast, the PTFs are supposed to be valid for theensemble of all characteristics. This problem is illustrated in Fig. 7, which shows retention data for anarrow selection of 47 loam samples with bulk densities between 1.3 and 1.4 g cm 23. The average retention curve, as estimated by H3, is also shown. We
expect to see measured retention data in a narrow
band, but the ®gure shows that there is a considerable
scatter. This variation may be caused by predictors
other than texture and bulk density or by systematicdifferences in measurement methodologies.

Fig. 8. Estimated vs. measured water contents for model H3 and H5 for 47 loam samples with bulk densities between 1.3 and 1.4 g cm 23 (cf.
Fig. 8).

M.G. Schaap et al. / Journal of Hydrology 251 (2001) 163±176173

Fig. 9. Schematic overview of the structure of rosetta.

Improved PTFs were obtained by Vereecken et al.
(1989) and Schaap and Bouten (1996), among others,
who used more particle size fractions. Additional
predictors can also be used to improve the performance of the models, such as organic matter content,
porosity, particle density, soil chemical parameters,
soil structure, mineralogy, and pedality (Rawls etal., 1991). However, using more predictors also
requires that they be available for both the calibrationof PTFs and their actual application. Of course, thedetermination of additional predictors may take aconsiderable effort, thereby diminishing the very
reason why one would want to use PTFs insteadof relying on the direct measurement of hydraulicproperties. From this perspective, the inclusion of
measured water retention points (Ahuja et al.,
1989; Messing 1989; Williams et al., 1992;
Schaap and Bouten, 1996) is a pragmatic way to
improve the prediction of hydraulic properties by
PTFs. One or two water retention points can beviewed as lumped parameters that contain implicit
information on hydraulic properties not provided
by soil texture or bulk density. In many cases,
one or two retention points can be measured relatively quickly or are available in national databases such as the NRCS database, whichcontains more than 120 000 soil horizons for the
USA (Soil Survey Staff, 1995). Using the samedata as in Fig. 7, we plotted estimated vs.
measured retention points for model H3 and H5in Fig. 8. While the agreement with the measured

data is not perfect, the estimations by model H5
are much better than the estimations by model H3.
In the many situations where retention points are
simply not available, models H1±H3 may still
make acceptable estimations Ð also consideringthat these models were calibrated on the samedata as models H4 and H5.
The ability of the hydraulic functions (Eqs. (1) and(2)) to match the hydraulic data is another importantfactor. Figs. 2 and 3 demonstrated that ®ts of Eq. (1)described water retention data well. For hydraulicconductivity however, we see that the direct ®t of
Eq. (2) has already large RMSEu near saturation anda predominantly negative MEu (Figs. 4 and 5). This
indicates that Eq. (2) is incapable of simultaneously®tting the wet and the dry part of the unsaturated
hydraulic conductivity curve. As a result, allmodels based on ®tted K0 and L will perform
poorly near saturation. Schaap and Leij (2000)
found that the ®tted K0 was often about oneorder of magnitude lower than the measured Ks
value, thus causing a discontinuity in hydraulicconductivity if Eq. (2) is evaluated at saturation.
They interpreted this difference in terms of macropores that predominantly in¯uenced Ks and properties of the soil matrix that determined K0. An
improved version of Eq. (2) may need to consider
the effects of macropores. Unfortunately, such aneffort will be hampered by the limited number ofhydraulic conductivity measurements near saturation (Fig. 4).

174

M.G. Schaap et al. / Journal of Hydrology 251 (2001) 163±176

5. Description of rosetta
Named somewhat whimsically after the Rosetta
Stone that allowed translation of ancient Egyptian
hieroglyphs into Old Greek, rosetta allows userfriendly access to models H1±H5 for water retention and saturated hydraulic conductivity andmodels C2-Fit and C2-H1±C2-H5 for unsaturated
hydraulic conductivity. In this section, we will
review the most important features of rosetta.
More information about various aspects of the
program and ®le speci®cations may be obtained
through the help system which can be accessedfrom anywhere within the program. rosetta is
primarily a Windows w1 based application whichuses a Microsoft access 97 w1 database ®le tostore its data and estimations. The Microsoft
access software, however, is not needed to run
rosetta. Command-line versions of rosetta(currently without database support) are available
for the MS-DOS w1 and the LINUX operating
systems. rosetta can be downloaded freely fromthe world-wide-web site: .
The ¯ow of data inside rosetta is illustrated inFig. 9. Input data can be entered manually or as aformatted ASCII ®le. Input and output data are
stored in various tables in the same database ®leand accessed by the program as needed. Basic soil
data (sand, silt, and clay percentages, bulk density
and the water contents at 330 and 15 000 cm
suction) are used by the hierarchical models(H1±H5) to estimate water retention parametersand Ks. Model C2 uses ®tted retention parameters
to estimate K0 and L (i.e. C2-Fit), but is also able
to use estimated retention as input as illustrated by
the model combinations C2-H1±C2-H5 in thisstudy.
The user interface of rosetta (not shown)consists of three menu-controlled and easy tounderstand screens. The ®rst screen provides
general database information, i.e. number ofrecords in the database. The second screen serves
to make estimations of the seven hydraulic parameters with models H1±H5 and C2-H1±C2-H5.
The third screen allows estimations of K0 and Lfrom ®tted retention parameters using model C2Fit.
6. Concluding remarks
This study presents the computer program rosetta
which implements a number of PTFs for estimation ofwater retention parameters, the saturated and unsaturated hydraulic conductivity as well as associateduncertainties. The models were characterized interms of their calibration data sets and the accuracyof their estimations. For the estimation of water retention and saturated hydraulic conductivity, it turned outthat the hierarchical models performed reasonably
well if more predictors were used (texture, bulk
density and one or two retention points). The estimations were less accurate when fewer predictors wereused, however, such predictions by these models may
still be useful when no data are available. The PTFs
provide uncertainty estimates of predicted hydraulicparameters allowing an assessment of rosetta's
reliability, even when no independent hydraulic data
are available.
A previous study (Schaap and Leij, 2000) established models that estimated unsaturated hydraulicconductivity parameters from ®tted retention parameters. This study showed that it was also possible
to get reasonable estimations of unsaturated hydraulicconductivity using estimated retention parameters
derived from the hierarchical models. However,some problems remain in the estimation of unsaturated hydraulic conductivity, notably the poor performance near saturation. Although the new models are
better than the `traditional' MVG model K 0  Ks andL  0:5 for suctions higher than a few centimeter,
they are unable to deal with a transition from saturated
to unsaturated hydraulic conductivity.
rosetta offers a user-friendly graphical interface
and combines the PTFs with a simple databasemanagement structure to facilitate parameter estimates and data management. The program is available
at the US Salinity Laboratory's World-Wide-Website.
Acknowledgements

1

Trade names are provided for the bene®t of the reader and do not
imply endorsement by the USDA.

The authors gratefully acknowledge the support byM.G. Schaap et al. / Journal of Hydrology 251 (2001) 163±176

NSF and NASA (EAR-9804902), and the ARO(39153-EV).
References
Ahuja, L.R., Cassel, D.K., Bruce, R.R., Barnes, B.B., 1989. Evaluation of spatial distribution of hydraulic conductivity using effective porosity data. Soil Sci. 148, 404±411.
Arya, L.M., Paris, J.F., 1981. A physico-empirical model topredict the soil moisture characteristic from particle-size
distribution and bulk density data. Soil Sci. Soc. Am. J.
45, 1218±1227.
Arya, L.M., Leij, F.J., van Genuchten, M.Th., Shouse, P.J., 1999a.
Scaling parameter to predict the soil water characteristic fromparticle-size distribution data. Soil Sci. Soc. Am. J. 63, 510±
519.
Arya, L.M., Leij, F.J., Shouse, P.J., van Genuchten, M.Th., 1999b.
Relationship between the hydraulic conductivity function andthe particle-size distribution. Soil Sci. Soc. Am. J. 63, 1063±
1070.
Bouma, J., van Lanen, J.A.J., 1987. Transfer functions and threshold values: from soil characteristics to land qualities. Quanti®ed
Land Evaluation, Beek, K.J. (Ed.). International Institute of
Aerospace Survey Earth Science ITC publication 6, 106±110.
Burdine, N.T., 1953. Relative permeability calculations from poresize distribution data. Trans. AIME 198, 71±77.
Carsel, R.F., Parrish, R.S., 1988. Developing joint probability distributions of soil water retention characteristics. Water Resour.
Res. 24, 755±769.
Efron, B., Tibshirani, R.J., 1993. An Introduction to the Bootstrap.
Monographs on Statistics and Applied Probability. Chapman &Hall, New York.
Haverkamp, R., Parlange, J.Y., 1986. Predicting the water-retention
curve from particle size distribution: 1. Sandy soils without
organic matter. Soil Sci. 142, 325±339.
Hoffmann-Riem, H., van Genuchten, M.Th., FluÈhler, H., 1999. A
general model of the hydraulic conductivity of unsaturated soils.
In: van Genuchten, M.Th., Leij, F.J., Wu, L. (Eds.). Proceedingsof International Workshop, Characterization and Measurementsof the Hydraulic Properties of Unsaturated Porous Media.
University of California, Riverside, CA, pp. 31±42.
Klute, A. (Ed.), 1986. Methods of Soil Analysis. Part 1. Physicaland Mineralogical Methods Monograph 9ASA and SSSA,
Madison, WI.
Kosugi, K., 1999. General model for unsaturated hydraulic conductivity for soils with lognormal pore-size distribution. Soil Sci.
Soc. Am. J. 63, 270±277.
Leij, F.J., van Genuchten, M.Th., 1999. Characterization andmeasurement of the hydraulic properties of unsaturated porous
media. In: van Genuchten, M.Th., Leij, F.J., Wu, L. (Eds.).
Proceedings of International Workshop, Characterization andMeasurements of the Hydraulic Properties of Unsaturated
Porous Media. University of California, Riverside, CA, pp.
31±42.
Leij, F.J., Alves, W.J., van Genuchten, M.Th., Williams, J.R., 1996.
Unsaturated Soil Hydraulic Database, UNSODA 1.0 User's

175

Manual. Report EPA/600/R-96/095, US Environmental Protection Agency, Ada, Oklahoma, 103 pp.
Messing, I., 1989. Estimation of the saturated hydraulic conductivity in clay soils from soil moisture retention data. Soil Sci. Soc.
Am. J. 53, 665±668.
Minasny, B., McBratney, A.B., Bristow, K., 1999. Comparisonof different approaches to the development of pedotransfer
functions for water-retention curves. Geoderma 93, 225±
253.
Mualem, Y., 1976. A new model predicting the hydraulic conductivity of unsaturated porous media. Water Resour. Res. 12, 513±
522.
Nelder, J., Mead, R., 1965. A simplex method for function minimization. Comput. J. 7, 308±313.
Nemes, A., Schaap, M.G., Leij, F.J., WoÈsten, J.H.M., 2001.
Description of the unsaturated soil hydraulic database
UNSODA Version 2.0. J. Hydrol. this issue.
Pachepsky, Ya.A., Timlin, D., Varallyay, G., 1996. Arti®cial neuralnetworks to estimate soil water retention from easily measurable
data. Soil Sci. Soc. Am. J. 60, 727±733.
Pachepsky, Ya.A., Timlin, D., Ahuja, L.R., 1999. Estimating saturated hydraulic conductivity using water retention data andneural networks. Soil Sci. 164, 552±560.
Press, W.H., Flannery, B.P., Teukolsky, S.A., Vetterling, W.T.,
1988. Numerical Recipes in C. ®rst ed. Cambridge University
Press, New York.
Rawls, W.J., Brakensiek, D.L., 1985. Prediction of soil water properties for hydrologic modeling. In: Jones, E.B., Ward, T.J.
(Eds.). Proceedings Symposium Watershed Management in
the Eighties. April 30±May 1, 1985, Denver, CO, Am. Soc.
Civil Eng., New York, NY, pp. 293±299.
Rawls, W.J., Gish, T.J., Brakensiek, D.L., 1991. Estimating soil
water retention from soil physical properties and characteristics.
In: Stewart, B.A. (Ed.). Advances in Soil Science. Springer,
New York.
Schaap, M.G., Bouten, W., 1996. Modeling water retention curvesof sandy soils using neural networks. Water Resour. Res. 32,
3033±3040.
Schaap, M.G., Leij, F.J., 1998. Database related accuracy anduncertainty of pedotransfer functions. Soil Sci. 163, 765±779.
Schaap, M.G., Leij, F.J., 2000. Improved prediction of unsaturated
hydraulic conductivity with the Mualem±van Genuchten model.
Soil Sci. Soc. Am. J. 64, 843±851.
Schaap, M.G., Leij, F.J., van Genuchten, M.Th., 1998. Neuralnetwork analysis for hierarchical prediction of soil water retention and saturated hydraulic conductivity. Soil Sci. Soc. Am. J.
62, 847±855.
Soil Survey Staff, 1995. Soil survey laboratory information manual.
Soil Survey Investigation Report No. 45. National Soil Survey
Center, Lincoln, NE.
Tyler, S.W., Wheatcraft, S.W., 1989. Application of fractal mathematics to soil water retention estimation. Soil Sci. Soc. Am. J.
53, 987±996.
van Genuchten, M.Th., 1980. A closed-form equation for predicting
the hydraulic conductivity of unsaturated soils. Soil Sci. Am. J.
44, 892±898.
van Genuchten, M.Th., Leij, F.J., 1992. On estimating the hydraulic176

M.G. Schaap et al. / Journal of Hydrology 251 (2001) 163±176

properties of unsaturated soils. In: van Genuchten, M.Th., Leij,
F.J., Lund, L.J. (Eds.). Indirect Methods for Estimating theHydraulic Properties of Unsaturated Soils. Proceedings of International Workshop, Riverside, CA, 11±13 October,
1989University of California, Riverside, CA, pp. 1±14.
Vereecken, H., Maes, J., Feyen, J., Darius, P., 1989. Estimating thesoil moisture retention characteristic from texture, bulk density,and carbon content. Soil Sci. 148, 389±403.

Williams, R.D., Ahuja, L.R., Naney, J.W., 1992. Comparison of
methods to estimate soil water characteristics from limited
texture, bulk density, and limited data. Soil Sci. 153, 172±184.
WoÈsten, J.H.M., Finke, P.A., Jansen, M.J.W., 1995. Comparison ofclass and continuous pedotransfer functions to generate soil
hydraulic characteristics. Geoderma 66, 227±237.