Journal of Hydrology 399 (2011) 93–99

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Journal of Hydrology
journal homepage: www.elsevier.com/locate/jhydrol

Deriving and validating pedotransfer functions for some calcareous soils
Habib Khodaverdiloo a, Mehdi Homaee b,⇑, Martinus Th. van Genuchten c, Shoja Ghorbani Dashtaki daDepartment of Soil Science, Urmia University, Urmia, Iran
Department of Soil Science, Tarbiat Modares University, Tehran 14115-336, Iranc
Department of Mechanical Engineering, COPPE/LTTC, Federal University of Rio de Janeiro, Rio de Janeiro, RJ, BrazildDepartment of Soil Science, Shahrekord University, Shahrekord 88186/34141, Iranb

a r t i c l e

i n f oArticle history:
Received 12 January 2010
Received in revised form 14 December 2010
Accepted 28 December 2010
Available online 6 January 2011
This manuscript was handled by P. Baveye,
Editor-in-Chief
Keywords:
Calcareous soils
Pedotransfer function
Soil hydraulic properties
Water retention curves u m m a r y
The unsaturated soil hydraulic properties are needed for many different applications in soil hydrology.
Pedotransfer functions (PTFs) have proven to be useful to indirectly estimate these parameters from moreeasily obtainable soil data. Until now no studies have been conducted to derive or verify PTFs for calcareous soils, which hydraulically may not behave the same as non-calcareous soils. The objectives of thisstudy were to assess the inﬂuence of soil CaCO3 on the soil water retention characteristics of some calcareous soils, and to derive PTFs for these soils. Two data sets were used to derive and evaluate the established PTFs. Data set 1 containing 220 samples was employed as a calibration set for multiple linear
regression. An independent data set containing 55 soil samples from a different location served to verify
the derived PTFs. No signiﬁcant difference in accuracy was found between the PTFs with and without
CaCO3 in terms of estimating speciﬁc soil water retention values or the van Genuchten soil hydraulicparameters. Compared with the Rosetta PTFs of Schaap et al. (2001), the derived point and parametric
PTFs provided better accuracy with average RMSE values of 0.028 and 0.107 cm3 cm3, respectively.
Ó 2010 Elsevier B.V. All rights reserved.

1. Introduction
Estimates of the unsaturated soil hydraulic properties areneeded for many agronomic, environmental and engineering applications involving water ﬂow and contaminant transport processes
in the vadose zone. A broad array of laboratory and ﬁeld methods
are currently available for direct measurement of the hydraulicproperties (e.g., Dirksen, 2000; Dane and Topp, 2002). Unfortunately, most or all methods are too time consuming and costly
for most applications (Wösten et al., 2001). Furthermore, due tohigh temporal and spatial variability in the hydraulic characteristics, a large number of samples is generally required to accurately
characterize ﬁeld conditions.
An alternative to direct measurement is the use of indirect
methods in which the hydraulic properties are estimated from
more easily measured or more readily available soils data (Bouma,
1989; Wösten et al., 2001). Methods that may be used for thispurpose include statistical pore-size distribution models, inverse
models and especially pedotransfer functions (PTFs). PTFs (Bouma
and van Lanen, 1987; Bouma, 1989) are based on the premise thatthe hydraulic properties can be related to basic soil properties suchas the particle size distribution, bulk density and/or organic matter⇑ Corresponding author. Tel.: +98 21 4829 2280; fax: +98 21 4419 6524.
E-mail address: mhomaee@modares.ac.ir (M. Homaee).
0022-1694/$ - see front matter Ó 2010 Elsevier B.V. All rights reserved.
doi:10.1016/j.jhydrol.2010.12.040

content. From a prediction point of view, PTFs can be distinguishedinto point and parametric PTFs. Point PTFs predict the watercontent at pre-deﬁned soil water pressure heads, while parametric
PTFs assume that the hydraulic properties can be described adequately with a hydraulic model containing a limited number ofparameters.
Iran, as many other countries, does not have sufﬁcient soil
hydraulic data for deriving local PTFs for relevant agricultural orenvironmental modeling applications. However, several large databases such as UNSODA (Leij et al., 1996), HYPRES (Lilly, 1997;
Wösten et al., 1999), WISE (Batjes, 1996) and the USDA-NRCS pedon soil characterization database (Soil Survey Staff, 2010a) havebeen established to facilitate analyses of the soil hydraulic properties. Consequently, it is attractive to use such databases to develop
PTFs for regions with less available data. Although the advantagesof existing PTFs are well discussed in the literature (e.g. Tietje andTapkenhinrichs, 1993; Espino et al., 1995; Wösten et al., 1995;
Minasny et al., 1999), their applicability to calcareous soils has
not been addressed thus far (Homaee and Farrokhian Firouzi,2008). Also, practical applications of most PTFs is often hamperedby their very speciﬁc data requirements.
Hydrologists in countries with insufﬁcient soil hydraulic ortaxonomic data are often confronted with situations where one
or more PTF input parameters is not available. The Rosetta package(Schaap et al., 2001) implements ﬁve hierarchical PTFs to predict
the WRC, as well as the saturated and unsaturated hydraulic94

H. Khodaverdiloo et al. / Journal of Hydrology 399 (2011) 93–99

conductivity. The hierarchy in PTFs allows prediction of van
Genuchten hydraulic parameters and the saturated hydraulic conductivity using limited (soil textural class only) to more extended(texture, bulk density, and one or two water retention points) input data. This makes Rosetta quite useful for countries having data
limitations.
Calcareous soils are widely distributed over the world andphysically may not behave the same as non-calcareous soils. Calcareous soils contain 5% or more (by volume) inorganic carbon or
CaCO3 equivalent (Soil Survey Staff, 1999). Soils of this type are
the dominant formation in many areas, particularly in arid andsemiarid regions. According to the FAO, about 65% of soils in Iranare calcareous (FAO/UNDP, 1972). Inorganic carbon in soils commonly exists in the form of the carbonate minerals calcite (CaCO3),
dolomite [Ca, Mg(CO3)2], and as magnesium calcites (Ca1x
MgxCO3). Other less common forms are aragonite (CaCO3) and siderite (FeCO3). Carbonates in soils may be of primary (inheritedfrom parent materials) or secondary (pedogenic) origin. Secondary
carbonates usually consists of aggregates made up of silt- and claysized calcite crystals, which are easily identiﬁed using grain mounttechniques. Large crystals of calcite or dolomite are mostly of primary origin (Doner and Lynn, 1989).
Qualitative and quantitative knowledge of Ca and Mg carbonates
is useful in many agronomic and environmental studies, such as forinvestigations of root growth, water movement, contaminant transport, soil pH (Nelson, 1982) and the nature of the exchange complex(Goh and Mermut, 2006). Studies that considered the effects of calcium carbonate precipitation on reductions in pore space suggestthat neither water retention nor the hydraulic conductivity is affected signiﬁcantly by calcium carbonate precipitation (Frenkel
et al., 1978). However, from water retention and adsorption energy
points of view, carbonates of the clay size can be treated as silt particles (Soil Survey Staff, 2010b). Thus, the hydraulic properties ofcalcareous soils may well differ from non-calcareous soils. Also, calcium carbonate is routinely removed from soil when soil texture isdetermined. The properties of soils with large CaCO3 contents hence
may well change during standard hydraulic analyses, which may
further complicate the use of PTFs for non-calcareous soils. Hence,
the applicability of available PTFs, such as those in the Rosetta package, to calcareous soils remains largely untested.
The objectives of this study were to (1) derive and verify pedotransfer functions of several typical calcareous soils, and to test
whether the inclusion of soil CaCO3 content as an input parameter
would improve the accuracy of the PTFs, and (2) to investigate if
the Rosetta PTFs, which were not derived speciﬁcally for calcareous
soils, can be applied to calcareous soils.

2. Materials and methods
2.1. Soil data and soil characterization
A large set of disturbed and undisturbed samples were collectedfrom the top 30 cm soil horizon of the Karaj, Karaj-Najm Abad,
Mohammad Abad, Mard Abad and Nazar Abad soil series near
the city of Karaj, Iran. The soils were classiﬁed as Torriorthents,
Calcixerepts, Haplocalcids and Haplocambids according to USDA
Soil Taxonomy (Soil Survey Staff, 2010b). In total, 275 undisturbed
cores (7.5 cm diameter by 5.0 cm height) and 275 disturbed samples were collected. The disturbed samples were ﬁrst air-dried
and then sieved through a 2 mm sieve. The particle size distributions of the samples were obtained using the hydrometer method(Gee and Or, 2002), while CaCO3 contents were determined usingpressure calcimetry (Sherrod et al., 2002).
To determine water retention values, the soil cores were slowly
saturated by soaking them in water at a level just below the top of

the core. This procedure was carried out over a period of 2 days toobtain as complete saturation as possible by minimizing entrappedand dissolved air in the cores. Soil water contents at saturation
were determined by oven-drying the saturated samples at 105 °C
for 24 h. After saturation, cores were placed on a saturated ceramic
plate inside a pressure plate apparatus and subjected to consecutive pressure heads of 100, 330, and 1000 cm to allow desaturation of the samples and measurement of the water content. Soilwater retention values at 3000, 5000, and 15,000 cm pressure
heads were similarly determined using a pressure plate apparatus
on disturbed soil samples in three replicates.
Particle size distributions of selected soil samples (ranging fromthose having the lowest to the highest CaCO3 contents) were determined after removing their calcium carbonate. Calcium carbonate
was removed using diluted HCl following procedures proposedby Kroetsch and Wang (2006) for removal of carbonates prior todetermining particle size distributions. The HCl-treated soil
samples were air-dried and grinded, after which the particle
size distributions and water retention values at 3000, 5000,
and 15,000 cm pressure heads were obtained, again using thepressure plate apparatus. A t-test was performed to verify statistical differences between the amounts of retained water and the soil
particle size distributions of paired samples (i.e., samples before
and after calcium carbonate removal).
To obtain a uniform description of all WRCs, we used the soil
water retention equation of van Genuchten (1980):hðhÞ ¼ hr þ

hs  hr

ð1Þ

ð1 þ jahjn Þ11=nwhere h is the volumetric water content (–), h is the soil water pressure head (L), hr and hs are the residual and saturated water contents(–), respectively, and a (L1) and n (–) are shape factors. The nonlinear least-squares optimization program RETC of van Genuchten
et al. (1991) was used to ﬁt the hydraulic parameters in Eq. (1) tothe measured retention data.
The geometric mean dg (L) and geometric standard deviation dg(–) of the soil particle diameters were determined using methods
proposed by Shirazi and Boersma (1984):

dg ¼ exp a;a ¼ 0:01

jX

fi ln M i

ð2Þ1

dg ¼ exp b;2

b ¼ 0:01

jX

2

fi ln M i  a2

ð3Þ1

where j is the number of soil separates (e.g., clay, silt, sand), Mi is
the mean diameter (in mm) of particles in soil separate i, and fi isthe percentage of total soil mass having a diameter equal to or lessthan Mi.
The entire soils database was divided into two subsets. Subset 1
containing 80% of the samples (n = 220) from the Karaj, Karaj-Najm
Abad, and Mard Abad soil series was used as the calibration set.
Subset 2 with the remaining 20% (n = 55) involving independent
samples from the Mohammad Abad and Nazar Abad soil series
was employed as a validation set. Table 3 gives details on the properties of the two data sets.
2.2. PTF development and WRC estimation
Multiple linear regression analyses were performed on the calibration subset to correlate soil water retention values at pressure
heads of 0, 100, 330, 1000, 3000, 5000, and 15,000 cm, as
well as the van Genuchten parameters, with available soil physicochemical parameters to develop several pairs of PTFs, i.e., PTFs withand without using CaCO3 as one of the predictors of the PTFs. The

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H. Khodaverdiloo et al. / Journal of Hydrology 399 (2011) 93–99

paired PTFs hence refer to using CaCO3 as input to the developed
PTFs, not to whether CaCO3 was or was not removed from the samples prior to the water content measurements.
The accuracies of the paired PTFs were compared using several
quantitative measures to provide a basis for selecting the best PTFs
for estimating soil water retention values. Water contents atpressure heads of 0, 100, 330, 1000, 3000, 5000, and15,000 cm were subsequently generated for both the calibrationand validation subsets using the selected PTFs, either directly as
point PTFs or by inserting the parametric PTFs into Eq. (1). The
van Genuchten retention equation was used next to computewater contents at all pressure heads at which water contents had
been measured. The water retention parameters were also predicted with the hierarchical PTFs of Rosetta using sand, silt andclay percentages, as well as the bulk density, of the validation subset as input data. We emphasize that the main aim of this study
was not necessarily to obtain very accurate predictions as such,but ﬁrst and foremost to derive PTFs that show possible effectsof CaCO3 on water retention.

ME ¼

RMSE ¼

d¼1

Cp ¼




SSEp
 ðm  2pÞ
MSEm

ð4Þ

where SSEp is the sum-of-squared error (SSE) of the best model having p parameters (including its intercept), and MSEm is the meansquare error (MSE) of the model using all m predictors. A small value of Cp indicates that the model is relatively precise (has a small
variance) in estimating the true regression coefﬁcients and predicting future responses (Ryan and Joiner, 1994). In this study wechoose a subset for which Cp approached the number of predictors,
p, in a given regression model (Daniel and Wood, 1980).
The degree of multicollinearity in each derived PTF was tested
using the ‘‘Variation Inﬂation Factor’’, VIF (Hocking, 2003; Ho,2006). We furthermore used the Durbin–Watson statistic to determine if the residuals showed any signiﬁcant correlation based on
the order in which the data were analyzed.
As predictive equations, PTFs are routinely evaluated in terms ofthe correspondence between measured and predicted values.
When the data used for evaluation are different from those used
to develop the equations, the ‘‘reliability’’ of the prediction is evaluated (Pachepsky and Rawls, 1999; Wösten et al., 2001). In thisstudy we evaluated the reliability of the derived PTFs, as well as
those obtained with Rosetta, using the independent data set from
the Mohammad Abad and Nazar Abad soil series.
A complete assessment of model performance should include
one ‘‘goodness-of-ﬁt’’ measure and at least one absolute error measure (Legates and McCabe, 1999). The mean error (ME), root meansquare error (RMSE), and index of agreement (d) were used to evaluate both the accuracy and the reliability of the derived PTFs. We
used the d statistic to circumvent certain problems associated withthe commonly used coefﬁcient of determination (R2). The index ofagreement reﬂects the degree to which the observations are accurately estimated by the predictions (Willmott, 1981). In contrast toR2, d is a measure of the degree at which model predictions are error free, rather than being a measure of correlation or association.
The mathematical expressions of the various statistics are as follows (Willmott, 1981):

ð5Þ

"Pn  p
 #1=2o 2i¼1 hi  hi
n

ð6Þ

Pn
p
o 2
i¼1 ðhi  hi Þ



h



i2
Pn  po  þ  hoi  ho 
i¼1  hi  hð7Þwhere hpi are the predicted values of the soil water content, hoi are
the observed soil water contents, n is the number of samples, while
over-lined symbols represent mean values. We furthermore evaluated the relative improvement (RI) of the PTFs with CaCO3 (shownby the subscript +CaCO3) over those without CaCO3 (subscript
CaCO3) as a PTF predictor in terms of the RMSE for all hðhÞ pairs
using:

RI ¼

2.3. Reliability, accuracy and validity of the PTFs
After analyzing for normality in the data, the subset regression
procedure was used to select the best group of independent variables. Our general approach was to select the smallest subset that
fulﬁlled certain statistical criteria. The Minitab software (Minitab,
1998) was used to obtain the R-squared (R2), adjusted R-squaredðR2adj Þ, and Cp statistics for this purpose. The Cp statistic is given by:n1Xðhp  hoi Þ
n i¼1 i

RMSECaCO3  RMSEþCaCO3
 100%
RMSECaCO3

ð8Þ

The relative improvement of region-speciﬁc PTFs over Rosetta
was similarly evaluated by replacing RMSECaCO3 and RMSE+CaCO3
in Eq. (8) with the RMSEs of the region-speciﬁc PTFs and the Rosetta predictions, respectively.
3. Results and discussion
Ranges in the particle size distribution, the calcium carbonate
content and water retained at pressure heads of 3000, 5000,
and 15,000 cm for some selected soil samples before and after
calcium carbonate removal are shown in Table 1. A t-test indicateda signiﬁcant (p 6 0.001) increase in retained water at these threepressure heads after removal of CaCO3 from the samples. While
any retained water was signiﬁcantly inﬂuenced by the particle
adsorption energy at the lower pressure heads, the reason for thismay be attributed to the fact that carbonates within the clay size
act more as silt from a water holding point of view. A comparisonof the particle size distributions in Table 1 of the soil samples before and after CaCO3 removal indicates, surprisingly, that the sandpercentage, and hence also the mean soil particle size, increased
after removing CaCO3. One may expect the opposite as carbonates
often act as a cementing agent to cluster smaller particle into larger units.
One way to explain the particle size increase is that the carbonate removal procedure preferentially eliminated smaller carbonate
particles while leaving the larger particles unchanged. Anotherexplanation may be that CaCO3 particles in calcareous soils could
act not only as a cementing agent to cluster primary particles into
secondary particles, but also as primary particles by themselves.
Hence, carbonate removal may have caused the preferential

Table 1
Ranges in soil properties before and after CaCO3 removal (in% of the material prior to
CaCO3 removal) for some selected soil samples (values in parentheses are meanvalues).

a

Soil property

Range before CaCO3
removalRange after CaCO3
removalC (%)aSi (%)S (%)
CaCO3 (%)
h3000cm (cm3 cm3)h5000cm (cm3 cm3)h15,000cm (cm3 cm3)

14–26 (22)40–50 (44)28–44 (34)
6.4–28 (11)0.13–0.17 (0.15)
0.11–0.16 (0.14)
0.10–0.14 (0.12)

9–29 (20)
13–52 (29)
34–67 (51)–0.18–0.25 (0.21)
0.15–0.23 (0.19)
0.13–0.21 (0.16)

C, Si, and S: clay, silt, and sand contents, respectively.

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H. Khodaverdiloo et al. / Journal of Hydrology 399 (2011) 93–99

A set of regression equations was obtained to estimate thevan Genuchten parameters as well as water retained at pressure
heads of 0, 100, 330, 1000, 3000, 5000, and 15,000 cm,
using the best subset regression method. Since our multiple
regression approach assumes normal distributions of the dependent variables, the degree of normality of the data was tested
using Ryan and Joiner’s (1994) method. The normality tests
showed that some of the variables were not normally distributed. Therefore, the data with non-normal distributions werenormalized as much as possible using some of the power andother transformations shown in Table 2. This table provides

removal of carbonate particles within the clay size. This suggeststhat determination of soil water retention of acid-treated soil samples may lead to unrealistic results when used for ﬁeld water management, or for agricultural or environmental modelingapplications. Table 1 also shows that in spite of a reduction in
the smaller particle sizes after CaCO3 removal, the retained water
increased in the soil samples. This supports the view that calcium
carbonate particles within the clay size did not act as clay particles
to retain soil water (Soil Survey Staff, 2010b). These results reﬂect
lower adsorption energy of the calcium carbonate than other soil
particles of approximately the same size.

Table 2Derived PTFs of calcareous soils that predict water retention at speciﬁc pressure heads, as well as van Genuchten parameters,with (+CaCO3) and without (CaCO3) using soil calcium carbonate content as an input parameter. The equations represent thebest subset regression results and their adjusted R2 ðR2adj Þ, root mean square error (RMSE), and relative improvement (RI) values.
The derived pedotransfer functions

R2adj (RMSE)+CaCO3hs = 0.380 + 0.00620 C/S + 0.108 qb  0.00306 CaCO3

0.57⁄⁄⁄(0.039)
4.9

CaCO3hs = 0.230 + 0.00110 C/S + 0.177 qba

0.42⁄⁄⁄(0.041)+CaCO3h100cm = 0.222 + 0.00946 C/S + 0.106 qb  0.00172 CaCO3

0.69⁄⁄⁄(0.022)
4.3

CaCO3h100cm = 0.306 + 0.0123 C/S + 0.0668 qb

0.71⁄⁄⁄(0.023)+CaCO3h330cm = 0.720 + 0.177 qb  0.936 dg –0.000044 CaCO3

CaCO3h330cm = 0.724 + 0.176 qb  0.938 dg+CaCO3h1000cm = 0.612 + 0.142 qb  0.796 dg  0.000025 CaCO3

CaCO3h1000cm = 0.614 + 0.141 qb  0.797 dg+CaCO3h3000cm = 0.529 + 0.109 qb + 0.00247 dg  0.723 dg  0.000183 CaCO3

CaCO3h3000cm = 0.544 + 0.105 qb + 0.00250 dg  0.731 dg+CaCO3h5000cm = 0.460 + 0.112 qb + 0.00230 dg  0.648 dg  0.000075 CaCO3

CaCO3h5000cm = 0.466 + 0.111 qb + 0.00231 dg  0.652 dg+CaCO3h15,000cm = 0.422 + 0.131 qb + 0.00113 dg  0.650 dg  0.000242 CaCO3

CaCO3

RI (%)

0:1

0.72⁄⁄⁄(0.026)
0.0

0:1

0.73⁄⁄⁄(0.026)

0:1

0.76⁄⁄⁄(0.020)
2.4

0:1

0.77⁄⁄⁄(0.016)
0:1

0.77⁄⁄⁄(0.017)
0.0

0:1

0.78⁄⁄⁄(0.017)

0:1

0.73⁄⁄⁄(0.017)
0.0

0:1

0.74⁄⁄⁄(0.017)

0:1

0.65⁄⁄⁄(0.021)
0.0h15,000cm = 0.402 + 0.136 qb + 0.00109 dg  0.638 dg

0:1

0.66⁄⁄⁄(0.021)+CaCO3hr = 0.103–0.00274 dg  0.873 h330cm + 1.98 h15,000cm  0.000736 CaCO3

0.71⁄⁄(0.026)
0.0CaCO3hr = 0.114–0.00328 dg  0.837 h330cm + 1.96h15000cm

0.70⁄⁄(0.026)+CaCO3a = 0.0142 + 0.000771 dg  0.000612 CaCO3

0.24⁄⁄⁄(0.008)
18.3

CaCO3a = 0.00230 + 0.00129 dg

0.06⁄⁄(0.010)+CaCO3n = 2.22–0.0217 dg  3.89 h330cm + 4.57 h15,000cm + 0.00292 CaCO3

0.30⁄⁄⁄(0.153)
0.8

CaCO3n = 2.27–0.0238 dg  3.74 h330cm + 4.48 h15,000cm

0.29⁄⁄⁄(0.155)

dg: geometric mean of the soil particle diameter (mm).
dg: geometric standard deviation of the soil particle diameter (–).
⁄⁄⁄
and ⁄⁄ indicate statistical signiﬁcance at the 0.001 and 0.01 conﬁdence level, respectively.
a
C, S, qb, and CaCO3: clay content (%), sand content (%), soil bulk density (g cm3), and soil calcium carbonate (%),
respectively.

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H. Khodaverdiloo et al. / Journal of Hydrology 399 (2011) 93–99

the derived point and parametric PTFs of the calcareous soils
with and without
CaCO3 as an input parameter, and their RMSE,
RI, and R2adj values. The derived PTFs showed VIF values thatwere always less than the critical value of 10 often used to indicate multicollinearity among the regressed variables (e.g., Ho,
2006), except for the hs and h100cm PTFs that used both the clay
and sand contents as independent predictors. To avoid multi-collinearity in this case, the clay to sand ratio (C/S) was used rather
than the original variables. Also, the Durbin–Watson value for allof the derived PTFs was found to be always larger than 1.4, thus
indicating that no signiﬁcant autocorrelation existed among theresiduals (Ho, 2006).
Compared with the point PTFs, the accuracy of the derived PTFs
for the a and n parameters was not as good. Our results indicatethat the derived PTFs could not accurately predict the hydraulicparameters. This may be caused by interdependency amongst theparameters, poor ﬁt of the model to the data, or over-parameterization of the model (van den Berg et al., 1997).
As shown in Table 2, using CaCO3 as an additional input parameter for the PTFs improved the predictions between 2.4% and18.3%, especially for the a hydraulic parameter. The relatively large
improvement for a may be related to changes in the pore-size distribution by secondary CaCO3, which would mainly affect a as discussed earlier. Still, in view of the relatively small differences
between the RMSE values (a maximum of 0.031 cm1 for a), thiswas not a signiﬁcant improvement, even for a itself which had
the highest RI (18.3%). Overall there was no signiﬁcant difference
between the paired PTFs (i.e., the PTFs with and without CaCO3)
to estimate soil water retention at either speciﬁc pressure heads
or via the van Genuchten parameters. This may be due to the factthat the other input parameters (such as bulk density and soil texture) already may have accounted for part of the possible effects of
CaCO3 on soil water retention, thus reducing the direct effects of
CaCO3 on the PTF results. To further test this hypothesis, we used
the PTFs with CaCO3 for a, and those without CaCO3 for the other
output variables to evaluate the accuracy of region-speciﬁc PTFs,
and to compare our results with those obtained using Rosetta.
Table 2 shows that CaCO3 had a negative effect on all water
retention values, both at relatively high and low water contents.
One possible reason for this is that CaCO3 clusters smaller particles
to larger ones, thus possibly increasing secondary porosity andhence the water content, except perhaps at or very near saturation.

At the same time, the low adsorption energy of CaCO3 at the dry
end of the curve may lead to its negative correlation with the watercontent (Table 1).
We note that the PTF’s in Table 2 are limited to the Iranian soil
samples used in our analysis. Table 3 shows ranges in observed
physical and chemical data of the soil samples in the calibration(set 1) and validation (set 2) data sets before CaCO3 removal, including of the soil particle size distribution, the soil bulk density qb, andthe CaCO3 content. The values in Table 3 can be used to avoid
extrapolation of the PTF predictions outside of the measurement
range.
We next applied the derived PTFs, as well as the Rosetta PTFs
using sand, silt and clay percentages and bulk density as input
data, to the validation subset (set 2). Table 4 provides a quantitative comparison of the reliability of the water contents predictedwith the derived point and parametric PTFs and Rosetta. Comparedwith Rosetta, the region-speciﬁc point-PTFs did lead to better accuracy with RMSE < 0.054 cm3 cm3. The average RMSEs were 0.028,
0.107, and 0.176 cm3 cm3 for the point, parametric, and Rosetta
PTFs, respectively. The region-speciﬁc parametric PTFs had a tendency to overestimate the water contents, while the Rosetta PTFs
underestimated the water contents. The average ME values were0.000, 0.085, and 0.148 cm3 cm3 for the point and parametric
PTFs and Rosetta, respectively. The differences seemed to be larger
at the higher water contents (Table 1 and Fig. 1a), which may beinterpreted as an inability of the bulk density to reﬂect the effects
of soil structure on the WRC. The average values of the index ofagreement, d, were 0.91 and 0.54 for the point and parametric
PTFs, respectively, which reﬂects reasonable performance of the
PTFs. The average value of d was 0.32 for Rosetta. In all, the results
indicate relatively good performance of the selected point andparametric PTFs in terms of the three statistics (see also Fig. 1a).
The average relative improvements of our region-speciﬁc point
and parametric PTFs over Rosetta were 83% and 36%, respectively.
Comparing the average RMSE value of Rosetta in this study(RMSE > 0.102 cm3 cm3) with that of Rosetta for its own data
(0.068 cm3 cm3; Schaap et al., 2001) shows that Rosetta did not
perform well for our calcareous soils. We note here that somestudies suggested that the accuracy of simulations using PTF-based
soil hydraulic properties may be acceptable for selected
applications when the RMSE values are on the order of about
0.065–0.070 cm3 cm3 (e.g., Nemes et al., 2003).

Table 3Ranges in particle size distribution, geometric mean particle diameter dg, geometric mean standard deviation of particle diameter dg, CaCO3 content, and soil bulk density qb used
as input data for calibration (set 1) and validation (set 2) of the pedotransfer functions.
Parameter

C (%)

S (%)

Si (%)

dg (mm)dg (–)

CaCO3 (%)

qb (g cm3)

Range for set 1
Range for set 2

11–48
12–48

17–54
17–53

6–71
6–56

0.0067–0.2468
0.0068–0.1157

7.35–20.34
7.58–20.22

4.5–47
6.4–28

1.20–1.83
1.20–1.83

Table 4
Calculated mean error ME, root mean square error, RMSE, and index of agreement, d, statistics for quantitative validation of the reliability of the derived PTF’s and Rosetta at
different volumetric water contents (h) for the validation data set. The values in bold are the relative improvement, RI, of region-speciﬁc PTFs over those of Rosetta.

ME (cm3 cm3)

RMSE (cm3 cm3)
RI (%)

Point PTF
Parametric PTF
Rosetta
Point PTF
Parametric PTF
Rosettad (–)

Point PTF
Parametric PTF
Rosettahsh100cmh330cmh1000cmh3000cmh5000cmh15000cm

0.001
0.000
0.121
0.057
67
0.054
69
0.172
–
0.892
0.845
0.363

0.000
0.076
0.260
0.025
91
0.095
68
0.297
–
0.871
0.588
0.218

0.000
0.150
0.193
0.029
87
0.174
22
0.222
–
0.919
0.377
0.294

0.0010.142
0.152
0.022
87
0.163
6
0.174
–
0.933
0.367
0.315

0.001
0.098
0.118
0.019
86
0.114
17
0.137
–
0.937
0.449
0.350

0.001
0.076
0.109
0.019
85
0.090
29
0.126
–
0.924
0.506
0.352

0.000
0.050
0.086
0.023
77
0.059
42
0.102
–
0.893
0.674
0.401

98

H. Khodaverdiloo et al. / Journal of Hydrology 399 (2011) 93–99(b) 0.4

Rosetta
Point PTFs
Parametric PTFs

Predicted AWC (cm3 cm-3)

Predicted Water Content (cm3 cm-3)(a) 0.8
0.6

0.4

0.2

0

0.3

0.2

0.1

0
0

0.2

0.4

0.6

0.8

0

0.1

0.2

0.3

0.4

Measured AWC (cm3 cm-3)

Measured Water Content (cm3 cm-3)

Fig. 1. Measured and predicted soil water retentions (SWR) at pressure heads of 0, 100, 330, 1000, 3000, 5000, and 15,000 cm (all together) (a) and available watercontent (AWC) (b) using the different PTFs for the validation data set. The solid lines indicate the 1:1 diagonals.

at FC and PWP were both estimated from the regression equations. Thus, any errors in those predictions were already included in the model and hence propagated into the estimatesfor AWC.

-330 cm-15000 cm

0.5

r = 0.63

Water content (-)

0.4
0.3

4. Conclusionsr = 0.67

0.2
0.1
0

0

15

30

45

60

Clay content (%)
Fig. 2. Relationships between the volumetric water contents at pressure heads of330 cm (ﬁeld capacity, FC) and 15,000 cm (permanent wilting point, PWP) withthe soil clay content.

The results so far indicate that differences between estimatesusing PTFs speciﬁcally developed for calcareous soils and the Rosetta package were not fully due to the inclusion of soil CaCO3
content into the PTFs, but likely resulted also from other factors
such as database-related uncertainty (Schaap and Leij, 1998) as
well as from differences between the invoked algorithms (Nemes
et al., 2003). However, in the case of the a parameter, part ofthese differences may be due to the fact that soil CaCO3 content
was not a parameter in the hierarchical PTFs of the Rosetta package. We next compared measured retention values with watercontents estimated with the point and parametric PTFs and theRosetta package (Fig. 1a) for the entire retention curve, as wellas measured and predicted values of the available water content,
AWC, (Fig. 1b), which is deﬁned as the difference between thewater contents at 330 cm (ﬁeld capacity, FC) and 15,000 cm(the permanent wilting point, PWP). We found a signiﬁcant correlation (p ¼ 0:001) between the measured and estimated watercontents for the entire retention curve. However, the correlation
for available water content was relatively weak. This may be related to the fact that the water content at both pressure heads(330 and 15,000 cm) increased with increasing clay content.
Fig. 2 shows the regression between water content and clay content for two different pressure heads. The best ﬁtted lines were
found to diverge slightly. One other reason for the weakness ofthe correlation may be due to the fact that the water contents

In this study we assessed the effect of soil CaCO3 content onwater retention, and derived PTFs to predict the water retention
curve and the van Genuchten parameters of calcareous soils. Relative improvements of the derived PTFs as compared to the Rosetta
PTFs were also evaluated. Our results suggest lower adsorption energy (and hence lower water contents) of soil calcium carbonate
than of other soil particles having approximately the same size.
We found no signiﬁcant difference between the paired PTFs (i.e.,with and without CaCO3 as an input parameter) in estimatingwater retention, neither for the point nor parametric PTFs. Thismay be attributed to the fact that the other input parameters(notably bulk density and soil texture) already may have accounted for part of the possible effects of CaCO3 on soil water
retention, thus reducing the direct effects of CaCO3 on the PTF results. Compared with Rosetta, the derived PTFs provided better
accuracy, with the RMSE not exceeding 0.174 cm3 cm3. Our results indicate that Rosetta may not be very effective in predicting
water contents of calcareous soils. A similar conclusion wasreached by Homaee and Farrokhian Firouzi (2008) regarding theuse of Rosetta to predict water retention data of gypsiferous soilsof Iran. This indicates that the performance of a PTF may be inﬂuenced by other factors such as the geographical source of the data
sets used for its development, differences in measurement techniques, or other dependencies that were not considered in theanalysis (e.g. Cornelis et al., 2001; Wagner et al., 2001; Ghorbani
Dashtaki et al., 2010). Soil bulk density, for example, is known toplay a signiﬁcant role at or near saturation (Lin et al., 1999). Therefore, further studies are needed to incorporate soil structure as an
input parameter to derive PTFs.
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