Soil Physics & Hydrology

A Comparative Study of Multiple Approaches
for Predicting the Soil–Water Retention Curve:
Hyperspectral Information vs. Basic Soil Properties
Ebrahim Babaeian
Mehdi Homaee*

Dep. of Soil Science
Tarbiat Modares University
Tehran, 14115-336
IranHarry Vereecken
Carsten Montzka

Institutes of Bio- and Geosphere
Agrosphere (IBG-3)
Forschungszentrum Jülich GmbH52425 Jülich
Germany

Ali Akbar Norouzi

Soil Conservation and Watershed
Management Research Institute
Tehran, IranMartinus Th. van Genuchten

Dep. of Mechanical Engineering
COPPE/LTTC
Federal University of Rio de Janeiro
Rio de Janeiro, RJ, 21945-970
BrazilandDep. of Earth Sciences
Utrecht University
Budapestlaan 43584 Utrecht
Netherlands

Information about the soil–water retention curve is necessary for modeling waterflow and solute transport processes in soils. Soil spectroscopy in the visible, nearinfrared, and shortwave infrared (Vis-NIR-SWIR) range has been widely used
as a rapid, cost-effective and nondestructive technique to predict soil properties. However, less attention has been paid to predict soil hydraulic properties
using soil spectral data. In this paper, spectral reflectances of soil samples fromthe Zanjanrood watershed, Iran, were measured in the Vis-NIR-SWIR ranges(350–2500 nm). Stepwise multiple linear regression coupled with the bootstrap
method was used to construct predictive models and to estimate the soil–water
retention curve. We developed point and parametric transfer functions based on
the van Genuchten (VG) and Brooks-Corey (BC) soil hydraulic models. Three different types of transfer functions were developed: (i) spectral transfer functions(STFs) that relate VG/BC hydraulic parameters to spectral reflectance values,(ii) pedotransfer function (PTFs) that use basic soil data as input, and (iii) PTFs
that consider spectral data and basic soil properties, further referred to as spectral pedotransfer functions (SPTFs). We also derived and evaluated point transfer
functions which estimate soil–water contents at specific matric potentials. The
point STFs and SPTFs were found to be accurate at low and intermediate watercontents (R2 > 0.50 and root mean squared error [RMSE] < 0.018 cm3 cm-3),
while the point PTFs performed better close to saturation. The parametric STFs
and SPTFs of both the VG and BC models performed similarly to parametric PTFs
in estimating the retention curve. The best predictions of soil–water contents
were obtained for all the three transfer functions when the VG and BC retention models were fitted to the retention points estimated by the point transfer
functions. Overall, our findings indicate that spectral data can provide useful
information to predict soil—water contents and the soil–water retention curve.
However, there is a need to extend and validate the derived transfer functions toother soils and regions.
Abbreviations: BC, Brooks and Corey; EF, model efficiency; MAE, mean absolute error;
PTF, pedotransfer function; RMSE, root mean squared error; SMLR, stepwise multiple
linear regression; SPTF, spectral pedotransfer function; STF, spectral transfer function; VG,
van Genuchten; Vis, Visible; NIR, near infrared; SWIR, shortwave infrared.

U

nsaturated soil hydraulic property information is necessary for predicting and managing water flow and solute transport processes in soils. The
accuracy with which these properties can be estimated has however asignificant effect on the quality of predicted soil hydrological fluxes and states(Montzka et al., 2011). Pedotransfer functions are now popularly used to estimate
the soil hydraulic functions from basic soil data such as the particle-size distribu-

Soil Sci. Soc. Am. J.
doi:10.2136/sssaj2014.09.0355
Received 6 Sept. 2014.
Accepted 8 Apr. 2015.
*Corresponding author(mhomaee@modares.ac.ir).
© Soil Science Society of America, 5585 Guilford Rd., Madison WI 53711 USA
All rights reserved. No part of this periodical may be reproduced or transmitted in any form or by
any means, electronic or mechanical, including photocopying, recording, or any information storage
and retrieval system, without permission in writing from the publisher. Permission for printing and forreprinting the material contained herein has been obtained by the publisher.

Soil Science Society of America Journal

tion, the bulk density, and the organic C content (Vereecken etal., 1989, 1990, 1992, 2010; Schaap et al., 1998, 2001; Jarvis et al.,
2002; Rawls and Pachepsky, 2002; Pachepsky and Rawls, 2004;
Pachepsky et al. 2006; Jana et al., 2007; Homaee and Farrokhian
Firouzi, 2008; Weynants et al., 2009; Ghorbani Dashtaki etal., 2010). Both point and parametric PTFs have been used forthis purpose. Point PTFs predict soil–water contents at specificmatric potentials, while continuous PTFs predict the hydraulicfunctions in their entirety. Parametric PTFs have attracted more
attention since they quickly provide soil hydraulic parameter
estimates for use in hydrological models. By comparison, fewerstudies have tried to estimate the soil hydraulic parameters by fitting retention functions to water contents obtained using point
PTFs (Baumer, 1992; van den Berg et al., 1997; Tomasella andHodnett, 1998; Tomasella et al., 2000).
In addition to basic soil data, supplementary information
has been used to improve the performance of PTFs including soil
structural information (Rawls and Pachepsky, 2002; Pachepsky etal., 2006; Lilly et al., 2008), the water content at selected matricpotentials (Børgesen and Schaap, 2005; Børgesen et al., 2008),
clay mineralogy and taxonomic information (Pachepsky andRawls, 2004), vegetation parameters (e.g., the leaf area index or thenormalized difference vegetation index) and topography attributes(e.g., elevation, slope, and aspect) (Pachepsky et al., 2001; Leij etal., 2004; Sharma et al., 2006; Jana and Mohanty, 2011).
During the past two decades, visible (Vis), near-infrared(NIR), and shortwave-infrared (SWIR) spectrometry has been
widely used to estimate a range of soil properties, and also as a
rapid and cheap method in digital soil mapping. Using spectral
data, measurements take a few seconds, several soil properties
can be estimated from a spectrum, soil analysis is cheap wherehigh spatial density is required, sample preparation involves only
drying and sieving and no (hazardous) chemicals are required.
Physical soil constituents and properties that affect the bulk soil
spectral reflectance the most are soil color, soil moisture, organicC, particle size and Fe- and Al- oxids (Stenberg et al., 2010). Thisis the fundamental principle behind using the spectral approachto estimate soil properties and its applications have been
extensively reviewed (Viscarra Rossel et al., 2006c; Stenberg etal., 2010; Soriano Disla et al., 2014).
Several studies have shown the capability of laboratory scale
Vis-NIR-SWIR (400–2500 nm) spectrometry to accurately
predict a range of soil properties, including particle-size
distribution (Gomez et al., 2008; Lagacherie et al., 2008; Janiket al., 2009; Lopez et al., 2013), soil aggregate-size distribution(Sarathjith et al., 2014a, 2014b), calcium carbonate (Lagacherie
et al., 2008; Gomez et al., 2008), pH (Viscarra Rossel andBehrens, 2010), organic C content (Nocita et al., 2013; Lopezet al., 2013) and the cation-exchange capacity ( Janik et al., 2009;
Savvides et al., 2010). Volume-based soil properties such as bulk
density are typically estimated from spectral information in an
indirect manner through correlation with basic soil properties
such as clay content and soil organic matter. Latter properties areoften better correlated with spectral properties. Bulk density is∆a key property that is required to obtain reasonable estimates of
the wet part of the soil moisture retention characteristic.
In addition to estimating basic soil properties fromspectral information, several studies explored the potential ofusing spectral information to estimate soil–water content at
specific pressure head values. Janik et al. (2007), used partial
least squares regression (PLSR) method to relate mid-infrared
spectral data (2500–20000 nm) to soil–water contents at matricpotentials of -100 and -15000 cm. They obtained coefficients ofdetermination, R2, equal to 0.67 and 0.87 for these two watercontents, respectively. Similarly, Minasny et al. (2008) used
mid-infrared spectroscopy to predict water content at matricpotential values of -10, -100, -3000, and -15000 cm. They foundthat water contents at the lower matric potentials (notably-15000 cm) could be estimated better (R2 = 0.51, RMSE =0.05 cm3 cm-3) than those at high matric potentials (-100 cm,
with R2 = 0.08 and, RMSE = 0.07 cm3 cm-3). Since current
hyperspectral satellites operate in the Vis-NIR-SWIR range,
mid-infrared spectroscopy at present cannot be used to estimate
soil properties by satellite imagery. For this reason, Lagacherie
et al. (2008) suggested using spectrotransfer functions that linkreflectance measurements to soil properties.
Rather than only estimating specific points of the soil
moisture retention characteristic, recent studies analyzed thepotential of spectral soil information to estimate soil hydraulicproperties using parametric PTFs. Santra et al. (2009) usedprincipal component transformed spectral data (350–2500 nm)
as well as mimicked Landstat-ETM+ spectral bands to estimate
van Genuchten–Mualem soil hydraulic parameters (a, n, and Ks)of the wet part (> −800 cm) of the retention curve. Their results
were promising for the parameter n, but they had difficulties toestimate a and Ks. One major weakness of this approach is thatthe soil hydraulic parameters are estimated from a limited rangeof measured water contents only. Also, none of the above studies(i.e., Janik et al., 2007; Minasny et al., 2008; Lagacherie et al.,2008; Santra et al., 2009) introduced clearly effective wavelengths
for use in predictive models, whereas it is very important tocharacterize sensitive spectral regions to better understand therelation between spectral response and the physical behaviorof soils. Recently, Babaeian et al. (2015) evaluated the generalpotential of hyper- and multi-spectral remote sensors to retrieve
Mualem-van Genuchten hydraulic parameters, and tested it withlaboratory- and soil-map-based HYPRES and Rosetta PTFs.
Results indicate that with the upcoming hyperspectral EnMAP
mission it is in principle possible to retrieve van GenuchtenMualem soil hydraulic parameters in adequate accuracy, while
the reduced spectral information of the Sentinel-2 sensor isprinciply not able to predict soil hydraulic parameters. The
presented STF approach does not require soil texture andorganic matter data, which is an advantage for areas that do nothave such basic information. Based on the data set obtained by
Babaeian et al. (2015), in this study we present a comparative
analysis of spectral information along with simple soil data forderiving and validating different types of point and parametric
Soil Science Society of America Journal

transfer functions. The innoviation lies in the estimation of the
VG and BC hydraulic parameters as well as soil–water contents
at specific matric potentials, which are applied to predict soil–
water retention characteristics.
To evaluate if visible and near-infrared spectroscopy can
improve predictions of VG and BC soil hydraulic parameters,
three different approaches were investigated; (i) STFs that predicthydraulic parameters from spectral reflectance data, (ii) PTFs
based on soil properties such as particle-size distribution, bulk
density, organic C content and geometric mean of soil particles
diameter, and (iii) SPTFs that predict hydraulic parameters fromthe joint use of spectral reflectance data and basic soil attributes.
We further evaluated point and parametric approaches to estimate
VG and BC parameters using a fit of the retention models to theestimated soil–water contents and hydraulic parameters obtainedwith the parametric transfer functions.

MATERIALS AND METHODS

Study Area, Soil Sampling, and Soil
Property Measurements
The number of disturbed and undisturbed (cores with adiameter of 6.8 cm and a height of 5 cm) soil samples (n = 2
× 174) were collected from the top 30 cm soil horizon of
Zanjanrood subwatershed, northwest of Iran. The soils wereclassified as Calcixerepts, Haploxerepts, and Xerorthents (USDA
Soil Taxonomy, Soil Survey Staff, 2010b). A more detailed
description of the study area is given in Babaeian et al. (2015).
Collected basic properties of the soil samples included
clay (C, < 2 mm), silt (Si, 2–50 mm), sand (S, 50–2000 mm),organic carbon content (OC), and dry bulk density (rb) whichwere measured using sedimentation (Gee and Bauder, 1986),
dichromate oxidation (Walkley and Black, 1934), and paraffincoated procedures. The geometric mean of the soil particle
diameter, dg , was determined using the method of Shirazi andBoersma (1984). Gravimetric water contents were measured on
the undisturbed cores at three matric potentials in the wet range(i.e., 0, -5, -10 cm) and on the disturbed samples at six matricpotential in the mid (-330, -1000) and the dry (i.e., -3000, -5000,-10000, and -15000 cm) ranges of the water retention curve using
sand-box apparatus (Eijkelkamp Agri-Equipment, Giesbeek, theNetherlands) and pressure plate extractor methods (Soil Moisture
Equipment Corp., Santa Barbara, CA; Vereecken et al. (2010),
see also Babaeian et al. (2015) for more details). The calibrationand validation subsets were selected to divide the study area intoa west and an east part. The data of the western part (n = 130)
were used as calibration set. While those of the eastern part (n =44) were used to provide a completely independent data set forvalidation of the derived transfer functions. Using independent
sample t test statistics, a comparison of the mean values of thecalibration and validation set confirmed no significant (p > 0.19)
at the 0.05 significance level.
The soil–water retention functions were parameterizedusing the equations of van Genuchten (1980) and Brooks-Corey( Brooks and Corey, 1964), given by Eq. [1] and [2], respectively,
www.soils.org/publications/sssaj

VGq(h) =q r + ( q s − q r ) 1+ ( aˆ VG h ) nq(h) =q r + ( q s − q r )  a BC h 

− l BC

−m

[1]
[2]

where q [cm3 cm-3] is the soil–water content at matric potential
h [-cm], â VG [cm-1] and aBC [cm-1] are shape parameters of the
VG and BC models, respectively (approximately equivalent to
the inverse of the air-entry value), nVG [-] and lBC [-] are poresize distribution parameters, m is an empirical constant that canbe related to n (i.e., m = 1–1/nVG), and qr and qs [cm3 cm-3]
are the residual and saturated water contents, respectively. Using
nonlinear least-squares optimization, the retention models
were fitted to measured soil–water content values to obtain thehydraulic parameters, that is, aBC, â VG , nVG, and lBC. During
the optimization process, the residual water content was found tobe very close to zero, and thus it was fixed at zero for all samples(Babaeian et al., 2015).

Laboratory Hyperspectral Reflectance Measurements
The soil samples were air-dried and sieved through a 2-mm
mesh sieve to obtain the fine earth fraction of soil. Spectraof the air-dried and sieved samples were recorded in the VisNIR-SWIR (350–2500 nm) range with 1.4 (350–100 nm)
to 2 (1000–2500 nm) nm sampling intervals. The measured
hydraulic parameters (i.e., water content at each matricpotential, the VG and the BC retention models parameters)
were then correlated with spectral reflectance data. We have notfocused on the spectral reflectance measurements at different
matric potentials, but measured the spectral reflectance for
air-dried and sieved soil samples. These measured spectra werethen used to derive STF and SPTF. Extensive research in thepast showed that spectral measurement of soil on air-dried andsieved samples is a standard and routine procedure which has
been widely used already at the laboratory scale (e.g., Ben-Dor
and Banin, 1995; Chang et al., 2005; Brown et al., 2006; Janiket al., 2009; Santra et al., 2009; Bilgili et al., 2010; Viscarra
Rossel and Behrens, 2010; Stenberg et al., 2010; Nocita et al.,2011; Lopez et al., 2013; Nocita et al., 2013). Lobell and Asner(2002) showed that soil water, when present in substantial
amounts, has strong absorption bands in the NIR-SWIR range,
which could interfere with the spectral features of other soil
components and reduces the performance of calibration results.
Although air-dried samples show a slight variation in boundwater content (hygroscopic water) due to variation in texture,
the inferential effect of such amount of water is negligible on
spectral measurements. In such case, the interferential effectof soil moisture is negligible on spectral measurements. It wasalso found that sample fineness has no significant effect on
the calibration results (Genot et al., 2011; Nduwamungu etal., 2009). The measurements were performed in a standard
and controlled dark laboratory environment using a handheld
FieldSpec3 spectroradiometer (Analytical Spectral Device,
ASD, Boulder, CO).
∆A spectral library of 174 soil reflectance spectra, which has
been described in detail in Babaeian et al. (2015), was obtainedby arithmetic averaging of the iterations for each soil sample.

Transformation of the Vis-NIR-SWIR ReflectanceSpectra and Preprocessing
Spectral transformations and data preprocessing wereused to render the data more suitable for analysis by correcting
for background effects (Viscarra Rossel, 2008), light scattering(Barnes et al., 1989), removing nonlinearities in the spectra(Viscarra Rossel, 2008) and improving calibration (Tian etal., 2013; Nocita et al., 2013; Viscarra Rossel, 2008). Various
preprocessing and pretreatment algorithms can be used forthis purpose, such as Savitzky-Golay and median filtering(for de-noising and smoothing of spectra), using first andsecond derivatives of the spectrum (to eliminate backgroundeffects; Viscarra Rossel, 2008), using standard normal variate
and multiplicative scatter correction (to remove light scatterand baseline correction) (Geladi and Kowalski, 1986), andabsorbance and continuum removal transformations (to reduce
nonlinearities in the spectra; Lagacherie et al., 2008).
Based on cross validation, we used continuum removed
spectra transformation after applying Savitsky–Golay smoothingwith a second-order polynomial in segments (of the observation
points) involving three points (Savitzky and Golay, 1964). Moredetails about continuum removal methods and the Savitzky-Golay
algorithm are given in the literature (Stenberg et al., 2010; Noomenet al., 2006; Lagacherie et al., 2008; Babaeian et al., 2015).

Before performing the spectral analyses, we excluded
spectral data obtained in the range between 350 and 399 nm
and 2451 and 2500 nm because of excessive noise (Viscarra
Rossel et al., 2006c). Since spectroradiometer data are very
repetitive and heavily over-sampled with a high degree ofcorrelation between neighboring bands, data redundancy was
reduced using data reduction and down-sampling. We did thisby averaging every five contiguous 1-nm wavelengths resulting
in 410 data points from 400 to 2450 nm for calibration (Lopezet al., 2013).

Model Development and Hydraulic
Property Estimation
Hyperspectral data with high spectral resolution (1 nm) andbroader wavelengths (350–2500 nm) have been used frequently
for estimating soil properties (Ben-Dor and Banin, 1995; Changet al., 2001; Islam et al., 2003; Viscarra Rossel et al., 2006a,
2006c). These spectral data always show considerable collinearityand heteroscedasticity, which should be avoided whendeveloping PTFs based on regression equations. Characterizing
relevant wavebands is hence important for developing reliableprediction models and spectral indices. For this reason, we
employed correlation analysis and stepwise multiple linear
regression statistics (SMLR), which allows the selection of bands
that have better correlations with each attribute.
Three different approaches were used to develop
pedotransfer functions: STFs, PTFs, and SPTFs (Fig. 1). These
approaches are briefly summarized below.

Fig. 1. Graphical representation of three approaches used to estimate hydraulic parameters from spectral data and/or basic soil information. C,
Si, S, rb, OC, dg represent clay, silt, sand, bulk density, organic carbon, and geometric mean of soil particles diameter, respectively; Rw is spectralreflectance at wavelength w; aVG and nVG are VG shape parameters; aBC and lBC are BC shape parameters; qs is saturated soil–water content; q
is soil–water content; and subscript L represents a particular matric potential.
∆

Soil Science Society of America Journal

Approach 1: Spectral Transfer Functions
In the first approach, spectral reflectance values, referred
to as Scenario I in Babaeian et al. (2015), were used as unique
predictor variables to derive bothpoint and parametric STFs.
Point STFs estimate the vector q ={q 1 ,..., q L } where q refers
to the soil–water content and the subscripts to matric potential
levels between 1 and L. We estimated water contents at thenine available matric potentials (L = 9): 0, -5, -10, -330, -1000,-3000, -5000, -10000, and -15000 cm. Parametric spectral
transfer functions developed in this paper estimate the unknownparameter vector p ={aˆ , n ,a , l , q } (later referred as Method I)
where â VG and nVG are VG shape parameters, aBC and lBC are
BC shape parameters, and qs is the saturated soil–water content.

The STFs relate the two parameter vectors p and q to spectralreflectance values using regression analysis: p  f Rw  and
q = f ( Rw ), where Rw is the spectral reflectance at wavelength w
and f refers to the regression equation.
We also fitted the VG and BC retention functions to estimatedsoil–water contents obtained from the point STFs (i.e., p = f ( q))to construct new sets of the VG and BC parameters (later referred as
Method II; see Fig. 1) and predict soil–water retention.
VG

VG

BC

BC

s

Approach 2: Pedotransfer FunctionsIn the second approach, p and q vectors are directly
related to basic soil properties, i.e., p = f ( s ) and q = f ( s ), wheres = {C ,Si,S, r b ,OC , d g } (Fig. 1), to derive parametric (MethodI) and point PTFs. Like in the first approach, both retention
models VG and BC were then fitted to the point PTFs (Method
II). Such new set of hydraulic parameters were used to predictsoil–water retention.

Approach 3: Spectral Pedotransfer Functions
The third approach is, in fact, a combination of the two
previous approaches in that first, relationships between thebasic soil properties ( s ) and the spectral reflectance data arederived, (i.e., s = f ( Rw )). Then the outputs are used as input
data into derivedpoint and parametric PTFs (i.e., Approach 2)to obtain p and q . The VG and BC models were then fitted tothe point SPTFs (i.e., Method II). Using two different sets ofhydraulic parameters for each parametric transfer function (i.e.,
Methods I and II), water contents at specific matric potentials
were generated (see Fig. 1) and were compared with measured
retention points.

General Statistical Analysis for Spectral Transfer
Functions, Pedotransfer Functions, and Spectral
Pedotransfer Functions
Before model development, descriptive statistics of the basic
soil properties and soil hydraulic parameters were calculated andtested for normality (at the 5% level of significance, p < 0.05) using
the Kolmogorov–Smirnov one sample test statistics (Babaeian etal., 2015). Transformations were performed for those variables
that did not follow a normal distribution. Pearson’s correlation
analyses were performed on the calibration subset to explore thewww.soils.org/publications/sssaj

correlation between basic soil variables and hydraulic properties(i.e., water content at each matric potential or the VG and the
BC retention models parameters) with the spectral reflectancedata. Variables showing a strong correlation (at significance levelsof 1 and 5%) with hydraulic parameters were included in SMLR
as three separate sets of predictors for deriving three different setsof transfer functions (see Fig. 1). Details on the SMLR and theestimation process used are given in Babaeian et al. (2015). To
avoid multicollinearity in each derived function, the ‘Variance
Inflation Factor’, VIF, was used (Hocking, 2003; Ho, 2006).
We additionally used the ‘Durbin-Watson statistic’ to checkautocorrelation among the residuals of the regression equations(Ho, 2006; Babaeian et al., 2015).
Multiple linear regressions coupled with the bootstrap
method (Efron and Tibshirani, 1993) are often used to provide
robust estimates. Briefly, bootstrapping is a non-parametrictechnique for deriving robust estimates of regression coefficients.
Bootstrapping is most useful as an alternative to parametricestimates when the assumptions of those methods are in doubt(as in the case of regression models with heteroscedastic residuals
fit to small samples).
The bootstrap method creates random subsets (realizations)from a calibration set of size N to obtain B bootstrap data sets,
each with size N, through repeated sampling with replacement.
The bootstrap dialog box in PASW statistics was employed to
specify the bootstrap analyses and to create the bootstrap samples.
The simple resampling method with replacement from the original
dataset, with a number of 1000 bootstrap samples, were specified
at a 95% percentile confidence interval. Linear regression coupledwith bootstrap provides descriptive statistics and coefficients tables
that support mean, standard deviation and bootstrap estimatesand significance tests for the regression coefficients.
Using the three approaches, soil–water contents at specificmatric potentials, as well as the VG and BC hydraulic parameters,
were estimated for both the calibration and validation data sets.
To adjust the coefficients of the transfer function, the coefficientsof each empirical equation (i.e., the STFs, SPTFs, and PTFs)
obtained by SMLR during the first step were considered as apriori sets. The empirical coefficients of each regression equation
obtained from the first step were then adjusted by minimizing
the sum of squared errors between the estimates from the firststep and the observed hydraulic parameters (Babaeian et al.,2015; see also Weynants et al. (2009), for more details).

Accuracy and Reliability Criteria
Accuracy may be defined as the difference between measured
and predicted values of the soil hydraulic properties used in thecalibration step (Guber et al., 2009; Vereecken et al., 2010). Since
derived transfer functions are a set of empirical equations, a test of
their accuracy should be performed using a separate dataset thatis independent of the calibration set. We further define reliability
as evaluating the performance of the predictions using measured
values that are different from those used in model development(Vereecken et al., 2010). Reliability was tested using a validation∆

Table 1. Criteria for evaluating the accuracy of the transfer functions.

mean value, ranges, and standard deviations of thebasic soil attributes and hydraulic parameters ofNboth the calibration and validation subsets.
MAE =(1/ N − p)∑ ˆyi − yiMean absolute error
0i=1Figure 2 depicts the mean and standardNdeviationof the raw and the continuum removed
MBE =(1/ N − p)∑ ˆyi − yiMean bias error0i=1
spectra of the soil samples. Corresponding withthe results from Babaeian et al. (2015), spectralN
2
Root mean squared error RMSE = (1/ N − p)∑ ( ˆyi − yi )0reflectance values were relatively low below 700
i=1
nm (the visible region) and high for the NIR and2
Coefficient of
N
N
N

2
SWIR spectral range, with maximum reflectance2
1
R 2 =  ∑ ( ˆyi − ˆy ) ( yi − y )/ ∑ ( ˆyi − ˆy ) ∑ ( yi − y ) determination==i 1 =i 1
values being about 0.38, which represents the i 1relatively small reflectance from the soils (the
N
N
2 
2

1
Model efficiencyEF =1−  ( N − p ) ∑ ( ˆyi − yi )  /  ( N − p ) ∑ ( yi − y ) maximum reflectance value of a white reference
=
i 1=
i 1

 

ˆ
† y iand y i , ith observed and predicted values; y and yˆ , mean of the observed and panel is equal to 1). The soil spectral reflectancepredicted values; p, number of predictors in derived functions; N, number of data pairs generally increases in the presence of calcium
consisting of yi and yˆ i .
carbonate, while organic matter and soil moisture
set. The goodness of fit of the point and parametric STFs, SPTFs,
tend to reduce the reflectance.
and PTFs was evaluated using the root mean squared error
As is clearly shown in Fig. 2, both the raw and continuum(RMSE), the mean absolute error (MAE), the mean bias error
removed spectra exhibit four diagnostic absorption features(MBE), the coefficient of determination (R2), and the modelaround 1414, 1915, 2212, and 2340 nm (Babaeian et al., 2015).
efficiency (EF) as defined in Table 1.
The absorption peaks near 1414 and 1915 nm are strongly
associated with the bending and stretching of the hydroxyl
RESULTS AND DISCUSSION(OH) features of hygroscopic or free water, while those near
Soil Properties and Soil Spectra
2212 nm are due to clay mineral lattice OH features (Clark,
Loam and clay loam were the predominant textural classes
1999; Viscarra Rossel et al., 2006c; Viscarra Rossel and Behrens,
covering about 30 and 50% of the soils in the study area,2010). Absorption in the Vis range (for example near 480 and
respectively (Babaeian et al., 2015). Table 2 summarizes the
650 nm) corresponds to iron oxides, which control soil color
such as red hematite and yellow goethite (Stenberg
Table 2. Descriptive statistics (minimum, maximum, mean, and standard devia- et al., 2010). The absorption peak near 2341 nmtion) of basic soil properties, water retention parameters [q(h)], Van Genuchten wavelength may be attributed to CO groups
3(VG) and Brook–Corey (BC) hydraulic parameters for the calibration and validain
carbonateminerals(Gaffey,
1986;
Gomez
et
tion sets.
al., 2008). It has been reported that soil CaCO3
Calibration subset (n = 130)
Validation subset (n = 44)
content has a significant effect on accuracy of point
Soil properties†
Min. Max. MeanSD
Min. Max. MeanSD
and parametric PTFs in estimating water retention
USDA clay, %
15
45
28
6.6
16
40
28.5
6.6
(Khodaverdiloo et al., 2011). These absorption
USDA sand, %
13
63
39.4
10.3
19
62
35.9
9.1
features are consistent with those found in other
USDA silt, %
21
52
32.6
5.4
22
43
35.5
5.0
studies (e.g., Ben-Dor and Banin, 1995; Ben-Dor
Organic carbon, %
0.06
1.56
0.636 0.25
0.23 1.95 0.656 0.34
et al., 1999; Gomez et al., 2008; Santra et al., 2009;
0.95
1.26
1.11
0.06
0.97 1.22 1.096 0.06
rb, g cm-3
Babaeian et al., 2015).
Statistic
d g*  d g0.5 ,Formula†0.098 0.400 0.219

0.064

Optimal value

0.119 0.387 0.203 0.056

mm0.5

qs, cm3 cm-3
0.407
q(-5 cm), cm3cm-30.324
q(-10 cm), cm3cm-30.299
q(-330 cm), cm3cm-30.186
q(-1000 cm), cm3cm-3 0.141
q(-3000 cm), cm3cm-3 0.119
q(-5000 cm), cm3cm-3 0.111
q(-10000 cm), cm3cm-3 0.095

0.608 0.507 0.048 0.375 0.572 0.492 0.047
0.583 0.469 0.051 0.314 0.546 0.459 0.054
0.552 0.439 0.048 0.284 0.509 0.432 0.052
0.340 0.251 0.026 0.216 0.306 0.252 0.013
0.272 0.206 0.024 0.166 0.260 0.208 0.012
0.261 0.167 0.022 0.130 0.208 0.165 0.009
0.240 0.156 0.021 0.117 0.184 0.152 0.010
0.226 0.145 0.021 0.098 0.182 0.140 0.008
q(-15000 cm), cm3cm-3 0.094 0.218 0.137 0.020 0.092 0.174 0.133 0.009-3.08 -0.92 -1.85 0.454 -2.70 -0.47 -1.76 0.493
aVG[= ln ( â VG )], cm-1
nVG, [-]
1.09
1.27
1.17
0.034 1.11 1.24 1.17
0.034
0.035 0.742 0.225 0.127 0.038 0.620 0.273 0.140
aBC, cm-1-2.49 -1.26 -1.84 0.218 -2.37 -1.45 -1.84 0.194
lBC [= ln (l)], [-]† rb, bulk density; dg*, geometric mean diameter of soil particles; qs, saturated water content[cm3 cm-3]; q, water retention at specific matric potentials [cm3 cm-3]; aVG and nVG,
shape parameters of VG model; aBC and lBC, shape parameters of BC model.
∆

Correlation Analysis of Variables usedin Transfer Functions
We used Pearson’s correlation coefficient, R, to
explore correlations between basic and soil hydraulicproperties with the spectral reflectance values atvarious wavelengths across the measured spectrum toidentify the most significant variables for inclusionin the point and parametric STFs, SPTFs, and PTFs.
Figure 3a shows correlation values between the soil–
water contents and spectral reflectance values acrossthe Vis, NIR, and SWIR range. Soil water retained
at matric potentials of -330, -1000, -3000, -10000,
and -15000 cm show maximum and significant (p <0.01) correlations with the spectral reflectance values
Soil Science Society of America Journal

at 587-, 1417-, 1957-, and 2307-nm wavelengths.
The largest correlation coefficients were observed
for water contents at matric potentials of -15000 (R= 0.673) and -10000 cm (R = 0.692), followed by-5000 (R = 0.671), -3000 (R = 0.658), -1000 (R =0.499), and -330 cm (R = 0.459) matric potentials.
For values larger than -330 cm, water contents showpoor correlations (R < 0.196) with spectral data inthe 400- to 2450-nm range (Fig. 3a). Soil–watercontents generally showed a similar and close trend
across all wavelengths, possibly due to positiveand strong correlations among the water contents
across a wide range of matric potentials. The watercontents at matric potentials below -3000 cm werealso significantly (p < 0.01) correlated with thespectral reflectance across the absorption features(i.e., negative correlations at 1414, 1915, 2212
nm and positive correlations at 2340 nm), withcorrelation coefficients <0.553. Similarly, VG andBC hydraulic parameters showed significant (p < Fig. 2. Mean and standard deviation of the raw (bottom) and continuum removed (top) spectral
0.01) correlations with the spectral reflectances reflectance of sampled soils for both the calibration and validation sets. Boxes depict absorption
feature regions centered near 1414, 1915, 2212, and 2340 nm (Babaeian et al., 2015).
across a wide range of wavelengths, particularly inmontmorillonite). The absorption near 2347 nm may represents
the SWIR region (Fig. 3b). The largest correlations
illite or mixtures of smectite and illite (Clark et al., 1990; Post andwere observed at wavelengths 2307 nm (for nVG, aBC and lBC
with R = −0.558, −0.517 and 0.517, respectively), 2317 nm (forNoble, 1993; Stenberg, 2010). In general, the weakest correlations
aVG with R = 0.463), 2347 nm (for lBC with R = 0.326), 2217
between reflectance values and basic/hydraulic parameters werenm (for nVG and aBC with R = 0.321 and 0.277, respectively),obtained at wavelengths between 800 and 1200 nm, possibly due
2222 nm (for aVG with R = -0.289), 1972 nm (for aVG with R =to the lack of strong absorption features in this range.
–0.309), 1957 nm (for nVG with R = 0.367) and 1417 nm (for aVG,
The correlation between particle-size distribution, OC,
nVG, and aBC with R = −0.274, 0.290, and 0.241, respectively).
bulk density, and the geometric mean soil particle diameter
According to the literature, peaks near 1417 nm and 1957–1972
with spectral reflectance values are also shown in Fig. 3c and
nm indicate the influence of water bound in the inter layer lattices
3d. As reported by Babaeian et al. (2015), clay content, sandof clay minerals (Bishop et al., 1994; Ben-Dor and Banin, 1995).
content, and silt content were significantly (p < 0.01) correlated
The absorption near 2217–2222 nm is due to the absorption ofwith spectral reflectance values at wavelengths corresponding
Al–OH, and the small absorption near 2307–2317 nm may beapproximately to those of the water content values, VG and BC
due to Fe–OH as Fe is substituted in the octahedral sheet (e.g., inhydraulic parameters. Comparing Fig. 3a and 3c clearly show

Fig. 3. Pearson’s correlation coefficients between spectral reflectance values and (a) soil–water content values; (b) VG and BC hydraulic parameters;(c) clay, silt and sand content; and (d) organic carbon, bulk density and geometric mean of soil particles diameter over Vis-NIR-SWIR range.
www.soils.org/publications/sssaj∆

Table 3. Pearson’s correlation coefficients among hydraulic parameters, water retained at specific matric potentials and basic
soil properties.†
USDA clay
aVG, ln(cm-1)
nVG, [-]
aBC, cm-1
lBC, [-]

0.263**-0.474**0.302**USDA sand

USDA silt––––––––––––%––––––––––-0.294**0.227**
0.491**-0.338**-0.311**0.212**

C/S, [-]

Organic C%

0.277**-0.493**0.323**-0.164*0.001-0.014rbg cm-3-0.263**0.374**-0.257**dg*[mm0.5]-0.276**0.477**-0.295**-0.538**0.548**-0.365**-0.569**-0.0740.408**
0.533**
0.196-0.110-0.0230.148
0.281*-0.607**-0.1470.209*-0.1330.004
0.171
0.231*-0.601**-0.1650.207*-0.129-0.0030.177
0.187-0.594**-0.1580.450**-0.488**0.360**
0.514**
0.142-0.283**-0.467**0.478**-0.500**0.350**
0.484**
0.272**-0.359**-0.498**0.719**-0.709**0.445**
0.738**
0.201**-0.550**-0.706**0.724**-0.696**
0.416**
0.734**
0.173*-0.561**-0.696**0.722**-0.663**0.356**
0.714**
0.144-0.575**-0.673**0.705**-0.662**0.374**
0.710**
0.112-0.595**-0.662*** indicate significant values at the 0.05 level.
** indicate significant values at the 0.01 level.
† C/S, clay to sand ratio [-]; aVG and nVG, shape parameters of VG model; aBC and lBC, shape parameters of BC model; qs, saturated watercontent [cm3 cm-3]; q, water retention at specific matric potentials [cm3 cm-3].
qs, m3 m-3
q(-5 cm), m3 m-3
q(-10 cm), m3 m-3
q(-330 cm), m3 m-3
q(-1000 cm), m3 m-3
q(-3000 cm), m3 m-3
q(-5000 cm), m3 m-3
q(-10000 cm), m3 m-3
q(-15000 cm), m3 m-3that soil–water contents below matric potential -330 cm werepositively correlated with clay and silt content, while negatively
correlated with sand content. One probable reason for thesimilar trend in correlation between the water content at low
matric potentials and the clay content is that clay particles have ahigh adsorption energy, especially in the dry part of the retention
curve, which causes more water to be retained. Similarly, the rb
and dg* were correlated with sand content, with maximum andsignificant (p < 0.01) correlation values of -0.692 and 0.505 at
2307 and 1877 nm wavelengths, respectively. Organic carbon
content showed the largest and significant (p < 0.01) correlation
at wavelengths of 1402 nm (R = 0.480) and 1877 nm (R = 0.505),
which are close to the absorption features of 1414 and 1915 nm(Fig. 3d). It has been identified that the 1400- and 1900-nm
wavelengths are effective for estimation of soil organic matter,
while they are at the same time also characteristic for O-H andwater molecules (Ben-Dor and Banin, 1995). The spectral ranges
characteristics for different compounds are therefore difficult
to identify with confidence (Ben-Dor et al., 1999; Brown et al.,2006; Clark, 1999; Stenberg, 2010). Significant correlations
between basic soil properties and spectral reflectance values
were also reported in studies by Bilgili et al. (2010), Somers et al.
(2010), and Santra et al. (2009).
To develop PTFs, the correlation between basic soil
properties (such as C, S, Si, OC, rb, and dg*) with the watercontents and hydraulic parameters was calculated (Table 3). As
an example, the largest and significant (p < 0.01) correlations
were found between the water content at matric potential of-15000 cm and C, Si, S, rb, and dg*, with correlation coefficientsequal to 0.705, 0.374, -0.662, -0.595, and -0.662, respectively.
The saturated water content only showed significant (p < 0.01
and 0.05) correlations with rb (R = −0.607) and OC (R =0.281). Significant (p < 0.01) correlations were also obtained
between the VG and BC shape parameters and the particle-size∆

distribution and bulk density. Since both basic and hydraulicproperties showed relatively high correlations with the spectralreflectance values over the Vis, NIR, and SWIR range, it may
be possible to predict soil hydraulic properties using STFs and
SPTFs from the available data.

Hydraulic Property Estimation
Spectral Transfer Functions
Table 4 shows the coefficient of determination, R2, and root
mean squared error, RMSE, of the derived point and parametric
spectral transfer functions to predict the water content at ninematric potentials, as well as the VG and BC shape parameters,
using spectral reflectance values at specific wavelengths. The point
STFs yielded R2 and RMSE values ranging between 0.02 and
0.64, and 0.012 and 0.054 cm3 cm-3, respectively. The parametric
STFs produced R2 values between 0.14 and 0.44. We included inthis study the STFs of aVG and nVG from Babaeian et al. (2015)
to provide a basis for comparision with the parametric PTFs and
SPTFs. These results can be particularly helpful for soil hydraulicproperties that do not have direct relationships with spectralreflectance data. As shown in Table 4, soil–water contents at low
matric potentials are predicted with better accuracy compared
to water contents in the mid and wet part of the retention curve.
Better correlations between water contents at the lower matricpotentials with the spectral data may be explained by the roleof clay content. Clay particles have high adsorption energies,
especially in the dry part of the retention curve, which causes
more water to be retained, thus directly affecting soil spectralreflectance values.
Significant (p < 0.01) predictors for the soil–water contents
and hydraulic parameters in the visible region (400–700 nm)
were found in the ranges between 442 and 457 nm (blue), 502
and 587 nm (green), and 602 and 687 nm (red), which seems
to represent the effects of type and content of iron oxides such
Soil Science Society of America Journal

Table 4. Derived point and parametric spectral transfer functions (STFs) for predicting soil–water contents as well as van Genuchten
and Brooks-Corey shape parameters, using spectral reflectance values as predictor variables. The functions express the best regression equations and their coefficient of determination, R2, and root mean squared error, RMSE, values.†
R2

Spectral transfer function

RMSE

q-15000 = -3.930+0.01 (0.123R442 – 0.588R602 – 1.749R662 + 5.237R2142 – 0.787R2227+ 0.909R2287 + 0.940R2327)

0.63***

0.0126q-10000 = -5.427+0.01 (0.020R442+0.172R532–2.170R662+5.278R2142+0.795R2152– 0.543R2202 + 1.608R2307+0.443R2327)

0.64***

0.0124q-5000 = -0.247+0.01 (-0.0119R447+0.2271R532–1.832R677+0.2941R2162+0.4869R2202+1.660R2307 + 0.5081R2322+0.0812R2447)

0.60***

0.0135q-3000 = -0.139+0.01 (0.0964R437–1.7761R662+0.0252R1732–0.4809R2222+0.9180R2302+1.146R2327- 0.6940R2367+1.083R2402)

0.59***

0.0142q-1000 = -3.832+0.01 (-0.910R457+1.492R502–0.615R1162+1.690R2287+1.152R2332+1.406)

0.53***

0.0167q-330 = -0.354+0.01 (-0.8527 R437+2.369 R507–1.872 R572–2.256 R2187–1.975 R2257+3.884 R2307+1.444 R2422)

0.52***

0.0178q-10 = -4.332+0.01 (3.386R2242+1.521R2427)

0.05**

0.0472q-5 = -4.710+0.01 (3.520R2242+1.801R2427)

0.05**

0.0496

qs = -2.888+0.01 (3.501R2242)

0.02*

0.0536aVG = -44.107+0.01 (-2.174R552+48.77R687 -0.494R1252 +0.530R1897–2.608R2222+19.654R2317–21.71R2447)§

0.33***

0.372

nVG = 3.739+0.01 (-0.200R552+0.116R1417 -0.385R1957 -1.885R2157+0.935R2222–2.820R2307+1.623R2427)§

0.38***

0.0268aBC = 4.762+0.01 (-9.104R2237+4.371R2347)

0.14***

0.1172lBC = -8.813+0.01 (-4.170R502+12.447R587 -51.518R2107 +48.890R2117+23.261R2242–22.319R2307)

0.44***

0.1650* p < 0.001** p < 0.01*** p < 0.05
†aVG and nVG, shape parameters of VG model; aBC and lBC, shape parameters of BC model; qs, saturated water content [cm3 cm-3]; q,water retention at specific matric potentials [cm3 cm-3]; Rw, spectral reflectance [%] in wavelength w in nm, R2 and RMSE are coefficient ofdetermination and root mean squared error, respectively.
§ Refers to Babaeian et al. (2015).

as hematite and goethite (Dematte and Garcia, 1999; Viscarra
Rossel and Behrens, 2010). Potential predictor variables werealso found in the NIR-SWIR range and more obviously between
wavelengths of 2100 and 2400 nm where spectral reflectancevalues between 2107 and 2187 nm, 2202 and 2287 nm, 2302
and 2367 nm, and 2402 and 2447 nm were the significant (p <0.01) variables to predict every soil–water content as well as the
VG and BC shape parameters (Table 4). Soil spectral features aremainly a result of overtone absorption and combination of bondvibrations in molecules of three functional groups in minerals:
OH, SO4, and CO3 (Hunt and Salisbury, 1970; Ben-Dor andBanin, 1995). The main spectral features near 2160 and 2208
nm are due to the Al-OH bend plus O-H stretch combination
vibrations in kaolinite (Viscarra Rossel and Behrens, 2010). The
absorption features near 2280 nm may be due to Fe-OH in theoctahedral sheet of clay minerals. Slight absorption near 2340,
2380, and 2450 nm represents the presence of some illite or
mixtures of illite and smectite (Post and Noble, 1993; Viscarra
Rossel and Behrens, 2010). The major absorption wavelengths
near 1417, 1950, and 2222 nm correspond to the bending andstretching vibrations of the O–H bonds from adsorbed water and
OH associated to phyllosilicates (Ben-Dor, 2002). The spectralfeature centered near 2336 nm may be attributable to carbonate
bands (Viscarra Rossel and Behrens, 2010). The spectral features
between 1160 and 1250 nm may be due to C-H bonds withinorganic compounds (Stuart, 2004). We found no explanation to
the spectral features obtained near 2107 nm.
The decrease in RMSE values from the wet range to thedry range of the water retention curve is in line with the results
reported by Minasny et al. (2008) who used mid-infrared
www.soils.org/publications/sssaj

spectroscopy to estimate volumetric water contents at two
different matric potentials of -100 and -15000 cm. They found R2
values of 0.08 and 0.51, and RMSEs equal to 0.07 and 0.05 m3 m-3,
respectively. Compared with these values, however, our results are
more accurate with RMSE values of 0.0126 cm3 cm-3 at matricpotential of -15000 cm and 0.0472 cm3 cm-3 at matric potentialof -100 cm. In a similar study, Tranter et al. (2008) used midinfrared spectroscopy to predict particle-size distribution andbulk density. They next implemented the spectral based estimates
within the PTFs as input variables and found improvements towater retention prediction by taking into account the effect ofstructure and adsorptive forces on water retention. They reported
poor predictions of the water content of intact structured soils,
particularly in the wet end of the retention curve (matric potentials
0 and -100 cm), while improved predictions were noted in thedry end (matric potential -15000 cm) where water contents areaffected mainly by the adsorptive forces of soil particles.
The R2 values obtained for estimating the a parameter ofthe BC model (R2 = 0.14) were smaller than those obtained
for water contents at low matric potentials (i.e., < −330 cm
with 0.52 < R2 < 0.63) and the lBC parameter (R2 = 0.44).
Our results produced lower RMSE values (see Table 4) of theestimated VG parameters compared with findings by Santra
et al. (2009) who obtained RMSE values larger than 0.06 and1.5 for nVG and the logarithmic form of â VG , respectively. One
possible reason for this poor accuracy may be attributed to
the relatively narrow range of their measurements (i.e., matricpotential range between 0 and -800 cm) compared with ourstudy (full range, matric potential between 0 and 15000 cm)
that were used to fit and estimate the shape parameters. When∆

Table 5. Derived point and parametric pedotransfer functions, PTFs, forpredicting moisture retention characteristic as well as van Genuchten
parameters using a set of basic soil properties as predictor variables.
The functions express the best regression equations and their coefficient of determination, R2, and root mean squared error, RMSE, values.

content were 0.53 and 0.0339, respectively. A large portionof this improvement at the higher matric potentials may be
due to the effect of bulk density on soil–water retention
close to saturation (Sharma et al., 2006; Schaap et al., 2001).
Pedotransfer function†
R2
RMSE
This is also shown by the high coefficients of determination
0.61*** 0.0129
q-15000 = 0.212 + 0.025 C/S- 0.087 rb
in the classical parametric PTFs or for point estimation of
0.62*** 0.0128
q-10000 = 0.173 + 0.00088 C + 0.016 C/S- 0.061 rb
soil–water content at saturation. A review of existing point
0.65*** 0.0126
q-5000 = 0.186- 0.055rb + 0.029 C/S + 0.01 OC
based PTFs by Vereecken et al. (2010) showed that the
0.66*** 0.0129
q-3000 = 0.153 + 0.026 C/S + 0.013 OC + 0.078dg*
largest RMSE values are often obtained for water contents
0.33*** 0.0200
q-1000 = 0.237- 0.00115 S + 0.021 OC
at matric potential values between -500 and -2500 cm (pF
0.29*** 0.0217
q-330 = 0.196 + 0.020 rb + 0.030 C/S + 0.013 OC
2.7–3.4), with values between 0.015 and 0.037 cm3 cm0.36*** 0.0356
q-10 = 0.8211- 0.2761 rb + 0.00046 C
3, While relatively low RMSE values are found at matric0.40*** 0.0360
q-5 = 0.8690- 0.2916 rb + 0.0258 OC
potential values between -2.5 (pF 0.4, 0.011 cm3 cm-3) and
0.53*** 0.0339
qs = 0.8690- 0.2916 rb + 0.0258 OC-30 cm (pF 1.5, 0.010 cm3 cm-3). In this study we found
0.10*** 0.4321
aVG = -2.1894 + 0.020 C- 0.3199 OC
greater errors in the wet range, which is in line with findingsnVG = 1.3312- 0.000076 C- 0.00069 Si- 0.9998 q-15000 0.44*** 0.0253
by Nemes et al. (2003) and Khodaverdiloo et al. (2011). The
0.10*** 0.1204
aBC = 0.4733- 0.1799 rb + 0.00182 C- 0.002304 S
particular source of this sizable difference is unknown, but
0.46***
0.1599lBC = -1.2573 + 0.004333 S- 5.4783 q-15000*** p < 0.001
the narrow range in the bulk density and the organic carbon†aVG and nVG, shape parameters of VG model; aBC and lBC, shape parameters content as the input parameters may explain part of thoseof BC model; qs, saturated water content [cm3 cm-3]; q, water retention at
errors. Another possible reason may be the heterogeneity of
specific matric potentials [cm3 cm-3]; rb, bulk density [g cm-3], dg*,
0.5
geometric mean diameter of soil particles [mm ], C, S, Si, and OC are clay, soils, loam, and clay loam being the dominant textures in thesand, silt and organic carbon content [%], respectively. R2 and RMSE are study area.
coefficient of determination and root mean squared error, respectively.
Table 5 shows that water contents are estimated with bettermeasured data are not available for the full range of the waterR2 values than the VG and BC hydraulic parameters. Like theretention curve, the fitted parameters will have poor definition,
STFs, the R2 of the VG and BC parameters in the PTFs weremaking it difficult to estimate them with certainty.
less than 0.50. This may be attributed to the poor fit of VG and
BC parameters to the water contents (mean RMSE value 0.014
Pedotransfer Functions
cm3 cm-3), narrow range of hydraulic parameters in the dataset (e.g.,
Table 5 shows the PTFs that predict soil–water contents at
nVG parameter) and interdependency between the parameters (e.g.,
specific matric potentials, as well as the VG and BC hydraulicaVG and nVG; aBC and lBC, see Fig. 3b) (van den Berg et al., 1997;
parameters. Laboratory determined clay, silt, and sand content,
Khodaverdiloo et al., 2011). Further reasons may be the nonlinearity
organic carbon content and bulk density attributes were usedof the models as well as the discrepancy in dominant influences withas predictors in the PTFs. To avoid the multicollinearity
respect to single retention points and the shape parameters which
between predictor variables in the PTFs, the clay/sand ratio
are controlled by a set of retention points. The moderate accuracy of
was utilized (Khodaverdiloo et al., 2011). Based on thethe PTFs in this study may have been caused by the narrow range inderived point PTFs, soil–water contents at matric potentials
the particle size distribution and bulk density as well as the organic
between 0 and -15000 cm were predicted with R2 and RMSE
carbon content (Bilgili et al. (2010), see Table 2), which leads tovalues ranging between 0.29 and 0.66 and 0.0126 and 0.0360
moderate correlation with soil–water retention values (see Table
cm3 cm-3, respectively. The largest RMSE values were obtained
3). Similar results for water retention predictions and hydraulicin the wet range (i.e., -5 and -10 cm), with a mean value ofparameters using PTFs were also reported by Khodaverdiloo et al.
0.0358 cm3 cm-3, while R2 and RMSE for saturated water(2011) and Tranter et al. (2008).
Table 6. The derived functions for estimating basic soil properties from spectral reflectance data, along with values of coefficientof determination, R2, and root mean squared error, RMSE.†
R2

RMSE

C = 6.931+0.01(0.4878R562 + 0.7998R617 – 7.607R687 + 0.1468R1827 – 7.654R2227 + 3.183R2327 + 3.767R2387)

0.65***

0.0391

S = –26.835 + 0.01(0.990R422 – 2.902R532+15.904R722+ 4.997R877 + 6.872R2052 – 2.402R2197 + 8.937R2222+7.735R2257– 8.700R2327 – 3.838R2432)

0.70***

0.0565Si = –30.379 + 0.01(24.757R762– 2.120R892 + 3.100R2312 + 2.813R2407 + 2.284R2432)

0.41***

0.0416

OC = –21.98 + 0.01(2.230R497 – 83.661R677 + 77.272R707 + 63.858R772 – 52.082R797+11.854R1402+5.133R1862+ 7.452R2342– 8.271R2447)

0.69***

0.1395Regression equation

rb = 5.990 + 0.01(4.925R677 – 1.418R1122 – 2.358R2247 – 6.215R2307)

0.57***

0.0428dg* = 0.159 + 0.01(0.586R422 – 1.940R537 + 0.415R1917 + 2.281R2037 +5.456R2227 – 3.821R2327 – 2.769R2432)

0.65***

0.0383*** p < 0.001.
† C, S, Si and OC: clay content [%], sand content [%], silt content [%] and organic carbon content [%], respectively; rb: bulk density [g cm-3], dg*:
geometric mean diameter of soil particles [mm0.5]; Rw: spectral reflectance [%] in wavelength w in nm.
∆

Soil Science Society of America Journal

Spectral Pedotransfer Functions
Table 6 summarizes the best regression equations forpredicting basic soil properties using different sets of spectralreflectance values at specific wavelengths. The best predictions
were observed for sand (R2 = 0.70, RMSE = 5.65%), organiccarbon (R2 = 0.69, RMSE = 0.14%), clay (R2 = 0.65, RMSE =3.91%), and the geometric mean of soil particle diameter (R2 =0.65, RMSE = 0.038 mm). Bulk density and silt content werepredicted with R2 values of 0.57 and 0.41, and RMSE values
equal to 0.043 g cm-3 and 4.16%, respectively. The R2 and RMSE
values in Table 6 are very much in line with literature values(e.g., Ben-Dor and Banin, 1995; Viscarra Rossel et al., 2006b;
Wetterlind et al., 2008b???; Islam et al., 2003; Chang et al., 2001;
Chang and Laird, 2002; Brown et al., 2006; Minasny et al., 2008;
Bilgili et al., 2010). As an example, Bilgili et al. (2010) used VisNIR spectral reflectance data and PLSR method to predict clay,
sand, silt, and organic matter content and obtained R2 valuesof 0.83, 0.70, 0.32, and 0.60, respectively. As expected, clay
content was better predicted due to the spectral signatures of clay
minerals typically dominating the NIR spectra (Stenberg et al.,2010). The sand fractions mainly consist of quartz and feldspars,
which are relatively featureless and have a large reñectance in the
Vis-NIR-SWIR range (Hunt and Salisbury, 1970). Sand andclay content are strongly correlated with each other and provide
correlation coefficients that are very close to 1. The silt fraction
can be assumed to be a mixture of sand and clay minerals andis therefore difðcult to distinguish in the Vis-NIR-SWIR range(Wetterlind and Stenberg, 2010).
Significant (p < 0.01) spectral bands in the predictivemodels of clay, silt, and sand content occurred between 422 and687 nm, 722 and 892 nm, 1827 and 2052 nm, 2197 and 2257
nm, and 2312 and 2432 nm wavelengths. However, it should be
noted that the position of these absorption bands may slightly
vary depending on the soil composition (Stenberg et al., 2010).
The regression equation for organic carbon content contained
spectral predictors from a wide range of wavelengths (see Table6), which agrees with several studies that identified wavelengths
near 1100, 1600, 1700 to 1800, 2000, and 2200 to 2400 nm forpredicting soil organic carbon and nitrogen (Dalal and Henry,
1986; Ben-Dor and Banin, 1995; Martin et al., 2002; Stenberg,2010). It has been reported that soil organic carbon have broad
absorptions in the Vis, which are dominated by the darknessof humic acid and absorptions in the NIR-SWIR from theovertones and combination absorptions of O–H, C–H, andN–H (Clark et al., 1990; Clark, 1999). Since basic soil properties(i.e., C, S, Si, OC, rb, and dg*) were well predicted from spectralreflectance data, they were used as predictors in the PTFs forpredicting soil–water content using SPTFs. Table 7 provides theaccuracy of point and parametric SPTFs for predicting watercontents as well as the VG and the BC hydraulic parameters. The
point SPTFs provided R2 and RMSE values ranging from 0.16
to 0.57 and 0.0145 to 0.0438 cm3 cm-3, respectively, with thebest values obtained in the dry part of the retention curve. The
parametric SPTFs gave R2 values between 0.06 and 0.36. For the
www.soils.org/publications/sssaj

Table 7. Accuracy of point and parametric spectral pedotransfer
functions (SPTFs) for predicting soil–water contents as well as van
Genuchten (VG) and Brooks-Corey (BC) parameters, using substitution of spectral reflectance based basic soil properties into thederived pedotransfer functions. Also shown are values of the coefficient of determination, R2, and root mean squared error, RMSE.†
q-15000

q-10000

q-5000q-3000R2
0.57
RMSE 0.0145

0.56
0.01450.56
0.01490.53
0.33
0.0159 0.0201

qs

aVG

nVG

q-5

q-1000

aBC

q-330

q-10

0.22
0.16
0.0230 0.0406
lBC

R2

0.20
0.23
0.13
0.36
0.06
0.34
RMSE 0.0418 0.0438 0.4272 0.0276 0.1228 0.1781† q, soil–water content at specific matric potentials [cm3 cm-3]; qs issaturated water content [cm3 cm-3]; aVGand nVG, shape parameters of
VG model; aBC and lBC, shape parameters of BC model.

shape parameters related to air-entry value (i.e., a), the RMSE
values of the SPTFs were slightly greater than those obtained by
STFs. The SPTFs performed well for the pore-size distribution
parameters nVG (with R2 equal to 0.36) and lBC (with R2
equal to 0.34). Nevertheless, the aBC and aVG parameters are
generally estimated with very comparable degree of variation to
the nVG and lBC, with only exception for aVG with the STFs
(see Tables 4, 5, and 7).
Using SPTFs it is possible to improve prediction ofproperties with poor spectral response (e.g., qs, q-5, and q-10, see
Table 4 and 7). Bulk density as the best proxy to estimate thesaturated water content and the very wet range of the soil–water
retention characteristics could be estimated well from spectralreflectance information (i.e., by SPTFs). In such case, it may bepossible to improve the accuracy of spectral predictions nearsaturation using such a two-step approach. The SPTF approach,unlike PTFs, does not require soil texture and organic matterdata directly. This can be regarded as an advantage for areas that
do not have such basic information. Besides, the SPTF approach
exploits soil spectroscopy as a cheap, rapid, and accurate providerof basic soil information, reducing the cost associated with PTF
input data capture. Including spectral information in classicalPTFs opens the pathway to use remotely sensed data in soil
hydraulic properties estimation. Using satellite imagery-based
SPTFs, like satellite imagery-based STFs, it may be possible todevelop temporally dynamic PTFs to explicitly take into accountthe effect of soil management practices (e.g., tillage) and erosion
on soil hydraulic parameter estimation.
Regression equations for water contents in the wet part of
the retention curve (between 0 and -10 cm) showed the lowest
R2 (0.16–0.23) and highest RMSE (0.0406–0.0438 cm3 cm-3)
values. The low predictability close to saturation may be becausethat input data (e.g., spectral-based estimated bulk density)
partially capture the influence of soil structure on water retention.
Compared with STFs, the indirect prediction of watercontents from spectral reflectance data (i.e., using SPTFs)
yielded worse prediction accuracy in the dry and middle parts of
the retention curve, with 9% higher RMSE and 14% lower R2.
This may be due to the inherent uncertainties associated with the
input parameters, which decrease the prediction accuracy.
∆

Table 8. Validation of the derived spectral transfer functions(STFs), spectral pedotransfer functions (SPTFs), and pedotransfer functions (PTFs) for different soil–water content prediction
approaches. Underlined values indicate the best performance foreach transfer function.†
MBE

MAE

RMSE

R2

EF

First approach (STFs)
Parametric‡
VG §-0.0025BC-0.0050
Point based fit¶
VG
0.0024BC
0.0012
Parametric
VG
BC
Point based fit
VG
BC

0.02470.02580.03500.0361

0.934
0.929

0.9196
0.91840.02270.03400.937
0.02480.03490.934
Second approach (PTFs)

0.93450.93090.01040.01040.02910.0281

0.914
0.917

0.90210.90280.00840.00810.02320.03640.932
0.02400.0368
0.930
Third approach (SPTFs)

0.92500.92330.0416
0.0414

Parametric
VG
0.0106
0.02640.03600.934
0.9267BC
0.01090.02710.03710.930
0.9221
Point based fit
VG
0.00790.02530.03500.935
0.9306
BC
0.00700.02510.03420.938
0.9335† MBE, mean bias error (cm3 cm-3); MAE, mean absolute error (cm3 cm-3);
RMSE, root mean squared error (cm3 cm-3); R2, determination coefficient (-);
EF, model efficiency (-); VG, van Genuchten model; BC, Brooks-Corey model.
‡ Parametric transfer functions using Method I.
§ Point transfer functions-based fit using Method II.
¶Refers to Babaeian et al. (2015).

Reliability of the Transfer Functions
Table 8 provides a quantitative comparison of theperformance and reliability of the different approaches forpredicting the water retention curve of the validation dataset. As
indicated, all transfer functions provided R2 and EF, greater than
0.90. The parametric STFs and SPTFs of both the VG and BC
models developed from spectral data performed similarly to theparametric PTFs in predicting the soil–water retention curve,
which validates the use of spectral data to estimate soil hydraulicproperties. Several studies have shown the potential of predictors
such as clay mineralogy and taxonomic information for accurate
prediction of soil hydraulic properties (e.g., Pachepsky andRawls, 2004) which have not yet been fully implemented
within todays PTF models. Besides, soil spectroscopy has beensuccessfully used to reflect the effects of soil minerals. Soilminerals (type, proportions and concentrations) such as ironoxides (e.g., goethite, hematite), clay minerals (e.g., kaolin,montmorillonite [smectite], illite) and carbonates (e.g., calcite,
gibbsite) ultimately determine important properties of a soil
such as texture, structure, cation exchange capacity (CEC), andspecific surface area (Ben-Dor and Banin, 1995; Stenberg et al.,2010). The STF/SPTF approaches can take into account such
attributes to provide more accurate soil hydraulic parameters inthis respect. Various studies have shown that some important∆soil properties, for example bulk density, could be obtained fromsome other basic soil attributes such as particle-size distribution
and organic carbon content (Martin et al., 2009). This may be
due to connection between bulk density and organic carbon(e.g., Rawls, 1983; Manrique and Jones, 1991; Heuscher et al.,2005), which substantially affect spectral information. Bulk
density, as a proxy for soil structure, is a good predictor for thesaturated water content as shown in many PTFs and soil studies(e.g., Vereecken et al., 1989; Schaap et al., 1998).
The good performance of spectral based transfer functions may
also be due to the sensitivity of Vis-NIR-SWIR to many organicand inorganic components affecting soil hydraulic properties andproviding accurate predictions of soil–water retention. A majoradvantage of spectral data for soil analysis is that from a single
spectrum many properties may be accurately determined, thus
offering the possibility for considerable cost savings and increased
efficiency over conventional laboratory analysis.
As given in Table 8, the best predictions were obtained withthe fit of the retention models to water contents estimated withpoint transfer functions (i.e., using Method II). We furthermore
compared measured soil–water contents with values predictedwith the three approaches using Methods I and II for the entire
water retention curve. Results are displayed in Fig. 4 and 5
for the VG model and BC model, respectively. The validationof the transfer functions yielded comparable results to theirrespective calibration performance. All transfer functions for
the VG and BC models provided reasonable accuracy in the
mid and dry parts of the retention curve for both calibration(Fig. 4a, 4b, 5a, and 5b) and validation (Fig. 4c, 4d, 5c, and 5d)sets, while relatively poor predictions were obtained at highmatric potentials, which are a lot more scattered around the
1:1 diagonal. Using the VG model and at the wet end (pF £1), the SPTFs (with RMSE = 0.0520 and 0.0527 for Methods
I and II, respectively), the STFs (with RMSE = 0.0550 and
0.0548 for Methods I and II, respectively) and the PTFs (withRMSE = 0.0606 and 0.0583 for Methods I and II, respectively)
performed similarly in terms of RMSE (see Table 9). Using the
BC model and at pF £ 1, the highest (0.0642, Method I) andlowest (0.0518, Method II) RMSE values were produced by the
PTFs and SPTFs, respectively. Similar results were obtained at
the dry end (pF~4.2) (Fig. 4c-d, see Table 9). The BC model
was found to perform equally well in some cases, and the best
performances at the dry end (pF~4.2) were obtained with the
PTFs and STFs, followed by the SPTFs. RMSE values for pF£ 1 were, on average, 3.9 times greater than for pF~4.2, whichraises concerns about predicting the wet range and the precise
determination of soil–water content at matric potentials close
to saturation (Vereecken et al., 2010).
Overall, all transfer functions slightly overestimated thewater contents, particularly in the wet range (i.e., pF £ 1, with
MBE 0.0017 for STFs, 0.0138 for SPTFs, and 0.0234 for PTFs)
of the retention curve (data not shown). Using the VG model,
the MBE varied between -0.0025 and 0.0106, with the largest
value being for the parametric SPTF (Method I) and the smallest
Soil Science Society of America Journal

one for the STFs (Method II). Evaluation of the
MBE for the BC model showed similar results
to the VG model (ranged from -0.0025 to
0.0106), with a large MBE equal to 0.0109 forparametric SPTFs and a slight decrease (MBE
= 0.0012) for STFs (method II) (see Table 8).

CONCLUSIONSIn this paper we used three different
approaches to derive point and parametrictransfer functions from spectral data in the VisNIR-SWIR region and basic soil properties.
Using stepwise multiple linear regression
coupled with bootstrapping, we derived andevaluated three types of point and parametrictransfer functions:(i) STFs, (ii) PTFs, and (iii)
SPTFs which respectively used spectral data,
basic soil properties and spectral based basic
soil predictions as their inputs. We further
evaluated a fit of the VG and BC retention
models to the predicted water contents
obtained with each approach.
Soil–water contents, the VG and BC Fig. 4. Scatter plots of observed versus predicted water contents at matric potentials of 0,
parameters as well as basic soil properties -5, -10, -330, -1000, -3000, -5000, -10000 and -15000 cm (all together) usingparametric (left) and point (right) transfer function for the van Genuchten retention model
showed significant (p < 0.01) correlation with as applied to the calibration (top) and validation (bottom) sets. The solid lines indicate 1:1
spectral reflectance values, especially for the diagonals. The “parametric STFs” originated from Babaeian et al. (2015).
SWIR region. The point STFs and SPTFs
performed similarly to the point PTFs interms of R2 and RMSE in estimating watercontents in the mid and dry parts of theretention curve. In the wet range, PTFs were
found to perform better than the other two
approaches. Compared to the STFs, however,
better water content estimates were obtainedusing the SPTFs in the wet range.
For the VG and BC shape parameters
related to air entry value (i.e., aVG andaBC), the best estimations were obtained by
the STFs, followed by SPTFs and PTFs that
performed similarly to each other. However,for the parameters that reflect the pore-size
distribution (i.e., nVG and lBC), the PTFs
performed better, followed by the STFs.
The parametric STFs and SPTFs(Method I) of both the VG and BC models
developed from spectral data performed
similar to parametric PTFs for the retention
curve. This conclusion is important in thatit indicates the feasibility of using spectral
data to predict hydraulic properties. The Fig. 5. Scatter plots of observed versus predicted water contents at matric potentials of 0, -5,
best predictions were obtained with a fit of -10, -330, -1000, -3000, -5000, -10000 and -15000 cm (all together) using parametric
the retention models to soil–water contents (left) and point (right) transfer function for the Brooks-Corey retention model as applied tothe calibration (top) and validation (bottom) sets. The solid lines indicate 1:1 diagonals. The
estimated with point transfer functions “parametric STFs” originated from Babaeian et al. (2015).
(Method II).
www.soils.org/publications/sssaj∆

Table 9. Validation of different approaches and methods at the wet
and dry ends of the soil–water retention curve in terms of RMSE.
pF £ 1

pF~4.2First approach (STFs)
Parametric†
VG‡
BC
Point based fit§
VG
BC

0.05500.05370.01450.01580.05480.05540.01250.0140

Second approach (PTFs)
Parametric
VG
BC
Point based fit
VG
BC

0.0606
0.06420.01410.01250.05830.0593
Third approach (SPTFs)

0.01140.0153

Parametric
VG
0.0520BC
0.0551
Point based fit
VG
0.0527BC
0.0518† Method I.
‡ Refers to Babaeian et al. (2015)§ Method II

0.01540.01700.01510.0165

Our findings suggest that spectral information, as apromising approach, may be used to predict soil–water contents,
and indirectly the water retention curve. Our results are basedon a relatively local database from Iran. More variability inthe basic soil properties could affect the performance of thepresented relationships, and thus a definite need exists toevaluate the derived transfer functions on soils from otherregions. Despite the geographic restriction of the presented
STFs/SPTFs, the method we have developed can serve as a guidefor future enhancements of such functions. Reflectance of a soil
is a dynamic soil property that can undergo rapid changes due tochange in soil composition, soil erosion, and biological processes.
Using spectral data as an input of PTFs offers a way of including
this temporal dynamic soil property in soil–water retention
predictions. Further research could focus on evaluating spectralbased transfer functions for different soils in other regions, as wellas improvement in the predictions near saturation by including
the effect of structure in the predictive models. A topic of further
research is the potential of STFs/SPTFs to retrieve soil hydraulicparameters at large scale and further investigation through airborne/space-borne hyperspectral remote sensing.

ACKNOWLEDGMENTS

This research was funded by Tarbiat Modares University, Iran.
Ebrahim Babaeian is grateful for support from the Research Center
Jülich, Agrosphere Institute (IBG-3), Germany. The authors are reallygrateful to the associate editor, and the two anonymous reviewers fortheir constructive and insightful comments, which led to a significant
improvement of this paper.

∆

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