Remote Sensing of Environment 187 (2016) 218–229

Contents lists available at ScienceDirect

Remote Sensing of Environment
journal homepage: www.elsevier.com/locate/rse

Soil moisture prediction of bare soil proﬁles using diffuse spectral
reﬂectance information and vadose zone ﬂow modeling
E. Babaeian a,1, M. Homaee a,⁎, C. Montzka b, H. Vereecken b, A.A. Norouzi c, M. Th. van Genuchten d,ea

Department of Soil Science, Tarbiat Modares University, Tehran 14115-336, IranInstitutes of Bio- and Geosphere: Agrosphere (IBG-3), Forschungszentrum Jülich GmbH, 52425 Jülich, Germany
Soil Conservation and Watershed Management Research Institute (SCWMRI), Tehran, Irand
Department of Mechanical Engineering, COPPE/LTTC, Federal University of Rio de Janeiro, Rio de Janeiro, RJ 21945-970, BrazileDepartment of Earth Sciences, Utrecht University, Utrecht, Netherlandsbca r t i c l e

i n f oArticle history:
Received 23 August 2015
Received in revised form 3 October 2016
Accepted 12 October 2016
Available online xxxx
Keywords:
Soil moisture
ASAR
Spectral reﬂectance
Soil hydraulic properties
Spectral transfer functionsa b s t r a c t
Soil hydraulic property information of the vadose zone is key to quantifying the temporal and spatial variability ofsoil moisture, and for modeling water ﬂow and contaminant transport processes in the near surface. This study
deals with exploring the feasibility of using diffuse soil spectral information in the visible, near-infrared andshortwave infrared range (350–2500 nm) to estimate coarse-scale soil hydraulic parameters and predict soil
moisture proﬁles using a topography-based aggregation scheme in conjunction with a 1D mechanistic waterﬂow model. Three different types of parametric transfer functions (so-called spectrotransfer functions, STFs;
pedotransfer functions, PTFs; and spectral pedotransfer functions, SPTFs) were aggregated from the point scale
to 1 km2 pixel size. to provide coarse scale estimates of van Genuchten-Mualem (VGM) hydraulic parameters.
The coarse scale hydraulic parameters were evaluated by simulating soil water dynamics of the 1 km2 pixels
across the Zanjanrood River sub-watershed (ZRS) in northwest Iran. Resultant soil water states were comparedwith ground-truth measurements and advanced synthetic aperture radar (ASAR) estimates of soil water content.
The topography-based aggregation scheme was found to provide effective values of the VGM hydraulic parameters across the ZRS study site. The coarse scale STFs performed best in terms of simulating surface, near-surface
and subsurface soil water dynamics, followed by the coarse scale SPTFs and PTFs, which performed similarly.
The average simulated soil water contents of the surface layer closely correlated with ASAR estimates during relatively wet periods. Simulated subsurface soil water dynamics matched well with the ground-truth measurements. These ﬁndings indicate the feasibility of using spectral data to predict VGM hydraulic parameters and,ultimately, to predict soil water dynamics at the larger scales.
© 2016 Elsevier Inc. All rights reserved.

1. Introduction
Proﬁle soil moisture, as a key dynamic state variable, plays a central
role in weather and climate predictions from the regional to the global
scale by controlling the exchange and partitioning of water and energy
ﬂuxes between the land surface and the atmosphere (Vereecken et al.,2008; Kornelsen and Coulibaly, 2014). Accurate knowledge of proﬁlesoil moisture at various spatial and temporal scales is also importantfor strategic management of water resources (Vereecken et al., 2016).
Soil moisture status and ﬂuxes vary considerably in both space andtime due to inherent variations in the soil hydraulic properties(Montzka et al., 2011), precipitation rates (Koster et al., 2004;⁎ Corresponding author.
E-mail address: mhomaee@modares.ac.ir (M. Homaee).
1
Present address: Soil, Water, and Environmental Science Department, The Universityof Arizona, Tucson, AZ 85721, USA.

http://dx.doi.org/10.1016/j.rse.2016.10.029
0034-4257/© 2016 Elsevier Inc. All rights reserved.

Rosenbaum et al., 2012), topographic features (Joshi and Mohanty,
2010; Jana and Mohanty, 2012b; Schröter et al., 2015), and vegetation
characteristics (Famiglietti et al., 1998; Guar and Mohanty, 2013).
A range of in-situ and remote soil water sensing techniques havebeen developed, tested, and used with varying levels of success during
the past several decades (Vereecken et al., 2014). In-situ techniques
are generally conﬁned to short-term ﬁeld experiments or point-scalesensor installations that are representative over a relatively small spatial
scales since soil water is subject to considerable spatial heterogeneity(Greifeneder et al., 2016). Indirect estimates of soil moisture can be obtained using active (Ulaby et al., 1996; Baghdadi et al., 2012; Jagdhuber
et al., 2013; Kornelsen and Coulibaly, 2013) and passive (Jonard et al.,2011; Montzka et al., 2013; Dimitrov et al., 2014, 2015) microwave remote sensors that have had the greatest success in estimating soil moisture in a spatially and temporally consistent behavior. These methods
provide surface soil moisture estimates of only the top few centimeters(0–5 cm) of a soil proﬁle (Kerr, 2007). The somewhat low spatial

E. Babaeian et al. / Remote Sensing of Environment 187 (2016) 218–229

resolution (several tens of kilometers) of passive microwave measurements has prompted research on downscaling to expand applicability(Pellenq et al., 2003; Merlin et al., 2008). However, non-invasive geophysical methods, such as ground penetrating radar (GPR)(Weihermuller et al., 2007; Jonard et al., 2011), electromagnetic induction (EMI) (Robinson et al., 2012), and electrical resistivity tomography(ERT) (Vanderborght et al., 2013), have been used to bridge the gap between point and satellite measurements of soil moisture.
Soil-vegetation-atmosphere-transfer (SVAT) models are commonlyused to numerically simulate state variables such as soil moisture, as
well as for estimating energy-mass exchange ﬂuxes. The performanceof SVAT models is usually conﬁned by uncertainty of the driving forces
and its parameters. While soil hydraulic properties are very importantin distributed SVAT models, they are mostly observed only at the
point scale or generalized to soil maps. A major challenge when runningthese models at a larger scale is obtaining accurate model inputs andphysically realistic hydraulic parameter values. Aggregation of soil hydraulic properties from ﬁeld to watershed or regional scales is criticalfor SVAT model performance at these scales (Zhu and Mohanty,
2002a, 2002b; Vereecken et al., 2007; Jana and Mohanty, 2012a,
2012b, 2012c; Vereecken et al., 2016). Hence, a need exists for upscaling
schemes that enable one to convert point scale data to much larger
extents.
Coarse scale characteristics of the soil hydraulic parameters aregoverned predominantly by soil texture and structure (especially at
the ﬁeld scale), and topography (especially at watershed scales and beyond) (Jana, 2010). Topography plays a key role in soil classiﬁcation.
Several studies have shown that topography-based scaling algorithms
are able to capture much of the variations in soil hydraulic parameters
required to generate equivalent ﬂows and soil moisture states in acoarsened domain (Wilson et al., 2004; Jana and Mohanty, 2012a,
2012b).
Practical methods for estimating soil moisture continuously overtime and relatively large spatial areas likely involve a combination of remote sensing and modeling (Entekhabi et al., 1999; Vereecken et al.,2014). Recent studies have demonstrated that proﬁle soil moisture
could be estimated well by assimilation of remotely sensed surface
soil moisture data into a hydrological model (Das et al., 2008a; Ines
and Mohanty, 2008a, 2009; Montzka et al., 2011; Han et al., 2013,2014; De Lannoy and Reichle, 2016; Vereecken et al., 2016). Despite
the important role of surface and subsurface soil moisture in hydrological and meteorological predictions, detailed spatial and temporalmodeling of proﬁle soil moisture at the large scale is often still lacking.
During the past few decades, visible, near-infrared and shortwave
infrared (Vis-NIR-SWIR) reﬂectance spectroscopy has been shown tobe an effective alternative to conventional in-situ or laboratory methods
for providing rapid, noninvasive and cost-effective estimates of a wide
range of soil properties. Many studies have shown the capability of laboratory scale Vis-NIR-SWIR (400–2500 nm) spectrometry to accurately
estimate basic soil properties such as the soil particle size distribution,organic carbon content, water content, and clay mineralogy (Gomez etal., 2008; Lopez et al., 2013; Minasny et al., 2008, among many others).
These properties are at the same time key input parameters for many
pedotransfer functions (PTFs) for estimating the unsaturated soil hydraulic properties (Vereecken et al., 2010). Despite extensive literature
on predictions of basic soil properties from Vis-NIR-SWIR data, more research is needed to more directly and reliably estimate the soil hydraulic properties. A few studies recently analyzed the potential of soil
spectral information in the Vis-NIR-SWIR region to estimate soil hydraulic properties using point (Janik et al., 2007; Minasny et al., 2008;
Lagacherie et al., 2008; Babaeian et al., 2015b) and parametric (Santra
et al., 2009; Babaeian et al., 2015b) transfer functions. These studies provided soil hydraulic parameters at point scale. While some scale mismatch between mostly point measurements of the soil hydraulicparameters and hydrological models appears to be unavoidable, a better
understanding of the required upscaling process is very much needed.

219

While the advantages of PTFs have been demonstrated for quantifying soil hydraulic properties (e.g., Vereecken et al., 1989; Schaap et al.,
2001; Homaee and Farrokhian Firouzi, 2008; Ghorbani Dashtaki et al.,2010; Khodaverdiloo et al., 2011), they are rarely implemented in hydrologic models where a broad deﬁnition and application of soil types
still dominate simulations of soil moisture. Parametric PTFs provide
soil hydraulic parameters that could be used directly in hydrologicalmodels. Guber et al. (2009) compared a number of published PTFs andthe HYDRUS-1D model (Šimůnek et al., 2005) to simulate water ﬂow
in a soil proﬁle.
The spectral behavior of a soil is a dynamic soil property that can undergo rapid changes because of changes in soil composition due to, forexample, agricultural activities, soil erosion and biological processes.
Using spectral data as PTF input provides an effective way of including
the temporal processes in hydrological models. Babaeian et al. (2015a,
2015b) recently derived and validated the accuracy of spectrotransfer
functions (STFs) and spectral pedotransfer functions (SPTFs) to predictthe unsaturated soil hydraulic properties. STFs relate the hydraulicproperties directly with spectral reﬂectance parameters, while SPTFs
use additional basic soil data such as the particle size distribution andbulk density.
In this paper we present a study to test the effectiveness and robustness of coarse-scale derived parametric PTFs, STFs, and SPTFs by studying surface, near-surface and subsurface soil water dynamics in a semiarid region, the Zanjanrood River sub-watershed (ZRS), in northwestern
Iran. The accuracy of simulated surface soil water states is tested against
estimates from microwave satellite imagery. Our primary objective wasto assess coarse scale values of the van Genuchten-Mualem soil hydraulic parameters (van Genuchten, 1980) to simulate surface, near-surface
and subsurface soil water dynamics at the 1 km × 1 km domain/pixel
size, while incorporating the inﬂuence of the local topography into theaggregation algorithm. Reference soil water states for comparison
were obtained from the advanced synthetic aperture radar (ASAR)
through the IEM algorithm developed by Rahman et al. (2008). Ourﬁndings will help to assess the value of air- and space-borne
hyperspectral data for studying the spatio-temporal dynamics of proﬁlesoil water contents.
2. Materials and methods
2.1. Study area
The Zanjanrood River sub-watershed (ZRS), located in the northwestern part of Iran, was selected as the test area for our study. TheZRS area of approximately 250 km2 was chosen for its variety in terrain
and land use characteristics, soil type and soil distribution patterns(Fig. 1). The topography consists of level to slightly undulating slopes
varying approximately from 0 to 4%, with elevations ranging fromapproximately 1380 to 2160 m above mean sea level. The climate issemi-arid, with an average annual precipitation of 320 mm. The maximum (43 °C) and minimum (−30 °C) yearly temperatures occur in August and January, respectively, while the average yearly temperature isabout 11 °C. Soil texture varies from clay to sandy loam, with the majority of soils classiﬁed as clay loam and loam. Rain-fed agriculture with aland cover of wheat (75%) and poor rangeland (25%) dominate landuse in the area. Using Arc GIS FishNet tool (ESRI), the entire ZRS was divided into a grid of 1 km × 1 km pixels to match the ASAR (global mode)
pixels. We selected 20 pixels across the study area for analysis so thatthey represent different locations, soil types, topographies and land
uses (see Fig. 1). A summary of various geophysical attributes of the selected pixels are given in Table 1.
2.2. Numerical simulations
The HYDRUS-1D software package was used to simulate verticalwater ﬂow in the soil domains (Šimůnek et al., 2005). HYDRUS-1D

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E. Babaeian et al. / Remote Sensing of Environment 187 (2016) 218–229

Fig. 1. Figure showing the Zanjanrood River sub-watershed (ZRS) study area, including locations of the sampling points, selected pixels, and the meteorological station (a), the soil type (b),and land-use (c) maps.

uses the Richard's equation to simulate unsaturated ﬂow, while incorporating a general sink term to account for root water uptake as follows:


∂θðhÞ
∂
∂h
¼
K ðhÞ −K ðhÞ −S
∂t
∂z
∂z

For the soil hydraulic properties (θ(h) and K(h)) in Eq. (1), we used
the original van Genuchten-Mualem (VGM) expressions as derived by
van Genuchten (1980):

ð1Þ
Se ¼

where θ is the soil water content [cm3 cm−3], h is the soil water pressure
head [cm], zis soil depth [cm], t is time [d], K is the hydraulic conductivity [cm d−1], and S is the sink term [d−1] (i.e., root water uptake).

θðhÞ−θr 
n −m¼ 1 þ jαhj
θs −θrK ðhÞ ¼ K s

ð2Þ


m i2
pﬃﬃﬃﬃﬃh
Se 1− 1−S1=með3ÞTable 1Land-use, average elevation, average slope, and soil texture classes of the selected ZRS pixels.

Pixel 1
Pixel 2
Pixel 3
Pixel 4
Pixel 5
Pixel 6
Pixel 7
Pixel 8
Pixel 9Pixel 10
Pixel 11
Pixel 12
Pixel 13
Pixel 14
Pixel 15
Pixel 16
Pixel 17
Pixel 18
Pixel 19
Pixel 20

Dominant land-use

Average elevation (m)Average slope (%)

Dominant soil type

Rangeland
Agriculture
Agriculture
Agriculture
Agriculture
Agriculture
Agriculture
Agriculture
Agriculture
Rangeland
Agriculture
Agriculture
Agriculture
Agriculture
Agriculture
Agriculture
Rangeland
Rangeland
Rangeland
Rangeland

1529
1682
1671
1719
1691
1779
1826
1846
1832
1577
1612
1660
1752
1770
1771
1859
1589
1536
1632
1540

1.81
1.94
1.85
2.28
1.95
3.04
3.56
4.16
3.40
2.13
1.93
1.75
2.50
2.70
2.30
3.15
2.30
2.18
2.38
1.92

Clay loam
Clay loam
Clay loam
Clay loam
Clay loam
Clay loam
Clay loam
Clay loam
Clay loam
Loam
Loam
Loam
Loam
Loam
Loam
Loam
Sandy loam
Sandy loam
Sandy loam
Sandy clay loam

Spring wheat is the dominant agriculture in the region

E. Babaeian et al. / Remote Sensing of Environment 187 (2016) 218–229

Evaporation

Precipitation

1 km
Flow ~ 0
1 km

Upward flux

Downward flux

Soil depth: 100 cm

Free drainage
Fig. 2. A pixel-scale non-interacting and homogeneous soil proﬁle used for the numericalexperiment across the study area.

where θr and θs are the residual and saturated water contents, respectively [cm3 cm−3], α is an empirical shape parameter approximately
equivalent to the inverse of the air entry value [cm−1], n is a pore size
distribution parameter [], and m = 1–1/n.
The numerical simulations were performed for all the 20 selected
pixels of 100-cm deep soil proﬁles, where each pixel assumed to be representative of each 1 km2 pixel. We did not employ numerical simulations for the rest of the study area, because these 20 pixels wereselected based on different locations, soil types, topographies and land
uses and thus can be considered as an indicator of the whole study
area. We used a non-interacting and homogeneous soil column

221

approach (Vereecken et al., 2007) in which the soil hydraulic properties
did not vary with depth (Fig. 2). The choice of uniform soils with depth
is justiﬁed by the fact that the horizontal extent of the study domain(comprised of 1 km × 1 km pixels) was much greater than the vertical
proﬁle (with 100-cm depth). We hence assumed that the effects ofchanges in the soil properties versus depth due to layering close to thesoil surface are relatively minor in the overall aggregation scheme.
The 100-cm deep soil proﬁles were discretized into 200 non-equidistant ﬁnite elements having a size of 0.5 mm at the soil surface anda size of 35 mm at the lower boundary (Scharnagl et al., 2011). Atmospheric time-dependent boundary conditions and a free drainage condition (∂h/∂z = 0) were imposed at the upper and lower boundaries ofthe soil proﬁles. As initial condition we assumed a linearly decreasingwater content from 0.4 cm3 cm−3 at the soil surface to 0.2 cm3 cm−3
at the bottom of the proﬁle (Montzka et al., 2011). A 30-day spin-up
time period was used to allow the assumed initial soil water distribution
in each of the 20 pixels to align with the local weather conditions. After
employing the aggregation scheme and providing coarse scale soil hydraulic parameters, each pixel area was considered ﬂat from a run-off/
run-on perspective, thus assuming that water ﬂow only occurred in
the vertical direction.
Aggregated effective VGM parameters (see Section 2.3) wereassigned to each selected coarse pixel. Wheat crops, being the dominant
vegetation cover in the study area, are commonly planted in the end of
March (DOY–90). Hence, we neglected transpiration and root water uptake processes due to sparsely vegetation cover, and only considered
evaporation. The Penman-Monteith approach, as implemented in
HYDRUS-1D, was used to estimate potential soil evaporation rates
based on atmospheric forcing data from the meteorological station in
the region (Šimůnek et al., 2008). We simulated a period of 100-days,
starting on January 1, 2012, with a temporal resolution of one day inthe precipitation/potential evaporation data. Fig. 3 demonstrates thereference potential evapotranspiration (ET) and precipitation patterns
during the study period.
2.3. Aggregation algorithm
The power average operator (PAO), a topography-based aggregation
algorithm as described by Yager (2001), was used in this study to coarsen the measured and retrieved VGM soil hydraulic parameters. The PAO
approach combines two aggregation methods, a mode-like method andFig. 3. Time series of the precipitation and evapotranspiration (left), air (min., max., mean) and soil (mean) temperature (right) forcing data from the meteorological station time starting
January 2012.

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E. Babaeian et al. / Remote Sensing of Environment 187 (2016) 218–229

a mean type aggregation, to provide a very useful tool for coarse scalesoil hydraulic parameters. In the mode-like method, the emphasis is
on ﬁnding the most probable value of a parameter from a given set,
while in mean-type aggregation the aim is to ﬁnd the mean value ofthe given set. The PAO is deﬁned as:XnP ðp1 ; p2 ; …; pn Þ ¼ Xi¼1n

½1 þ T ðpi Þpi

ð4Þ

½1 þ T ðpi Þi¼1hRMS =Lc ¼ g ðΔσ ∘ Þ2ð9ÞUsing the backscatter coefﬁcient obtained for dry surface conditions(σ∘dry), it is possible to derive both hRMS and Lc as follows:σ ∘dry ¼ hðhRMS ; Lc Þ

ð10Þ

Using Eqs. (9) and (10), and substituting terms, it is possible to solve
for the two roughness parameters, hRMS and Lc, to obtainin which
T ðpi Þ ¼

proportional to the ratio of hRMS and Lc:

n
X



Sup pi ; p j

ð5Þ

i¼1
j≠i



Lc ¼ ω Δσ ∘ ; σ ∘dry

ð11Þ



hRMS ¼ ϕ Δσ ∘ ; σ ∘dry

ð12Þ

where P⁎ is the power average of parameter values p1,p2, …,pn, Sup(pi,pj) is the support of pi from pj in which Sup(pi, pj)∈[0.1]. A generalform of the support equation is

The resulting roughness parameters are used to parameterize the
IEM model and to retrieve the soil water content. The values of theroughness parameters can be then substituted in Eq. (9):
2Sup pi ; p j ¼ e−ηðpi −p j Þσ ∘moist ¼ λ Δσ ∘ ; σ ∘dry ; θð6Þwhich can be inverted to obtain the soil water content:

where



θ ¼ λ−1 Δσ ∘ ; σ ∘dry ; σ ∘moist

rﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ
ﬃ


η¼

z jmax −z jminzi −z j2

xi −x j2

þ yi −y j2þ zi −z j

S

ð14Þ

2

ð7Þ

where η is the scale factor (η ≥ 0)), x, y and z are the Cartesian coordinates of the point, and S is the scale (resolution) to which the hydraulicparameters are being aggregated (i.e., 1 km). In nature scale factor canbe affected by many factors such as variation in atmospheric parameters, vegetation cover, soil type, distance between observations and topography. Here we constrained the other factors and considered η as afunction of difference in topography (elevation) and distance between
sampling points.
A more detailed description of the PAO is provided by Jana andMohanty (2012a, 2012b). The PAO was used separately for providing
coarse scale VGM hydraulic parameters (pi) so that aggregated values(estimated/measured parameters) were obtained using the difference
in distance (horizontal and vertical) between the sampling points andtheir values. The elevation data were used to determine vertical distance between the sample points.
2.4. Radar model and soil water content retrieval
The Integral Equation Model (IEM) is a widely used analytical andphysically based radar backscatter model developed for bare soils(Zribi and Dechambre, 2002; Rahman et al., 2008). In general, IEM
quantiﬁes the backscattering coefﬁcient as a function of soil water content and surface roughness, which are unknown, and the radar conﬁguration:σ ∘ ¼ f ðhRMS ; Lc ; θÞ

ð13Þ

ð8Þ

where σ∘ is the backscattering coefﬁcient [decibel, dB], hRMS is the root
mean squared height variation of the surface at the centimeter scale[cm], Lc is the correlation length of the height variation, and θ is thesoil water content as before.
Zribi and Dechambre (2002) indicated that differences in the backscatter coefﬁcient, Δσ∘, generated with the IEM model using two different incidence angles while keeping all other parameters constant, is
proportional to the surface roughness only. They also found that Δσ∘ is

We used the method developed by Rahman et al. (2008) to provide
estimates of roughness parameters (hRMS, Lc) from multi-angle radar
images at two incidence angles from two dry images in August and September 2011. Dry backscatter coefﬁcient (σ∘dry) was also obtained from
ASAR images in this two dates. We used Next ESA SAR Toolbox(NEST) software (https://earth.esa.int/web/nest) for computing backscatter coefﬁcients.
2.5. Data collection and analysis
Basic soil attributes (i.e., clay content, silt content, sand content, bulk
density, organic carbon content and geometric mean of the soil particle
diameter) and VGM hydraulic parameters (i.e., θr, θs, α, n and Ks) of the
ZRS study area were obtained for 174 soil samples (point scale with average distance about 1.5 km) collected from the study area using a combination of relatively standard ﬁeld soil sampling procedures andlaboratory measurements (Dane and Topp, 2002). The saturated hydraulic conductivity was measured using constant- and falling-head
methods in the laboratory. Gravimetric water contents were measured
at nine matric potentials (i.e., 0, − 5, − 10, − 330, − 1000, − 3000,− 5000, − 10,000, and − 15,000 cm) of the water retention curveusing sand-box apparatus and pressure plate extractor methods in thelaboratory (Vereecken et al., 2010). Using nonlinear least-squares optimization, the retention models were ﬁtted to the measured soil–watercontent values to obtain the hydraulic parameters (see also Babaeian
et al., 2015a, 2015b for more details). These laboratory-based hydraulicparameters were considered as observed VGM parameters.
Using these basic soil properties and laboratory-measured spectral
reﬂectance data in the visible, near-infrared and shortwave-infrared region (350–2500 nm), three different types of parametric transfer functions were developed to provide estimated sets of hydraulicparameters. The transfer functions included spectral transfer functions(STFs), pedotransfer function (PTFs) and spectral pedotransfer functions (SPTFs). A detailed description of how the soil spectral data were
processed and used to derive the transfer functions is given by
Babaeian et al. (2015b).
The PAO aggregation scheme was subsequently used to aggregate i)estimated VGM parameters from the transfer functions, and ii) observed

E. Babaeian et al. / Remote Sensing of Environment 187 (2016) 218–229

VGM parameters from the laboratory so that they could be used to simulate soil water dynamics at the pixel scale (1 km × 1 km). The soil proﬁle for this purpose was divided into three layers: 0 to 5, 5 to 10, and 10
to 30 cm. The three parameters α, n and θs in Eq. [2] and the one additional parameter Ks in Eq. [3], were estimated for each layer using thederived parametric STFs, PTFs and SPTFs proposed by Babaeian et al.
(2015b). Brieﬂy, the parametric STFs, PTFs and SPTFs are simple linear
regression equations which use spectral data, basic soil properties andspectral based basic soil predictions, respectively, as their inputs to estimate VGM parameters. In-situ soil water content data (n = 15) of thebare proﬁles were collected using time domain reﬂectometry (TDR)
method (Topp et al., 1980) at ﬁve different times and at two depths (z– 0–10 cm, z – 30 cm) along transects within one ﬁeld site (with area
~ 1 km2) close to the meteorological station (Fig. 1). Elevation data
were provided at a 30 m resolution. Meteorological data (e.g., daily precipitation, maximum and minimum temperature, relative humidity,
wind speed and solar radiation) were obtained from a meteorologicalstation located north of the study area (Fig. 1) for the months of January
through March 2012. Time series of daily average precipitation andevapotranspiration are shown in Fig. 3. As can be seen, relatively wet
and dry periods alternated during the study period.
Using ENVISAT/ASAR active microwave data (C-band, Global Modewith a resolution of 1 km × 1 km, ascending pass) and the inversion algorithm of IEM, surface soil water contents were retrieved for 13 days ofthe year 2012. The sensor measured the total soil backscatter at pixels of
1 km × 1 km, as stated earlier, which were then used to provide soil
water estimates. Surface roughness values needed for the IEM model
were derived from a set of two ASAR images at dry soil conditions, covering the study area at different view angles (Verhoest et al., 2008). In
order to validate the estimates, we used measured surface soil watercontents at the ﬁeld scale. ASAR-based surface soil water contents within the study area, valid for the top centimeter of the soil (Mohanty et al.,2013; Adams et al., 2013), were considered as a basis to evaluate simulated surface soil water contents obtained with HYDRUS-1D. We used
the mean error (ME), the root mean squared error (RMSE) andPearson's correlation coefﬁcient (r) of the simulated and measured

223

values to evaluate the accuracy of our numerical experiments and theperformance of the coarse scale transfer functions (Zarei et al., 2010):
ME ¼

N
1X
ðSi −M i Þ
N i¼1

vﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ
u N
u1 X
ðS −M i Þ2
RMSE ¼ t
N i¼1 iXN Si −S Mi −M
i¼1r ¼ rﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ
2 XN
XN 
2
Si −S
Mi −M
i¼1
i¼1

ð15Þ

ð16Þ

ð17Þ

where Si and Mi denote the ith simulated (estimated) and measured
values, S and M are means of simulations (estimations) and measured
values respectively, N is the number of data pairs consisting of Si and
Mi. Also, we added the p value (1 and 5%) of the correlations.
3. Results and discussion
3.1. Accuracy of coarse scale transfer functions for the VGM hydraulicparameters
In this section we show the performance of the PAO scheme in termsof coarse scale soil hydraulic parameters and providing effective valuesof the VGM parameters. Fig. 4 shows a comparison between observed
and estimated VGM hydraulic parameters that were aggregated using
the PAO scaling scheme from the ﬁne scale to the 1 km2 coarse resolution for the 20 selected pixels (1 km × 1 km) within the study area. As
can be seen, the coarse scale estimates for each parameter are slightly
different from the coarse scale observations. Relatively large differenceswere observed for the saturated water content, θs (Fig. 4a). The coarse
scale transfer functions (estimated VGM parameters) showed a similar
and very close trend with the observed values of α, n and lnKs acrossFig. 4. Aggregated values of the estimated and observed VGM hydraulic parameters for 20 pixels across the ZRS.

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Table 2Comparison between coarse-scale estimated and observed VGM hydraulic parametersacross all selected pixels of the ZRS.
Coarse scale θs[cm3cm−3]
r
STFs
PTFs
SPTFs

RMSE

α[cm−1]r

0.321 0.0294 0.648
0.554b 0.0427 0.309
0.123 0.0374 0.366

RMSEb

lnKs[cm ⋅ d−1]

n[−]
r

RMSE

r

b

RMSE
b

0.0545 0.703 0.0148 0.863 0.2471
0.0676 0.655b 0.0137 0.555a 0.3678
0.0656 0.659b 0.0139 0.681b 0.3774

r and RMSERMSE are correlation coefﬁcient and root mean squared error, respectively. Superscripts ‘a’ and ‘b’ represent signiﬁcance at the 0.05 and 0.01 levels, respectively.

all pixels (Figs 4b, d). The coarse scale transfer functions overestimatedθs for most of the pixels, with the largest value being for the PTFs (ME =0.034) and the smallest one for the STFs (ME = 0.005). The coarse scaletransfer functions slightly underestimated α, n and lnKs of most pixels,
with ln(Ks) having the largest ME values (− 0.066, − 0.064 and− 0.013 for the PTFs, SPTFs and STFs, respectively), and n having
smallest ME values (ME = −0.007, −0.003 and −0.003 for the STFs,
PTFs and SPTFs, respectively).
Table 2 provides a comparison between VGM parameters from thecoarse scale transfer functions and those obtained from coarsening theobserved values, in terms of Pearson's correlation coefﬁcient (r) and
RMSE information for providing effective VGM parameters. As indicated, coarse scale STFs performed the best for parameters α (r = 0.648,
p b 0.01, and RMSE = 0.0545), n (r = 0.703, p b 0.01, and RMSE =0.0148) and lnKs (r = 0.863, p b 0.01, and RMSE = 0.2471), followedby the coarse scale SPTFs. By comparison, the r values for θs were quite
low (r b 0.55). The coarse scale PTFs performed best for θs, having r
and RMSE values equal to 0.554 (p b 0.01) and 0.0427, respectively.
Overall, the strong and signiﬁcant correlations between the coarsescale estimated and observed VGM parameters are indications that the
PAO scheme used to aggregate the ﬁne scale soil hydraulic parameters
is providing an appropriate set of VGM hydraulic parameters at thecoarse scale.
3.2. Coarse scale transfer functions and soil water dynamics
The temporal dynamics of soil water contents of the selected pixels
at three soil depths as simulated using the three sets of coarse scaletransfer functions are shown in Figs. 5, 6 and 7, along with the observed

values (using measured VGM parameters) and ASAR estimates. The
three curves in each plot represent daily model outputs of the watercontent using the coarse scale led transfer functions. Two additional
curves show the ﬁne- and coarse-scale daily outputs when observed
VGM parameters were used in the forward run. Ground-truth measurements of soil water and ASAR estimates are marked by symbols. As expected, the surface soil (z – 0–1 cm) exhibited more variations in the soil
water contents (range between 0.10 and 0.45 cm3 cm−3) than the othertwo depths where the variations are gradually weakened (Figs. 6 and 7).
Results indicate that at the beginning of the simulated period, due toseveral precipitation events, the surface layer nearly reached saturation.
Soil water contents reﬂected rapid inﬁltration of water during precipitation events at DOY 29, 34, 90 and 94 due to dry soil condition. During thestrongest precipitation events (i.e., DOY 34, 91 and 95), the upper andlower soil layers reached saturation, which persisted for several days.
At the mid of the simulation period (DOY between 50 and 90), the soil
surface dried out rapidly within a few days, with water contents
reaching a constant value of about 0.15 cm3 cm−3. This was due inpart to used residual water content (θr = 0.05), initial/boundary conditions, and less precipitation, while evaporation rates continued from thesurface soil. The evapotranspiration (ET) values (see Fig. 3) are larger
than precipitation values between DOY 50 and 88. So this could resultin non-response to the precipitation events during this period.
According to the meteorological station data, on several days, however, the mean air and soil temperatures went down to below 0 °C
(see Fig. 3). It should be noted that these values were obtained fromone meteorological station located in the northwest of the study areaand elevation about 1800 m. This was consistent with the presence ofa snow cover and a frozen surface soil as observed in the meteorologicalstation site. Inﬁltration and water ﬂow is essentially non-existent in afrozen soil.
The results of Figs. 5, 6 and 7 also show that the transfer functionbased soil water signatures closely followed each other as well as theobserved (ﬁne and coarse scale) signatures for most pixels. A comparison of the various curves gives additional information about the role ofprecipitation as a key factor controlling surface soil water status. For example, the coarse scale transfer functions produced very similar time series that were shifted in various degrees with respect to each other. The
scatter in the simulated water contents was found to be substantial at
the deeper layers, particularly during dry period (Figs. 6 and 7). Noticefurther that simulations obtained with the coarse-scale transfer

Fig. 5. Simulated time series (January through March 2012) of surface (0–1 cm) soil water contents using coarse scale transfer functions, versus ﬁne and coarse scale observations (fromobserved VGM parameters) and ASAR-based estimates for 20 pixels of the ZRS study site. Ground-truth (measured) values are shown for pixel 13.

E. Babaeian et al. / Remote Sensing of Environment 187 (2016) 218–229

225

Fig. 6. Simulated time series (January to March 2012) of near-surface (z – 5 cm) soil water contents using coarse scale transfer functions versus ﬁne and coarse scale observations (fromobserved VGM parameters) for 20 pixels of the ZRS study site.

functions continuously over-predicted soil water contents of the near(z – 5 cm) and subsurface (z – 30 cm) layers. The coarse scale PTFs
and SPTFs also tended to over-predict the water contents of most pixels.
Fig. 8 shows ME and the RMSE values between the average daily soil
water contents for the selected pixels at three soil depths as obtainedusing the coarse-scale observed VGM parameters and those calculatedusing three different sets of coarse scale transfer functions in the
HYDRUS-1D simulations. As can be seen, for most of the pixels at
three soil depths, the coarse scale STFs performed the best with mean
RMSE and ME values of 0.012 and 0.004 cm3 cm−3, respectively, followed by the coarse scale SPTFs (mean RMSE and ME equal to 0.019 and
0.010 cm3 cm− 3, respectively) and the PTFs (mean RMSE and ME
equal to 0.021 and 0.015 cm3 cm−3, respectively). While the simulated
water contents were overestimated in many pixels, in general they

were reasonable accurate. This signiﬁes that the simulated soil watercontents were relatively close to the reference values. Results suggest
the feasibility of using spectral data to estimate VGM parameters andpredict the soil water dynamic at the larger scale.

3.3. Comparison of simulated soil water contents with ASAR estimatesFig. 5 illustrates average daily soil water contents of the surface soil
(z – 0–1 cm) as simulated using the coarse-scale observed VGM parameters and those obtained with the coarse scale transfer functions, alongwith the ASAR-based estimates for the selected pixels. As can be seen,
the estimated (ASAR) and simulated soil water trends show a good
match with the precipitation pattern (see Figs. 3 and 5).

Fig. 7. Simulated time series (January to March 2012) of subsurface (z – 30 cm) soil water content using coarse scale transfer functions versus ﬁne and coarse scale observations (fromobserved VGM parameters) for 20 pixels of the ZRS study site. Ground-truth (measured) values are shown for pixel 13.

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E. Babaeian et al. / Remote Sensing of Environment 187 (2016) 218–229

Fig. 8. ME and RMSE values between average daily simulated soil water contents using three different sets of transfer functions, and those obtained using the coarse-scale observed VGM
parameters for each pixel at three soil depths.

We found that the lowest simulated soil water contents were about
0.10 cm3 cm− 3, while the ASAR-based estimates were less than thesimulated values (b 0.10 cm3 cm− 3) (Fig. 5). This indicates that the
ASAR data were more sensitive during relatively dry conditions.
Except for a few cases, the ASAR estimates produced lower watercontents for about half of the selected pixels (i.e., pixels 1, 2, 6, 9,
10, 11, 12, 15 16 and 19) during the study period. This may pointout that the probability of underestimation is about 50%. However,more investigations are needed to improve our estimations. This difference in water contents may be attributed to soil roughness () and soil
freezing (Jagdhuber et al., 2014). They pointed out that as soon as
the soil temperatures fall below 0 °C, a distinct drop occurs in the dielectric constant for all soil types. This then keeps the dielectric level
close to the lower physical limit for all freezing states (Jagdhuber etal., 2014). In such case, the soil medium will show dielectric propertiesof a dry soil.
Part of the differences may be due also to some differences in the effective sensing depths of the ASAR sensor and TDR probes (Wang et al.,2011). The surface layer of a soil is commonly drier than the subsurface
layers, particularly in arid and semi-arid regions (Wang et al., 2011).
ASAR signals (C-band, 5.33 GHz) essentially perceive the dielectric
properties of the surface soil layer (at about 1 cm or less). For the
TDR-based ground-truth measurements we used for the validation,
the detected water content is the integral value of the entire sampledlayer (0–10 cm) in the measured soil volume. This could partly explain
the underestimation of the water content, as suggested also in the literature. However, this does not explain all of the underestimated soil
water measurements. Another source of errors may be related to assumptions about the roughness estimation. In our study the surface
roughness was considered to be temporally stable, with the roughness
parameterizations assuming dielectric properties for dry soil conditions,while soil management practices (e.g., agricultural land preparation, soil
erosion) may change the surface roughness between relatively dry andwet periods. Soil roughness can also change due to change in soil waterconditions.

Correlations of the average daily water contents simulated with thecoarse scale transfer functions with those from the ASAR-based estimates are given in Table 3. The data show that the average simulated
surface water contents from the coarse scale transfer functions generated good correlations with ASAR estimates for all pixels across wet, intermediate and dry days, with the r-values being between 0.10 and 0.84.
Signiﬁcant correlations were found for pixels 1, 4, 5, 10, 12, 13, 18, 19,
20, which showed r values between 0.62 and 0.84. This may illustratethat the probability of 50% for correlation/uncorrelation within thesepixels. However, no signiﬁcant differences in correlations were observed between simulated water contents from the coarse scale transfer
functions (Table 3).
3.4. Comparison of average simulated soil water contents and ground-truth
measurements
For each coarse scale transfer function, we analyzed the r, ME and
RMSE of simulated water contents for the surface (z – 0–1 cm) and subsurface (z – 30 cm) soil layers for which ground-truth measurements(deﬁned as measured) and ASAR estimates were available. Results areshown in Table 4. While the previous section provided insight into theperformance of the PAO scheme with respect to providing effective
VGM hydraulic parameters, the ultimate test of the practical applicability of the scheme is how well the simulated soil water states match themeasurements. Accordingly, we compared the coarse-scale simulated
water contents to the average of the values (n = 15) from one experimental ﬁeld site, which arithmetically were resampled to the 1 km
scale, as well as the remotely sensed ASAR soil water estimates. Our approach could be validated only for one pixel (pixel 13) because of a lackof sufﬁcient in-situ measurements. Still, this provides a base of judging
the performance and robustness of the coarse scale transfer functions
and the hydrologic simulation model.
Table 4 shows that for surface layer the correlations were relatively
good (r values between 0.499 and 0.581), but that the biases (errors)
between the simulated and the ground-truth measurements wereE. Babaeian et al. / Remote Sensing of Environment 187 (2016) 218–229

227

Table 3
Correlation coefﬁcient (r) between simulated soil water content from coarse scale transfer functions and ASAR-based estimates (z – 0–1 cm) for the selected pixels at ZRS.

Pixel 1
Pixel 2
Pixel 3
Pixel 4
Pixel 5
Pixel 6
Pixel 7
Pixel 8
Pixel 9Pixel 10
Pixel 11
Pixel 12
Pixel 13
Pixel 14
Pixel 15
Pixel 16
Pixel 17
Pixel 18
Pixel 19
Pixel 20

Coarse scale STFs

Coarse scale SPTFs

Coarse scale PTFs

Coarse scale measurements

0.62‡
0.10
0.51
0.62‡
0.73§
0.09
0.36
0.28
0.31
0.82§
0.24
0.82§
0.72§
0.57
0.33
0.56
0.49
0.84§
0.72§
0.73§

0.63‡
0.10
0.51
0.62 ‡
0.75§
0.10
0.35
0.26
0.33
0.82§
0.24
0.82§
0.73§
0.57
0.32
0.56
0.49
0.84§
0.73§
0.75§

0.65‡
0.10
0.51
0.63 ‡
0.75§
0.10
0.36
0.26
0.33
0.82§
0.24
0.81§
0.73§
0.57
0.32
0.57
0.49
0.83§
0.73§
0.74§

0.62‡
0.10
0.50
0.62‡
0.73§
0.10
0.37
0.24
0.32
0.82§
0.24
0.80§
0.71§
0.56
0.32
0.56
0.49
0.87§
0.75§
0.71§

Superscripts ‡ and § represent p b 0.05 and p b 0.01 respectively.

considerable (RMSE values between 0.107 and 0.138 cm3 cm−3 and ME
values between 0.004 and −0.015 cm3 cm−3). For the subsurface layer,
however, the transfer functions were found to perform much better
than for the surface layer. At the ﬁne scale and in the subsurface layer,
the simulated water contents matched the in-situ measurements very
well (r = 0.999, ME = 0.016 and RMSE = 0.015 cm3 cm−3). At the
pixel scale, the simulated soil water dynamics also closely matched
the in-situ measurements. The best results were obtained with thecoarse-scale observed hydraulic parameters (r = 0.995, ME = 0.010,
RMSE = 0.009 cm3 cm− 3) and the estimated hydraulic parametersfrom the STFs (r = 0.998, ME = 0.018, RMSE = 0.018 cm 3 cm− 3),followed by the SPTFs (r = 0.896, ME = 0.033, RMSE = 0.034 cm 3cm−3) and PTFs (r = 0.871, ME = 0.035, RMSE = 0.036 cm 3 cm−3),
with the SPTFs and PTF performing very similarly. These ﬁeld validation
results support the robustness of the coarse scale spectral transfer functions as shown earlier also in Section 3.2.
4. Summary and conclusions
In this paper we presented results of the newly developed diffuse
spectral reﬂectance-based transfer functions of Babaeian et al.
(2015a, 2015b), and used a topography-based aggregation scheme

Table 4
Summary of performance of the coarse scale transfer functions in simulating surface(z – 0–1 cm) and subsurface (z – 30 cm) soil water contents for the pixel 13 of the ZRS
study site.
Simulated versus Measuredz – 0–1 cm
Fine scale (Obs.)
Coarse scale (Obs.)
Coarse scale PTFs
Coarse scale SPTFs
Coarse scale STFsz – 30 cm
Fine scale (Obs.)
Coarse scale (Obs.)
Coarse scale PTFs
Coarse scale SPTFs
Coarse scale STFs

r

ME

RMSE

0.537
0.581
0.532
0.499
0.578

0.027
0.004
−0.010−0.010−0.015

0.132
0.107
0.140
0.138
0.123

0.999⁎⁎
0.995⁎⁎
0.871
0.896⁎
0.998⁎⁎

0.016
0.010
0.035
0.033
0.018

0.015
0.009
0.036
0.034
0.018

* and ** represent p b 0.05 and p b 0.01, respectively.

(PAO) to assess coarse-scale transfer functions (i.e., STFs, SPTFs andPTFs). The ultimate objective was to predict surface and near-surface
soil water dynamics at a semi-arid region, ZRS, in northwestern Iran.
Using the PAO algorithm, which is based only on topographic attributes (elevation), we aggregated point-scale estimated and observed VGM hydraulic parameters to a coarse resolution (1km2 pixel size). The equivalence of the coarse scale transfer functions was subsequently tested by simulating soil water dynamics
for 20 pixels through the watershed. Simulated soil water contentsof the surface and subsurface layers were compared across scale,and also with the ground-truth measurements as well as withthose made using the ASAR spaceborne radar sensor in combination
with the IEM model.
We found signiﬁcant correlations between aggregated values of theestimated and observed VGM hydraulic parameters for the selected
pixels of the ZRS site. The coarse scale STFs performed the best for parameters α, n and lnKs, followed by the coarse scale SPTFs. The coarse
scale PTFs performed best for θs,. The coarse scale STFs performed bestin simulating surface and near-surface soil water dynamics in terms of
RMSE and ME values, followed by the coarse scale SPTFs and PTFs,
which produced very similar results. While the simulated water contents were slightly overestimated in many pixels, in general they produced reasonable accurate values. Average simulated water contentsof the surface layer showed signiﬁcant correlations with the ASAR estimates for most pixels, particularly during wet periods. The simulated
soil water dynamics matched the ground-truth measurements well, especially in the root zone layer.
Overall, the PAO scheme used to aggregate the ﬁne-scale soil hydraulic parameters provided a useful set of VGM hydraulic parameters
for the coarse scale. Our ﬁndings point out the feasibility of using spectral data to estimate VGM hydraulic parameters and, ultimately, to provide predictions in time and space of prevailing soil water contents.
Future work could be designed to implement and test this approach at
the larger scale using air-borne and space-borne hyperspectral (e.g.,
EnMAP, Hyperion) and multi-spectral (e.g., Landsat-8, Sentinel-2) remote sensors. This study was conducted during the winter time,
where soil water measurements through the experimental ﬁeld were
only available for a short period corresponding to this season. Since
ASAR data is recorded in C-band, they signiﬁcantly are affected bydense vegetation cover of agricultural lands in summer. Thus this
could provide uncertain estimates of soil water during the summer
time.

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