Estimation of Soil Moisture Applying Modiﬁed
Dubois Model to Sentinel-1; A Regional Study from
Abhilash Singh 1, Kumar Gaurav 1,*, Ganesh Kumar Meena 1and Shashi Kumar 2
1Department of Earth and Environment Sciences, Indian Institute of Science Education and Research,
Bhopal 462066, Madhya Pradesh, India; email@example.com (A.S.); firstname.lastname@example.org (G.K.M.)
2Department of Photogrammetry and Remote Sensing, Indian Institute of Remote Sensing, ISRO,
Dehradun 248001, Uttarakhand, India; email@example.com
*Correspondence: firstname.lastname@example.org; Tel.: +91-755-669-1383
Received: 11 May 2020; Accepted: 3 June 2020; Published: 15 July 2020
Surface soil moisture has a wide application in climate change, agronomy, water resources,
and in many other domain of science and engineering. Measurement of soil moisture at high
spatial and temporal resolution at regional and global scale is needed for the prediction of
drought, planning and
management of agricultural productivity to ensure food security.
in microwave remote sensing, especially after the launch of Sentinel operational
satellites has enabled the scientiﬁc community to estimate soil moisture at higher spatial and temporal
resolution with greater accuracy. This study evaluates the potential of Sentinel-1A satellite images
to estimate soil moisture in a semi-arid region. Exactly at the time when satellite passes over the
study area, we have collected soil samples at 37 different locations and measured the soil moisture
below the ground surface using ML3 theta probe. We processed the soil samples in
laboratory to obtain volumetric soil moisture using the oven dry method. We found soil moisture
measured from calibrated theta probe and oven dry method are in good agreement with Root Mean
Square Error (RMSE) 0.025 m
and coefﬁcient of determination (R
) 0.85. We then processed
Sentinel-1A images and applied modiﬁed Dubois model to calculate relative permittivity of the soil
from the backscatter values (
). The volumetric soil moisture at each pixel is then calculated by
applying the universal Topp’s model. Finally, we masked the pixels whose Normalised Difference
Vegetation Index (NDVI) value is greater than 0.4 to generate soil moisture map as per the Dubois
soil moisture accord with the measured values with RMSE = 0.035
= 0.75. We found a small bias in the modelled soil moisture (
). However, this has
reduced signiﬁcantly (
) after applying a bias correction based on Cumulative Distribution
Function (CDF) matching. Our approach provides a ﬁrst-order estimate of soil moisture from
Sentinel-1A images in sparsely vegetated agricultural land.
Keywords: soil moisture; theta probe; Sentinel-1A; NDVI; modiﬁed Dubois model
Soil moisture is a temporary storage of water in soil pores that controls various processes occurring
at the air–soil interface [
]. Quantiﬁcation of soil moisture is required on a regular basis for predicting
ﬂood, drought, agricultural productivity, hydrological modelling and climate studies [
the speciﬁc application, soil moisture is needed at different spatial and temporal scales. At a local
scale, it can be measured in the ﬁeld using Time Domain Reﬂectometry (TDR) or gravimetric methods.
These measurement techniques provide a more accurate estimate of soil moisture, but they are tedious
Remote Sens. 2020,12, 2266; doi:10.3390/rs12142266 www.mdpi.com/journal/remotesensing
Remote Sens. 2020,12, 2266 2 of 19
and time-consuming. This limits the use of in-situ measurement techniques to measure soil moisture
on global or regional scales.
An alternative to in-situ measurements, surface soil moisture, can be modelled from remote
sensing images. Active microwave remote sensing, speciﬁcally Synthetic Aperture Radar (SAR)
imaging has emerged as an effective tool to estimate surface soil moisture. The SAR sensors transmit
microwave electromagnetic pulses and record the backscattered energy from the earth’s surface.
The microwave pulses have high sensitivity towards the dielectric properties of the target and surface
]. At a given incidence angle, when a SAR signal interacts with the soil-water mixture,
a permittivity (
) gradient exists between the dry soil (
= 2) and water (
= 80), that reﬂects in the
intensity of radar backscatter [13–16].
To retrieve the relative soil permittivity and surface roughness component from the SAR
backscatter, various empirical, semi-empirical and theoretical models have been proposed [
These models are developed for the quad polarised SAR images and are mainly applicable on barren
land. However, the Water Cloud and Dubois models have been successfully used to estimate soil
moisture over barren and sparsely vegetated land [25–28].
In a study, Zribi et al.
have applied Water Cloud Model (WCM) on L-band PALSAR/ALOS-2
satellite data to estimate soil moisture in a tropical agricultural area under dense vegetation cover
conditions. Yang et al.
have used the fully polarimetric C-band Radarsat-2 SAR data for
soil moisture mapping in Juyanze Basin, China. They concluded that increasing the number of
polarimetric parameters at C-band can provide a more robust estimate of surface soil moisture.
El Hajj et al. 
and Bousbih et al.
have shown that the synergic use of radar (Sentinel-1) and
optical (Sentinel-2) data can be utilised to estimate soil moisture at higher spatial resolution at ﬁeld
scale. They have used
a neural network
(NN) model to estimate soil moisture by the inversion of
radar signals. In doing so,
generated a synthetic database of the backscattering coefﬁcient
in the VV and HH polarisation for a range of soil moisture, surface roughness and NDVI values by
the parameterisation of coupled WCM and modiﬁed Integral Equation Model (IEM). They concluded
that their approach can be used to estimate soil moisture in agricultural plots having NDVI less than
0.75. Further, Qiu et al.  used the similar WCM and IEM coupled model to evaluate the impact of
different vegetation indices (NDVI, Enhanced Vegetation Index, and Leaf Area Index) in the estimation
of soil moisture. They reported the accuracy of estimated soil moisture is independent of the choice of
speciﬁc vegetation indices.
Hachani et al. 
used sentinel-1 images to estimate soil moisture in an
arid climate in Tunisia. They have developed an artiﬁcial neural network (ANN) using the training
samples obtained by combining satellite measurements and the simulated backscatter values using
the Integral Equation Model (IEM). They claimed their model is almost site independent and able
to simulate soil moisture content with limited or no ancillary information (i.e., DEM, local Incidence
angle, NDVI). More recently,
Ezzahar et al. 
have used Support Vector Machine (SVM), IEM and
Oh models to estimate soil moisture over bare agricultural soil in the Tensﬁt basin of Morocco from
sentinel-1 satellite images.
Hosseini and McNairn
applied WCM-Ulaby model on C-band (Radarsat-2) and L-band
(UAVSAR) SAR data to estimate soil moisture and biomass in wheat ﬁelds in western Canada. Some
] have used modiﬁed Dubois model and dual polarised (HH and HV) RISAT-1, C-band
data to estimate soil moisture of the Bhal region in Gujrat, India. They found promising results with
good correlation during the initial period of the crop. However, the accuracy decreases greatly at the
locations of dense canopy cover and higher NDVI values in the study area.
After the launch of Sentinel-1A satellite mission in April 2014, the global coverage of SAR data is
easily available at higher spatial and temporal resolution, and is being widely used for soil moisture
]. Sentinel-1A satellite sensor operates in C-band at frequency 5.405 GHz and acquire
information about the earth’s surface in selectable single (HH or VV) and dual polarisation (HH + HV,
VV + VH) [
]. This data is freely available and is widely used in various applications, including soil
moisture estimation [34,38,41–43].
Remote Sens. 2020,12, 2266 3 of 19
This study uses dual polarised Sentinel-1A satellite images to estimate soil moisture in a semi-arid
region in central India. We used modiﬁed Dubois model to calculate the relative soil permittivity from
SAR backscatter values. Eventually, we input the relative soil permittivity in universal Topp’s model
to obtain volumetric soil moisture in barren or sparsely vegetated farmlands.
2. Study Area
This study is conducted in Bhopal district of Madhya Pradesh in central India (Figure 1).
divided into two administrative blocks, Berasia in the north and Phanda in the south having
area of about 1424 km
and 1348 km
respectively (Figure 1). Climatically, Bhopal lies in
zone and is typically covered by agriculture land (64.5%), barren land (7.3%), forest (13%), and water
bodies (4.6%) [
]. The average elevation in the study area varies between 450 and 550 m from the
mean sea level with the gently undulated landscape. The average air temperature ranges between 6
and 41 ◦C. About 75% of the study area is covered by black cotton soil formed due to the weathering
of basaltic rocks. The remaining 25% is covered with yellowish-red, mixed soils [45,46].
Not in scale
In-situ locations (N=37)
Landsat-8 image in False Color Composite (FCC) shows the administrative blocks (Phanda
and Berasia) of Bhopal district, Madhya Pradesh. Circles in Yellow and triangles in black are the
locations of soil moisture measurement in the ﬁeld. Grid on the top right illustrates the random
sampling strategy to collect soil moisture.
In this study, we have considered Phanda block as a test site to estimate soil moisture. About 44%
of the area of Phanda is cultivable and used for agricultural purposes. The agricultural practice in the
region largely depends on the Indian summer monsoon in June, July, August, and September (JJAS),
where it receives about 92% of total rainfall.
In recent years, the frequency of droughts in central India has increased, which has adversely
impacted the agricultural productivity [
]. To obtain the frequency of drought events in the study
Remote Sens. 2020,12, 2266 4 of 19
area, we have calculated Standardized Precipitation Index (SPI) for the monsoon period (JJAS) from
1990 to 2018 using gridded (0.25
) rainfall data obtained from the Indian Meteorological
]. SPI is used to characterise meteorological drought. For example, SPI values in
0.99 to 0.99) is considered normal, whereas SPI values less than
1 and greater
than 1 are considered to be dry and wet period respectively [
]. The SPI values of Phanda block
(Figure 2), clearly suggests that the frequency of drought events has increased in last two decades.
events (2002, 2004, 2010, 2014, 2015, and 2017) have occurred between the years
2000 to 2018 (Figure 2).
In this scenario, monitoring soil moisture at higher spatial and temporal resolution has become
important in planning and management of agricultural productivity, water resources and ensuring
food security. The landuse, geology, and soil types of the Phanda block makes it an ideal ﬁeld site to
study the soil moisture.
1990 1995 2000 2005 2010 2015
Normal - 0.99 to 0.99 Wet 1 to ≥ 2 Dry -1 to ≤ -2
Standarised Precipition Index (SPI)
Areal averaged Standardized precipitation Index (SPI) for Indian summer monsoon (June, July,
August, September) from 1990 to 2018. Shaded region (SPI
0.99 to 0.99) shows the normal precipitation
condition. SPI in range (−1≤ −2 ) and (1 ≥2) suggests drought and wet condition respectively.
3. Material and Methods
3.1. Satellite Data
This study uses microwave and optical satellite images (Table 1) to estimate soil moisture.
downloaded publicly available Sentinel-1A images of two consecutive pass, i.e., 17 and 29 January
2019 from European Space Agency (https://scihub.copernicus.eu/). Sentinel-1A, C-band SAR records
the backscatter signals day and night, independent of the illumination and weather conditions.
microwave images in four exclusive modes; Stripmap (SM), Interferometric Wide swath
Extra Wide swath (EW)
, Wave (WV). It can capture images (in terms of polarization) using same
set of transmitted pulses by using its antenna. Depending upon the acquisition mode, Sentinel-1
can acquires images in dual polarisation modes, Vertical–Vertical (VV) and Vertical–Horizontal (VH),
or in single polarisation (HH or VV) at 10 m
10 m cell size with a swath 250 km. At this swath,
the incidence angle ranges between 29
for near and far range respectively. It has a temporal
resolution of 12 days (in combination with Sentinel-1B the temporal resolution is 6 days). Microwave
signals at C-band can penetrate up to 5 cm deep below the soil surface [
]. The Sentinel-1A level-1
data is categorised into two product types: Ground Range Detected (GRD) and Single Look Complex
(SLC). Wide range of applications requires Sentinel-1A GRD product with standard corrections.
Remote Sens. 2020,12, 2266 5 of 19
After applying standard corrections, the Sentinel-1A GRD images will have square pixels (consisting
of amplitude) with reduced speckle [
]. We have also downloaded Landsat 8 images from the
United States Geological Survey (https://earthexplorer.usgs.gov/) pertaining to the date closest to
the Sentinel-1A images. The Landsat 8 satellite mission carries a two-sensor payload, the Operational
Land Imager (OLI) and the Thermal Infrared Sensor (TIRS). The OLI sensor consists of nine spectral
) and acquire images at 16 days revisit time with the spatial resolution 15 m for the
panchromatic band (0.50–0.68µm) and 30 m for the remaining bands .
Table 1. Details of the Sentinel-1 and Landsat 8 images used in this study.
Date Polarisations Incidence angle
(m ×m) Direction
17/01/2019 VH + VV 38.4 10 ×10 NE
29/01/2019 VH + VV 38.5 10 ×10 NE
Row/Path Band Wavelength
15/01/2019 44/145 4, 5 0.64–0.67, 0.85–0.88 30
22/01/2019 43/146 4, 5 0.64–0.67, 0.85–0.88 30
3.2. Field Measurement
We have used ML3 theta probe sensor and gravimetric method to measure soil moisture in the
ﬁeld. Theta probe works on the principle of TDR, and it measures the bulk soil relative permittivity
) at a frequency 100 MHz. This bulk relative permittivity is then converted into volumetric soil
moisture by applying a soil speciﬁc calibration of TDR. We have calibrated the theta probe for three
different dominant soil types of our study area. A detailed procedure of calibration is mentioned in the
Appendix A. To measure soil moisture, we have conducted a ﬁeld campaign on 17 and
29 January 2019
in Bhopal, Madhya Pradesh. These dates coincide with the Sentinel-1A pass over Bhopal at 5:50 a.m.
(IST). At the time of satellite passes, we have measured the soil moisture at 37 locations.
To conduct measurements, we overlay a square grid of
3 km ×3 km
on our study area [
randomly select few grids to measure the soil moisture. At the centre of each grid,
the soil moisture by inserting the metal rod of the theta probe at 5 cm below the ground
surface and record the soil moisture value (
) in the data logger and acquired their locations
handheld GPS (Figure 3a). We repeated this procedure at least in 8 to 10 different
locations within the grid and ﬁnally averaged them to get soil moisture (Figure 1). Simultaneously
at each location, we have collected about 100 g of soil samples at 5 cm below the ground surface
using tubular samplers (Figure 3b). We used these samples to measure soil moisture by oven drying
). At each of the measurement location, we have also taken observations on land
, vegetation height and weather parameters (temperature, precipitation, etc.). Table 2
reports the detailed characteristics and location of our sampling sites.
Remote Sens. 2020,12, 2266 6 of 19
Measurement of soil moisture using (
) ML3 sensor and (
) Collection of soil samples in
the ﬁeld. Photograph (
) Shows the sample processing in the laboratory for oven drying to calculate
Remote Sens. 2020,12, 2266 7 of 19
Table 2. Details of the ground condition and soil moisture measured in the ﬁeld using ML3 theta probe.
Date Site ID Latitute Longitude Elevation
(msl) Land Use Sampling Depth
17-01-2019 1 23.22913 77.26613 516 Agriculture land (Chickpeas) 5 10–15 0.291 ±0.053
17-01-2019 2 23.22978 77.28679 517 Agriculture land (Chickpeas) 5 15–20 0.170 ±0.028
17-01-2019 3 23.22081 77.31552 515 Agriculture land (Chickpeas) 5 0–5 0.167 ±0.020
17-01-2019 4 23.20669 77.34076 538 Barren land 5 0 0.043 ±0.017
17-01-2019 5 23.18931 77.38358 507 Barren land 5 0 0.109 ±0.032
17-01-2019 6 23.16962 77.33730 532 Agriculture land (Mustard) 5 20–30 0.185 ±0.025
17-01-2019 7 23.16144 77.31003 546 Barren land 5 0 0.111 ±0.014
17-01-2019 8 23.31624 77.41531 495 Agriculture land (Wheat) 5 15–20 0.266 ±0.052
17-01-2019 9 23.33788 77.39777 497 Agriculture land (Wheat) 5 30–35 0.175 ±0.022
17-01-2019 10 23.33280 77.35484 494 Agriculture land (Coriander) 5 10–15 0.275 ±0.046
17-01-2019 11 23.31749 77.32511 503 Agriculture land (Mixed) 5 20–30 0.198 ±0.032
17-01-2019 12 23.32754 77.25596 529 Agriculture land (Wheat) 5 20–30 0.255 ±0.051
17-01-2019 13 23.32683 77.29851 510 Agriculture land (Chickpeas) 5 10–15 0.254 ±0.037
17-01-2019 14 23.34099 77.36872 502 Agriculture land (Wheat) 5 30–40 0.098 ±0.015
17-01-2019 15 23.38717 77.39961 488 Agriculture land (Daikon) 5 0 0.270 ±0.042
17-01-2019 16 23.43098 77.37777 487 Agriculture land (Chickpeas) 5 15–20 0.218 ±0.038
17-01-2019 17 23.50044 77.40357 476 Agriculture land (Wheat) 5 20–25 0.285 ±0.052
17-01-2019 18 23.53360 77.40742 478 Agriculture land (Chickpeas) 5 10-15 0.186 ±0.021
29-01-2019 19 23.41329 77.39910 484 Agriculture land (Wheat) 5 30–40 0.189 ±0.025
29-01-2019 20 23.35487 77.40400 483 Agriculture land (Wheat) 5 40–50 0.174 ±0.024
29-01-2019 21 23.34471 77.43551 490 Agriculture land (Wheat) 5 20–25 0.175 ±0.024
29-01-2019 22 23.35516 77.47569 512 Agriculture land (Wheat) 5 10–15 0.270 ±0.060
29-01-2019 23 23.37469 77.45610 492 Agriculture land (Wheat) 5 40–50 0.129 ±0.018
29-01-2019 24 23.39272 77.44480 478 Agriculture land (Wheat) 5 20–25 0.069 ±0.013
29-01-2019 25 23.36028 77.45131 501 Agriculture land (Mixed) 5 10–15 0.262 ±0.033
29-01-2019 26 23.32369 77.48873 518 Agriculture land (Wheat) 5 30–40 0.099 ±0.024
29-01-2019 27 23.28805 77.51691 491 Agriculture land (Chickpeas) 5 15–20 0.267 ±0.041
29-01-2019 28 23.29685 77.27975 516 Barren land 5 0 0.221 ±0.042
29-01-2019 29 23.29730 77.99768 519 Agriculture land (Chickpeas) 5 20–25 0.180 ±0.027
29-01-2019 30 23.29316 77.26544 528 Agriculture land (Wheat) 5 15–20 0.267 ±0.042
29-01-2019 31 23.29380 77.28096 520 Agriculture land (Wheat) 5 10–15 0.159 ±0.027
29-01-2019 32 23.28579 77.28620 523 Agriculture land (Mixed) 5 5–10 0.234 ±0.046
29-01-2019 33 23.28255 77.28209 519 Agriculture land (Wheat) 5 40–50 0.117 ±0.026
29-01-2019 34 23.28405 77.28794 520 Agriculture land (Chickpeas) 5 10–15 0.153 ±0.028
29-01-2019 35 23.29396 77.26690 526 Agriculture land (Wheat) 5 40–50 0.276 ±0.032
29-01-2019 36 23.25948 77.27253 511 Barren land 5 0 0.102 ±0.034
29-01-2019 37 23.26410 77.29583 515 Agriculture land (Chickpeas) 5 10–15 0.124 ±0.029
Note: Temperature range (at 2 m): (18.4–19.1) ◦C; Earth surface temperature: (13.7–18.1) ◦C; Precipitation: Nil (Source: Weather station Bhopal).
Remote Sens. 2020,12, 2266 8 of 19
3.3. Data Processing
3.3.1. Soil Samples
We processed the soil samples in laboratory to measure their moisture content. We took about
each of soil samples from a grid and placed them in a separate beaker (Figure 3c). We placed the
samples in an electric oven at 105
C for about 24 h [
]. Once the samples are completely dried,
them. The difference between initial and dry weight provides the amount of moisture
present in the soil samples. Eventually, we divide the weight of moisture content with the dry weight
of soil samples. This quantity is the gravimetric soil moisture (mg) and expressed in [kg/kg].
Since theta probe measures the volumetric soil moisture (
), we need to convert our laboratory
measurement into comparable metric for any meaningful comparison. We multiply the gravimetric
soil moisture (
) to the density ratio of soil (
) and water (
) to compute the volumetric soil
moisture (mv) in [m3/m3] according to;
3.3.2. Satellite Images
We have used Sentinel Application Platform (SNAP) v6.0 to process the Sentinel-1A images.
The processing involves four major steps, radiometric calibration, multilook, speckle noise reduction
using reﬁned Lee ﬁlter, and terrain correction. Terrain or geometric calibration uses the Shuttle Radar
Topography Mission (SRTM) digital elevation model of spatial resolution 30 m. The resulting image
pixels contain the true backscatter (
) values on a linear scale. Finally, we convert the backscatter
values into decibel scale (
) according to,
. We have also processed Landsat-8
images to compute NDVI. It helps to measure the intensity of vegetation cover in terms of vegetation
density and vegetation height. We take the ratio of the difference between band 5 (Near Infrared) and
band 4 (Red) to the sum of band 5 and band 4 of Landsat-8 images. The NDVI is required to specify
the validity range (NDVI ≤0.4) of modiﬁed Dubois model for soil moisture.
3.4. Soil Moisture Modelling
We have used the backscatter values of Sentinel-1A images and incidence angle in the modiﬁed
Dubois model to calculate the relative soil permittivity. Finally, we used the relative permittivity in
universal Topp’s model to compute volumetric soil moisture.
3.4.1. Radar Backscattering Model
Dubois et al.
developed an empirical model to calculate the relative soil permittivity from
quad polarised SAR images. Initially, this model was developed for L-, C- and X-band data obtained
from scatterometer and later applied on airborne images as well. The model structure is developed on
a strong physical reasoning; however, some of the unknown coefﬁcients are obtained by ﬁtting to the
experimental data. The backscattering coefﬁcient for HH and VV polarisation is given by Equations (2)
HH =10−2.75 cos1.5 θ
sin5θ!100.028etan θ(k.s. sin θ)1.4λ0.7 (2)
VV =10−2.35 cos3θ
sin3θ!100.046etan θ(k.s. sin θ)1.1λ0.7 (3)
is the incidence angle,
is the relative soil permittivity, sis the surface roughness (cm),
is the wavenumber, and
is the SAR wavelength. These parameters can be grouped
into two; sensor parameters (
) and target parameters (
and s). In Equations (2) and (3),
Remote Sens. 2020,12, 2266 9 of 19
are unknown. These equations can be inverted to compute the relative soil
permittivity and surface roughness parameters.
Dubois model is applicable for the SAR images acquired at incidence angle
and in the frequency range between 1.5–11 GHz. Further, this model is valid on the region having
sparsely vegetation or barren land. The performance of the Dubois model is maximum where NDVI of
the image pixels is less than 0.4 (Dubois NDVI criterion) or in the region on SAR images where the
ratio of cross-polarised σ◦
VV is less than −11 dB .
Dubois model was initially developed for quad polarised SAR images; it can not be directly
applied to dual polarised data. In a study Rao et al.
modiﬁed the Dubois model by incorporating
in-situ measurements and ﬁeld conditions and used the Equation (2) to calculate the soil moisture
from the SAR images acquired in HH polarisation.
To derive the unknown parameter (surface roughness) of Equation (3), we obtain the parameter
from regression model proposed by Srivastava et al.
. Once surface roughness is known,
Equation (2) or (3) can be solved to compute the other unknown, the relative soil permittivity.
A ﬂowchart in Figure 4illustrates the detailed methodology used for in-situ data acquisition,
image processing and modelling to estimate soil moisture.
(VV + VH)
(VV + VH)
Regression model Identification of sparse
vegetation and bare land
over bare land
& Geometrical correction
& Geometrical correction,
Voltage of the
dry & wet soil
of the soil
Flow chart illustrates the methodology used for the estimation of soil moisture from
3.4.2. Estimation of Soil Moisture
To estimate soil moisture, we used Topp’s model [
]. It takes the relative soil permittivity
derived from Sentinel-1A image as an input to estimate volumetric soil moisture content according to
. This model does not require a priori knowledge of soil properties (texture, grain size)
and is proven to be a robust approach for the estimation of soil moisture .
mv=−5.3 ×10−2+2.92 ×10−2e−5.5 ×10−4e2+4.3 ×10−6e3(4)
Remote Sens. 2020,12, 2266 10 of 19
4.1. Performance of Calibrated Theta Probe
We compared the soil moisture measured from the theta probe and oven dry method.
no obvious difference, despite a mild scatter, all data points seem to gather around a single line
). This suggests a good agreement between (R
= 0.84 with RMSE = 0.025 m
) both the
methods, provided theta probe is correctly calibrated for the speciﬁc soil types in the study area.
Hereafter we will use the measurements of theta probe for further analysis.
0.1 0.15 0.2 0.25 0.3
Oven dry SM [m3/m3]
TDR SM [m3/m3]
N = 37, RMSE = 0.025, R2= 0.85
Soil moisture measured using theta probe as a functions of gravimetric method. Shaded gray
region is the 95% conﬁdence level of the regression curve.
4.2. Soil Moisture from Sentinel-1A
Once we calculated the soil moisture from Sentinel-1A images, we evaluated their accuracy with
the in-situ measurement. We ﬁrst identiﬁed the valid region for modiﬁed Dubois model using the
Dubois NDVI criterion. For the locations where ground measurement is valid, we extracted the
corresponding pixels from the modelled soil moisture maps. For both the dates, we observed
) between the measured and modelled soil moisture (Figure 6).
However, at some
locations, the difference between the modelled and measured values of soil moisture is comparatively
large. This is probably due to the spatial scale mismatch, heterogeneous ﬁeld conditions, measurement
uncertainty, and model bias. When in-situ measurement is compared with the satellite derived soil
moisture, a representative error arises due to the difference in the spatial scale of in-situ measurement
and satellite observation. The spatial scale mismatch becomes more prominent when the land surface
is heterogeneous. This limits the competency to compare the point measurement with the satellite [
The error in the retrieval of soil moisture increases with the heterogeneity in land surface
Further, the measurement uncertainty is mainly due to the error associated with in-situ measurement.
For example, error resulting from the conversion of dielectric constant to soil moisture in TDR, presence
Remote Sens. 2020,12, 2266 11 of 19
of organic matter in the soil, overestimation of drying condition in oven and difference in the sampling
depth of the in-situ and satellite measurements .
To reduce the measurement uncertainty, we have calibrated the TDR, removed the organic matter
from soil the soil samples, and collected soil samples in the ﬁeld according to the simulated penetration
depth of the C-band SAR signal in the ground [
]. Model error (or bias) is mainly due to the
assumptions followed by its use.
0.05 0.1 0.15 0.2 0.25
TDR SM [m3/m3]
Satellite SM [m3/m3]
N = 37, Bias = 0.018 m3/m3, R2= 0.75
Regression curve between satellite derived and in-situ (TDR) measured soil moisture.
Shaded gray region is the 95% conﬁdence level of the regression curve.
To overcome the systematic errors (instrument calibration and model error), we performed a bias
correction by applying the CDF matching approach [
]. This is one of the widely used statistical
methods to minimise the bias in satellite-derived soil moisture [
]. In principle, we adjusted the
satellite-derived soil moisture according to the CDF of in-situ (TDR) soil moisture to minimise their
difference (Figure 7).
Applying the CDF correction on our data, biases in the soil moisture derived from Sentinel-1A
has reduced from 0.02 m
to 0.001 m
. Finally, we used the bias corrected values to generate
soil moisture maps for 17 and 29 January 2019 (Figure 8) of the study area.
Remote Sens. 2020,12, 2266 12 of 19
0.05 0.1 0.15 0.2 0.25 0.3 0.35
Soil moisture [m3/m3]
TDR SM (Reference)
Sentinel 1A SM (Biased)
Sentinel 1A SM (Corrected)
Bias correction using the CDF matching technique. Solid black line is the CDF of in-situ
measured soil moisture using TDR, dashed and dotted lines in black are the CDF of biased and
corrected soil moisture estimated from sentinel-1A respectively.
00.05 0.1 0.15 0.2 0.25 0.3 0.35
Soil moisture [m3/m3]
Spatial distribution of soil moisture estimated from Sentinel-1. Pixels shown in white
correspond to the region where modiﬁed Dubois model is not valid.
Remote Sens. 2020,12, 2266 13 of 19
This study uses modiﬁed Dubois model to estimate soil moisture from dual polarised (VV and VH)
Sentinel-1A images. Our result suggests that the model derived soil moisture accord well (
and RMSE = 0.035 m
) with the in-situ measurement (Figure 6). This is consistent with the range
of RMSE (0.03–0.04) m3/m3reported by other researchers .
The modelled soil moisture is subject to bias due to various geometric, atmospheric and modelling
errors. The magnitude of these uncertainties depends on various factors such as choice of a backscatter
model, frequency of SAR images, ground condition and vegetation types. Several methods such as
mean based (linear, local intensity and variance scaling) and the distribution-based (quantile and CDF
matching) have been developed to correct the bias from the modelled soil moisture values [
We have used the CDF matching approach to minimize the bias from our modelled soil moisture.
In doing so, we have adjusted the CDF of biased values according to the CDF of reference data.
signiﬁcantly reduced the bias from our modelled soil moisture. Figure 9, shows the relative
soil moisture values estimated from Sentinel-1A images before and after the CDF correction.
5 10 15 20 25 30 35
Relative soil moisture [m3/m3]
TDR SM (Reference) Sentinel 1A SM (Biased) Sentinel 1A SM (Corrected)
Relative soil moisture plotted at their corresponding sample location ID. Difference between
the measured (solid line) and modelled (dotted lines) soil moisture is shown before and after the
We observed, at some locations the modelled soil moisture is overestimated or underestimated
with respect to the measured values. The underestimation is probably related to low backscattering
coefﬁcients from relatively smooth surfaces. Similarly, the overestimation of soil moisture could be
associated with the high surface roughness resulting in high backscattering coefﬁcients.
Though Sentinel-1A images provide a ﬁrst-order estimation of soil moisture, modelling soil
moisture from satellite images has substantial limitations and challenges. Most of the backscatter
models used for the estimation of the relative soil permittivity from SAR backscatter are only valid for
a speciﬁc range of soil moisture. For example, the modiﬁed Dubois model is valid for soil moisture in
a range between 0 and 0.35
. Microwave SAR images with appropriate backscatter models can
estimate soil moisture only upto a few cms below the soil surface. In our case, we have estimated the soil
moisture from the top about 5 cm below the ground surface. Further, many of the existing backscatter
models are applicable for speciﬁc landuse and landcover classes. For example, Oh and water cloud
models are applicable for barren and vegetated lands, respectively. The modiﬁed Dubois model can
be applied on both barren and sparsely vegetated (NDVI
0.4) land. In summary, modiﬁed Dubois
model performs well over the semi-arid region on agriculture and barren land. The performance is
further improved when the bias correction method is used.
Moreover, estimation of soil moisture from C-band SAR is sensitive to various parameters such
as; the incidence angle, polarisation, vegetation height and vegetation indices, i.e., Leaf Area Index
Remote Sens. 2020,12, 2266 14 of 19
observed that in a typical agricultural ﬁeld (LAI
0.5), the effect of vegetation is
more prominent in the radar backscatter compared to other target properties.
As a consequence, when the vegetation effect starts dominating, it complicates the soil moisture
retrieval. The backscatter values results from the combined signature of vegetation and underlying
soil water [
]. In such condition we can not ignore the attenuation due to vegetation. To minimise the
effect of vegetation, scattering model such as the WCM can be implemented [79–83].
We have shown that the modiﬁed Dubois model provides a good estimate (R
= 0.75) of soil
moisture in a region of heterogeneous land cover. The modelled soil moisture is subject to error due to
the model (systematic) and sampling (random) errors. We have shown that the systematic error (also
called systematic bias) can be largely minimised by the CDF matching technique. Whereas random
errors can be reduced by increasing the number of sample size.
We found that the VV polarisation of Sentinel-1A is suitable for soil moisture monitoring.
mainly because the VV polarisation is more sensitive to the soil contribution. In contrast,
is more sensitive to the volume scattering, and it describes the vegetation contribution
more effectively. Since our model is only for VV or HH, we have used the VV polarisation based on
the polarisation of the Sentinel-1A data.
Further, the potential of VV and HH polarisation of Sentinel-1A may be evaluated, especially for
the models (i.e., WCM) that can estimate soil moisture in diverse vegetation condition. Finally, our
ﬁrst-order analysis calls for a more detailed study on soil moisture modelling from Sentinel-1A images
in diverse soil, landuse and landcover conditions.
This study is a step towards monitoring the surface soil moisture at higher spatial and temporal
resolution from remote sensing data. Our methodology can be used to predict and monitor
meteorological droughts, agricultural productivity and managing water resources in the region.
Conceptualization, A.S. and K.G.; methodology, A.S., G.K.M. and K.G.; software,
A.S. and K.G.; validation, G.K.M., A.S. and K.G.; formal analysis, A.S. and G.K.M.; investigation, K.G. and
A.S.; resources, K.G. and S.K.; data curation, G.K.M., A.S. and K.G.; writing—original draft preparation, A.S.
and K.G.; writing—review and editing, K.G. and A.S.; visualization, K.G. and S.K.; supervision and project
administration, K.G.; funding acquisition, K.G. and S.K. All authors have read and agreed to the published version
of the manuscript.
Funding: This research was funded by the Space Applications Centre (SAC-ISRO) under NASA-ISRO Synthetic
Aperture Radar (NISAR) mission through grant Hyd-01.
We would like to acknowledge IISER Bhopal for providing institutional support.
PhD is supported by the Department of Science and Technology (DST), Government of India
through DST-INSPIRE fellowship. We gratefully acknowledge S.K. Tandon for fruitful suggestions. We thanks to
the editor and all the three anonymous reviewers for providing helpful comments and suggestions.
Conﬂicts of Interest: The authors declare no conﬂict of interest.
Theta probe (ML3 sensor) requires an intensive soil speciﬁc and a sensor speciﬁc calibration
before being used for data acquisition in the ﬁeld. The soil speciﬁc calibration explores a functional
relationship between the relative soil permittivity and soil moisture. In contrast, the sensor speciﬁc
calibration explores the functional relationship between the relative soil permittivity and ML3 output
(volts). Both the soil and sensor speciﬁc calibration equations are combined to ﬁnally convert the
sensor output directly into soil moisture. The soil speciﬁc calibration allows to ﬁnd the two constants
(a0,a1) of Equation (A1). √e=a0+a1·mv(A1)
Remote Sens. 2020,12, 2266 15 of 19
For sensor calibration, ML3 sensor measures the bulk relative soil permittivity using the empirical
relation given by Equation (A2);
√e=1.0 +6.175 ·V+6.303 ·V2−73.578 ·V3+183.44 ·V4−184.78 ·V5+68.017 ·V6(A2)
where, Vis the voltage in Volt. Combining soil and sensor speciﬁc calibration equation reads
Before the ﬁeld campaign, we have calibrated the theta probe at three different locations in the
study area (Figure A1).
Soil samples used from three different ﬁelds for the calibration of MLT-3 theta probe.
Samples from S1 and S3 corresponds to agricultural lands composed of black cotton soil and rich
in organic matters. S2 consists of black soil with granules rubble (about 20–25%) formed due to the
subsequent weathering of Deccan basalt.
The corresponding values of the calibration constant is given Table A1.
Table A1. Field derived calibration constants for MLT-3 theta probe.
Measuring Unit Site 1 (S1) Site 2 (S2) Site 3 (S3)
Ls(cm3) 563 563 563
Ww(gm) 491 505 504
Vw(mV) 342 333 350
W0(gm) 410 415 421
V0(mV) 101 72 90
a01.6 1.5 1.6
a17.1 7.4 7.6
, we have measured two voltage from Equation (A2).
to the dry and wet samples respectively. We have also measured wet weight (
) and dry weight (
of the samples.
Calculation of a0
: For dry soil (i.e.,
=0), Equation (A1), is reduced to
in Equation (A2), we have calculated the value of
. Eventually we calculated
Calculation of a1: For wet soil, we calculated the soil moisture as;
Remote Sens. 2020,12, 2266 16 of 19
is the volume occupied by the sample in the beaker. By substituting the value of
Equation (A2), we have calculated the values of √em. Finally a1is calculated according to;
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