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remote sensing
Article
Retrieval of Soil Moisture Content Based on
a Modified Hapke Photometric Model: A Novel
Method Applied to Laboratory Hyperspectral and
Sentinel-2 MSI Data
Yuan Zhang 1,†, Kun Tan 1,2,3,*,†, Xue Wang 2,3 and Yu Chen 1
1
Key Laboratory for Land Environment and Disaster Monitoring of NASG, China University of Mining and
Technology, Xuzhou 221116, China; ts18160052a31@cumt.edu.cn (Y.Z.); chenyu@cumt.edu.cn (Y.C.)
2
Key Laboratory of Geographic Information Science (Ministry of Education), East China Normal University,
Shanghai 200241, China; xwang@geo.ecnu.edu.cn
3School of Geographic Sciences, East China Normal University, Shanghai 200241, China
*Correspondence: tankun@geo.ecnu.edu.cn; Tel.: +86-021-5434-1227
†Y.Z. and K.T. contributed equally to this work.
Received: 6 June 2020; Accepted: 10 July 2020; Published: 13 July 2020
Abstract:
Soil moisture is the crucial carrier of the global hydrologic cycle and the dynamic energy
balance regulation process. Therefore, it is of great significance to monitor surface soil moisture
content (SMC) accurately for the study of the natural ecological environment. The Hapke model is
the most widely used photometric model in soil remote sensing research, but the development of this
model is limited by the lack of valid multi–angular data. The main innovations of this paper have
two aspects: (1) A novel soil moisture retrieval approach based on the Hapke (SMR–Hapke) model
is derived by exploring the relationship between single scattering albedo (SSA) and SMC on the
optical bands from 400 to 2400 nm. The performance of the proposed model was verified on a dataset
consisting of four different soil samples, and the experimental results indicated that the inverted
soil moisture from SMR–Hapke model coincided with the measurement values, with the R
2
being
generally more than 0.9 in the solar domain. (2) The SMR–Hapke model has been reduced to a linear
form on the SWIR field and a physically-based normalized difference soil moisture index
NDSMIHapke
has been proposed. Based on the laboratory-based hyperspectral data, we compared the performance
of
NDSMIHapke
with other traditional soil moisture indices using linear regression analysis, and the
results demonstrate that the proposed
NDSMIHapke
had a great potential for estimating SMC with R
2
values of 0.88. Finally, high–resolution SMC map was produced by combining the Sentinel–2 MSI
data with
NDSMIHapke
. This study provides a novel extended Hapke model for the estimation of
surface soil moisture content.
Keywords:
soil moisture content; Hapke photometric model; reflectance spectroscopy; Sentinel–2 MSI
1. Introduction
Soil moisture, one of the main ingredients of terrestrial ecosystems, links the global energy and
hydrologic cycles by modulating the partitioning of sensible and latent heat fluxes [
1
], and profoundly
affects the spatio–temporal variation of climatic conditions [
2
]. The monitoring of surface soil moisture
content (SMC) can provide key information for precision agriculture [
3
] and a reference for regional
hydrological studies [
4
,
5
]. Although traditional manual methods show a high accuracy in estimating
soil moisture, it is difficult to reflect the spatial distribution of SMC at the macro level with expensive in
situ measurements and a time–consuming spatial sampling process. As a technology for observing the
Remote Sens. 2020,12, 2239; doi:10.3390/rs12142239 www.mdpi.com/journal/remotesensing
Remote Sens. 2020,12, 2239 2 of 21
Earth, many low–cost and timely remote sensing methods have been developed to realize the dynamic
monitoring of SMC in large areas [6].
The main SMC retrieval methods can be classified into two major categories, based on the
difference of the spectral response principles: microwave remote sensing methods and optical remote
sensing methods. Microwave remote sensing systems have achieved significant success in recent
years, including the Advanced Microwave Scanning Radiometer for the Earth Observing System
(AMSR–E) [
7
], the Soil Moisture and Ocean Salinity missions (SMOS) [
8
,
9
], and the Soil Moisture Active
and Passive (SMAP) missions [
10
]. However, it is worth mentioning that the coarse spatial resolution
of the microwave soil moisture products (mostly in the range of 25–40 km) limits their application in
local areas, especially in the field of precision irrigation and agricultural drought assessment. Optical
remote-sensing methods are also essential for soil moisture estimation because of their higher spatial
resolutions. The spectral regions used by the optical methods cover the thermal infrared and visible
and near-infrared (VNIR) bands. Examples of such optical methods include: (i) Physically-based
or empirical radiative transfer model [
11
,
12
]; (ii) Empirical indices model of soil moisture [
13
,
14
];
(iii) Hyperspectral-based models [
15
]; (iv) Triangular or trapezoidal method of two-dimensional
space [
16
,
17
]. The optical methods are easy to operate and the computational complexity is low.
From the perspective of practical application, the microwave remote-sensing method is applicable
to the global scale, the VNIR–thermal method is suitable for watershed, and the soil moisture index
model is more effective on the regional or field scales. With the development of machine learning,
statistical models combining hyperspectral data for soil moisture retrieval have emerged in recent
years [
18
,
19
], such as support vector machine (SVM) [
20
,
21
], artificial neural networks (ANNs) [
22
,
23
],
etc. However, these statistical models have certain limitations in explaining the variation of reflectance
in terms of the spectral mechanism.
The interaction of radiation with soil (scattering, absorption, refraction, and reflection) depends
on the optical properties of media, which are strongly related to the moisture content, organic carbon,
metal oxide, etc. [
24
,
25
]. Modeling the processes of interaction can give useful information about
surface properties [
26
,
27
]. In the optical domain (400–2500 nm), radiative transfer equation (RTE)
is an important tool for retrieving information about soils. It can explicitly relate bidirectional
reflectance to the optical properties of soil such as the single scattering reflectance (SSA), absorption
and backscattering coefficients, porosity factor and scattering phase function [
28
,
29
]. Although various
SMC estimation methods have their advantages, they are often empirical. Comparatively, physical
models or semi-empirical models based on the RTE are more complicated than statistical methods,
but provide a more general approach to analyzing different samples. To date, some research has
demonstrated the retrieval method of SMC based on the RTE physical process. Bach and Mauser [
30
]
ascribed the general darkening of soil to the internal reflection of incident radiation in the soil water
layer, and the water-specific absorption phenomena were formulated by the Beer–Lambert–Bouguer
law.
Sadeghi et al.
[
31
] presented a physically–based soil moisture retrieval model in the solar
domain that was based on the Kubelka–Munk two-flux radiative transfer theory. Roosjen et al. [
32
]
studied the effects of SMC on anisotropic reflectance with the Rahman–Pinty–Verstraete (RPV) model,
and the results indicated that reflectance anisotropy contains more information on SMC than spectral
reflectance. Bablet et al. [
11
] derived a semi–empirical multilayer radiative transfer model of soil
reflectance (MARMIT), considering the multiple reflection and refraction processes between air, water,
and soil. Yuan et al. [
12
] deduced the relationship between SMC and diffuse reflectance using the
absorption coefficient and scattering coefficient related to SMC, and proposed the SMC retrieval
model based on the Kubelka–Munk theory. The main SMC retrieval models based on a physical
process are summarized in Table 1, which also lists the corresponding expressions and the meanings of
the parameters. The physical methods often require prior information that is difficult to determine,
and their application is limited due to a lack of explicit equations that relate the bidirectional reflectance
parameters to soil properties.
Remote Sens. 2020,12, 2239 3 of 21
The Hapke photometric model [
33
] is the most widely used kind of Bidirectional Reflectance
Distribution Function (BRDF) model in the soil remote sensing research. However, the Hapke model
does not consider soil moisture, which limits its application in soil moisture inversions using remote
sensing data. Yang et al. [
34
] extended the SOILSPECT model [
35
] with the soil equivalent water
thickness to establish the SWAP–Hapke soil directional radiation model. The SWAP–Hapke model is
based on multi–angle data, while the valid spaceborne multi–angular data set is not much. The major
contributions of this study are as follows: (i) proposed and evaluated a novel soil moisture retrieval
model based on Hapke model (SMR–Hapke model), which can be applied to single–angular reflectance
data. The model contains five physical and empirical parameters to determine the conversion between
moisture content and reflectance; (ii) developed a new normalized difference soil moisture index
(
NDSMIHapke
) from the linearized SMR–Hapke model in the shortwave infrared (SWIR) region,
and compared the performance with other moisture index models; (iii) high-resolution SMC map was
produced combining the Sentinel–2 MSI multispectral data and NDSMIHapke .
Table 1. Summary of the SMC retrieval models based on physical processes.
Reference Expression Remark
Bach and Mauser
[30]
ρ=ρ0
n2(1−ρ0)+ρ0
R=R0·e(−α·l)
ρ,R: spectral reflectance of moist soil
ρ0,R0: spectral reflectance of dry soil
n: refractive index of liquid
l: active thickness of water layer
free parameters: l
Sadeghi et al. [31]R=nw−nα
nw+nα2θ+1+r(θ)−q[r(θ)]2+2r(θ)
r=σrd(1−θ
θs)+rs(θ
θs)
σ(1−θ
θs)+(θ
θs)
r(θ): transformed volume reflectance
free parameters: rd,rs,σ
Bablet et al. [11]
Rmod =ε×Rws +(1−ε)×Rd
Tw=e−αBL
Rws =r12 +t12t21 RdT2
w
1−r21RdT2
w
Tw: transmittance
αB: the specific absorption coefficient of in
situ water
L: the thickness of the water layer
free parameters: ε,L
Yuan et al. [12]r(θ)=r11−θ
1−θ1+a1θ−θ1
1−θ1
1−θ
1−θ1
r1=(1−R1)2
2R1
a1: the ratio of the absorption coefficient of
soil water to the scattering coefficient of soil
with a water content of θ1
free parameters: a1
Yang et al. [34]
rw=r0×e(−α·ξ)
r(θs,θo,φ)=
ω
41
cosθs+cosθoP(g,g0)[1+B(g)] +H(cosθs)H(cosθo)−1
P(g)=1+bcos g +c(3cos2g−1)
2+b0cos g0+c0(3cos2g0−1)
2
B(g)=B0
1+(1/h)tan(g/2)
r(θs,θo,φ): the soil bidirectional
reflectance model
α: absorption coefficient
ξ: equivalent water thickness
free parameters : ω,B0,h,b,c,b0,c0,ξ
2. Background and Methods
2.1. Description of SMR–Hapke Model
The formulation of the radiative transfer theory derived by Hapke [
36
] describes the interaction
of light with a medium, and taking the physical, geometry, and optical parameters of the particles
into account. It is the most widely used photometric model in planetary astronomy, earth observation
research and mineralogical information estimation [
37
,
38
], and this model is simple and can reproduce
the photometric response of bare surfaces well [
39
]. In the Hapke model, the bidirectional reflectance
r(µ0,µ)can be derived using Equation (1):
r(µ0,µ)=ω
4
1
µ0+µP(g)[1+B(g)] +H(µ0)H(µ)−1, (1)
where
ω
is the single scattering albedo (SSA) of soil medium;
µ0
and
µ
are the cosines of the
incidence zenith angles and emittance zenith angles, respectively;
g
is the phase angle and
B(g)
is
Remote Sens. 2020,12, 2239 4 of 21
the backscattering function. The phase function
P(g)
describes the angular distribution of the light
scattered from a soil surface. The H(x)function is Chandrasekhar ’s isotropic scattering function:
H(x)=1+2x
1+2x√1−ω. (2)
For dense mixed media, the incident light will usually interact with the particles of the mixture
many times before reaching the sensor. The parameter
ω
is defined as the probability that the photons
would be scattered by the particle:
ω=S
E=S
S+A, (3)
where Sand Aare the average scattering coefficient and average absorption coefficient of the medium,
respectively; Eis the average extinction coefficient of the medium, equal to
S+A
. It can be reasonably
assumed that the Sand Avalues are the summed function of the absorption and scattering coefficients
of its components [
31
,
40
]. Considering the effect of moisture content, Sand Acan be expressed as
follows:
A=Ad+Awθ,
S=Sd+Swθ.(4)
where
Ad
and
Aw
denote the absorption coefficients of dry soil and soil moisture, respectively;
Sd
and
Sw
represent the scattering coefficients of dry soil and soil moisture, respectively; and
θ
is the volumetric
moisture content (VMC), which can be calculated by Equation (5):
θ=(m−m0)/ρwater
m0/ρb
, (5)
where
m
and
m0
are the mass of wet and dry soil, respectively;
ρb
represents the bulk density of soil;
and
ρwater
is the density of water (1.0 g
·
cm
–3
). With the increase in the
θ
, the absorption and scattering
coefficients of saturated soil can be formulated as:
As=Ad+Awθs,
Ss=Sd+Swθs.(6)
where
θs
indicates the saturated moisture content.
F
denotes equal to the ratio
A/S
, combining
Equations (3) to (6) yields:
F=1−ω
ω=A
S=As−Aw(θs−θ)
Ss−Sw(θs−θ). (7)
Equation (7) reflects the relationship between SSA and SMC. However, Equation (1) is relatively
complex and requires more input parameters, so it is difficult to calculate the value of SSA directly.
Hapke simplified Equation (1) by making the following assumption [
41
]: (1) the opposition effect can
be ignored when the phase angle is large enough, and
B(g)=
0; (2) with the assumption of isotropic
scattering properties, P(g) =1. Then the analytic solution for the SSA can be calculated from r(µ0,µ):
ω(r(µ0,µ)) =1−
q(u0+u)2−(4u0u+Γ)(1−Γ)−(u0+u)
4u0u+Γ
2
, (8)
Γ=(1+2u0)(1+2u)
4(u0+u)r(µ0,µ). (9)
In cases of high moisture content, especially near saturation or oversaturation, the influence of
Fresnel reflection, which is typically only a small fraction of the total reflectance, needs to be considered.
The optical properties of soil moisture are difficult to determine due to the suspended particles and
Remote Sens. 2020,12, 2239 5 of 21
dissolved organic matter. Therefore, in order to simplify the modeling process, the reflectance of pure
water is used to represent Fresnel reflection RF:
RF=nw−1
nw+12
, (10)
where
nw
represents the refractivity of pure water. The calculated spectral reflectance of pure water is
shown in Figure 1using the measurements of Segelstein [42].
Remote Sens. 2020, 12, x FOR PEER REVIEW 5 of 22
(,)=1−
(+)−(4+)(1−)–(+)
4+ , (8)
=(1+2)(1+2)
4(+)(,) . (9)
In cases of high moisture content, especially near saturation or oversaturation, the influence of
Fresnel reflection, which is typically only a small fraction of the total reflectance, needs to be
considered. The optical properties of soil moisture are difficult to determine due to the suspended
particles and dissolved organic matter. Therefore, in order to simplify the modeling process, the
reflectance of pure water is used to represent Fresnel reflection :
=−1
+1, (10)
where represents the refractivity of pure water. The calculated spectral reflectance of pure water
is shown in Figure 1 using the measurements of Segelstein [42].
Figure 1. Spectral reflectance of pure water [42].
Then a total reflectance () model of wet soil is established by adding the Fresnel reflectance to
the volume bidirectional reflectance from the Hapke model:
=∙+(,)=−1
+1+
41
+()() , (11)
subject to:
= 1
1+ , (12)
=−(−)
1−(−) , (13)
with =
⁄, =
⁄, and =
⁄. The parameter is utilized to adjusting the surface
effect of the soil moisture. In order to facilitate the practical application in remote sensing, Equations
(11)–(13) are further rearranged so that SMC can be directly calculated according to :
=−−
− , (14)
=1−(−)
(−) . (15)
The () function is calculated by Equations (8) and (9). Five parameters (,,,,and )
were introduced into the soil moisture retrieval model, which renamed the SMR–Hapke model.
represents the saturated moisture content of the soil, which is independent of the wavelength.
Figure 1. Spectral reflectance of pure water [42].
Then a total reflectance (
Rt
) model of wet soil is established by adding the Fresnel reflectance to
the volume bidirectional reflectance from the Hapke model:
Rt=ε·RF+r(µ0,µ)=εnw−1
nw+12
+ω
4
1
µ0+µH(µ0)H(µ), (11)
subject to:
ω=1
1+F, (12)
F=rs−t1(θs−θ)
1−t2(θs−θ), (13)
with
rs=As/Ss
,
t1=Aw/Ss
, and
t2=Sw/Ss
. The
ε
parameter is utilized to adjusting the surface
effect of the soil moisture. In order to facilitate the practical application in remote sensing, Equations
(11)–(13) are further rearranged so that SMC can be directly calculated according to Rt:
θ=θs−F−rs
Ft2−t1
, (14)
F=1−ω(Rt−εRF)
ω(Rt−εRF). (15)
The
ω(x)
function is calculated by Equations (8) and (9). Five parameters (
ε
,
rs
,
t1
,
t2
,
and θs
)
were introduced into the soil moisture retrieval model, which renamed the SMR–Hapke model.
θs
represents the saturated moisture content of the soil, which is independent of the wavelength.
ε
controls the proportion of Fresnel reflection by the water film on the soil surface.
rs
,
t1
and
t2
are
the functions of the surface roughness, observation geometry, and refractive index, which are closely
related to the absorption and scattering characteristics of the soil and are difficult to obtain by direct
measurement. If the corresponding parameter values of each sample at different wavelengths are
calculated, the mutual conversion of
Rt
and
θ
can be realized. The variables and their definitions of
SMR–Hapke model are summarized in Table 2.
Remote Sens. 2020,12, 2239 6 of 21
Table 2. Description of the parameters of SMR–Hapke model.
Symbol Description
RtThe total reflectance received from sensor.
RFFresnel reflection at the air–soil interface due to differences in the refractive indices of the
soil and surrounding air.
µ0,µThe cosines of incidence zenith angles and emittance zenith angles.
r(µ0,µ)The bidirectional reflectance from the Hapke model.
nwThe refractivity of pure water.
εThe parameter to adjusting the surface effect of the soil moisture.
ω
Single scattering albedo (SSA), which is defined as the ratio of the amount of light scattered
from the medium to the combined amount of light scattered and absorbed at a
given wavelength.
H(x)The approximation of Chandrasekhar’s isotropic scattering function.
S,AThe average scattering coefficient and average absorption coefficient of the medium.
FThe ratio of absorption coefficients to scattering coefficient.
2.2. NDSMIHapke : Normalized Difference Soil Moisture Index Based on the Hapke Model
Since the optical properties of soil depend on the physical and chemical properties of the
components, the parameters in the proposed Equation (11) should also vary greatly with the
heterogeneity of the soil, and the nonlinear form of SMR–Hapke model increases the complexity of
inversion. It should be noted that the scattering effect of soil moisture is much weaker than that of soil
particles in the Shortwave Infrared (SWIR) field (especially on the sensitive bands of moisture), so we
assumed that the effects of
t2
were inconsequential and could be ignored. With this consideration,
Equation (14) can be reformulated as:
θ=F
t1
+t1θs−rs
t1
, (16)
Equation (16) reflects the linear relationship between
θ
(SMC) and
F
. In the practical application
using satellite remote sensing, under the assumption that Fresnel reflection is negligible,
F
can be
calculated from bidirectional reflectance according to Equations (7)–(9) and the moisture content can
be obtained by simple linear regression method with Equation (16).
The sensitive bands of soil moisture retrieval in laboratory spectrometry are near 1450 and 1900 nm,
which are shown in Figure 2. However, these bands are usually not used in satellite remote sensing
imagery due to the strong interference of atmospheric water-vapor. The European Space Agency
launched Sentinel-2, which carries an innovative wide-swath, high-resolution, multispectral imager
(MSI) with 13 spectral bands covering the visible, near-infrared (VNIR) and the shortwave-infrared
(SWIR) spectral region. Spectral band 11 (1610 nm) and band 12 (2190 nm) are less affected by water
vapor absorption and present a well sensitivity with the fluctuations of moisture, which have greater
potential to be applied for the SMC estimation. Therefore, these two bands were utilized to establish
the soil moisture index model.
Remote Sens. 2020,12, 2239 7 of 21
Remote Sens. 2020, 12, x FOR PEER REVIEW 7 of 22
Figure 2. Absorption coefficient of pure water [43,44].
Single-band SMC retrieval with traditional broadband remote-sensing data may cause the lower
performance. While the combination of different bands can reduce the effects of soil type and
instrumental errors. Figure 3a,b illustrate the soil reflectance and the corresponding F calculated by
Equations (7) to (9), respectively. The difference value (−) indicates a significant linear
relationship with SMC (Figure 3d).
Figure 3. (a) Reflectance of Mollisol soil; (b) F value of Mollisol soil calculated by Equations (7) to (9);
(c) Value of −; (d) Difference value and SMC.
Considering the correlation between SMC and the difference of F on two shortwave–infrared
bands, a normalized difference soil moisture index based on the Hapke model was developed:
=−
+ . (17)
where and represent the value of F at 2190 nm and 1610 nm calculated from Equations
(7) to (9). To date, some indices have been proposed to determine and map soil moisture. Five indices
are listed in Table 3, which are mainly calculated by the reflectance of the SWIR bands.
Table 3. Soil moisture indices found in the literature.
Figure 2. Absorption coefficient of pure water [43,44].
Single-band SMC retrieval with traditional broadband remote-sensing data may cause the lower
performance. While the combination of different bands can reduce the effects of soil type and
instrumental errors. Figure 3a,b illustrate the soil reflectance and the corresponding Fcalculated by
Equations (7) to (9), respectively. The difference value (
F2190 −F1610
) indicates a significant linear
relationship with SMC (Figure 3d).
Remote Sens. 2020, 12, x FOR PEER REVIEW 7 of 22
Figure 2. Absorption coefficient of pure water [43,44].
Single-band SMC retrieval with traditional broadband remote-sensing data may cause the lower
performance. While the combination of different bands can reduce the effects of soil type and
instrumental errors. Figure 3a,b illustrate the soil reflectance and the corresponding F calculated by
Equations (7) to (9), respectively. The difference value (−) indicates a significant linear
relationship with SMC (Figure 3d).
Figure 3. (a) Reflectance of Mollisol soil; (b) F value of Mollisol soil calculated by Equations (7) to (9);
(c) Value of −; (d) Difference value and SMC.
Considering the correlation between SMC and the difference of F on two shortwave–infrared
bands, a normalized difference soil moisture index based on the Hapke model was developed:
=−
+ . (17)
where and represent the value of F at 2190 nm and 1610 nm calculated from Equations
(7) to (9). To date, some indices have been proposed to determine and map soil moisture. Five indices
are listed in Table 3, which are mainly calculated by the reflectance of the SWIR bands.
Table 3. Soil moisture indices found in the literature.
Figure 3.
(
a
) Reflectance of Mollisol soil; (
b
)Fvalue of Mollisol soil calculated by Equations (7) to (9);
(c) Value of F2190 −F1610; (d) Difference value and SMC.
Considering the correlation between SMC and the difference of Fon two shortwave–infrared
bands, a normalized difference soil moisture index based on the Hapke model was developed:
NDSMIHapke =F2190 −F1610
F2190 +F1610
. (17)
where
F2190
and
F1610
represent the value of Fat 2190 nm and 1610 nm calculated from Equations (7) to
(9). To date, some indices have been proposed to determine and map soil moisture. Five indices are
listed in Table 3, which are mainly calculated by the reflectance of the SWIR bands.
Remote Sens. 2020,12, 2239 8 of 21
Table 3. Soil moisture indices found in the literature.
Soil Moisture Index Equation Reference
NSMI (B1800 −B2119)/(B1800 +B2119 )Haubrock et al. [4]
NINSOL (B2076 −B2230)/(B2076 +B2230 )Fabre et al. [14]
NINSON (B2122 −B2230)/(B2122 +B2230 )OltraCarrióet al. [45]
STR (1−B2185)2/2B2185 Sadeghi et al. [46]
NSDSI1 (B1694 −B2230)/B1694 Yue et al. [13]
3. Research Area and Data
3.1. Data Preparation for SMR–Hapke Model
In this section, the accuracy of the proposed SMR–Hapke model was evaluated using laboratory
spectral data of four soils at different SMC gradients, as shown in Table 4. Spectral data of Aridosol,
Endisol and Mollisol were measured and published by Lobell [
47
]. The quartz sand’s data are from
J. Tian [48].
Table 4. Summary of the main information on the datasets.
Soil Type SMC Angles Bulk Density
(g·cm3)
Levels Range Incidence Emittance
Aridosol 10 0–0.319 15◦0◦1.54
Endisol 7 0–0.442 15◦0◦1.35
Mollisol 9 0–0.696 15◦0◦0.64
Quartz sand 9 0–0.354 – 0◦1.44
The Quartz sand’s incidence zenith angle is not provided in the literature [
48
], and set to 15
◦
in this article. Considering the correlation of adjacent bands, the spectra were resampled at 10 nm
intervals, and then the Savitzky–Golay method was adopted for denoising. The size of the filtering
window was set to 9. The final spectral curves are depicted in Figure 4.
All soil systems are spatially heterogeneous, and soil spectra are controlled by many factors such as
mineral composition, organic matter content, surface roughness, and observed geometry. Under natural
conditions, the physical and chemical properties of the soil change slowly with time. In contrast, soil
moisture greatly affects the optical properties of the soil. Generally speaking, moist soil has a lower
reflectance than dry soil, with a varying decreasing rate in the optical bands (400–2400 nm). It is clear that
the reflection spectra of the different soil types are diverse, as shown in Figure 4. From the absorption
characteristics, it can be seen that there are two strong water absorption bands near 1400 nm and
1900 nm, which dominate the reflectance in the SWIR bands. As a result of the differences in soil texture,
the absorption peaks of the different soils types vary in depth, width, and displacement. However,
the spectral curves at different SMC levels show similar shapes, which present an approximately
parallel trend. Compared with the SWIR bands, the visible bands (400–700 nm) show a lower response
to the fluctuations of moisture content, with no significant change of the curve shape.
Remote Sens. 2020,12, 2239 9 of 21
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Figure 4. Spectral reflectance of the four soil samples under various levels of volumetric soil water
content.
3.2. Data Preparation for
3.2.1. Research Area and Experiments
In order to explore the application of the proposed model, soil samples were
collected in Yitong County, Jilin province, China (E: 125°19'12", N: 43°19'48", Figure 5), during May
2019. This area belongs to the humid monsoon climate zone, which is in the middle temperate zone
of China. The region is hilly, with an average annual temperature of 5.5℃. The annual average
precipitation is 651.7 mm, and the sunshine is sufficient. Yitong River runs through the whole
research area from southeast to northwest. The average altitude of the study area is 305 m, the lowest
altitude is 262 m, and the highest altitude is 446 m. The soil types in the area are mainly dark brown
forest soil, meadow soil, black soil and alluvial soil.
Figure 4.
Spectral reflectance of the four soil samples under various levels of volumetric soil
water content.
3.2. Data Preparation for NDSMIHapke
3.2.1. Research Area and Experiments
In order to explore the application of the proposed
NDSMIHapke
model, soil samples were collected
in Yitong County, Jilin province, China (E: 125
◦
19
0
12”, N: 43
◦
19
0
48”, Figure 5), during May 2019.
This area belongs to the humid monsoon climate zone, which is in the middle temperate zone of China.
The region is hilly, with an average annual temperature of 5.5
◦
C. The annual average precipitation
is 651.7 mm, and the sunshine is sufficient. Yitong River runs through the whole research area from
southeast to northwest. The average altitude of the study area is 305 m, the lowest altitude is 262 m,
and the highest altitude is 446 m. The soil types in the area are mainly dark brown forest soil, meadow
soil, black soil and alluvial soil.
Remote Sens. 2020, 12, x FOR PEER REVIEW 10 of 22
Figure 5. Location of the study area and sampling points. The red and blue points indicate the
calibration and verification sites, respectively.
The farmland soil can be available due to the ploughing of the fields. The principle of soil
sampling in this study is to arrange the sampling points in the farmland area as evenly as possible
according to the traffic conditions. A total of 65 sites were surveyed in the study area, and three soil
samples at different depths (1–5cm, 20–40cm, and 60–80cm) for each sampling point were collected.
Surface soil (1–5cm) was collected by five–point sampling method for verification of Sentinel MSI
Images. All the samples were immediately put into impermeable sealed bags, and a total of 195
samples were collected. Almost all the soil samples are characterized as clay loam, and a small
amount of sandy loamy soil are present in the area (Figure 6).
Figure 6. Texture of the studied soil samples. The size of the soil particles was divided into clay (≤2
μm), silt (2–50μm) and sand (50–2000 μm) according to the United States Department of Agriculture
(USDA) classification.
3.2.2. Laboratory Measurement of Soil Moisture and Hyperspectral Reflectance
The hyperspectral data and SMC data were collected as follows. Firstly, the soil samples were
removed from the impervious sealed bags, and each sample was divided into two parts. For one part,
an ML3X soil moisture meter was used to record the volumetric moisture content of the soil.
Meanwhile, the other part was evenly placed into a petri dish, and an ASD FieldSpec 3 portable
Figure 5.
Location of the study area and sampling points. The red and blue points indicate the
calibration and verification sites, respectively.
The farmland soil can be available due to the ploughing of the fields. The principle of soil sampling
in this study is to arrange the sampling points in the farmland area as evenly as possible according to
the traffic conditions. A total of 65 sites were surveyed in the study area, and three soil samples at
Remote Sens. 2020,12, 2239 10 of 21
different depths (1–5 cm, 20–40 cm, and 60–80 cm) for each sampling point were collected. Surface soil
(1–5 cm) was collected by five–point sampling method for verification of Sentinel MSI Images. All the
samples were immediately put into impermeable sealed bags, and a total of 195 samples were collected.
Almost all the soil samples are characterized as clay loam, and a small amount of sandy loamy soil are
present in the area (Figure 6).
Remote Sens. 2020, 12, x FOR PEER REVIEW 10 of 22
Figure 5. Location of the study area and sampling points. The red and blue points indicate the
calibration and verification sites, respectively.
The farmland soil can be available due to the ploughing of the fields. The principle of soil
sampling in this study is to arrange the sampling points in the farmland area as evenly as possible
according to the traffic conditions. A total of 65 sites were surveyed in the study area, and three soil
samples at different depths (1–5cm, 20–40cm, and 60–80cm) for each sampling point were collected.
Surface soil (1–5cm) was collected by five–point sampling method for verification of Sentinel MSI
Images. All the samples were immediately put into impermeable sealed bags, and a total of 195
samples were collected. Almost all the soil samples are characterized as clay loam, and a small
amount of sandy loamy soil are present in the area (Figure 6).
Figure 6. Texture of the studied soil samples. The size of the soil particles was divided into clay (≤2
μm), silt (2–50μm) and sand (50–2000 μm) according to the United States Department of Agriculture
(USDA) classification.
3.2.2. Laboratory Measurement of Soil Moisture and Hyperspectral Reflectance
The hyperspectral data and SMC data were collected as follows. Firstly, the soil samples were
removed from the impervious sealed bags, and each sample was divided into two parts. For one part,
an ML3X soil moisture meter was used to record the volumetric moisture content of the soil.
Meanwhile, the other part was evenly placed into a petri dish, and an ASD FieldSpec 3 portable
Figure 6.
Texture of the studied soil samples. The size of the soil particles was divided into clay
(
≤
2
µ
m), silt (2–50
µ
m) and sand (50–2000
µ
m) according to the United States Department of Agriculture
(USDA) classification.
3.2.2. Laboratory Measurement of Soil Moisture and Hyperspectral Reflectance
The hyperspectral data and SMC data were collected as follows. Firstly, the soil samples were
removed from the impervious sealed bags, and each sample was divided into two parts. For one
part, an ML3X soil moisture meter was used to record the volumetric moisture content of the soil.
Meanwhile, the other part was evenly placed into a petri dish, and an ASD FieldSpec 3 portable
spectrometer with spectral range of 350–2500 nm and sampling interval of 1 nm was used to measure
the soil hyperspectral reflectance. As shown in Figure 7, a halogen lamp is used as the light source with
the illumination zenith Angle set to 40
◦
. We collected each spectrum five times, and then performed
outlier elimination and splice correction, taking the average spectra as the final actual reflectance
data. To prevent water evaporation from affecting the measurement results, the measurement of SMC
and the collection of the spectra were performed immediately after the soil samples were removed
from the sealed bags. In total, 195 sets of volumetric moisture content data and hyperspectral data
were acquired.
Remote Sens. 2020, 12, x FOR PEER REVIEW 11 of 22
spectrometer with spectral range of 350–2500 nm and sampling interval of 1 nm was used to measure
the soil hyperspectral reflectance. As shown in Figure 7, a halogen lamp is used as the light source
with the illumination zenith Angle set to 40°. We collected each spectrum five times, and then
performed outlier elimination and splice correction, taking the average spectra as the final actual
reflectance data. To prevent water evaporation from affecting the measurement results, the
measurement of SMC and the collection of the spectra were performed immediately after the soil
samples were removed from the sealed bags. In total, 195 sets of volumetric moisture content data
and hyperspectral data were acquired.
Figure 7. Experimental equipment and measured soil reflectance data.
3.2.3. Sentinel–2 MSI Data and Image Processing
Sentinel–2 is an earth observation mission developed by the European Space Agency (ESA) and
carries an innovative wide swath high-resolution multispectral instrument (MSI) with 13 spectral
bands, covering the Vis–NIR–SWIR electromagnetic frequency domains. We acquired the Sentinel–2
MSI data from the ESA Sentinel Scientific Data Hub (https://scihub.copernicus.eu/dhus/#/home), and
the satellite transit time (2019–05–04) was two days after the field sampling (2019–05–02).
Atmospheric corrections were applied to the MSI images to obtained the surface reflectance using
the ESA SNAP (version 7, http://step.esa.int/main/download/snap–download/) and Sen2Cor
packages (version 2.8 http://step.esa.int/main/third–party–plugins–2/sen2cor/sen2cor_v2–8/).
Reflectance at the two SWIR band [band 12 (central wavelength: 2185 nm) and band 11 (central
wavelength:1610nm)] was utilized for the calculation of the , and images were
resampled to 10-m resolution with the cubic convolution interpolation method. Using the
Classification tools based on Support Vector Machine (SVM) in the ENVI software to extract the bare
soil in the research area. Finally, the reflectance data of field sampling points of Sentinel–2 MSI images
were extracted by the Geospatial Data Abstraction Library (GDAL) package. Flow charts illustrate
the sequence of image-processing steps for mapping the surface soil moisture with in
Figure 8.
Figure 7. Experimental equipment and measured soil reflectance data.
Remote Sens. 2020,12, 2239 11 of 21
3.2.3. Sentinel–2 MSI Data and Image Processing
Sentinel–2 is an earth observation mission developed by the European Space Agency (ESA) and
carries an innovative wide swath high-resolution multispectral instrument (MSI) with 13 spectral bands,
covering the Vis–NIR–SWIR electromagnetic frequency domains. We acquired the Sentinel–2 MSI
data from the ESA Sentinel Scientific Data Hub (https://scihub.copernicus.eu/dhus/#/home), and the
satellite transit time (2019–05–04) was two days after the field sampling (2019–05–02). Atmospheric
corrections were applied to the MSI images to obtained the surface reflectance using the ESA SNAP
(version 7, http://step.esa.int/main/download/snap--download/) and Sen2Cor packages (version 2.8
http://step.esa.int/main/third--party--plugins--2/sen2cor/sen2cor_v2--8/). Reflectance at the two SWIR
band [band 12 (central wavelength: 2185 nm) and band 11 (central wavelength: 1610 nm)] was utilized
for the calculation of the NDSMIHapke , and images were resampled to 10-m resolution with the cubic
convolution interpolation method. Using the Classification tools based on Support Vector Machine
(SVM) in the ENVI software to extract the bare soil in the research area. Finally, the reflectance data of
field sampling points of Sentinel–2 MSI images were extracted by the Geospatial Data Abstraction
Library (GDAL) package. Flow charts illustrate the sequence of image-processing steps for mapping
the surface soil moisture with NDSMIHapke in Figure 8.
Remote Sens. 2020, 12, x FOR PEER REVIEW 12 of 22
Figure 8. Flowcharts illustrating the sequence of Sentinel–2 MSI data analyses steps for mapping
surface soil moisture content with
3.3. Performance Metrics
The coefficient of determination (R2), root mean square error (RMSE), and mean absolute error
(MAE) were used to evaluate the performance of model.
=1−∑( −)
∑(−
)
(18)
RMSE=∑( −)
(19)
MAE=∑|
−|
(20)
where and are the estimated and measured values of SMC, respectively;
is the
average measured value; and is the sample number. Mathematically, a higher R2 value
corresponds to a smaller RMSE and MAE, and represents a better modeling accuracy.
4. Results
4.1. SMR–Hapke Model Application
4.1.1. Parameter Calculation
Model inversion is achieved by searching the optimal values of unknown model parameters
(,,, and ), which minimizes the merit function. We use the mean–square error (MSE) as the
merit function to measure the difference between the measured and estimated values of reflectance:
MSE(,,,, ) = 1
()−(,)
(21)
where () is the measurement at a given wavelength (nm), and (,) is the simulated
reflectance described in Equation (11).
Figure 8.
Flowcharts illustrating the sequence of Sentinel–2 MSI data analyses steps for mapping
surface soil moisture content with NDSMIHapke .
3.3. Performance Metrics
The coefficient of determination (R
2
), root mean square error (RMSE), and mean absolute error
(MAE) were used to evaluate the performance of model.
R2=1−PN
i=1θmeas
i−θest
i2
Pn
i=1θmeas
i−θmeas2(18)
RMSE =sPN
i=1θest
i−θmeas
i2
N(19)
MAE =PN
i=1θest
i−θmeas
i
N(20)
Remote Sens. 2020,12, 2239 12 of 21
where
θest
and
θmeas
are the estimated and measured values of SMC, respectively;
θmeas
is the average
measured value; and
N
is the sample number. Mathematically, a higher R
2
value corresponds to
a smaller RMSE and MAE, and represents a better modeling accuracy.
4. Results
4.1. SMR–Hapke Model Application
4.1.1. Parameter Calculation
Model inversion is achieved by searching the optimal values of unknown model parameters
(
ε
,
rs
,
t1
,
t2and θs
), which minimizes the merit function. We use the mean–square error (MSE) as the
merit function to measure the difference between the measured and estimated values of reflectance:
MSE(ε,rs,t1,t2,θs)=1
N
N
X
k=1hRtrue(λ)−Rpred (λ,θk)i2(21)
where
Rtrue(λ)
is the measurement at a given wavelength
λ
(nm), and
Rpred(λ,θk)
is the simulated
reflectance described in Equation (11).
In this study, the optimal solutions of Equation (21) for each band are obtained by fitting the
model based on the laboratory spectral data of four soils (Aridosol, Endisol, Mollisol, and Quartz
sand), using the genetic algorithm of coupled nonlinear programming, implemented in Matlab R2019b.
By combining the global search capability of the genetic algorithm with the local search advantage of
the nonlinear programming algorithm, the merit function
MSE(ε,rs,t1,t2,θs)
can be minimized to
obtain the global optimal solution of the inverse problem.
As an illustration, Figure 9demonstrates that the MSE between the measured and the modeled
reflectance spectra of four soils is generally lower than 3
×
10
−4
in the whole band, indicating that
the proposed SMR–Hapke model shows a good performance and can accurately reflect the variation
trend of soil reflectance with moisture content. The calculated optimal values are displayed in
Figure 10, which reflects the variation curves of the five unknown parameters for the four samples.
Figure 10 indicates that parameters
ε
,
rs
,
t1
and
t2
vary greatly in range of 1200–2500 nm, and there are
obvious peaks and troughs in the two water absorption bands. Therefore, the proposed SMR–model
has high sensitivity in SWIR region. Note that the value of
θs
barely changes in the SWIR bands,
which can be ascribed to the saturated moisture content being only related to the physical and chemical
properties of the soil, instead of the wavelength. The significant wave peaks of
rs
and
t1
appear near
1400 nm and 1900 nm, which are due to the strong absorption of water in these spectral intervals,
and result in a small scattering coefficient for the soil.
Remote Sens. 2020, 12, x FOR PEER REVIEW 13 of 22
In this study, the optimal solutions of Equation (21) for each band are obtained by fitting the
model based on the laboratory spectral data of four soils (Aridosol, Endisol, Mollisol, and Quartz
sand), using the genetic algorithm of coupled nonlinear programming, implemented in Matlab
R2019b. By combining the global search capability of the genetic algorithm with the local search
advantage of the nonlinear programming algorithm, the merit function MSE(,,,, ) can be
minimized to obtain the global optimal solution of the inverse problem.
As an illustration, Figure 9 demonstrates that the MSE between the measured and the modeled
reflectance spectra of four soils is generally lower than 3×10 in the whole band, indicating that
the proposed SMR–Hapke model shows a good performance and can accurately reflect the variation
trend of soil reflectance with moisture content. The calculated optimal values are displayed in Figure
10, which reflects the variation curves of the five unknown parameters for the four samples. Figure
10 indicates that parameters ε, , and vary greatly in range of 1200–2500 nm, and there are
obvious peaks and troughs in the two water absorption bands. Therefore, the proposed SMR–model
has high sensitivity in SWIR region. Note that the value of barely changes in the SWIR bands,
which can be ascribed to the saturated moisture content being only related to the physical and
chemical properties of the soil, instead of the wavelength. The significant wave peaks of and
appear near 1400 nm and 1900 nm, which are due to the strong absorption of water in these spectral
intervals, and result in a small scattering coefficient for the soil.
Figure 9. The MSE(,,,, ) values of four soil samples.
Figure 10. Parameters (,,,,and ) of the six soils at different wavelengths.
4.1.2. SMC Estimation
Using the Equations (14) to (15), the performance of the SMR–Hapke model was verified. Figure
11 shows the variation of the R2 and RMSE values in the range of 400–2400 nm, which indicates that
the proposed model has a high retrieval accuracy and stability. For the four soils, the R2 values are
generally more than 0.9 on the NIR–SWIR bands, and the RMSE values are all less than 5%. The
Figure 9. The MSE(ε,rs,t1,t2,θs)values of four soil samples.
Remote Sens. 2020,12, 2239 13 of 21
Remote Sens. 2020, 12, x FOR PEER REVIEW 13 of 22
In this study, the optimal solutions of Equation (21) for each band are obtained by fitting the
model based on the laboratory spectral data of four soils (Aridosol, Endisol, Mollisol, and Quartz
sand), using the genetic algorithm of coupled nonlinear programming, implemented in Matlab
R2019b. By combining the global search capability of the genetic algorithm with the local search
advantage of the nonlinear programming algorithm, the merit function MSE(,,,, ) can be
minimized to obtain the global optimal solution of the inverse problem.
As an illustration, Figure 9 demonstrates that the MSE between the measured and the modeled
reflectance spectra of four soils is generally lower than 3×10 in the whole band, indicating that
the proposed SMR–Hapke model shows a good performance and can accurately reflect the variation
trend of soil reflectance with moisture content. The calculated optimal values are displayed in Figure
10, which reflects the variation curves of the five unknown parameters for the four samples. Figure
10 indicates that parameters ε, , and vary greatly in range of 1200–2500 nm, and there are
obvious peaks and troughs in the two water absorption bands. Therefore, the proposed SMR–model
has high sensitivity in SWIR region. Note that the value of barely changes in the SWIR bands,
which can be ascribed to the saturated moisture content being only related to the physical and
chemical properties of the soil, instead of the wavelength. The significant wave peaks of and
appear near 1400 nm and 1900 nm, which are due to the strong absorption of water in these spectral
intervals, and result in a small scattering coefficient for the soil.
Figure 9. The MSE(,,,, ) values of four soil samples.
Figure 10. Parameters (,,,,and ) of the six soils at different wavelengths.
4.1.2. SMC Estimation
Using the Equations (14) to (15), the performance of the SMR–Hapke model was verified. Figure
11 shows the variation of the R2 and RMSE values in the range of 400–2400 nm, which indicates that
the proposed model has a high retrieval accuracy and stability. For the four soils, the R2 values are
generally more than 0.9 on the NIR–SWIR bands, and the RMSE values are all less than 5%. The
Figure 10. Parameters (ε,rs,t1,t2, and θs) of the six soils at different wavelengths.
4.1.2. SMC Estimation
Using the Equations (14) to (15), the performance of the SMR–Hapke model was verified. Figure 11
shows the variation of the R
2
and RMSE values in the range of 400–2400 nm, which indicates that the
proposed model has a high retrieval accuracy and stability. For the four soils, the R
2
values are generally
more than 0.9 on the NIR–SWIR bands, and the RMSE values are all less than 5%. The performance
of the SMR–Hapke model is relatively poor in the visible region, which is due to the insensitivity of
visible light to the fluctuations of SMC.
Remote Sens. 2020, 12, x FOR PEER REVIEW 14 of 22
performance of the SMR–Hapke model is relatively poor in the visible region, which is due to the
insensitivity of visible light to the fluctuations of SMC.
Figure 11. R2 and RMSE at different wavelengths for four soils.
The SMC retrieval results in the whole band (400–2400 nm) are displayed in Figure 12, from
which it can be clearly observed that there was a significant linear relationship between the estimated
and measured SMC.
Figure 12. SMC measured and estimated using Equation (14).
4.2. Performance Evaluation of
4.2.1. Evaluation Using Laboratory Spectral Data
The retrieval algorithm of unknown parameters used in this study can acquire the optimal value,
but each soil sample needs to measure the spectra under different moisture contents, which increases
the complexity of the calculation and optimization steps. Equation (16) is a simplification of the SMR–
Hapke model, in which the volumetric moisture content can be expressed as a linear function of the
F. As an illustration, Figure 13 shows the linear relationship between F and θ for the four soils on the
SWIR bands (1610 nm and 2190 nm), which verifies the applicability of Equation (16).
Figure 11. R2and RMSE at different wavelengths for four soils.
The SMC retrieval results in the whole band (400–2400 nm) are displayed in Figure 12, from which
it can be clearly observed that there was a significant linear relationship between the estimated and
measured SMC.
Remote Sens. 2020, 12, x FOR PEER REVIEW 14 of 22
performance of the SMR–Hapke model is relatively poor in the visible region, which is due to the
insensitivity of visible light to the fluctuations of SMC.
Figure 11. R2 and RMSE at different wavelengths for four soils.
The SMC retrieval results in the whole band (400–2400 nm) are displayed in Figure 12, from
which it can be clearly observed that there was a significant linear relationship between the estimated
and measured SMC.
Figure 12. SMC measured and estimated using Equation (14).
4.2. Performance Evaluation of
4.2.1. Evaluation Using Laboratory Spectral Data
The retrieval algorithm of unknown parameters used in this study can acquire the optimal value,
but each soil sample needs to measure the spectra under different moisture contents, which increases
the complexity of the calculation and optimization steps. Equation (16) is a simplification of the SMR–
Hapke model, in which the volumetric moisture content can be expressed as a linear function of the
F. As an illustration, Figure 13 shows the linear relationship between F and θ for the four soils on the
SWIR bands (1610 nm and 2190 nm), which verifies the applicability of Equation (16).
Figure 12. SMC measured and estimated using Equation (14).
Remote Sens. 2020,12, 2239 14 of 21
4.2. Performance Evaluation of NDSMIHapke
4.2.1. Evaluation Using Laboratory Spectral Data
The retrieval algorithm of unknown parameters used in this study can acquire the optimal value,
but each soil sample needs to measure the spectra under different moisture contents, which increases
the complexity of the calculation and optimization steps. Equation (16) is a simplification of the
SMR–Hapke model, in which the volumetric moisture content can be expressed as a linear function of
the F. As an illustration, Figure 13 shows the linear relationship between Fand
θ
for the four soils on
the SWIR bands (1610 nm and 2190 nm), which verifies the applicability of Equation (16).
Remote Sens. 2020, 12, x FOR PEER REVIEW 15 of 22
Figure 13. Relationship between SMC and F of four soil in 1610nm and 2185nm.
With field sampling and laboratory measurements, we acquired a total of 195 sets of SMC and
laboratory spectral data to evaluate the performance of . The partition of the datasets is
based on the joint x–y distances (SPXY) method [49]. Of this total, 130 datasets were used as the
calibration set to analyze the relationship between and soil moisture content, and the
remaining 65 datasets were used for the validation (Figure 14).
Figure 14. Box-plots, histograms, and descriptive statistics of SMC: (a) the whole set; (b) the
calibration set; and (c) the verification dataset. Min: minimum, Max: maximum, SD: standard
deviation, CV: coefficient of variation, n: the number of soil samples.
Based on the laboratory–based calibration dataset, we compared the accuracy of the model with
other soil moisture indices by linear regression analysis. The other five soil moisture indices are listed
in Table 3.
Figure 15 presents the relationships between the six indices and the SMC. The Normalized Index
of NSWIR domain for SMC estimation from Linear regression (NINSOL, Figure 15b) and Normalized
Index of NSWIR domain for SMC estimation from Nonlinear correlation (NINSON, Figure 15c)
correlate negatively with SMC, whereas the Normalized Difference Soil Moisture Index (NSMI,
Figure 15a), Soil Transformed Reflectance (STR, Figure 15d), Normalized Shortwave–infrared
Difference Bare Soil Moisture Index (NSDSI1, Figure 15e), and the proposed (Figure
15f) have a positive correlation with SMC. Table 5 presents the equations between SMC and the soil
moisture indices. Moreover, the corresponding R2, RMSE, and MAE values are also given. The results
shown in Table 5 reflect that NSMI, NINSOL, STR, and NSDSI1 have good predication ability for
SMC, with the R2 more than 0.7. In general, with the increase in the water content, the sensitivity of
each index decreases. Table 5 also indicates that the proposed have great potential for
estimating field SMC, with R2 values of 0.8138, RMSE values of 0.033, and MAE values of 0.0263,
respectively.
Figure 13. Relationship between SMC and Fof four soil in 1610 nm and 2185 nm.
With field sampling and laboratory measurements, we acquired a total of 195 sets of SMC and
laboratory spectral data to evaluate the performance of
NDSMIHapke
. The partition of the datasets
is based on the joint x–y distances (SPXY) method [
49
]. Of this total, 130 datasets were used as the
calibration set to analyze the relationship between
NDSMIHapke
and soil moisture content, and the
remaining 65 datasets were used for the validation (Figure 14).
Remote Sens. 2020, 12, x FOR PEER REVIEW 15 of 22
Figure 13. Relationship between SMC and F of four soil in 1610nm and 2185nm.
With field sampling and laboratory measurements, we acquired a total of 195 sets of SMC and
laboratory spectral data to evaluate the performance of . The partition of the datasets is
based on the joint x–y distances (SPXY) method [49]. Of this total, 130 datasets were used as the
calibration set to analyze the relationship between and soil moisture content, and the
remaining 65 datasets were used for the validation (Figure 14).
Figure 14. Box-plots, histograms, and descriptive statistics of SMC: (a) the whole set; (b) the
calibration set; and (c) the verification dataset. Min: minimum, Max: maximum, SD: standard
deviation, CV: coefficient of variation, n: the number of soil samples.
Based on the laboratory–based calibration dataset, we compared the accuracy of the model with
other soil moisture indices by linear regression analysis. The other five soil moisture indices are listed
in Table 3.
Figure 15 presents the relationships between the six indices and the SMC. The Normalized Index
of NSWIR domain for SMC estimation from Linear regression (NINSOL, Figure 15b) and Normalized
Index of NSWIR domain for SMC estimation from Nonlinear correlation (NINSON, Figure 15c)
correlate negatively with SMC, whereas the Normalized Difference Soil Moisture Index (NSMI,
Figure 15a), Soil Transformed Reflectance (STR, Figure 15d), Normalized Shortwave–infrared
Difference Bare Soil Moisture Index (NSDSI1, Figure 15e), and the proposed (Figure
15f) have a positive correlation with SMC. Table 5 presents the equations between SMC and the soil
moisture indices. Moreover, the corresponding R2, RMSE, and MAE values are also given. The results
shown in Table 5 reflect that NSMI, NINSOL, STR, and NSDSI1 have good predication ability for
SMC, with the R2 more than 0.7. In general, with the increase in the water content, the sensitivity of
each index decreases. Table 5 also indicates that the proposed have great potential for
estimating field SMC, with R2 values of 0.8138, RMSE values of 0.033, and MAE values of 0.0263,
respectively.
Figure 14.
Box-plots, histograms, and descriptive statistics of SMC: (
a
) the whole set; (
b
) the calibration
set; and (
c
) the verification dataset. Min: minimum, Max: maximum, SD: standard deviation,
CV: coefficient of variation, n: the number of soil samples.
Based on the laboratory–based calibration dataset, we compared the accuracy of the model with
other soil moisture indices by linear regression analysis. The other five soil moisture indices are listed
in Table 3.
Figure 15 presents the relationships between the six indices and the SMC. The Normalized Index
of NSWIR domain for SMC estimation from Linear regression (NINSOL, Figure 15b) and Normalized
Index of NSWIR domain for SMC estimation from Nonlinear correlation (NINSON, Figure 15c) correlate
negatively with SMC, whereas the Normalized Difference Soil Moisture Index (NSMI, Figure 15a),
Soil Transformed Reflectance (STR, Figure 15d), Normalized Shortwave–infrared Difference Bare Soil
Moisture Index (NSDSI1, Figure 15e), and the proposed
NDSMIHapke
(Figure 15f) have a positive
Remote Sens. 2020,12, 2239 15 of 21
correlation with SMC. Table 5presents the equations between SMC and the soil moisture indices.
Moreover, the corresponding R
2
, RMSE, and MAE values are also given. The results shown in Table 5
reflect that NSMI, NINSOL, STR, and NSDSI1 have good predication ability for SMC, with the R
2
more
than 0.7. In general, with the increase in the water content, the sensitivity of each index decreases.
Table 5also indicates that the proposed
NDSMIHapke
have great potential for estimating field SMC,
with R2values of 0.8138, RMSE values of 0.033, and MAE values of 0.0263, respectively.
Remote Sens. 2020, 12, x FOR PEER REVIEW 16 of 22
Figure 15. Linear fitting of the six moisture indices and VWC using the calibration data.
Table 5. Comparison of the SMC accuracy.
SMC Indices Equation R2 RMSE MAE
NSMI SMC = 1.568×NSMI + 0.0194 0.8477 0.0298 0.0229
NINSOL SMC = −2.418×NINSOL + 0.0719 0.7737 0.0363 0.0279
NINSON SMC = −4.757×NINSON + 0.1793 0.4414 0.0571 0.0431
STR SMC = 0.1029×STR + 0.0244 0.7165 0.0407 0.0289
NSDSI1 SMC = 0.8714×NSDSI1 − 0.0150 0.8041 0.0338 0.0253
SMC = 0.7458× + 0.0138 0.8138 0.033 0.0263
The validation dataset was used to estimate the SMC by the linear equations listed in Table 5.
Figure 16 presents the estimated and measured SMC values of the six indices and the corresponding
R2, RMSE, and MAE values. The proposed indicated favorable performance with an R2
of 0.8801, an RMSE of 0.0212, and an MAE of 0.0167, respectively. Therefore, can be
used to reasonably estimate the soil moisture for regions with large spatial variability. Moreover, as
a simplified single calibration equation, can be obtained based on linear regression
analysis with less measured data, which greatly reduces the complexity of SMC retrieval compared
with the SMR–Hapke model.
Figure 15. Linear fitting of the six moisture indices and VWC using the calibration data.
Table 5. Comparison of the SMC accuracy.
SMC Indices Equation R2RMSE MAE
NSMI SMC =1.568 ×NSMI +0.0194 0.8477 0.0298 0.0229
NINSOL SMC =−2.418 ×NINSOL +0.0719 0.7737 0.0363 0.0279
NINSON SMC =−4.757 ×NINSON +0.1793 0.4414 0.0571 0.0431
STR SMC =0.1029 ×STR +0.0244 0.7165 0.0407 0.0289
NSDSI1 SMC =0.8714 ×NSDSI1 −0.0150 0.8041 0.0338 0.0253
NDSMIHapke SMC =0.7458 ×NDSMIHapke +0.0138 0.8138 0.033 0.0263
The validation dataset was used to estimate the SMC by the linear equations listed in Table 5.
Figure 16 presents the estimated and measured SMC values of the six indices and the corresponding
R
2
, RMSE, and MAE values. The proposed
NDSMIHapke
indicated favorable performance with an R
2
of 0.8801, an RMSE of 0.0212, and an MAE of 0.0167, respectively. Therefore,
NDSMIHapke
can be
used to reasonably estimate the soil moisture for regions with large spatial variability. Moreover,
as a simplified single calibration equation,
NDSMIHapke
can be obtained based on linear regression
analysis with less measured data, which greatly reduces the complexity of SMC retrieval compared
with the SMR–Hapke model.
Remote Sens. 2020,12, 2239 16 of 21
Remote Sens. 2020, 12, x FOR PEER REVIEW 17 of 22
Figure 16. Estimated and measured SMC for the six soil moisture indices on the verification set.
4.2.2. Evaluation and SMC Mapping Using Sentinel–2 MSI Data
In order to explore the application of in broadband satellite remote sensing images,
the surface reflectance of the 65 field sampling points were extracted using Sentinel–2 MSI data, of
which 43 sites were used as the calibration and 22 sites for the validation (Figure 5). The data are
partitioned using the SPXY method. According to the remote sensing image metadata, the solar
zenith angle at satellite transit time is 29°8'22.29". Since the image has been orthogonally rectified,
the emittance angle is set to 0°. was calculated by Equation (17).
Figure 17a shows a weak correlation between surface reflectance and SMC. Figure 17b,c present
the SMC estimated and measured by using the at calibration and validation sites. The
result shows that has high potential for estimating soil moisture at a regional scale, the
R2 of calibration and validation sites is generally more than 0.6. For comparison, the performance of
the other two soil moisture indexes (STR and NSDSI1) were given on the SWIR Sentinel–2 bands, as
shown in Figure 18. The NSMI, NINSOL and NINSON are not located in Sentinel–2 bands and
therefore did not participate in the comparison.
Figure 16. Estimated and measured SMC for the six soil moisture indices on the verification set.
4.2.2. Evaluation and SMC Mapping Using Sentinel–2 MSI Data
In order to explore the application of
NDSMIHapke
in broadband satellite remote sensing images,
the surface reflectance of the 65 field sampling points were extracted using Sentinel–2 MSI data, of
which 43 sites were used as the calibration and 22 sites for the validation (Figure 5). The data are
partitioned using the SPXY method. According to the remote sensing image metadata, the solar
zenith angle at satellite transit time is 29
◦
8
0
22.29”. Since the image has been orthogonally rectified,
the emittance angle is set to 0◦.NDSMIHapke was calculated by Equation (17).
Figure 17a shows a weak correlation between surface reflectance and SMC. Figure 17b,c present the
SMC estimated and measured by using the
NDSMIHapke
at calibration and validation sites. The result
shows that
NDSMIHapke
has high potential for estimating soil moisture at a regional scale, the R
2
of
calibration and validation sites is generally more than 0.6. For comparison, the performance of the
other two soil moisture indexes (STR and NSDSI1) were given on the SWIR Sentinel–2 bands, as shown
in Figure 18. The NSMI, NINSOL and NINSON are not located in Sentinel–2 bands and therefore did
not participate in the comparison.
Remote Sens. 2020, 12, x FOR PEER REVIEW 17 of 22
Figure 16. Estimated and measured SMC for the six soil moisture indices on the verification set.
4.2.2. Evaluation and SMC Mapping Using Sentinel–2 MSI Data
In order to explore the application of in broadband satellite remote sensing images,
the surface reflectance of the 65 field sampling points were extracted using Sentinel–2 MSI data, of
which 43 sites were used as the calibration and 22 sites for the validation (Figure 5). The data are
partitioned using the SPXY method. According to the remote sensing image metadata, the solar
zenith angle at satellite transit time is 29°8'22.29". Since the image has been orthogonally rectified,
the emittance angle is set to 0°. was calculated by Equation (17).
Figure 17a shows a weak correlation between surface reflectance and SMC. Figure 17b,c present
the SMC estimated and measured by using the at calibration and validation sites. The
result shows that has high potential for estimating soil moisture at a regional scale, the
R2 of calibration and validation sites is generally more than 0.6. For comparison, the performance of
the other two soil moisture indexes (STR and NSDSI1) were given on the SWIR Sentinel–2 bands, as
shown in Figure 18. The NSMI, NINSOL and NINSON are not located in Sentinel–2 bands and
therefore did not participate in the comparison.
Figure 17.
(
a
) Sentinel-2 MSI B11 (1610 nm) and B12 (2185 nm) vs SMC. (
b
) SMC estimated and measured
by using
NDSMIHapke
(calibration sites). (
c
) SMC estimated and measured by using
NDSMIHapke
(validation sites).
Remote Sens. 2020,12, 2239 17 of 21
Remote Sens. 2020, 12, x FOR PEER REVIEW 18 of 22
Figure 17. (a) Sentinel-2 MSI B11 (1610nm) and B12 (2185nm) vs SMC. (b) SMC estimated and
measured by using (calibration sites). (c) SMC estimated and measured by using
(validation sites).
Figure 18. The SMC estimated and measured by using: (a) STR, calibration sites; (b) STR, validation
sites; (c) NSDSI1, calibration sites; (d) NSDSI1, validation sites.
In Table 6, The R2 values of STR calibration and validation are 0.515 and 0.475, respectively. The
R2 values of NSDSI1 calibration and validation are 0.612 and 0.576, respectively. Table 6 indicates that
the proposed perform better than the other indices in estimating SMC using the
broadband Sentinel-2B MSI data. As shown in Figure 19, the spatial distribution of SMC was obtained
according to the linear regression equation.
Table 6. Relationship between SMC and SMC indices in broadband Sentinel-2 data.
Indices Equation Calibration Validation
R2 RMSE R2 RMSE
STR SMC = 0.05×STR + 6.11 0.515 0.031 0.475 0.043
NSDSI1 SMC = -1.58×NSDSI1 + 6.25 0.612 0.027 0.576 0.038
SMC = 0.9322× + 0.0353 0.656 0.026 0.642 0.035
Figure 18.
The SMC estimated and measured by using: (
a
) STR, calibration sites; (
b
) STR, validation
sites; (c) NSDSI1, calibration sites; (d) NSDSI1, validation sites.
In Table 6, The R
2
values of STR calibration and validation are 0.515 and 0.475, respectively. The R
2
values of NSDSI1 calibration and validation are 0.612 and 0.576, respectively. Table 6indicates that the
proposed
NDSMIHapke
perform better than the other indices in estimating SMC using the broadband
Sentinel-2B MSI data. As shown in Figure 19, the spatial distribution of SMC was obtained according
to the linear regression equation.
Table 6. Relationship between SMC and SMC indices in broadband Sentinel-2 data.
Indices Equation Calibration Validation
R2RMSE R2RMSE
STR SMC =0.05 ×STR +6.11 0.515 0.031 0.475 0.043
NSDSI1 SMC =−1.58 ×NSDSI1 +6.25 0.612 0.027 0.576 0.038
NDSMIHapke SMC =0.9322 ×NDSMIHapke +0.0353 0.656 0.026 0.642 0.035
Remote Sens. 2020,12, 2239 18 of 21
Remote Sens. 2020, 12, x FOR PEER REVIEW 19 of 22
Figure 19. (a) Sentinel–2 MSI image of study area, satellite transit time: 2019–05–04; (b) Extraction of
bare soil; (c) SMC map of study areas.
5. Conclusions and Prospect
The Hapke model is the most widely used photometric model in the scientific community and
has been successfully applied to soil remote sensing research. However, multi-angle data are
infrequent in the practical application of remote sensing, which is the barrier to the development of
the Hapke model in SMC retrieval. In this regard, this paper built a SMR–Hapke model to investigate
the relationship between single scattering albedo and soil moisture content. Moreover, a physically
based normalized difference soil moisture index from the SMR–Hapke model is
proposed. The advantage of the proposed SMR–Hapke model is that it may be applied to any
observation geometry, and is not confined to multi angle data. The genetic algorithm of coupled
nonlinear programming used in this study is independent of the initial values, and can start from a
random solution to find the optimal solution. The results displayed in Figures 11 and 12 indicate that
the proposed model could be applied for the retrieval of SMC among different types of soils, with a
high prediction accuracy in the solar domain (400–2500nm).
To handle the spatial variation of the model parameters caused by the heterogeneity of soil, we
reduced the SMR–Hapke model to a linear form and further proposed the . The
performance of was validated by 195 sets of SMC and laboratory spectral data from
Yitong County, Jilin province. The results show that the simplified model has a superior ability to
predict the moisture content, and has a better applicability over a wide range of areas. To date, there
have been few studies of the physically based soil moisture index. To our knowledge, we are the first
to extend the Hapke model for the practical soil moisture index. Compared with other empirical
indices, this model has a definite physical basis. After simple calibration steps with measured data, a
wide range of soil surface moisture can be estimated rapidly according to the . The
proposed approach presents a great potential for the retrieval of surface soil moisture on cultivated
land.
The penetration depth of optical methods is very limited, and this inherent limitation makes it
only able to monitor surface moisture. However, the dramatic fluctuations of soil surface moisture
change the overall shape of the reflecting spectra, hence the variations in moisture are considered as
the major challenges for the in-field application of soil imaging spectroscopy. The proposed SMR–
Figure 19.
(
a
) Sentinel–2 MSI image of study area, satellite transit time: 2019–05–04; (
b
) Extraction of
bare soil; (c) SMC map of study areas.
5. Conclusions and Prospect
The Hapke model is the most widely used photometric model in the scientific community and has
been successfully applied to soil remote sensing research. However, multi-angle data are infrequent in
the practical application of remote sensing, which is the barrier to the development of the Hapke model
in SMC retrieval. In this regard, this paper built a SMR–Hapke model to investigate the relationship
between single scattering albedo and soil moisture content. Moreover, a physically based normalized
difference soil moisture index
NDSMIHapke
from the SMR–Hapke model is proposed. The advantage
of the proposed SMR–Hapke model is that it may be applied to any observation geometry, and is not
confined to multi angle data. The genetic algorithm of coupled nonlinear programming used in this
study is independent of the initial values, and can start from a random solution to find the optimal
solution. The results displayed in Figures 11 and 12 indicate that the proposed model could be applied
for the retrieval of SMC among different types of soils, with a high prediction accuracy in the solar
domain (400–2500 nm).
To handle the spatial variation of the model parameters caused by the heterogeneity of soil, we
reduced the SMR–Hapke model to a linear form and further proposed the
NDSMIHapke
. The performance
of
NDSMIHapke
was validated by 195 sets of SMC and laboratory spectral data from Yitong County,
Jilin province. The results show that the simplified model has a superior ability to predict the moisture
content, and has a better applicability over a wide range of areas. To date, there have been few studies
of the physically based soil moisture index. To our knowledge, we are the first to extend the Hapke
model for the practical soil moisture index. Compared with other empirical indices, this model has
a definite physical basis. After simple calibration steps with measured data, a wide range of soil surface
moisture can be estimated rapidly according to the
NDSMIHapke
. The proposed approach presents
a great potential for the retrieval of surface soil moisture on cultivated land.
The penetration depth of optical methods is very limited, and this inherent limitation makes it
only able to monitor surface moisture. However, the dramatic fluctuations of soil surface moisture
change the overall shape of the reflecting spectra, hence the variations in moisture are considered as the
major challenges for the in-field application of soil imaging spectroscopy. The proposed SMR–Hapke
Remote Sens. 2020,12, 2239 19 of 21
model could be used as a spectral correction approach to eliminate the influence of moisture, which is
beneficial to quantifying other information of interest such as heavy metals, total nitrogen content,
organic matter content, or texture. The
NDSMIHapke
index can be used as a sensitive variable to realize
the rapid prediction of surface moisture distribution. The soils in the field are influenced by other types
of soil surface variation, including vegetation coverage, particle size distribution, dust accumulation,
and the formation of physical/biogenic crusts. How to reduce the influence of the above environmental
conditions on the optical properties of soil, and how to extend the model for field and large-scale
applications, will be the focus of our future research.
Author Contributions:
K.T. and Y.Z. conceived and designed the experiments. Y.Z. performed the experiments
and analyzed the results. K.T. and Y.Z. wrote the manuscript. X.W., and Y.C. gave comments and suggestions
on the manuscript and proofread the document. All authors have read and agreed to the published version of
the manuscript.
Funding: This research is supported in part by National Natural Science Foundation of China (No. 41871337).
Conflicts of Interest: The authors declare no conflict of interest.
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