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IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING, VOL. 60, 2022 4303415
Global Sensitivity Analysis of the MEMLS Model
for Retrieving Snow Water Equivalent
Shuo Gao ,ZhenLi ,Member, IEEE, Ping Zhang , Quan Chen , Jiangyuan Zeng ,Senior Member, IEEE,
Changjun Zhao , Chang Liu , and Zhaojun Zheng
Abstract— Sensitivity analysis (SA) of model parameters is of
great importance for understanding, development, and applica-
tion of models. However, the influence of snow microstructure
variability on snow water equivalent retrieval from passive
microwave measurements is still unclear. This article explores the
parameter sensitivity of the microwave emission model of layered
snowpacks (MEMLS) with improved born approximation (IBA)
by using a quantitative global SA method, the extended Fourier
amplitude sensitivity test (EFAST) algorithm. A deep analysis is
conducted, including the sensitivity of passive microwave emission
to snow parameters, the sensitivity variation analysis for different
snow conditions, and the temporal properties of the parameter
sensitivity. The results show the exponential correlation length,
snow depth, and snow density are the three most sensitive
parameters for snow without salt in the MEMLS model for
the brightness temperature gradient at 18.7 and 36.5 GHz.
For snow with a small salt content, the exponential correlation
length, snow depth, snow temperature, and snow density are
the four most sensitive parameters. Second, snow parameter
variability highly affects the microwave radiation. The sensitivity
values of microwave brightness temperature to snow depth
gradually increase when the exponential correlation length is
less than 0.25 mm and then slightly decreases with the increase
of exponential correlation length and decreases along with the
increase of snow density. Finally, our analysis highlights the
Manuscript received March 25, 2021; revised August 24, 2021 and
November 22, 2021; accepted December 2, 2021. Date of publication
December 10, 2021; date of current version March 1, 2022. This work was
supported in part by the National Key Research and Development Program of
China under Grant 2018YFA0605403, in part by the Science and Technology
Basic Resources Investigation Program of China “Investigation on Snow
Characteristics and their distribution in China” under Grant 2017FY100502,
in part by the National Natural Science Foundation of China under Grant
41976171, in part by the Key Deployment Program of AIRCAS under Grant
Y950930Z2F, and in part by the Youth Innovation Promotion Association
CAS under Grant 2018082. (Corresponding author: Ping Zhang.)
Shuo Gao and Chang Liu are with the Key Laboratory of Digital Earth
Science, Aerospace Information Research Institute, Chinese Academy of
Sciences, Beijing 100094, China, and also with the College of Resources and
Environment, University of Chinese Academy of Sciences, Beijing 100049,
China (e-mail: gaoshuo@radi.ac.cn; liuc5@radi.ac.cn).
Zhen Li, Ping Zhang, and Quan Chen are with the Key Laboratory of
Digital Earth Science, Aerospace Information Research Institute, Chinese
Academy of Sciences, Beijing 100094, China (e-mail: lizhen@radi.ac.cn;
zhangping@radi.ac.cn; chenquan@radi.ac.cn).
Jiangyuan Zeng is with the State Key Laboratory of Remote Sensing
Science, Aerospace Information Research Institute, Chinese Academy of
Sciences, Beijing 100101, China (e-mail: zengjy@radi.ac.cn).
Changjun Zhao is with the Northwest Land and Resources Research
Center, Shaanxi Normal University, Xi’an 710119, China (e-mail:
zhaocj@snnu.edu.cn).
Zhaojun Zheng is with the Key Laboratory of Radiometric Calibration and
Validation for Environmental Satellites, China Meteorological Administration,
National Satellite Meteorological Center, Beijing 100081, China (e-mail:
zhengzj@cma.gov.cn).
Digital Object Identifier 10.1109/TGRS.2021.3134695
importance to include the snow density, especially for deep
snow depth, in the combination of sensitive factors in future
multiparameter retrievals.
Index Terms—Extended Fourier amplitude sensitivity
test (EFAST) method, global sensitivity analysis (GSA),
microwave emission model of layered snowpacks (MEMLS)
model, passive microwave remote sensing, snow microstructure,
snow water equivalent (SWE).
I. INTRODUCTION
SNOW water equivalent (SWE) is well recognized as
a significant variable in many hydrological, ecological,
and climate models and plays a pivotal role in the study
of terrestrial water cycle, Earth’s energy balance, and cli-
mate change [1], [2]. Good knowledge of the spatial and
temporal distributions of SWE can help understand the role
of hydrological cycles and climate processes in the climate
system [3]. Despite the particular value of SWE, it is very
difficult to quantitatively measure SWE at different spatial
scales (especially at large scales) using traditional meteoro-
logical stations due to the heterogeneity of the land surface
and the snow distribution itself [4]. Passive microwave remote
sensing provides a viable and effective way to characterize
the distribution of snow depth/SWE at regional and global
scales [4], [5]. Due to the nature of the passive microwave
observations, the SWE retrieval is reliable only in areas with
dry snow cover. The principle of SWE detection using passive
microwave measurements is based on the volume scattering
of snow particles in dry snowpack [6]. Passive microwave
remote sensing also has the advantage of all-weather coverage
without depending on solar illumination [6]–[8]. At present,
this technique is the most efficient method to retrieve snow
depth/SWE at large scales [4], [6], [9].
However, snow depth/SWE retrieval is a challenging work,
not just because the snow particle size has a strong effect
on the magnitude of the microwave volume scattering in
dry snowpack [10]. Indeed, there are many snow parameters
that affect the snow emission characteristics, including the
physical temperature, depth, density, particle size, moisture
content, and characteristics of the underlying medium of the
snow [6], [11]. The numerous parameters and high hetero-
geneity of snowpack are great challenges for snow depth
retrieval from passive microwave remote sensing. Although
passive microwave remote sensing has provided long time
series estimates of the northern hemisphere [4], [12] or global
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4303415 IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING, VOL. 60, 2022
SWE [5], there are still many uncertainties [13], [14]. The
main error source is the influence of the seasonal evolution
of snow microstructure parameters on microwave scattering
in the SWE inversion model [15]. It is well known the snow
radiative transfer models usually require a large number of
input parameters that are difficult to estimate. In addition,
since snow cover exists on the ground close to its melting
point, its physical parameters transform with time depend-
ing on the snow environment during the snow season [16].
Meanwhile, the accuracy of snow depth/SWE estimates varies
with time and space, especially trends to underestimate in the
late stage of snow season [13], [17], [18]. Snow parameter
variability highly affects the microwave radiation. However,
at present, the temporal properties of the snow parameter
sensitivity are not clear during the snow season. For this
reason, a comprehensive and quantitative analysis of the role
and importance of the input parameters in the snow model
is of great significance for better understanding the accuracy
of existing SWE products and improving the SWE retrieval
algorithms.
In snow microwave remote sensing, a reasonable parame-
terization of the snow radiative transfer model used to sim-
ulate snow emission can improve the capability of retrieving
snow depth/SWE from satellite microwave observations [19].
Brightness temperature observed at the snow surface is deter-
mined by the volume scattering and absorption inside the
snowpack and surface scattering at the snow-soil bound-
ary [16], [20], [21]. Recent work using brightness temperature
combined with a forward model for microwave emission has
shown potential in estimating snow depth/SWE [4], [10],
[22]–[28]. Snow emission models published in the previ-
ous literature include the Helsinki University of Technology
model (HUT) [12], [21], the dense media radiative transfer-
multilayer model (DMRT-ML) [29], the dense media radia-
tive transfer-quasi-crystalline approximation Mie scattering of
sticky spheres (DMRT-QMS) [30], and the microwave emis-
sion model of layered snowpacks (MEMLS) with improved
Born approximation (IBA) [31], [32]. HUT is a semiempirical
snow emission model and the others are based on theoretical
approaches. From a physical point of view, according to Loewe
and Picard [33], MEMLS and DMRT-ML are in fact very
similar. Pan et al. [34] compared HUT and MEMLS models
with observations of natural snow cover at Sodankylä, Finland;
Churchill, Canada; and Colorado, USA. The results showed
that the HUT model tends to underestimate brightness temper-
ature for deep snow and MEMLS with IBA performed better
by comparing with in situ observations. Royer et al. [19]
compared and analyzed the four commonly used snow radia-
tive transfer models using the same extensively measured
physical snowpack properties and comparisons with ground-
based radiometric measurements showed that the MEMLS
model converged to better results. In this article, we focus
on the MEMLS model with IBA. MEMLS is a six-flux snow
radiative transfer emission model and calculates the microwave
brightness temperature of multiple-layer snow with layered
snowpacks information [16].
A thorough and quantitative investigative process of snow
radiative transfer models, namely, the sensitivity analysis (SA),
is of great importance to distinguish the sensitivities of the
parameters [27], [35]. In previous studies [27], [36], [37],
a method of local SA (LSA) was commonly adopted to
investigate the sensitivity of passive microwave brightness
temperatures to the physical parameters of the snowpack.
However, the LSA method can only analyze one input parame-
ter at one time by holding the other parameters fixed at their
nominal values, which cannot quantify the interaction effects
among the parameters [38], [39]. It is common knowledge that
many parameters (e.g., snow depth and snow density) usually
vary simultaneously in the natural world. In addition, the
application of LSA to nonlinear and non-monotonic models
may be questionable [40]–[42]. The snow radiative transfer
model is a high-dimensional nonlinear and non-monotonic
model, which limits the use of LSA.
Compared with the LSA algorithms, the global SA (GSA)
method can analyze the output uncertainties when all the
parameters simultaneously vary over the entire parameter
space [43]. Moreover, GSA can determine the interaction
effects of the parameters on the model output, which is
appropriate for nonlinear and non-monotonic models [39],
[44], [45]. Therefore, the GSA method can be more effective
and reliable to determine the sensitive and insensitive para-
meters and their interactions in the snow radiative transfer
models. GSA methods could be divided into three types:
screening method, regression-based method, and variance-
based method [45], [46]. The screening method is able to
obtain the ranking of the model parameters, though the
variance-based method is capable of quantifying the contri-
bution of each parameter to the unconditional variance of
the model output [47]. The GSA method has been popularly
used in various scientific fields because of its advantages
[48]–[51]. The extended Fourier amplitude sensitivity
test (EFAST) algorithm is a variance-based and quantitative
GSA method that could be used to perform the SA of the com-
plex physical models [52], [53]. The EFAST method is devel-
oped based on the Fourier Amplitude Sensitivity Test (FAST)
algorithm [54] and Sobol’s algorithm [55]. The advantage of
the FAST algorithm is a high sampling efficiency that is based
on a defined search curve to scan the entire parameter space.
However, the method cannot compute the interactions among
parameters [41], [43]. Sobol’s algorithm is able to compute
the sensitivity index and present an indication of the overall
effect of a given parameter through thinking about all probable
interactions of the factor with the others. Yet, Sobol’s method
has a high computational demand based on the Monte Carlo
algorithm [55]. The EFAST method integrates the advantages
of both high efficiency and accuracy from the FAST algorithm
and the ability to compute the parameter interaction effects
from Sobol’s algorithm. Due to the advantages, the EFAST
method has been widely applied to hydrological and ecolog-
ical models [51], crop and environmental models [45], [56],
and radiative transfer and discrete scattering models of soil
moisture [38], [39], [43], [44]. In this article, we investigate,
for the first time, the effect of snow parameters on microwave
radiation based on the EFAST algorithm.
In Section II, the theoretical backgrounds of the
MEMLS model and EFAST method are briefly introduced.
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GAO et al.: GSA OF THE MEMLS MODEL FOR RETRIEVING SWE 4303415
Then, the parameters required for model runs and three numer-
ical experiment schemes for SA are described in Section III.
The results of this study are discussed in detail in Section IV.
Finally, Section V summarizes the main conclusions of
the study.
II. MODEL AND METHOD
A. MEMLS Model
The snow radiative transfer model is essential for under-
standing passive microwave brightness temperature observa-
tions and retrieving snow parameters [18]. The simulation of
passive microwave brightness temperatures for snow-covered
areas is accomplished by MEMLS with IBA as it is capable
of predicting absorption well and volume scattering behavior
in snowpacks at a frequency range of 5–100 GHz. Developed
and tested in Switzerland, the MEMLS model is based on a
radiative transfer approach using six-flux theory to describe
absorption and volume scattering, including radiation trapping
through a homogeneous snowpack of a certain depth. If the
snowpack is assumed plane-parallel, the change of microwave
brightness temperature in the transmission direction could be
simplified into two directions: the observing direction and
the inverse of the observation direction. The two directions
could simply be called “upward” and “downward” directions
respectively. The change of microwave brightness temperature
in the propagation direction of zenith angle θ0and azimuth
angle ∅0at any vertical location zcould be written as
∂Tupz
∂z=−keTupz+kaT+kforward
sTupz
+kbackward
sTdnz(1a)
−∂Tdnz
∂z=−keTdnz+kaT+kforward
sTdnz
+kbackward
sTupz(1b)
where z=z·secθ0,Tupzis the upward brightness tempera-
ture; Tdnzis the downward brightness temperature; keis the
extinction coefficient (ke=ka+ks);andkais the absorption
coefficient. Tis the physical temperature of snow; kforward
sand
kbackward
sare the forward scattering coefficient and backward
scattering coefficient respectively; and ksis the sum of kforward
s
and kbackward
s. These are the differential snow emission radiative
transfer equations used in MEMLS [16].
Mätzler [32] developed and tested the IBA to calculate the
bistatic volume scattering coefficient as
kbi
sθ,∅,θ,φ=v(1−v)(εi−1)2K2Ik4sin2χ(2)
where (θ,∅)is the scattered angle; θ,φis the incident
angle; vis the ice volume fraction; εiis the ice permittivity;
K2is the ratio of the mean-squared electric fields inside
and outside of ice particles; Iis the integral of the spatial
autocorrelation function; and χis the angle between the
direction of the electric field of the incident wave and the
propagating direction of the scattered wave. The IBA model
provides a method of calculating the radiation attenuation for
the MEMLS model and turns it into a physically based snow
emission model.
When solving the radiative transfer equation in 3-D space,
MEMLS takes into account the internal reflection in the snow
medium owing to the higher permittivity of snow compared to
air. The internal reflection traps the radiation along a subset of
directions in the snowpack, and the MEMLS model describes
the trapped radiation by four horizontal fluxes [16]. Since
the model assumes that the snowpack is plane-parallel, the
gradient of the trapped radiation is 0. Thus, the MEMLS
model divides the radiation into six fluxes in total including
the upward, downward radiation, and trapped radiation. The
validity of the MEMLS model in simulating the microwave
brightness temperature has been extensively evaluated and
examined in many studies [16], [19], [34]. For detailed
descriptions of the MEMLS, refer to [16], [31], and [34].
B. EFAST Method
The EFAST is a GSA method that can be applied to
high-order nonlinear and non-monotonic models [41], [52].
In this article, the EFAST algorithm was used to quantify
the parameter sensitivity of the MEMLS model. The EFAST
adopts the method of model variance analysis and believes
that the variance of the model output is caused by the input
parameters and the interaction among the parameters, which
can reflect the sensitivity of the model output to the input
parameters [41]. EFAST has been widely used in agricultural,
hydrological, and ecological models due to its favorable char-
acteristics [39], [43], [45], [51], [57]–[59].
The variance-based EFAST algorithm mainly includes
two procedures. First, high-efficiency sampling is performed
through a transformation function. Next, the total sensitivity
index (TSI) and the main sensitivity index (MSI) are quanti-
tatively calculated through the FAST [41].
For any considered model simplified as
y=f(x),x=(x1,x2,...,xn)(3)
where the model output yis calculated through the model
fwith the total set of ninput parameters x1to xn.First,
the multidimensional input parameter space is supposed to be
converted into a 1-D space through the Fourier transformation
functions called the searching curves as follows:
xi(s)=1
2+1
πarcsin[sin(ωis+ϕi)](4)
where i=1,2,...,n,ωiis the Fourier frequency, ϕiis
the random phase shift within the range of [0, 2π),ands
represents the sample order from 1 to the total number of
samples. In this process, selecting a set of values within the
value range of each parameter is named resampling. The key
to this process is to set some key parameters. The explicit
computation formula is elaborated as
Ns=Nr(2Mωmax +1)(5)
where Nsis the sample size for each input parameter, Nris the
number of searching curves, Mis the given interference factor
(M=4),andωmax stands for the largest sampling frequency.
In order to determine the number of random samples, the
proposed parameters of Nrand ωmax can be selected based
on a simple ratio rule as ωmax /Nrin the range of 16–64 [43].
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4303415 IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING, VOL. 60, 2022
Second, two sensitivity indices (SIs), namely, the MSI and
TSI for each input parameter, are computed. In this process,
the randomly sampled values are input into the model, and
then the model outputs are expanded by Fourier series
y=f(s)=
+∞
j=−∞ Ajcos(js)+Bjsin(js)(6)
where j∈Z={−∞,...,−1,0,1,...,+∞};Ajand Bj
stands for the two Fourier coefficients expressed as
Aj=1
2ππ
−π
f(s)cos(js)ds (7a)
Bj=1
2ππ
−π
f(s)sin(js)ds.(7b)
The total variance of the model output is obtained as
ˆ
D=1
2ππ
−π
f2(s)ds −1
2ππ
−π
f(s)ds2
≈2
+∞
j=1A2
j+B2
j.(8)
Then, the partial variance ˆ
Diof the individual parameter xi
is estimated based on the Fourier coefficients Ajand Bjwith
respect to its specific Fourier frequency ωias
ˆ
Di=
+∞
−∞
jωi=2
+∞
j=1A2
jωi+B2
jωi(9)
where is the spectrum of the Fourier series expansion
determined as j=A2
j+B2
j.
Finally, the model outputs SIs including MSI and TSI for
each parameter xiare defined as
MSIi=
ˆ
Di
ˆ
D(10a)
TSIi=1−
ˆ
D−i
ˆ
D(10b)
where ˆ
D−istands for the partial variance of all other para-
meters for the ith factor, defined as ˆ
D−i=ˆ
Dk,k= i.
MSIiis the main sensitivity index, which can also be called
the first-order sensitivity index, which represents the direct
contribution of the ith parameter to the total variance of the
model output, and TSIiis the total (including higher-order
effects) sensitivity index. Compared to the SIs of the FAST
method, the TSI sensitivity index of the new EFAST considers
the interaction effects between the other parameters, which
makes it more appropriate for complex nonlinear and non-
monotonic models in the SA. The higher values of the SIs
represent greater sensitivity to the model outputs. The dif-
ference between TSI and MSI (i.e., TSI-MSI) indicates the
interactions among the parameters. For a detailed description
and theoretical derivations of EFAST, readers can refer to [41]
and [60]. The source code of EFAST can be downloaded
from the website: http://malthus.micro.med.umich.edu/lab/
usadata.
TAB L E I
INPUT PARAMETERS AND THEIR DISTRIBUTIONS
AND RANGES IN THE MEMLS MODEL
III. MATERIALS AND PARAMETER SA TESTS
A. Parameters
To perform the SA tests, it is necessary to have a detailed
and quantitative understanding of the parameters in the
MEMLS model. The snow parameters and their distributions
and variation ranges in the MEMLS model are presented in
Table I.
The incident angle is set to 55◦, which is consistent with the
setting of the Advanced Microwave Scanning Radiometer 2
(AMSR2) sensor onboard the Global Change Observation
Mission–Water 1 (GCOM-W1) mission. Ground reflectivity at
different frequencies corresponds to bare soil with a surface
roughness of 1 cm and a ground permittivity of 4 [26],
which is a reasonable assumption for frozen ground [61].
The reflectivity of the snow–soil interface at 10.7, 18.7,
36.5, and 89 GHz are 0.07, 0.06, 0.05, and 0.035 in the
horizontal polarization and 0.06, 0.05, 0.03, and 0.02 in the
vertical polarization, calculated using an empirical model [62].
The sky background brightness temperatures are 5, 15, 25,
and 35 K at the frequency of 10.7, 18.7, 36.5, and 89 GHz,
respectively [63]. The liquid water content is assumed to be 0
because the snow depth/SWE retrieval is reliable only in areas
with seasonal dry snow cover [64].
The ground temperature (TG) provides background bright-
ness temperature. In this study, TG is assumed to be the same
as the snow temperature (TS) [65]. For passive microwave
remote sensing, previous studies believed that TS can affect
the accuracy of the SWE retrievals to some extent. Kelly
et al. [66] assumed that the TS is constant, but Dai et al. [23]
established an empirical formula from the snow depth and
daily minimal air temperature to calculate the TS for the
depth less than 30 cm and assumed the TS is constant in the
case of snow depth deeper than 30 cm in Xinjiang, China.
Field observations show that the snow density (ρ) in the
former Soviet Union is about 210–310 kg ·m−3[67], and
in North America, it is approximately 240–380 kg ·m−3
[19]. However, the average ρin China’s three stable snow
areas (including northern Xinjiang, northeast, and Qinghai-
Tibet Plateau) is about 175 kg ·m−3. The distribution of snow
density shows obvious spatial differences. The exponential
correlation length (Pe c ) of dry snow, or any isotropic two-
component granular medium in 3-D space, is defined to
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GAO et al.: GSA OF THE MEMLS MODEL FOR RETRIEVING SWE 4303415
characterize the impact of size and distribution of scatters
(such as snow particles) on scattering [68]. The values of
Pec are used as inputs for the MEMLS model to describe the
snow microstructure metrics [16]. According to in situ field
experiments, the measured snow geometric grain size (Dmax )
inside the snowpack is usually less than 5 mm in Churchill,
Canada [19], Sodankylä, Finland [34], and SnowEx field
observations at Grand Mesa, USA [69]. However, the particle
size of snow may be much larger when a snow deep hoar
develops especially for the shallow snow and steep temperature
gradients in the snowpack, such as the Arctic Coastal Plain of
Alaska [70] and the Qinghai-Tibet Plateau [71]. Hall et al. [70]
found that a snow-deep hoar generally develops in Alaska, and
the snow particle size can reach 10–15 mm. In Central Asia,
western China, and the Qinghai-Tibet Plateau, the size of Dmax
in some natural layers may reach 25 mm [17], [71], [72]. Field
surveys have shown that there is distinct spatial heterogeneity
in the distribution of snow particle size. The values of Pec can
be calculated in three ways: 1) from the observed linear rela-
tionship between Pec and mean Dmax [19]; 2) from the optical
grain size radius (measurements of snow specific surface area)
and fractional volume [73]; and 3) from the mean Dmax and
fractional volume [14]. Snow on land has zero salt content, and
snow on sea ice is considered to contain weak salt content [16].
Based on the field observations and model recommendations,
a wide range of the parameters in the model (given in Table I)
is set to guarantee a comprehensive understanding of their
influence on the model outputs. According to [39], [44],
and [45], the parameter SA results generally depend less on
the parameter distribution function than the value ranges, and
a uniform distribution was commonly assumed for the input
factors. Therefore, a uniform distribution is assumed for all
the input parameters in this experiment.
B. SA Tests
Three numerical experiment tests of the parameter SA in
the MEMLS model are designed to be analyzed in the EFAST
method by using the parameters listed in Table I and the field
experimental data.
Test 1—ParametersSensitivity Comparison Analysis: The
goal of the parameter SA is to identify the sensitive parameters
with reasonable sampling samples in the entire parameter
space. Ten channels simulated by the MEMLS model, includ-
ing 10.7, 18.7, 36.5, and 89 GHz and brightness temperature
difference at 18.7 and 36.5 GHz for vertical and horizontal
polarizations, are selected since they play important roles for
SWE retrieval. In this text, all parameters given in Table I
were analyzed by the EFAST method. The sensitivities indexes
including TSI and MSI were analyzed to determine the pri-
mary sensitive factors in the MEMLS model. The magnitude
of the TSI and MSI values characterizes the relative impor-
tance of the input parameters on the brightness temperature
as predicted by the MEMLS model. The differences between
TSI and MSI values indicate the interaction effects among the
input parameters.
Test 2—ParametersSensitivity Variation Analysis: In this
study, all parameters in Table I, except for SD,Pe c ,orρ,were
included in the MEMLS model in the EFAST method. The
brightness temperature differences at 18.7 and 36.5 GHz for
different polarizations are selected since they can characterize
the volume scattering of the snowpacks to some extent, which
is critical for the SWE retrieval. The TSI values characterize
the sensitivity of the input parameters and also reflect the
feasibility of each parameter to be retrieved, and the variations
of the TSI values then indicate the stability of their retriev-
ability for different snow conditions. The sensitivity values of
these parameters were computed and their TSI variations were
analyzed to explore the possible sources of retrieval errors and
the potential enlightenment in the view of inversion.
Test 3—Temporal attributes of the parameter sensitivity:
The snow parameters vary significantly during the snow sea-
son. The evolution of the snow parameters has a high impact
on the microwave radiation of snowpacks. Therefore, the
temporal attributes of the parameter sensitivity were analyzed
to investigate the microwave response to the snow parameters
inside the snowpacks through a case study in Xinjiang, China.
The evolution trends of snow parameters over time were
obtained based on the field observations and meteorological
stations during the two snow seasons for 2017–2018 and
2018–2019. The variation ranges of snow parameters over
time were set into the MEMLS model by the EFAST
method to obtain the temporal characteristics of the parameter
sensitivities.
IV. RESULTS AND DISCUSSION
A. Test 1: ParametersSensitivity Comparison Analysis
In this text, all parameters listed in Table I are ana-
lyzed by the EFAST method. At present, the development
of snow depth or SWE inversion algorithms is mainly based
on the fact that the brightness temperature decreases with
the increase of snow depth and the brightness temperature
difference at 18 and 36 GHz increases with the increase of
snow depth [6], [74]. However, in the development of regional
snow depth retrieval algorithms, other frequencies were also
considered. For example, Dai et al. [23] introduced 10.7 GHz
to detect deep snow, and Kelly et al. [66] and Jiang et al. [75]
used the high frequency of 89 GHz to further separate shallow
snow. Fig. 1 shows the TSI, MSI, and their differences of
all parameters for dry snowpack at four different frequencies
of 10.7, 18.7, 36.5, and 89 GHz. To compare the differences
between GSA and LSA, Fig. 2 shows the local sensitivity
analysis results for the different frequencies brightness tem-
perature variations as a function of Pe c or ρin a simple
synthetic case defined by one layer of 50 cm snow depth.
Fig. 3 shows the sensitivity results of brightness temperature
difference at 18.7 and 36.5 GHz. It can be clearly observed
from Figs. 1 and 3 that the values of MSI of each parameter
are correspondingly smaller than the values of TSI for the
nonlinear MEMLS model. The sum of MSI values of all
parameters is approximately 0.9, while the total values of TSI
are slightly higher than 1. Compared with MSI, the higher
value of TSI is due to the interaction among parameters,
and the values of MSI and TSI keep the same trends as the
frequency increases. As a result, the TSI results are selected
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4303415 IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING, VOL. 60, 2022
Fig. 1. TSI and MSI of all parameters in the MEMLS model. The left side
represents the snow without salt (Sppt =0). The right side represents the
snow with a small salt content Sppt of 0‰–0.1‰. (a) and (b) For 10.7 GHz.
(c) and (d) For 18.7 GHz. (e) and (f) For 36.5 GHz. (g) and (h) For 89 GHz
(for shadow snow depth of 0–20 cm).
for a comprehensive analysis for the consideration of the
completeness of the sensitivity indexes.
For snow without salt content, as shown in
Fig. 1(c), (e), and (g), Pe c is the most sensitive factor
in the MEMLS model for different frequencies of 18.7,
36.5, and 89 GHz, with the TSI values varying between
approximately 0.3 and 0.8 individually. As for 10.7 GHz,
TG is the most sensitive factor in the MEMLS model,
which means the background radiation of the soil under the
snowpack cannot be ignored. As the frequency increases,
the TSI values of TG decrease in different degrees, and the
decrease of TG is particularly obvious. On the contrary,
the results of TS show a slightly increasing trend. Note that
the rankings of the sensitivity indexes of parameters vary at
different frequencies. At 10.7 GHz for vertical polarization,
TG,Pec,andSD are the three most sensitive parameters
Fig. 2. Brightness temperature variation as a function of the exponential
correlation length, Pec and the snow density, ρfor different frequencies and
polarizations. (a) For the Pe c,ρ=250 kg ·m−3. (b) For the ρ,Pe c =
0.25 mm. SD =50 cm, TG =263 K, TS =263 K, and Sppt =0. The
incidence angle of brightness temperature simulations is 55◦.
with the TSI being about 0.3–0.65 and the remaining two
parameters of TS and ρbeing with the TSI values less
than 0.05. However, TG,ρ,Pec,andSD are the four most
sensitive parameters with the TSI value of ρhaving a
substantial increase of around 0.35 at horizontal polarization.
At 18.7 GHz for vertical polarization, the parameters Pec,TG,
and SD become the three most sensitive factors, with the TSI
value of the others less than 0.03. In addition, the TSI value
of ρalso has a great increase over that of SD at 18.7 GHz
in the horizontal polarization. At 36.5 GHz, the parameters
Pec and SD become the two most sensitive factors, with the
TSI value of the others less than 0.05 for both vertical and
horizontal polarizations. At 89 GHz for shadow snow depth
of 0–20 cm, the TSI value of Pec continues to increase to
about 0.75, however, the TSI value of SD is slightly less
than 0.25. Meanwhile, the sensitivity values of TS and TG
can be ignored with the TSI values less than 0.05. The total
interactions among all parameters decrease with the increase
of the frequencies and the results of TSI and MSI are similar
for both vertical and horizontal polarizations at different
frequencies.
For snow with a small salt content Sppt of 0‰–0.1‰, the
sensitivity results are presented in Fig. 1(b), (d), (f), and (h) for
10.7, 18.7, 36.5, and 89 GHz, respectively. The comparison
between the TSI and MSI results for snow with a weak salt
content is akin to that for snow without salt, with the main
disparities that the sensitivity results of TS in the MEMLS
model are much higher than those for snow without salt.
According to Wiesmann et al. [16], TS and Sppt work together
on calculating the imaginary part of the relative permittivity
of impure ice, thereby affecting the dielectric constant of the
snow, and the effects of the two factors are interactive rather
than independent. The increase in snow salinity together with
TS will increase the imaginary part of the snow dielectric
constant [32], which will affect the calculation of the scattering
coefficient inside the snowpack, thereby affecting the bright-
ness temperature. Therefore, the sensitivity values of bright-
ness temperature to TS will increase with the increase of Sppt.
As the LSA results show in Fig. 2, the brightness temperatures
simulated by the MEMLS model decrease with the Pe c and
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GAO et al.: GSA OF THE MEMLS MODEL FOR RETRIEVING SWE 4303415
Fig. 3. TSI and MSI of all parameters in the MEMLS model for brightness
temperature difference at 18.7 GHz and 36.5 GHz for dry snowpack. (a) For
the snow without salt. (b) For the snow with a small salt content Sppt of
0‰–0.1‰.
slightly increase with the ρ, which are consistent with previous
studies [19]. The differences between EFAST and LSA are
mainly the following three points. First, the prerequisites for
parameter changes are different. LSA can only analyze one
input parameter at one time by holding the others as fixed
values, which is an idealized condition and does not conform
to the real situation in nature. EFAST can analyze the output
uncertainties when all the parameters simultaneously vary over
the entire parameter space. Second, EFAST can obtain the
sensitivities indexes based on the variance of the model output.
Third, EFAST can examine the overall impact of changes
in multiple parameters and analyze the parameter interaction
effects.
As the GSA results show in Fig. 3(a), Pe c ,SD,andρare the
three most sensitive factors for snow without salt at the bright-
ness temperature difference of 18.7 and 36.5 GHz with the TSI
values of about 0.05–0.82 for dry snowpack. In addition, the
TSI value of Pec is intriguingly about four times that of SD for
both vertical and horizontal polarizations. It indicates Pe c is
the most critical snow parameter affecting snow depth or SWE
retrieval. Moreover, snow parameters inside the snowpacks,
particularly snow grain size, change throughout the whole
snow season [76], [77]. The metamorphosis of the snow grains
is mainly controlled by the bulk temperature gradient through
the snowpack [74], [76]. The snow microstructure parameter
Pec evolves with the change of the snow grains [23], [68].
Algorithms that ignore the effect of snow microstructure
parameters can yield erroneous estimates of snow depth or
SWE. Therefore, the prior information about the snow particles
is of great importance in the snow depth or SWE inversion
due to the high sensitivity results of Pec for both vertical and
horizontal polarizations. Furthermore, the sensitivity results of
SD at vertical polarizations are about 0.02 higher than those
of horizontal polarizations. Thus, the vertical polarizations
are recommended if the brightness temperature differences of
18.7 and 36.5 GHz are considered to be used in the snow
depth or SWE algorithm.
For snow with a weak salt content, Pec ,SD,TS,andρare
the four most sensitive factors in the MEMLS model at the
brightness temperature difference of 18.7 and 36.5 GHz. The
sensitivity results of the parameters are generally consistent
with those for snow without salt. Nevertheless, the TSI results
of SD are about 0.03 lower than those of snow without salt.
Fig. 4. TSI variations of all parameters but SD in the MEMLS model for
brightness temperature differences at 18.7 and 36.5 GHz for dry snowpack.
(a) and (b) For vertical polarization. (c) and (d) For horizontal polarization.
(a) and (c) For snow without salt. (b) and (d) For snow with a small salt
content Sppt of 0‰–0.1‰.
Additionally, the sensitivity indexes of TS are much higher
compared with the results of the snow without salt. The total
interactions among all parameters increase when the snowpack
contains weak salinity. It implies that, compared with the snow
without salt, the snow depth or SWE retrieval from passive
microwave remote sensing is more complicated for dry snow
with weak salinity.
B. Test 2: ParametersSensitivity Variation Analysis
In this text, all parameters but SD,Pec,orρare
included in the MEMLS model in the EFAST method, and
their insensitive values of TSI are analyzed under different
snow depth, snow grain size, and snow density conditions.
As explained in test 1, the TSI values can illustrate the
feasibility of the input parameters to be retrieved. Furthermore,
the variations of TSI values delineate the stability of the
retrievability of each parameter under different snowpack
conditions.
The spatial and temporal distributions of the snow
depth/SWE vary significantly in the whole snow season.
Therefore, it is indispensable to figure out the changes in
the sensitivity of various parameters with the change of SD.
The TSI variations can be analyzed to determine the potential
error sources and improve the current retrieval method of the
snow depth/SWE. The variations of the TSI for all parameters
but SD under different snow depths are shown in Fig. 4.
In essence, Fig. 4 is similar to Fig. 3 except for the different
input number of MEMLS model parameters in the EFAST
method.
For snow without salt, as shown in Fig. 4(a) and (c) for
vertical polarization and horizontal polarization, respectively,
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4303415 IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING, VOL. 60, 2022
Fig. 5. Scattering coefficients, absorptions coefficients, and snow layer
emissivity response with different snow depth and snow density at 18.7 and
36.5 GHz, evaluated by MEMLS. Fixed parameters: Pec =0.2 mm, TS =
263 K, TG =263 K, and the incidence angle =55◦.
though the Pec sensitivity decreases from about 0.95–0.85
with the increase of SD, its TSI values retain the highest
among all the parameters, which indicates the consistently
high possibility of Pe c to be the error resource in the
snow depth/SWE retrieval. Correspondingly, the consistently
increasing TSI values of ρfrom about 0.03–0.11, TS from
about 0.004–0.04, and TG from approximately 0.005–0.025
are observed. Generally, the variations of TSI values of vertical
polarization are basically the same as those of horizontal
polarization. The main divergence is that the TSI values
of ρincrease slightly faster under horizontal polarization.
A uniform distribution function was used for snow density
at different snow depth conditions. However, the natural snow
density conditions may be more complicated for deep snow
depth. The increase of TSI values of ρcannot be ignored
with the increase of SD, which means it has an important
impact on the deep snow. As is shown in Fig. 5, scattering
coefficients [Fig. 5(a)] and absorption coefficients [Fig. 5(b)]
are constant results along with the increase of SD for different
snow densities. As is shown in Fig. 5(c), the results of snow
emissivity increase with the increase of snow depth and snow
density in varying degrees at 18.7 and 36.5 GHz, and the
increase at 36.5 GHz is faster than that of 18.7 GHz, especially
for dense snow density. The results indicate that the increasing
TSI values of ρwith the increase of SD are mainly affected
by the thermal emission inside the snowpack. For snow with
a weak salt content, the variations of sensitivity results of all
parameters but SD are given in Fig. 4(b) and (d). The TSI
values of Pe c decrease slightly faster for snow with a weak salt
compared with those of snow on land without salt. According
to the TSI variations results, the sensitivity values of TS are
similar to those of ρfor vertical polarization and the sensitivity
values of TS are about 0.06 less than those of ρfor horizontal
polarization. The TSI values of Sppt are small with the TSI
Fig. 6. TSI variations of all parameters but Pec in the MEMLS model for
brightness temperature differences at 18.7 and 36.5 GHz for dry snowpack.
(a) and (b) For vertical polarization. (c) and (d) For horizontal polarization.
(a) and (c) For snow without salt. (b) and (d) For snow with a small salt
content Sppt of 0‰–0.1‰.
values always less than 0.015, which can be ignored in the
multiparameter inversion.
In summary, the aforementioned findings emphasize the
primary importance of the snow microstructure parameter Pec
to be provided in the snow depth/SWE retrieval regardless of
whether the snow contains salt. Additionally, the TSI values
of all parameters but SD vary slightly under different snow
depths, which indicates the different impact of these factors
on the snow multiparameter retrieval. When SD is less than
50 cm, Pec is the main factor with the TSI values about
higher than 0.95 and the TSI values of the other parameters
lower than 0.05. When SD is higher than 50 cm, apart from
the impact of Pec, the effect of ρneeds to be noticed for
both vertical and horizontal polarizations with the TSI values
greater than 0.05 with the increase of SD, especially for
horizontal polarization. Moreover, since snow salinity affects
the calculation of the snow dielectric constant, the TSI values
of TS are much higher, which indicates snow multiparameter
retrieval is more complicated for snow with weak salt.
As stated before, the spatial distribution of snow grain
size has obvious differences due to the impact of micro-
topography and temperature changes according to the field
observations [23], [70]. The TSI variations of all parameters
but Pec in the MEMLS model for brightness temperature
differences at 18.7 GHz and 36.5 GHz for dry snowpack were
investigated, as shown in Fig. 6.
First, there is an increasing SD sensitivity from about
0.2 to 0.8 with the increase of the Pec for both vertical and
horizontal polarizations. Meanwhile, the TSI values of SD
increase quickly when the Pec is about less than 0.2 mm, and
then the TSI values of SD tend to be stable and even show a
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GAO et al.: GSA OF THE MEMLS MODEL FOR RETRIEVING SWE 4303415
Fig. 7. Scattering coefficients, absorptions coefficients, and snow layer
emissivity response with different exponential correlation lengths and snow
density at 18.7 and 36.5 GHz, evaluated by MEMLS. Fixed parameters:
SD =50 cm, TS =263 K, TG =263 K, and the incidence angle =55◦.
slight downward trend, especially for horizontal polarization
in the case of Pe c higher than 0.2 mm. The increasing TSI
results suggest the increasing retrievability of SD with the
increase of Pec, particularly on the condition that Pe c is around
0.25 mm, in the traditional snow depth/SWE retrieval method
based on the brightness temperature differences at 18.7 and
36.5 GHz. Second, the sensitivities of ρincrease generally
from about 0.05–0.4, while the rate of increase becomes
greater with the trends opposite to that of SD in the case of
Pec higher than 0.2 mm. As is shown in Fig. 7, the results
of scattering coefficients [given in Fig. 7(a)] increase with
the increase of Pec, especially for 36.5 GHz. Additionally,
the values of scattering coefficients increase with the increase
of ρand the influence of ρon the scattering coefficients
gradually increases with the increase of Pe c , especially at
36.5 GHz. The absorption coefficients [given in Fig. 7(b)] are
constant results along with the increase of Pec for different
snow densities. As is shown in Fig. 7(c), snow layer emissivity
increases slightly at 18.7 GHz with the increase of Pec and ρ,
respectively. At 36.5 GHz, the results of snow emissivity
gradually increase when Pec is less than 0.25 mm and then
slightly decreases. Moreover, the influence of ρon snow
emissivity at 36.5 GHz is greater than that of 18.7 GHz. The
results indicate that the increasing TSI values of ρwith the
increase of Pec is mainly affected by the volume scattering and
thermal emission inside the snowpack. Third, the sensitivities
of TS are greater than those of SD in case that Pec is less than
0.1 mm, which indicates the impact of TS is important in the
snow depth/SWE inversion in the case of snow with a small
grain size. Additionally, other parameters including Sppt and
TG for Pec greater than 0.2 mm usually have low sensitivities
and have no particular distinct fluctuation for both vertical and
horizontal polarizations, except for the factor of TS with the
Fig. 8. TSI variations of all parameters but ρin the MEMLS model for
brightness temperature differences at 18.7 and 36.5 GHz for dry snowpack.
(a) and (b) For vertical polarization. (c) and (d) For horizontal polarization.
(a) and (c) For snow without salt. (b) and (d) For snow with a small salt
content Sppt of 0‰–0.1‰.
TSI values from about 0.4–0.3 on the condition that snow has
a weak content in Fig. 6(b) and (d).
The density of snow varies over space according to the
field observations and is a function of formation conditions
in the clouds and the atmospheric conditions through which
the snow crystals fall. [15], [23], [77]. The density of snow
also tends to increase over time due to snowpack settlement
and compaction during and after a snowfall event. How-
ever, the current northern hemisphere SWE retrieval scheme
of GlobSnow SWE product utilizes a fixed constant ρof
240 kg/m3[4]. As is shown in Fig. 4, snow density indeed
has an important effect on deep snow. This is consistent
with existing SWE validation results that underestimation
occurs in deep snow especially in the middle and late of the
snow season [13], [78], when the snow density is relatively
higher than the fixed value. Therefore, we investigated the
TSI variations of all parameters but ρin the MEMLS model
for brightness temperature differences at 18.7 and 36.5 GHz
for dry snowpack, presented in Fig. 8.
As shown in Fig. 8, the most evident findings are that
the sensitivities of SD decrease consistently, while the Pec
sensitivities increase slowly and always keep a high value
as the increase of snow density. The sensitivities values of
SD decrease generally from about 0.27–0.13 and the TSI
results for horizontal polarization are slightly lower than
those of vertical polarization, which means snow density has
an important influence. According to Mätzler [79], the real
part of the dielectric permittivity for dry snow is the unary
cubic function of ρand increases with the increase of ρ.
Thereby, the effective path length in the snowpack decreases
with the increase of the real part of dielectric permittivity
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4303415 IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING, VOL. 60, 2022
for dry snow [16] in the case of the incident angle of 55◦.
Therefore, the sensitivity values of SD will decrease with the
increase of ρ. The TSI values of TS are consistently low in
Fig. 8(a) and (c) for snow without salt, being about 0.08 and
with a slightly increasing trend to about 0.04, and keep the TSI
values around 0.1 shown in Fig. 8(b) and (d) as the ρincrease.
Finally, the sensitivities of TG and Sppt are very low and their
values almost do not fluctuate regardless of the ρvalue.
The results suggest the decreasing retrievability of SD in
the traditional method based on the brightness temperature
differences at 18.7 and 36.5 GHz when snow density is higher,
which can be partially improved by using spatial and temporal
dynamic snow density rather than the fixed or empirical
constant [4], [66] during the whole snow season. The constant
density used in GlobSnow SWE retrieval is much large for
the early snow season and small for the late snow season [78].
The GlobSnow product overestimates the SWE for small SWE
values for early snow season and underestimates the SWE for
large SWE conditions, especially for late snow season when
the snowpacks are usually denser than the constant density
applied [13], [18], [78], [80]. The errors of GlobSnow are sup-
posed to be mainly caused by the constant ρ, underestimation
of snow grain size for small SD, and overestimation of snow
grain size for large SD, as well as the lack of representativeness
of the meteorological sites [78], [80]. Venäläinen et al. [80]
used snow transect snow density from Eurasia and Canada
and automated snow observations from the USA to post-
process the GlobSnow v.3.0 SWE product by a simple ratio of
dynamic and constant snow density. On the one hand, it may
be a potential method to replace the constant density with
spatiotemporal dynamic interpolation based on observations
from meteorological stations in the iterative snow inversion
model to improve the baseline GlobSnow SWE retrieval
methodology. On the other hand, the constant density in the
GlobSnow product can also be replaced by the values simu-
lated by the snow process models [81]. From the perspective of
improvement of snow depth/SWE retrieval algorithm, it would
be an effective solution to include snow density into the com-
bination in the new multiparameter retrieval methods for the
future.
C. Test 3: Temporal Attributes of the Parameter Sensitivity
The snow parameters vary significantly during the snow
season. Traditional retrieval algorithms assume the empirical
or average snow grain size and snow density to estimate snow
depth/SWE based on the relationship between snow depth and
microwave radiation, which is the reason that the conventional
static methods perform well in average snow season [66].
However, the accuracy of snow depth/SWE estimates varies
with time and space, especially trends to underestimate in
the late stage of the snow season [13] due to the seasonal
metamorphism of snowpacks. Therefore, we analyzed the tem-
poral attributes of the parameter sensitivity to investigate the
microwave response to snow parameters inside the snowpacks
through a case study in Xinjiang, China.
In situ snow parameters are collected from the Xinjiang
province that is located in the Northwest of China (Fig. 9).
Fig. 9. Spatial distribution of field sampling observations (52 yellow square
points) and meteorological stations (65 pink dot points) in Xinjiang, China.
The southern and northern parts of Xinjiang are dominated
by sparse grassland, while the central area is mainly bare
land [82]. The Xinjiang province is a stable snow area located
in Central Asia, which is suitable for studying the influence of
snow parameters on snow depth inversion [23]. From January
2018 to March 2018 and December 2018 to early March
2019, six field survey experiments were conducted in northern
Xinjiang during the two snow seasons. During the field obser-
vations, a large number of snow pits were measured. In these
snow pits, the snow density, depth, grain size, temperature, and
temperature at the snow-ground interface of snowpack were
measured in detail at different stages of the snow season. The
snow density was obtained by measuring a known volume
of snow. The snow grain diameter inside the snowpack was
measured by an optical microscope. According to the field
measurements, the snow grain size and snow density gradually
increase from top to bottom inside snowpacks as shown in
Fig. 10(a) and (b). Fig. 10(d) presents the averaged snow
depth according to 65 meteorological stations with daily snow
depth values for two snow seasons from 2017 to 2018 and
2018 to 2019. According to the field observations, we argue
that the averaged snow depth can be used to determine the
number of snow layers, and the snowpacks can be up to
three layers. When the snow depth is less than 10 cm in
the early snow season, the snowpack is characterized as one
layer. When the snow depth is between 10 and 20 cm in
the middle snow season, the snowpack is regarded as two
layers and the thicknesses of the top layer and bottom layer
are equal. When the snow depth is greater than 20 cm in
the late snow season, the snowpack is characterized as three
layers and the thickness of the top layer is equal to the middle
layer and twice the depth of the bottom. In this numerical
experiment, ±50% perturbation of the averaged snow depth
is set as the upper and lower limits of the parameter vari-
ation for the fluctuation of snow depth distribution. Snow
temperature changes over time within one day, however, the
measurements of snow pits were usually obtained during the
daytime. The automatic temperature detectors were set at
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GAO et al.: GSA OF THE MEMLS MODEL FOR RETRIEVING SWE 4303415
Fig. 10. Mean evolution trends of snow microstructure parameters over time during the two snow seasons for 2017–2018 and 2018–2019 based on the field
observations and meteorological stations. (a) Snow grain diameter and standard deviation. (b) Snow density and standard deviation. (c) correlation length and
standard deviation. (d) Snow depth and standard deviation. (e) Snow temperature. (f) Soil temperature.
Aletai station to automatically collect the snow temperature
[given in Fig. 10(e)] and soil temperature [given in Fig. 10(f)]
data every ten minutes per day. Since the temperature inside
the snowpacks changes little at night and the TSI values are
small analyzed in Test 1 and Test 2, the snow temperature
inside the snowpacks is considered equal. Since the study
area is located inside the Eurasian away from the ocean, the
parameter of Sppt is set to 0. According to the meteorological
station, the highest snow temperature was lower than 0 ◦C
from December to mid-March at night in this region. Thus,
snow is considered dry and the liquid water is set to 0.
Additionally, a comparative experiment is designed based on
field observations to study the influence of the snow layers. For
a single snow layer during the entire snow season, the variation
ranges of snow parameters correspond to the maximum range
inside the snowpacks. For the multilayer snow, the ranges of
snow parameters over time follow the extents of the natural
layer [given in Fig. 10]. The ranges of these parameters
change over time and were set in the MEMLS model for
brightness temperature differences at 18.7 and 36.5 GHz to
understand the temporal variations performed by the EFAST
method.
The temporal characteristics of the parameter sensitivities
are presented in Fig. 11. For a single layer during the entire
snow season as shown in Fig. 11(a) and (b), three parameters
of Pec,SD,andρare sensitive throughout the entire snow
season for both vertical and horizontal polarizations for dry
snow. The sensitivities of TG and TS are very low with the
TSI values of TG consistently lower than 0.005 and those of TS
consistently lower than 0.008 during the whole snow season.
In general, the sensitivity values of SD decrease consistently
from about 0.45–0.15 with a slight fluctuation. The sensitiv-
ity results of Pe c increase from about 0.45–0.75 over time
before mid-February, and then decrease gradually from about
0.75–0.65. Interestingly, the TSI values of ρremain stable at
around 0.1 before mid-February, and increase gradually from
about 0.1–0.2 and are higher than those of SD, especially at
horizontal polarization from late February. In view of snow
depth/SWE retrieval, the effect of ρis important in the late
stage of the snow season. In particular, the TSI values of
SD at vertical polarization are approximately 0.02 higher
than those at horizontal polarization. For multilayer snow,
the sensitivity results are presented in Fig. 11(c) and (d) for
vertical polarization and horizontal polarization, respectively.
The parameters of Pe c ,SD,andρare still sensitive throughout
the entire snow season and the trend of the sensitivity value
of each parameter over time is generally similar to the single-
layer result. However, the most evident difference is that
the sensitivity values of SD are higher than those for the
single-layer snow. The second observable difference is that
the sensitivity values of Pec are slightly lower than those for
the single-layer snow. The TSI values of SD decrease generally
from about 0.45–0.2 with a slight fluctuation and the TSI
values of vertical polarization are slightly higher than those
of horizontal polarization. From the view of snow depth/SWE
retrieval, more information of snow layers can enhance the
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4303415 IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING, VOL. 60, 2022
Fig. 11. Mean temporal attributes of the parameter sensitivity in the MEMLS model for 2017–2018 and 2018–2019 two snow seasons for brightness
temperature differences at 18.7 and 36.5 GHz for dry snowpack during the snow season in Xinjiang, China. (a) Single snow layer for vertical polarization.
(b) Single snow layer for horizontal polarization. (c) Multiple snow layers for vertical polarization. (d) Multiple snow layers for horizontal polarization.
sensitivity of SD and is helpful for the retrieval. The sensitivity
values of Pe c gradually increase from about 0.45–0.68 and TSI
values of Pe c keep the highest among all the parameters during
the entire snow season. In addition, the results also show that
the influence of snow density increases in the late snow season
especially for horizontal polarization.
From the temporal dynamic evolution of parameter sensitiv-
ity, except for TG and TS with almost non-variable sensitivity,
the sensitivity values of Pe c ,SD,andρare variable. The
results prove that the temporal characteristics of parameter
sensitivity are quite important, which means the evolution of
the snow parameters has a high impact on the microwave radi-
ation of snowpacks. From the perspective of snow depth/SWE
algorithms in the northern hemisphere or global area, the prior
information or accurate multiparameter retrieval methods for
the sensitivity parameters of Pe c and ρare needed rather
than empirical equations [5], [66] or fixed constants [4].
Additionally, the information of snow layers also contributes
to snow depth/SWE retrieval.
V. C ONCLUSION
This article explored the sensitivity of snow microstructural
parameters of the MEMLS model by using a variance-based
GSA technique. The MEMLS model was adopted to simulate
passive microwave brightness temperature at a 55◦incidence
angle that is the same as the configuration of AMSR2.
The EFAST method was used to quantify the microwave
radiation to physical parameters and the interactions among
the parameters. The method is conducive to studying the
possible error resources and potential improvements for the
SWE retrieval method. Three different SA test schemes were
designed. To our knowledge, it is the first time to use a
GSA algorithm to identify the sensitivity of snow physical
parameters and the effect of snow microstructure variation on
snow depth/SWE retrievals from passive microwave remote
sensing.
The results show that the sensitivity indexes (TSI, MSI,
and their difference) of the parameters vary for different fre-
quencies and the brightness temperature gradient of 18.7 and
36.5 GHz. Exponential correlation length, snow depth, and
snow density are the three main sensitivity parameters for
snow without salt in the MEMLS model for the brightness
temperature gradient. For snow with small salt content, the
exponential correlation length, snow depth, snow temperature,
and snow density are the four most sensitive parameters. The
results prove the retrievability of the snow depth in the tradi-
tional gradient-based retrieval method. Meanwhile, the results
provide a new choice to include the snow density, especially
for deep snow depth, in the combination of sensitive factors in
the future multiparameter retrievals. The sensitivity variation
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GAO et al.: GSA OF THE MEMLS MODEL FOR RETRIEVING SWE 4303415
analysis of these parameters also emphasizes the significance
of correlation length and snow density under different snow
conditions. Another interesting finding is that the global sensi-
tivities of snow depth at vertical polarization are always higher
than those of horizontal polarization. Moreover, the global
sensitivities of snow depth are lower for snow with a weak salt
content than those of snow without salt. The EFAST technique
is also valuable in exploring the temporal characteristics of the
parameter SA due to the evolution of snow parameters. The
temporal evolution of parameter sensitivity values is dynamic
variably during the snow season. The temporal variation of
the TSI values also indicates that the exponential correlation
length and snow density are the two main influential factors
in the snow depth/SWE inversion. Consequently, a new snow
depth/SWE retrieval method may need to consider the dynamic
effect of the evolution of the snow particles and snow density
in the future.
ACKNOWLEDGMENT
The authors would like to thank Prof. Andreas Wiesmann
for providing the MEMLS model. They would also like
to thank the National Meteorological Information Center,
Beijing, China, for providing the meteorological data.
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Shuo Gao received the B.S. degree in remote sens-
ing science and technology from Shandong Agri-
cultural University, Taian, China, in 2016. He is
currently pursuing the Ph.D. degree in cartogra-
phy and geographic information system with the
Key Laboratory of Digital Earth Science, Aerospace
Information Research Institute, Chinese Academy of
Sciences, Beijing, China.
His research interests include passive microwave
data processing, evaluation and application of snow
radiation model, and retrieval methods of snow
parameters.
Zhen Li (Member, IEEE) received the B.S. degree
in photogrammetry and remote sensing from Wuhan
University, Wuhan, China, in 1988, and the Ph.D.
degree in natural geography from the Lanzhou Insti-
tute of Glaciology and Geocryology, Chinese Acad-
emy of Sciences, Lanzhou, China, in 1998.
He is currently a Professor with the Key Labora-
tory of Digital Earth Science, Aerospace Information
Research Institute, Chinese Academy of Sciences,
Beijing, China. He has authored more than 100 jour-
nal articles and has authored and coauthored four
books in collaboration with others. His research interests include microwave
remote sensing, cryosphere environment, and disaster remote sensing.
Ping Zhang received the Ph.D. degree in communi-
cation and information systems from the Institute of
Electronics, Chinese Academy of Sciences, Beijing,
China, in 2009.
She is currently an Associate Professor with the
Key Laboratory of Digital Earth Science, Aerospace
Information Research Institute, Chinese Academy of
Sciences. She has authored more than ten articles
and is responsible for three books chapters. Her
research activities are concentrated in remote sensing
data processing, signal processing, and calibration of
synthetic aperture radar (SAR).
Quan Chen received the B.S. degree in photogram-
metry and remote sensing from Wuhan University,
Wuhan, China, in 2003, and the Ph.D. degree in
geographic information systems from the Institute
of Remote Sensing Applications, Chinese Academy
of Sciences, Beijing, China, in 2008.
He is currently an Associate Professor with
the Airborne Remote Sensing Center, Institute of
Remote Sensing and Digital Earth, Chinese Acad-
emy of Sciences. He has authored or coauthored over
40 journal articles. His research interests include
airborne remote-sensing data processing, and active and passive microwave
remote-sensing applied to hydrology.
Jiangyuan Zeng (Senior Member, IEEE) received
the B.S. degree from Wuhan University, Wuhan,
China, in 2010, and the Ph.D. degree from the Insti-
tute of Remote Sensing and Digital Earth, Chinese
Academy of Sciences, Beijing, China, in 2015.
He is currently an Associate Professor with the
State Key Laboratory of Remote Sensing Science,
Institute of Remote Sensing and Digital Earth,
Chinese Academy of Sciences. His research interests
include microwave remote sensing of geophysical
parameters (particularly soil moisture), hydrological
applications of satellite remote sensing, and bistatic scattering of soil surfaces.
Dr. Zeng has been a member of the Editorial Board of Remote Sensing of
Environment since 2020. He received several international awards, including
the International Society for Photogrammetry and Remote Sensing (ISPRS)
Best Young Author Award in 2020, the Young Scientist Award (including Cash
Award) from the Progress in Electromagnetics Research Symposium (PIERS)
in 2018, and the Young Scientist Award from the International Union of Radio
Science (URSI) in 2017.
Changjun Zhao received the B.S. degree from
Beijing Normal University, Beijing, China, in 2014,
and the Ph.D. degree in cartography and geography
information system from the Aerospace Information
Research Institute, Chinese Academy of Sciences,
Beijing, China, in 2020.
He is currently a Lecturer with the Northwest
Land and Resources Research Center, Shaanxi Nor-
mal University, Xi’an, China. His research inter-
ests include synthetic aperture radar (SAR) image
denoising and multitemporal interferometric SAR
techniques.
Chang Liu received the B.S. degree in remote sens-
ing science and technology from Shandong Univer-
sity of Science and Technology, Shandong, China,
in 2017. She is currently pursuing the Ph.D. degree
in cartography and geographic information system
with the Key Laboratory of Digital Earth Science,
Aerospace Information Research Institute, Chinese
Academy of Sciences, Beijing, China.
Her research interests include the assessment and
application of snow products and microwave remote
sensing of snow parameters.
Zhaojun Zheng received the B.S. degree in
atmospheric science from Nanjing University,
Nanjing, China in 2000, and the M.S. degree in
atmospheric physics and atmospheric environment
from Peking University, Beijing, China, in 2008.
He has been with the Satellite Meteorologi-
cal Institute, China Meteorological Administration,
National Satellite Meteorological Center, Beijing,
since 2000, focusing on cryosphere remote sensing
and analysis of cryospheric change.
Mr. Zheng was awarded the Research Associate
in 2009.
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