Developing a Long Short-Term Memory (LSTM)-Based Model for Reconstructing Terrestrial Water Storage Variations from 1982 to 2016 in the Tarim River Basin, Northwest China

Abstract

Estimating terrestrial water storage (TWS) not only helps to provide a comprehensive insight into water resource variability and the hydrological cycle but also for better water resource management. In the current research, Gravity Recovery and Climate Experiment (GRACE) data are combined with the available hydrological data to reconstruct a longer record of terrestrial water storage anomalies (TWSA) prior to 2003 of the Tarim River basin (TRB), based on a Long Short-Term Memory (LSTM) model. We found that the TWSA generated by LSTM using soil moisture, evapotranspiration, precipitation, and temperature best matches the GRACE-derived TWSA, with a high correlation coefficient (r) of 0.922 and a normalized root mean square error (NRMSE) of 0.107 during the period 2003–2012. These results show that the LSTM model is an available and feasible method to generate TWSA. Further, the TWSA reveals a significant fluctuating downward trend (p < 0.001), with an average annual decline rate of 0.03 mm/year during the period 1982–2016 in the TRB. Moreover, the TWS amount in the north of the TRB was less than that in the south of the basin. Overall, our findings unveiled that the LSTM model and GRACE data can be combined effectively to analyze the long-term TWS in large-scale basins with limited hydrological data.

Full text

remote sensing
Article
Developing a Long Short-Term Memory (LSTM)-Based Model
for Reconstructing Terrestrial Water Storage Variations from
1982 to 2016 in the Tarim River Basin, Northwest China
Fei Wang 1,2 , Yaning Chen 1 ,*, Zhi Li 1, Gonghuan Fang 1, Yupeng Li 1, Xuanxuan Wang 1,2, Xueqi Zhang 1,2
and Patient Mindje Kayumba 1,2


Citation: Wang, F.; Chen, Y.; Li, Z.;
Fang, G.; Li, Y.; Wang, X.; Zhang, X.;
Kayumba, P.M. Developing a Long
Short-Term Memory (LSTM)-Based
Model for Reconstructing Terrestrial
Water Storage Variations from 1982 to
2016 in the Tarim River Basin,
Northwest China. Remote Sens. 2021,
13, 889. https://doi.org/10.3390/
rs13050889
Received: 3 January 2021
Accepted: 22 February 2021
Published: 26 February 2021
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Copyright: © 2021 by the authors.
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4.0/).
1State Key Laboratory of Desert and Oasis Ecology, Xinjiang Institute of Ecology and Geography,
Chinese Academy of Sciences, Urumqi 830011, China; wangfei172@mails.ucas.ac.cn (F.W.);
liz@ms.xjb.ac.cn (Z.L.); fanggh@ms.xjb.ac.cn (G.F.); liyupeng14@mails.ucas.ac.cn (Y.L.);
wangxuanxuan17@mails.ucas.edu.cn (X.W.); zhangxueqi19@mails.ucas.ac.cn (X.Z.);
patientestime001@mails.ucas.ac.cn (P.M.K.)
2University of Chinese Academy of Sciences, Beijing 100049, China
*Correspondence: chenyn@ms.xjb.ac.cn; Tel.: +86-991-782-3169
Abstract:
Estimating Terrestrial Water Storage (TWS) not only helps to provide a comprehensive
insight into water resource variability and the hydrological cycle but also for better water resource
management. In the current research, Gravity Recovery And Climate Experiment (GRACE) data are
combined with the available hydrological data to reconstruct a longer record of Terrestrial Water
Storage Anomalies (TWSA) prior to 2003 of the Tarim River Basin (TRB), based on a Long Short-
Term Memory (LSTM) model. We found that the TWSA generated by LSTM using soil moisture,
evapotranspiration, precipitation, and temperature best matches the GRACE-derived TWSA, with a
high correlation coefficient (r) of 0.922 and a Normalized Root Mean Square Error (NRMSE) of 0.107
during the period 2003–2012. These results show that the LSTM model is an available and feasible
method to generate TWSA. Further, the TWSA reveals a significant fluctuating downward trend
(
p< 0.001
), with an average decline rate of 0.03 mm/month during the period 1982–2016 in the TRB.
Moreover, the TWSA amount in the north of the TRB was less than that in the south of the basin.
Overall, our findings unveiled that the LSTM model and GRACE data can be combined effectively to
analyze the long-term TWSA in large-scale basins with limited hydrological data.
Keywords: terrestrial water storage; Tarim River Basin; LSTM model; climate change
1. Introduction
Terrestrial Water Storage (TWS) is a crucial indicator to measure the health of hydro-
logical regimes and ecosystems [
1
–
3
]. On top of that, TWS is the main element in water,
food, and energy cycles [
4
]. Globally, endorheic systems experienced widespread water
loss (106.3 Gt yr
−1
) during the period 2002–2016, along with a net decline in endorheic
water storage, according to Gravity Recovery And Climate Experiment (GRACE) data [
5
].
These observations suggested that the decline in TWS mostly may be induced by both
climate change and human activities [
6
,
7
]. Additionally, TWS has recently shown signifi-
cant decreasing trends and experienced obvious seasonal variations in Northwest China,
including the Tarim River Basin (TRB) [
8
,
9
]. The TRB is the largest inland basin in China,
but also the heart of the Belt and Road Initiative [
10
]. Serious environmental problems
resulted in the TRB disintegration mostly emanate from desertification, over-consumption
of groundwater, and hydraulic disconnections due to water shortages [
11
]. From a global
perspective, the TRB is one of the main water-scarce regions in the world, and the irrigation
water requirement accounts for 95% of total water consumption. Furthermore, the increase
in agricultural irrigation water requirements has led to a decrease in regional water stor-
age [
12
]. In this extremely arid area, water storage is vulnerable to subtle flux perturbations,
Remote Sens. 2021,13, 889. https://doi.org/10.3390/rs13050889 https://www.mdpi.com/journal/remotesensing

Remote Sens. 2021,13, 889 2 of 17
which are exacerbated by unceasing warming and human activities. Increasing bouts of
warming and drying have triggered observable perturbations to the water balance, which
is further intensified by damming, diversions, and human water withdrawals in arid/semi-
arid endorheic regions [
13
–
15
]. TWS is an important indicator for measuring significant
changes in the hydrological cycle and water resources management [
16
]. Consequently,
continuous monitoring of TWS would not only lead to a better understanding of the hy-
drological cycle, but also it could be employed to analyze hydrological hazards, estimate
water availability, and manage water resources [
6
,
17
]. Thus, as a contributive effort in the
study area, it is crucial to monitor longer period spatial–temporal variations in total TWSA
in the TRB region (a full list of acronyms is provided in Table 1).
Table 1. List of acronyms used in this paper.
Acronym Meaning
LSTM Long Short-Term Memory
TWS Terrestrial Water Storage
GRACE Gravity Recovery And Climate Experiment
TWSA Terrestrial Water Storage Anomalies
TRB Tarim River Basin
FO Follow-On
TWSCs Terrestrial Water Storage Changes
CNN Convolutional Neural Network
ANN Artificial Neural Network
RNN Recurrent Neural Network
YRB Yarkand River Basin
KGRB Kaxgar River Basin
ARB Aksu River Basin
HRB Hotan River Basin
WKRB Weigan-Kuqa River Basin
DRB Dina River Basin
KRB Keriya River Basin
KKRB Kaidu-Kongque River Basin
QRB Qarqan River Basin
DEM Digital Elevation Model
APHRODITE Asian Precipitation-Highly-Resolved Observational Data Integration
Towards Evaluation
CRU Climatic Research Unit
PUSHGBC Princeton University and University of Southampton
Hydro-climatology Group Bias Corrected
GPCC Global Precipitation Climatology Centre
P Precipitation
ET Evapotranspiration
SM Soil Moisture
T Temperature
GLDAS-1 Global Land Data Assimilation system, version 1
GLDAS-2 Global Land Data Assimilation system, version 2
JPL Jet Propulsion Laboratory
CSR Center for Space Research
r correlation coefficient
NRMSE Normalized Root Mean Square Error
NSE Nash–Sutcliffe efficiency
BIAS Relative BIAS
Due to the obstructions caused by mountains (e.g., Tienshan Mountains, Kunlun
Mountains) and deserts (e.g., Taklimakan Desert) in the basin, there are no effective and
feasible datasets or approaches for estimating spatio-temporal changes of TWS [
18
]. In
addition, the study area is too large to observe hydrological fluxes [
11
]. However, the
GRACE satellite mission successfully launched in 2002 [
19
,
20
] has offered a new method
to quantify the monthly variations of TWS since it comprises soil moisture storage, sur-

Remote Sens. 2021,13, 889 3 of 17
face water, groundwater, glaciers, and snow. Despite its coarse resolution [
21
], GRACE
provides globally a “big picture” of TWS variations in real-time. Furthermore, GRACE
data combined with hydrological data have been used in numerous researches to estimate
groundwater storage [
22
–
27
], regional terrestrial water storage changes [
28
–
33
], drought
evaluation [
34
–
37
], flood monitoring [
38
–
40
], and ice sheet mass changing [
41
]. All the
aforementioned studies demonstrated that GRACE data are well-suited for monitoring
variations in TWS.
GRACE has provided a nearly continuous record of global TWS dynamics (2002–
2017) [
21
]. Monthly TWSA GRACE data are available, but there is a 2- to 6-month latency
period before the release of data [
42
]. Since mid-2018, the GRACE satellite Follow-On
(FO) mission has continued [
43
]. Nevertheless, the TWSA data before the GRACE launch
are crucial for generating long-term terrestrial water storage changes (TWSCs) and for
predicting future TWSCs. Several approaches have been made to reconstruct the TWS
time series prior to the 2003 GRACE launch, by using GRACE data. Yin et al. [
44
] rebuilt
the monthly, seasonal, and inter-annual variability of TWS for 1980 to 2015 based on
the water balance method in the Beishan area. A two-parameter water balance model
to reconstruct changes in annual groundwater storage and terrestrial water storage [
45
].
Meanwhile, Hasan et al. [
46
] charted a 66-year record of TWS for nine transboundary
river basins in Africa, based on an autoregressive model with exogenous variables. The
continuous development of deep learning techniques opens up new paths for the research
of hydrology and related fields [
47
–
50
]. Deep learning methods including data mining and
data reconstruction among others have proven to be effective in solving some traditionally
difficult problems [
51
]. In fact, there has been an increasing interest in the use of deep-
learning models to evaluate hydrological variables by understanding the relationship
between the input and output variables [
52
–
55
]. Sun et al. [
21
] reconstructed GRACE
data by combining a deep convolutional neural network (CNN) and hydrological models.
Lately, they demonstrated that the CNN model can effectively and accurately improve the
performance of LSMs [
21
]. In subsequent work, Sun et al. [
56
] reconstructed TWSA data by
using three different models (MLR, DNN, and SARIMAX), and discovered that the DNN
and SARIMAX models perform better than MLR models in majority grid cells. In China,
especially in Northwest China, the RF method is considered optimal for reconstructing
TWSA [
9
,
57
]. At the same time, the developed artificial neural network (ANN) models
worked well in reconstructing the monthly mean TWSA for the region [
39
]. Likewise,
Xie et al. [
58
] proposed an ANN model to build a relationship between TWSA and other
available hydrological data during the period 2003–2010 and then applied it to generate
TWSA before 2003. By using both ET and soil moisture, these results showed that the
ANN model is a feasible method to reconstruct TWSA, as it matches best with the GRACE-
derived TWSA.
In the current study, a long short-term memory (LSTM) model was used to build the cor-
rection between TWSA and hydrological variables (precipitation, ET, SM, and temperature),
with the aim of developing a long-term record of TWSA in the TRB. Moreover, LSTM, which
is a kind of Recurrent Neural Network (RNN) that performs well in coping with longer
record data, was selected because of its sophisticated network structure [
22
]. The LSTM
model has been widely applied to numerous researches in the forecasting of meteorological
variables and water resources management, such as flood forecasting [
59
], precipitation fore-
casting [
60
], streamflow forecasting [
61
,
62
], rainfall-runoff simulation [
63
,
64
], and low-flow
hydrological forecasting [
65
]. Although LSTM cannot directly show the internal mecha-
nism of water balance, it can analyze the cell-states and correlate them to hydrological
patterns [
63
]. Recently, Yang et al. [
40
] suggested that a combination of machine learning
techniques and classical flood simulation could be a more robust and efficient method for
flood risk assessment by using an LSTM model to enhance GHMs-based flood simulations.
Zhang et al. [
22
] proved that the LSTM model can learn previous information well by
developing it hence the prediction of water table depth with a higher prediction accuracy.
From these findings, it is clear that LSTM models showed great superiority over traditional

Remote Sens. 2021,13, 889 4 of 17
hydrological models, notably when there are complex nonlinear interrelationships in the
processes. This is due to LSTM modeling which is a nonparametric method that does not
depend on the true underlying function [63,66].
In recent decades, various studies have been undertaken to estimate TWS and water
budgeting in the TRB. For instance, Yang et al. [
18
] estimated TWS based on four hydrology
products from GRACE and GLADS in the TRB from 2003 to 2011. Zhao and Li, [
67
] found
that the TWS slightly decreased with a declining trend value of
−
1.4069
±
0.5060 mm yr
−1
in the TRB during the period 2002–2015, similarly, Yang et al. [
68
] reported that the TWS
in the TRB experienced a decreasing trend (1.6
±
1.1 mm/a) during the period 2002–2015.
Nevertheless, these studies covered only a relatively short term period, as the long-term
GRACE data were not yet available. Thus, to further understand the variations of TWS in
the TRB, we attempt to evaluate a long-term period of TWSA for the first time, based on
both GRACE data and the LSTM model.
Therefore, the specific objectives of this research include: (1) The estimation of total
water storage anomalies based on GRACE data in the TRB; (2) estimation of the long-term
time series of meteorological data (precipitation, ET, SM, and temperature) and correlations
between meteorological data and TWSA; and (3) propose an LSTM model to reconstruct
a long-term record of TWSA for 1982–2016. To the best of our knowledge, only a few
attempts have been made to calculate the TWSA from both GRACE data and the LSTM
model. Thus, reconstructing longer record TWSA data could estimate the influence of
climate change on the hydrological cycle and provide insights into the impact of water
resources management in the region.
2. Materials and Methods
2.1. Study Area
The Tarim River basin (Figure 1) covers an area of 1.02
×
10
6
km
2
and is located in the
northwest arid region of China. The inland basin is bordered by the Tienshan Mountains
to the north and the Kunlun Mountains to the south and includes the headwaters of the
Tarim River as well as nine other river basins, namely, the Yarkand River Basin (YRB), the
Kaxgar River Basin (KGRB), the Aksu River Basin (ARB), the Hotan River Basin (HRB),
the Weigan-Kuqa River Basin (WKRB), the Dina River Basin (DRB), the Keriya River Basin
(KRB), the Kaidu-Kongque River Basin (KKRB), and the Qarqan River Basin (QRB). The
Tarim River is a dissipative inland river whose runoff is mainly supplied by meltwater
from glaciers and snow.
2.2. Data
2.2.1. Meteorological Data
Precipitation (P) is deemed some of the most important data in the TRB’s water
cycle [
69
]. Due to the harsh climatic and environmental conditions, there are few me-
teorological stations in the TRB. Thus, this research adopts four published global high-
resolution precipitation datasets, namely (1) Asian Precipitation-Highly-Resolved Observa-
tional Data Integration Towards Evaluation (APHRODITE V1101 and V1101EX_R1) [
70
];
(2) The monthly 0.5
◦
grid data of precipitation series generated by the Climatic Research
Unit from the University of East Anglia in conjunction with the Hadley Centre (at the
UK Met Office) [
71
]; (3) Princeton University and University of Southampton Hydro-
climatology Group Bias Corrected Meteorological Forcing Dataset Versions 3 (PUSHGBC);
and (4) Global Precipitation Climatology Centre (GPCC). All of these products can be used
to offer accurate estimates of precipitation in the TRB.
On the other hand, Evapotranspiration (ET) is one of the most difficult hydrological
variables to obtain [
72
], especially in a region with sparse long-term hydrological data
like the TRB. So in this study, five types of ET products are proposed, including two
land surface models (Global Land Data Assimilation System, version 1 and 2 (hereafter,
GLDAS-1 and GLDAS-2)). The five products are: (1) GLDAS1-CLM; (2) GLDAS1-Mosaic;
(3) GLDAS1-Noah; (4) GLDAS1-VIC; and (5) GLDAS2-Noah. Bear in mind that ET is also

Remote Sens. 2021,13, 889 5 of 17
an essential variable and proposed as an input factor to reconstruct TWSA based on the
LSTM model in this study.
Remote Sens. 2021, 13, x FOR PEER REVIEW 5 of 18
Figure 1. Location of study region on the Tarim River Basin, including the headwaters of the Yarkand (YRB), Kaxgar
(KGRB), Aksu (ARB), Hotan (HRB), Weigan-Kuqa (WKRB), Dina (DRB), Keriya (KRB), Kaidu-Kongque (KKRB), and
Qarqan (QRB) River Basin; and glaciers, lakes, and elevations. DEM = digital elevation model.
2.2. Data
2.2.1. Meteorological Data
Precipitation (P) is deemed some of the most important data in the TRB’s water cycle
[69]. Due to the harsh climatic and environmental conditions, there are few meteorological
stations in the TRB. Thus, this research adopts four published global high-resolution pre-
cipitation datasets, namely (1) Asian Precipitation-Highly-Resolved Observational Data
Integration Towards Evaluation (APHRODITE V1101 and V1101EX_R1) [70]; (2) The
monthly 0.5° grid data of precipitation series generated by the Climatic Research Unit
from the University of East Anglia in conjunction with the Hadley Centre (at the UK Met
Office) [71]; (3) Princeton University and University of Southampton Hydro-climatology
Group Bias Corrected Meteorological Forcing Dataset Versions 3 (PUSHGBC); and (4)
Global Precipitation Climatology Centre (GPCC). All of these products can be used to of-
fer accurate estimates of precipitation in the TRB.
On the other hand, Evapotranspiration (ET) is one of the most difficult hydrological
variables to obtain [72], especially in a region with sparse long-term hydrological data like
the TRB. So in this study, five types of ET products are proposed, including two land
surface models (Global Land Data Assimilation System, version 1 and 2 (hereafter,
GLDAS-1 and GLDAS-2)). The five products are: (1) GLDAS1-CLM; (2) GLDAS1-Mosaic;
(3) GLDAS1-Noah; (4) GLDAS1-VIC; and (5) GLDAS2-Noah. Bear in mind that ET is also
an essential variable and proposed as an input factor to reconstruct TWSA based on the
LSTM model in this study.
Apart from P and ET, we also considered the influence of SM and temperature on
TWSA when building our LSTM model. Mean monthly temperature readings from CRU
and GLDAS-2 are also adopted due to temperature that may indirectly affect evaporation
from the soil. Moreover, it has been revealed by numerous studies that a strong correlation
appears between SM with GRACE-derived TWSA [39,58,73]. Further, it was illustrated
that SM from GLDAS-2 has the best performance [58]. Consequently, we select the
monthly SM data (kg/m2) from GLDAS-2 (0.25° × 0.25°) as an input factor to simulate
TWSA based on the LSTM model.
Figure 1.
Location of study region on the Tarim River Basin, including the headwaters of the Yarkand (YRB), Kaxgar (KGRB),
Aksu (ARB), Hotan (HRB), Weigan-Kuqa (WKRB), Dina (DRB), Keriya (KRB), Kaidu-Kongque (KKRB), and Qarqan (QRB)
River Basin; and glaciers, lakes, and elevations. DEM = digital elevation model.
Apart from P and ET, we also considered the influence of SM and temperature on
TWSA when building our LSTM model. Mean monthly temperature readings from CRU
and GLDAS-2 are also adopted due to temperature that may indirectly affect evaporation
from the soil. Moreover, it has been revealed by numerous studies that a strong correlation
appears between SM with GRACE-derived TWSA [
39
,
58
,
73
]. Further, it was illustrated
that SM from GLDAS-2 has the best performance [
58
]. Consequently, we select the monthly
SM data (kg/m
2
) from GLDAS-2 (0.25
◦×
0.25
◦
) as an input factor to simulate TWSA based
on the LSTM model.
2.2.2. GRACE Data
In this study, we selected two different GRACE data to estimate the changes in
terrestrial water storage. The first source is Jet Propulsion Laboratory (JPL) GRACE
RL05 mascon products (https://grace.jpl.nasa.gov/data/get-data/jpl_global_mascons/
(accessed on 1 January 2021)), and the other is GRACE RL05 Center for Space Research
(CSR) mascon products [
74
], retrieved from the GRACE Tellus website of the University
of Texas (http://www2.csr.utexas.edu/grace/RL05_mascons.html (accessed on 1 January
2021)). The subtle difference between the product of TWSA from JPL and CSR is mostly
caused by the methods and parameters [
75
]. Based on Long’s method, seventeen months
of missing data were interpolated [
33
]. The datasets used for additional information are
presented (Table 2).

Remote Sens. 2021,13, 889 6 of 17
Table 2. Brief Description of Datasets Used.
Data Data Sources Spatial
Resolution
Temporal
Resolution Date
Precipitation
APHRODITE 0.25◦daily 1982–2015
PUSHGBC 0.25◦daily 1982–2016
CRU 0.5◦Monthly 1982–2016
GPCC 0.5◦Monthly 1982–2016
ET
GLADS1-CLM 1◦Monthly 1982–2016
GLADS1-Mosaic 1◦Monthly 1982–2016
GLADS1-Noah 1◦Monthly 1982–2016
GLADS1-VIC 1◦Monthly 1982–2016
GLADS2-Noah 0.25◦Monthly 1948–2016
Temperature CRU 0.5◦Monthly 1982–2016
GLADS2-Noah 0.25◦Monthly 1982–2016
Soil moisture GLADS2-Noah(V2.0) 0.25◦Monthly 1948–2014
GLADS2-Noah(V2.1) 0.25◦Monthly 2000–2016
TWSA GRACE-JPL 0.5◦Monthly 2002–2017
GRACE-CSR 0.5◦Monthly 2002–2017
2.3. Methods
2.3.1. TWS Calculations
In this study, the JPL and CSR GRACE products were analyzed using the GRACE RL05
mascon solutions method. The two GRACE mascon datasets showed good performance
at the basin scale. However, as the original GRACE data may be noisy because of the
influences of atmospheric changes, some corrections and adjustments should be made
when evaluating TWSA. The correction of a glacial isostatic adjustment was used to
remove glacial rebound effects in a 3-D finite-element model [
76
]. The replacement of
Earth’s oblateness scale (C20) coefficient was also done because C20 values have larger
uncertainty [
77
]. For this, the degree-1 coefficients were calculated by using the Swenson
method [78].
According to Equation (1), the terrestrial water storage changes (TWSCs) are computed
using TWSA from the GRACE data in the TRB. The TWSCs for each month should be
evaluated by the two different time derivatives of TWSA [
79
]. The changes in terrestrial
water storage can be calculated as follows [80]:
ds
dt =TWS(t+1)−TWS(t−1)
2∆t(1)
where
ds
dt
denotes TWSC for month t. Note that TWS is estimated as the average of two
different TWSA products from JPL and CSR, such that TWS (t+ 1) and TWS (t
−
1) are
terrestrial water storage for month t+ 1 and t
−
1, respectively. The time
∆
tis considered
as 1 month to maintain consistency with the estimation of terrestrial water storage.
2.3.2. Design and Architecture of LSTM Deep Learning Models
We used deep learning-based models (i.e., LSTM, Figure 2) to reconstruct the TWSA
data at set time scales under the Python software in this study. Long short-term memory
network, the most advanced deep learning model, is a special kind of RNN. LSTM models
are designed to overcome the weaknesses of conventional RNNs with regard to learning
long-term dependencies. This model consists of three sections: an input layer, a few hidden
layers, and an output layer. The LSTM not only provides input data but also remembers the
states of the hidden neurons of the previous time steps. We set up four hidden layers, the
number of neurons in each layer is 50, 50, 60, and 10, respectively. The optimizer that we
used the LSTM model is Adam. The Time Step is 5 and the Batch Size is 10. As well, these
models simplify solving the autocorrelation and the temporal lag of the data and avoid
vanishing gradients [
81
]. The LSTM layer plays an important role in learning the time series
data and maintaining previous information. At the same time, the fully connected layer on

Remote Sens. 2021,13, 889 7 of 17
the top of the LSTM layer improves the fitting and learning ability of the model. Hence, the
LSTM can serve as an alternative for reconstructing TWSA in places where long-time series
hydrogeological data are difficult to get and complex hydrogeological characteristics.
Remote Sens. 2021, 13, x FOR PEER REVIEW 7 of 18
2.3.2. Design and Architecture of LSTM Deep Learning Models
We used deep learning-based models (i.e., LSTM, Figure 2) to reconstruct the TWSA
data at set time scales under the Python software in this study. Long short-term memory
network, the most advanced deep learning model, is a special kind of RNN. LSTM models
are designed to overcome the weaknesses of conventional RNNs with regard to learning
long-term dependencies. This model consists of three sections: an input layer, a few hid-
den layers, and an output layer. The LSTM not only provides input data but also remem-
bers the states of the hidden neurons of the previous time steps. We set up four hidden
layers, the number of neurons in each layer is 50, 50, 60, and 10, respectively. The opti-
mizer that we used the LSTM model is Adam. The Time Step is 5 and the Batch Size is 10.
As well, these models simplify solving the autocorrelation and the temporal lag of the
data and avoid vanishing gradients [81]. The LSTM layer plays an important role in learn-
ing the time series data and maintaining previous information. At the same time, the fully
connected layer on the top of the LSTM layer improves the fitting and learning ability of
the model. Hence, the LSTM can serve as an alternative for reconstructing TWS in places
where long-time series hydrogeological data are difficult to get and complex hydrogeo-
logical characteristics.
Figure 2. (a) Chain-like structure of the Long Short-Term Memory (LSTM). (b) A graphical representation of LSTM’s
memory block.
Various LSTM models have been used for flood forecasting, water table depth pre-
diction, and water resources management [60,65]. A special multilayer recurrent neural
network method [81], which is one of the most widely used LSTMs, is used jointly with
the activation function of relu to reconstruct TWSA during the period 1982–2016. The mul-
tiple datasets of the four variables (P, ET, SM, and T) and TWS unified the temporal reso-
lution and spatial resolution. The multiple datasets of each variable are averaged and then
a
b
Figure 2.
(
a
) Chain-like structure of the Long Short-Term Memory (LSTM). (
b
) A graphical representation of LSTM’s
memory block.
Various LSTM models have been used for flood forecasting, water table depth pre-
diction, and water resources management [
60
,
65
]. A special multilayer recurrent neural
network method [
81
], which is one of the most widely used LSTMs, is used jointly with
the activation function of relu to reconstruct TWSA during the period 1982–2016. The
multiple datasets of the four variables (P, ET, SM, and T) and TWSA unified the temporal
resolution and spatial resolution. The multiple datasets of each variable are averaged
and then put into the LSTM model for training. The input variables are P, ET, SM, and
T, while the output data are the TWSA. Since the reconstruction of the data (1982–2003)
is backward reconstruction, the time period of the model needs to be backward. For the
LSTM model, GRACE-derived TWSA data covering 120 months (December 2012 to January
2003) are divided into three periods of the training (December 2012 to January 2006, 70%
of all samples), validation (December 2005 to July 2004, 15% of all samples), and testing
(June 2004 to January 2003, 15% of all samples). The training of the LSTM model is one of
the nonlinear optimization problems, the purpose of which is to minimize the difference
between the simulated results of the output layer and the observed results [
21
]. In this
study, the activation function of relu is applied to train the network, as it requires less time
in the convergence process. What is noteworthy is that multiple training will produce
different results. Thus, in this process, statistical indicators (r and NRMSE) are used to
select the suitable optimal network which is then used to reconstruct the TWSA during the
period 1982–2002 in the TRB. The workflow exhibiting the reconstruction of TWSA based
on the LSTM model across the TRB is shown in Figure 3.

Remote Sens. 2021,13, 889 8 of 17
Remote Sens. 2021, 13, x FOR PEER REVIEW 8 of 18
put into the LSTM model for training. The input variables are P, ET, SM, and T, while the
output data are the TWSA. Since the reconstruction of the data (1982–2003) is backward
reconstruction, the time period of the model needs to be backward. For the LSTM model,
GRACE-derived TWSA data covering 120 months (December 2012 to January 2003) are
divided into three periods of the training (December 2012 to January 2006, 70% of all sam-
ples), validation (December 2005 to July 2004, 15% of all samples), and testing (June 2004
to January 2003, 15% of all samples). The training of the LSTM model is one of the nonlin-
ear optimization problems, the purpose of which is to minimize the difference between
the simulated results of the output layer and the observed results [21]. In this study, the
activation function of relu is applied to train the network, as it requires less time in the
convergence process. What is noteworthy is that multiple training will produce different
results. Thus, in this process, statistical indicators (r and NRMSE) are used to select the
suitable optimal network which is then used to reconstruct the TWSA during the period
1982–2002 in the TRB. The workflow exhibiting the reconstruction of TWSA based on the
LSTM model across the TRB is shown in Figure 3.
Figure 3. The workflow of reconstruction the changes of terrestrial water storage.
2.3.3. Performance Metrics
In this study, evaluation criteria including Correlation Coefficient (r), Normalized
Root-Mean-Square Error (NRMSE), Nash–Sutcliffe efficiency (NSE) coefficient [82], and
relative bias (BIAS) are chosen to evaluate the simulated performance of the LSTM model.
These criteria are calculated as follows:
= ∑(−




)(−




)



∑(−




)

 ×∑(−




)

 (2)
=∑( −)


∑()

 (3)
=1−∑(−)


∑(−




)

 (4)
=∑( −)


∑

 (5)
where  represents the estimated monthly values;  denotes the observed monthly
values; N indicates the number of months used for testing; and 




and 




are the mean
values of  and , respectively.
Figure 3. The workflow of reconstruction the changes of terrestrial water storage.
2.3.3. Performance Metrics
In this study, evaluation criteria including Correlation Coefficient (r), Normalized
Root-Mean-Square Error (NRMSE), Nash–Sutcliffe efficiency (NSE) coefficient [
82
], and
relative bias (BIAS) are chosen to evaluate the simulated performance of the LSTM model.
These criteria are calculated as follows:
r=∑N
i=1(xei −xei )(xoi −xoi)
q∑N
i=1(xei −xei )2×∑N
i=1(xoi −xoi )2(2)
NRMSE =v
u
u
t
∑N
i=1(xei −xoi )2
∑N
i=1(xoi )2(3)
NSE =1−∑N
i=1(xei −xoi )2
∑N
i=1(xoi −xoi )2(4)
BI AS =∑N
i=1(xei −xoi )
∑N
i=1xoi
(5)
where
xei
represents the estimated monthly values;
xoi
denotes the observed monthly
values; Nindicates the number of months used for testing; and
xei
and
xoi
are the mean
values of xei and xoi , respectively.
3. Results
3.1. Evaluation of GRACE TWSCs and Their Spatiotemporal Variability
The observations of GRACE can provide the monthly mean TWSA on a global scale.
Figure 4shows the monthly TWSA from JPL and CSR during the period 2002–2017. Results
showed a significant correlation between the TWSA derived from JPL and CSR, with a
correlation coefficient of 0.83. Additionally, it can reach a maximum and a minimum
almost simultaneously. The uncertainty of TWSA can be computed from JPL (https://
grace.jpl.nasa.gov/data/get-data/jpl_global_mascons.html (accessed on 1 January 2021)),
and the uncertainty of CSR-derived TWSA can be determined using an uncertainty value of
2 cm equivalent water thickness (http://www2.csr.utexas.edu/grace/RL05_mascons.html
(accessed on 1 January 2021)).
The mean monthly TWSA is computed as the average of JPL-derived TWSA and
CSR-derived TWSA with the view of diminishing the noise of equivalent water height.
From Figure 4, the range for the mean monthly TWSA is between
−
59.47 and 41.47 mm in
the TRB (relative to the baseline period from January 2004 to December 2009). Specifically, it
shows a distinct seasonal cycle. The minimum and maximum values of TWSA were found
in the winter (December to February) and summer (June to August). The monthly average
water storage in the region was
−
4.53 mm, with the highest value in June 2005 (41.47 mm)
and the lowest value in February 2015 (
−
59.47 mm). From 2002 to 2017, TWSA showed a
significant downward trend (p< 0.001), with an average decline rate of 0.20 mm/month
Moreover, according to Equation (1), TWSC can be obtained from GRACE-derived TWSA in
the study area. Then, the error can be calculated for the monthly TWSA to be approximately
9.6 mm, which is attributable to the measurement errors from 2002 to 2017 in the TRB.

Remote Sens. 2021,13, 889 9 of 17
Figure 5displays the spatial distribution of the TWSA from April 2002 to January 2017,
averaged for different seasons. The TWSA shows obvious seasonal differences from spring
to winter. It also reveals that the TWSA declined over a decade in the Tienshan Mountains,
highlighting the phenomenon of the sum of TWSA in the north of the basin being less than
that in the south of the basin from 2002 to 2017. Thus further, we found that the TWSA in
spring declined significantly after 2014 (Figure 5e). It is believed that the decline in TWSA
during the spring-time led to the decline of TWSA across the entire region. It is worth
mentioning that this decline in spring-time terrestrial water storage may be related to the
decrease in snow and glaciers cover in the Tienshan Mountains.
Remote Sens. 2021, 13, x FOR PEER REVIEW 9 of 18
3. Results
3.1. Evaluation of GRACE TWSCs and Their Spatiotemporal Variability
The observations of GRACE can provide the monthly mean TWSA on a global scale.
Figure 4 shows the monthly TWSA from JPL and CSR during the period 2002–2017. Re-
sults showed a significant correlation between the TWSA derived from JPL and CSR, with
a correlation coefficient of 0.83. Additionally, it can reach a maximum and a minimum
almost simultaneously. The uncertainty of TWSA can be computed from JPL
(https://grace.jpl.nasa.gov/data/get-data/jpl_global_mascons.html (accessed on 1 January
2021)), and the uncertainty of CSR-derived TWSA can be determined using an uncertainty
value of 2 cm equivalent water thickness (http://www2.csr.utexas.edu/grace/RL05_mas-
cons.html (accessed on 1 January 2021)).
Figure 4. The spatial–temporal distribution of Gravity Recovery and Climate Experiment (GRACE) terrestrial water stor-
age anomalies (TWSA) derived from Jet Propulsion Laboratory (JPL) and Center for Space Research (CSR) during the
period 2002–2017. ((a): spatial distribution of TWSA; (b): changing rate of annual TWSA; (c): temporal changes of average
TWSA(mm) and TWSC(mm/month)).
The mean monthly TWSA is computed as the average of JPL-derived TWSA and
CSR-derived TWSA with the view of diminishing the noise of equivalent water height.
From Figure 4, the range for the mean monthly TWSA is between -59.47 and 41.47 mm in
the TRB (relative to the baseline period from January 2004 to December 2009). Specifically,
it shows a distinct seasonal cycle. The minimum and maximum values of TWSA were
found in the winter (December to February) and summer (June to August). The monthly
average water storage in the region was −4.53 mm, with the highest value in June 2005
(41.47 mm) and the lowest value in February 2015 (−59.47 mm). From 2002 to 2017, TWS
showed a significant downward trend (p < 0.001), with an average decline rate of 0.20
mm/year. Moreover, according to Equation (1), TWSC can be obtained from GRACE-de-
rived TWSA in the study area. Then, the error can be calculated for the monthly TWS to
be approximately 9.6 mm, which is attributable to the measurement errors from 2002 to
2017 in the TRB. Figure 5 displays the spatial distribution of the monthly TWSA from
April 2002 to January 2017, averaged for different seasons. The total water storage shows
obvious seasonal differences from spring to winter. It also reveals that the TWS declined
over a decade in the Tienshan Mountains, highlighting the phenomenon of the sum of
TWS in the north of the basin being less than that in the south of the basin from 2002 to
2017. Thus further, we found that the TWS in spring declined significantly after 2014 (Fig-
ure 5e). It is believed that the decline in TWS during the spring-time led to the decline of
Figure 4.
The spatial–temporal distribution of Gravity Recovery and Climate Experiment (GRACE) terrestrial water storage
anomalies (TWSA) derived from Jet Propulsion Laboratory (JPL) and Center for Space Research (CSR) during the period
2002–2017. ((
a
): spatial distribution of TWSA; (
b
): changing rate of TWSA; (
c
): temporal changes of average TWSA(mm)
and TWSC(mm/month)).
3.2. Estimation of Long-Term Time Series of Meteorological Data and Their Uncertainties
Figure 6a presents the seasonal cycles of four precipitation datasets (APHRODITE,
PUSHGBC, CRU, and GPCC) was selected for the TRB., Findings disclosed that the precip-
itation from PUSHGBC is higher than that from the other three datasets, especially for the
summertime, while the precipitation from APHRODITE is the lowest. The uncertainty of
the overall average precipitation ranges from 0.49 to 32.68 mm/month, with the highest
value observed in summer (40.21 mm) and the lowest in winter (0.22 mm). Note that the
uncertainty of precipitation in 2016 cannot be obtained due to the lack of APHRODITE data.
However, we assume that the average monthly precipitation in the region was 7.99 mm
and the changes in precipitation from 1982 to 2016 were relatively stable. Despite the slight
increase, the changing trend was not significant (p= 0.32), and the highest increase rate
was detected in the upper reaches of the Tienshan Mountains.

Remote Sens. 2021,13, 889 10 of 17
Remote Sens. 2021, 13, x FOR PEER REVIEW 10 of 18
TWS across the entire region. It is worth mentioning that this decline in spring-time ter-
restrial water storage may be related to the decrease in snow and glaciers cover in the
Tienshan Mountains.
Figure 5. The spatial–temporal distribution of the mean TWSA(mm) in different seasons from April 2002 to January 2017,
(a,e) Spring (March–May), (b,f) Summer (June–August), (c,g) Autumn (September–November), and (d,h) Winter (Decem-
ber–February) in the Tarim River basin (TRB).
3.2. Estimation of Long-Term Time Series of Meteorological Data and Their Uncertainties
Figure 6a presents the seasonal cycles of four precipitation datasets (APHRODITE,
PUSHGBC, CRU, and GPCC) was selected for the TRB., Findings disclosed that the pre-
cipitation from PUSHGBC is higher than that from the other three datasets, especially for
the summertime, while the precipitation from APHRODITE is the lowest. The uncertainty
of the overall average precipitation ranges from 0.49 to 32.68 mm/month, with the highest
value observed in summer (40.21 mm) and the lowest in winter (0.22 mm). Note that the
uncertainty of precipitation in 2016 cannot be obtained due to the lack of APHRODITE
data. However, we assume that the average monthly precipitation in the region was 7.99
mm and the changes in precipitation from 1982 to 2016 were relatively stable. Despite the
slight increase, the changing trend was not significant (p = 0.32), and the highest increase
rate was detected in the upper reaches of the Tienshan Mountains.
Figure 5.
The spatial–temporal distribution of the mean TWSA(mm) in different seasons from April 2002 to January
2017, (
a
,
e
) Spring (March–May), (
b
,
f
) Summer (June–August), (
c
,
g
) Autumn (September–November), and (
d
,
h
) Winter
(December–February) in the Tarim River basin (TRB).
For large regions, it is difficult to obtain the actual ET at the in-situ measurements site,
especially like the TRB, which has limited hydrological and meteorological data. For that,
this study adopted five types of ET datasets to overcome these shortcomings. Therefore,
Figure 6b shows the monthly ET rates, ranging from 5.99 to 211.11 mm following seasonal
changes. In an overall perception, the ET increased from January to June, but decreased
rapidly till December. The monthly average ET in the region was 69.59 mm. From 1982
to 2016, evapotranspiration showed a significant increasing trend (p< 0.005), and the
average rate of change was 0.03 mm/month. The uncertainty of the monthly ET was
calculated, ranging from approximately 0.47 to 263.04 mm. It is noteworthy that the value
of ET in 1987 is abnormal, which may be the result of the difference between the five ET
products. Nonetheless, these have a slight effect on the estimation of TWSA for the whole
study period.
The climate of the TRB is predominantly temperate continental. Precipitation in the
TRB shows clear seasonal variations (Figure 7a). The summer (June to August) accounts
for about 50–70% of the annual total precipitation. Moreover, as displayed by
Figure 7b
,
there is a good correspondence between the precipitation and the average ET, while
Figure 7c
demonstrates that the maximum TWSA occurred in July, which is consistent
with the precipitation exhibited in
Figure 7a
. The nature of these findings unveils that the

Remote Sens. 2021,13, 889 11 of 17
reduction in precipitation over different seasons will lead to the modifications in TWSA
correspondingly. Consequently, climate change has not only affected the variations in
precipitation and ET but also the variations in TWSA.
Remote Sens. 2021, 13, x FOR PEER REVIEW 11 of 18
Figure 6. (a) Comparisons of the four precipitation datasets from APHRODITE, PUSH-
GBC, CRU and GPCC during the period 1982–2016 in the TRB. (b) As in (a) but for five
evapotranspiration (ET) datasets.
For large regions, it is difficult to obtain the actual ET at the in-situ measurements
site, especially like the TRB, which has limited hydrological and meteorological data. For
that, this study adopted five types of ET datasets to overcome these shortcomings. There-
fore, Figure 6b shows the monthly ET rates, ranging from 5.99 to 211.11 mm following
seasonal changes. In an overall perception, the ET increased from January to June, but
decreased rapidly till December. The monthly average ET in the region was 69.59 mm.
From 1982 to 2016, evapotranspiration showed a significant increasing trend (p < 0.005),
and the average rate of change was 0.03 mm/year. The uncertainty of the monthly ET was
calculated, ranging from approximately 0.47 to 263.04 mm. It is noteworthy that the value
of ET in 1987 is abnormal, which may be the result of the difference between the five ET
products. Nonetheless, these have a slight effect on the estimation of TWS for the whole
study period.
The climate of the TRB is predominantly temperate continental. Precipitation in the
TRB shows clear seasonal variations (Figure 7a). The summer (June to August) accounts
for about 50–70% of the annual total precipitation. Moreover, as displayed by Figure 7b,
there is a good correspondence between the precipitation and the average ET, while Fig-
ure 7c demonstrates that the maximum TWSA occurred in July, which is consistent with
the precipitation exhibited in Figure 7a. The nature of these findings unveils that the re-
duction in precipitation over different seasons will lead to the modifications in TWSA
correspondingly. Consequently, climate change has not only affected the variations in
precipitation and ET but also the variations in TWSA.
Figure 6.
(
a
) Comparisons of the four precipitation datasets from APHRODITE, PUSHGBC, CRU
and GPCC during the period 1982–2016 in the TRB. (
b
) As in (
a
) but for five evapotranspiration
(ET) datasets.
Remote Sens. 2021, 13, x FOR PEER REVIEW 12 of 18
Figure 7. The mean monthly (a) P, (b) ET, and (c) TWSA during the period 2003–2016 in the TRB.
3.3. Terrestrial Total Water Storage Anomalies Simulated from LSTM Models
The time scale of the GRACE data limits further estimations of terrestrial total water
storage in the TRB. So, an LSTM model is used to establish the relationship between TWSA
and hydrological data (P, ET, T, and SM) from 2003 to 2012 and accordingly apply it to
reconstruct TWSA before 2003. Related researches indicated that SM has a significant cor-
relation with TWSA. Thereby, we selected SM as an essential predictor and combined hy-
drological data. Additionally, we realized that the dataset of GLDAS-2 gives the best per-
formance (r = 0.65) from 2003 to 2012, as shown in Figure 8.
Figure 8. Correlations between precipitation (P), ET, temperature (T), and soil moisture (SM) with TWSA. The results in
parentheses represent the correlation coefficients between hydrological data with TWSA from 2003 to 2012.
To evaluate the effectiveness of the LSTM model, two performance metrics were se-
lected, namely correlation coefficient and NRMSE. The LSTM model is proved to have
satisfactory performance once the correlation coefficient is closer to 1 and a lower NRMSE
value. Thereby, All of the LSTM predictors with their performances are presented, hence
the comparison of the TWSA generated from GRACE and the LSTM model in different
stages (Table 3).
Table 3. Comparison Between LSTM-Generated TWSA and GRACE-Generated TWSA (2003–
2012).
LSTM Predictors Performance in Different Stages (r/NRMSE)
Training (70%) Validation (15%) Test (15%) All (100%)
SM_P 0.847/0.148 0.591/0.197 0.596/0.146 0.831/0.161
SM_T 0.879/0.136 0.659/0.128 0.625/0.127 0.857/0.135
SM_ET 0.873/0.133 0.669/0.161 0.633/0.116 0.855/0.139
SM_P_ET 0.796/0.161 0.877/0.128 0.507/0.123 0.818/0.150
SM_P_T 0.914/0.118 0.673/0.134 0.615/0.108 0.881/0.122
SM_ET_T 0.930/0.099 0.738/0.162 0.415/0.142 0.890/0.125
SM_ET_P_T 0.935/0.096 0.742/0.134 0.763/0.095 0.922/0.107
Note: the bolded value represents the best combination with 70%, 15%, 15%, and 100% represent-
ing the corresponding proportions to all samples in different pe-riods.
Figure 7. The mean monthly (a) P, (b) ET, and (c) TWSA during the period 2003–2016 in the TRB.
3.3. Terrestrial Water Storage Anomalies Simulated from LSTM Models
The time scale of the GRACE data limits further estimations of terrestrial total water
storage in the TRB. So, an LSTM model is used to establish the relationship between TWSA
and hydrological data (P, ET, T, and SM) from 2003 to 2012 and accordingly apply it to
reconstruct TWSA before 2003. Related researches indicated that SM has a significant
correlation with TWSA. Thereby, we selected SM as an essential predictor and combined
hydrological data. Additionally, we realized that the dataset of GLDAS-2 gives the best
performance (r = 0.65) from 2003 to 2012, as shown in Figure 8.

Remote Sens. 2021,13, 889 12 of 17
Remote Sens. 2021, 13, x FOR PEER REVIEW 12 of 18
Figure 7. The mean monthly (a) P, (b) ET, and (c) TWSA during the period 2003–2016 in the TRB.
3.3. Terrestrial Total Water Storage Anomalies Simulated from LSTM Models
The time scale of the GRACE data limits further estimations of terrestrial total water
storage in the TRB. So, an LSTM model is used to establish the relationship between TWSA
and hydrological data (P, ET, T, and SM) from 2003 to 2012 and accordingly apply it to
reconstruct TWSA before 2003. Related researches indicated that SM has a significant cor-
relation with TWSA. Thereby, we selected SM as an essential predictor and combined hy-
drological data. Additionally, we realized that the dataset of GLDAS-2 gives the best per-
formance (r = 0.65) from 2003 to 2012, as shown in Figure 8.
Figure 8. Correlations between precipitation (P), ET, temperature (T), and soil moisture (SM) with TWSA. The results in
parentheses represent the correlation coefficients between hydrological data with TWSA from 2003 to 2012.
To evaluate the effectiveness of the LSTM model, two performance metrics were se-
lected, namely correlation coefficient and NRMSE. The LSTM model is proved to have
satisfactory performance once the correlation coefficient is closer to 1 and a lower NRMSE
value. Thereby, All of the LSTM predictors with their performances are presented, hence
the comparison of the TWSA generated from GRACE and the LSTM model in different
stages (Table 3).
Table 3. Comparison Between LSTM-Generated TWSA and GRACE-Generated TWSA (2003–
2012).
LSTM Predictors Performance in Different Stages (r/NRMSE)
Training (70%) Validation (15%) Test (15%) All (100%)
SM_P 0.847/0.148 0.591/0.197 0.596/0.146 0.831/0.161
SM_T 0.879/0.136 0.659/0.128 0.625/0.127 0.857/0.135
SM_ET 0.873/0.133 0.669/0.161 0.633/0.116 0.855/0.139
SM_P_ET 0.796/0.161 0.877/0.128 0.507/0.123 0.818/0.150
SM_P_T 0.914/0.118 0.673/0.134 0.615/0.108 0.881/0.122
SM_ET_T 0.930/0.099 0.738/0.162 0.415/0.142 0.890/0.125
SM_ET_P_T 0.935/0.096 0.742/0.134 0.763/0.095 0.922/0.107
Note: the bolded value represents the best combination with 70%, 15%, 15%, and 100% represent-
ing the corresponding proportions to all samples in different pe-riods.
Figure 8.
Correlations between precipitation (P), ET, temperature (T), and soil moisture (SM) with TWSA. The results in
parentheses represent the correlation coefficients between hydrological data with TWSA from 2003 to 2012.
To evaluate the effectiveness of the LSTM model, two performance metrics were
selected, namely correlation coefficient and NRMSE. The LSTM model is proved to have
satisfactory performance once the correlation coefficient is closer to 1 and a lower NRMSE
value. Thereby, All of the LSTM predictors with their performances are presented, hence
the comparison of the TWSA generated from GRACE and the LSTM model in different
stages (Table 3).
Table 3.
Comparison Between LSTM-Generated TWSA and GRACE-Generated TWSA (2003–2012).
LSTM
Predictors
Performance in Different Stages (r/NRMSE)
Training (70%) Validation
(15%) Test (15%) All (100%)
SM_P 0.847/0.148 0.591/0.197 0.596/0.146 0.831/0.161
SM_T 0.879/0.136 0.659/0.128 0.625/0.127 0.857/0.135
SM_ET 0.873/0.133 0.669/0.161 0.633/0.116 0.855/0.139
SM_P_ET 0.796/0.161 0.877/0.128 0.507/0.123 0.818/0.150
SM_P_T 0.914/0.118 0.673/0.134 0.615/0.108 0.881/0.122
SM_ET_T 0.930/0.099 0.738/0.162 0.415/0.142 0.890/0.125
SM_ET_P_T 0.935/0.096 0.742/0.134 0.763/0.095 0.922/0.107
Note: the bolded value represents the best combination with 70%, 15%, 15%, and 100% representing the corre-
sponding proportions to all samples in different pe-riods.
Taking note that the bolded value represents the best combination with 70%, 15%, 15%,
and 100% representing the corresponding proportions to all samples in different periods.
From Table 3, the optimal combination of predictors is SM, ET, P, and T, which can
best capture the characteristics of TWSA compared with remained combinations. Thus,
using SM, ET, P, and T as predictors during the period 2003–2012, we simulated TWSA
for the TRB based on the LSTM model, then again reconstructed the TWSA values from
1982 to 2002. Figure 9displays the comparison of TWSA developed from both LSTM
and GRACE. As can be depicted, TWSA generated by LSTM agrees well with GRACE’s
one from 2003 to 2012, with a correlation efficient (r) of 0.922 and an NRMSE of 0.107,
respectively. This indicates that the LSTM model indeed performs well in simulating time
series data. Meanwhile TWSA exhibits an obvious seasonal cycle from 1982 to 2002. The
monthly average water storage in the region is
−
1.60 mm, with the highest value in June
2005 (41.47 mm) and the lowest value in February 2015 (-59.47 mm). From 1982 to 2016,
water storage unveiled a downward trend (p< 0.001), with an average decline rate of 0.03
mm/month. These data indicate that variables of SM, ET, P, and T in the LSTM model
not only offer the simulation of TWSA, but also reconstruct the TWSA with a long-term
time scale.

Remote Sens. 2021,13, 889 13 of 17
Remote Sens. 2021, 13, x FOR PEER REVIEW 13 of 18
Taking note that the bolded value represents the best combination with 70%, 15%,
15%, and 100% representing the corresponding proportions to all samples in different pe-
riods.
From Table 3, the optimal combination of predictors is SM, ET, P, and T, which can
best capture the characteristics of TWSA compared with remained combinations. Thus,
using SM, ET, P, and T as predictors during the period 2003–2012, we simulated TWSA
for the TRB based on the LSTM model, then again reconstructed the TWSA values from
1982 to 2002. Figure 9 displays the comparison of TWSA developed from both LSTM and
GRACE. As can be depicted, TWSA generated by LSTM agrees well with GRACE’s one
from 2003 to 2012, with a correlation efficient (r) of 0.922 and an NRMSE of 0.107, respec-
tively. This indicates that the LSTM model indeed performs well in simulating time series
data. Meanwhile TWSA exhibits an obvious seasonal cycle from 1982 to 2002. The monthly
average water storage in the region is -1.60 mm, with the highest value in June 2005 (41.47
mm) and the lowest value in February 2015 (-59.47 mm). From 1982 to 2016, water storage
unveiled a huge downward trend (p < 0.001), with an average annual decline rate of 0.03
mm/year. These data indicate that variables of SM, ET, P, and T in the LSTM model not
only offer the simulation of TWSA, but also reconstruct the TWSA with a long-term time
scale.
Figure 9. Comparisons between the mean monthly TWSA from GRACE and LSTM-generated TWSA.
4. Discussion
Deep learning methods have been proven to be very helpful in solving some tradi-
tionally difficult problems (e.g., data reconstruction) [51]. In our study, TWSA generated
by both LSTM and GRACE agrees well with each other’s from 2003 to 2012, with a high
correlation efficient (r) of 0.922 and an NRMSE of 0.107, respectively. Likewise, Yang et al.
[40] used the LSTM model to simulate the GHMs-based flood, and found the correlation
coefficients to be 0.95, 0.98, and 0.99. These results indicated that the LSTM model presents
a good performance in simulating time series data. Similarly, Sun et al. [21] reconstructed
GRACE data by combining the CNN model and hydrological models. Generally, deep-
learning techniques (e.g., LSTM model, CNN model) will promote the development of
hydrology and related fields in the future [48–50]. Furthermore, in terms of predictor se-
lection, we selected SM as an essential predictor and combined hydrological data, con-
sistent with related researches that also mentioned SM to have a significant correlation
with TWSA [80]. The Tarim River basin’s climate is predominantly temperate continental,
which is the most common inland drought system in the world [71]. Figure 5 illustrates
that the TWS declined over a decade in the Tienshan Mountains, highlighting the phe-
nomenon of the sum of TWS in the north of the basin is less than that in the south of the
basin from 2002 to 2017. Yang et al. [11] also reported the same phenomenon, but for a
slightly shorter period (2002 to 2015). Furthermore, we realized that TWS exhibited a sig-
nificant downward trend (p < 0.001), with an average decline rate of 0.20 mm/year from
Figure 9. Comparisons between the mean monthly TWSA from GRACE and LSTM-generated TWSA.
4. Discussion
Deep learning methods have been proven to be very helpful in solving some tradition-
ally difficult problems (e.g., data reconstruction) [
51
]. In our study, TWSA generated by
both LSTM and GRACE agrees well with each other’s from 2003 to 2012, with a high corre-
lation efficient (r) of 0.922 and an NRMSE of 0.107, respectively. Likewise,
Yang et al. [40]
used the LSTM model to simulate the GHMs-based flood, and found the correlation coeffi-
cients to be 0.95, 0.98, and 0.99. These results indicated that the LSTM model presents a
good performance in simulating time series data. Similarly, Sun et al. [
21
] reconstructed
GRACE data by combining the CNN model and hydrological models. Generally, deep-
learning techniques (e.g., LSTM model, CNN model) will promote the development of
hydrology and related fields in the future [
48
–
50
]. Furthermore, in terms of predictor
selection, we selected SM as an essential predictor and combined hydrological data, consis-
tent with related researches that also mentioned SM to have a significant correlation with
TWSA [
80
]. The Tarim River basin’s climate is predominantly temperate continental, which
is the most common inland drought system in the world [
71
]. Figure 5illustrates that the
TWSA declined over a decade in the Tienshan Mountains, highlighting the phenomenon
of the sum of TWSA in the north of the basin is less than that in the south of the basin
from 2002 to 2017. Yang et al. [
11
] also reported the same phenomenon, but for a slightly
shorter period (2002 to 2015). Furthermore, we realized that TWSA exhibited a significant
downward trend (p< 0.001), with an average decline rate of 0.20 mm/month from 2002
to 2017. Similar findings were produced by Zhao and Li, [
67
] who found the TWS to
slightly decrease with a declining trend of
−
1.4069
±
0.5060 mm yr
−1
in the TRB from
2002 to 2015. However, the reduction rate is slightly different due to the distinction in the
selected timescale.
In general, the amplitudes of TWSA with the LSTM model are slightly higher than the
TWSA from GRACE for the 1982–2016 period. However, this overestimation is reasonable
when considering the groundwater storage changes [
22
]. This overestimation may come
from the inherent uncertainty of TWSA. Even though the LSTM model provides an effective
method for estimating TWSA, it still poses some uncertainties and errors. The uncertainty
of the reconstructed TWSA could be attributed to two reasons: the uncertainty of the re-
analysis datasets and the uncertainty of the LSTM model. Primarily, due to limited training
sample data in this study, the results may be affected [
22
]. Moreover, there is a range of
uncertainty in P and ET, which may result in either underestimation or overestimation of
TWSA due to the complex geographical conditions in TRB’s areas
(Figure 6)
. Secondly, the
LSTM model provides a mathematically effective, pattern recognition technique that can
generate complex algorithms describing the relationships among several input and output
variables, and the model can be used to deal with the non-linear and seasonal tendencies
data. Generally, the LSTM model cannot explain the physical dynamics in TWS since it is a
relative “black box” compared with the logistic regression model [
81
]. This may reduce
the confidence of the LSTM models. At the same time, this forecast result produced by the

Remote Sens. 2021,13, 889 14 of 17
LSTM model may have some fluctuations, which is also quite normal [
58
]. The short-term
prediction effect of this model is better, and the long-term trend volatility is indeed a bit
large. Moreover, the determination of the appropriate LSTM model structure is another
factor that affects the accuracy of the model, which calls for more and in-depth calibration
of the model structure. In the current study, the best structure model was selected among
seven combinations (Table 3) by comparing the errors between results and observations.
More LSTM models with different architectures applied for evaluating results will improve
the accuracy and reduce the uncertainty. Notwithstanding the goodness of LSTM in timing
simulations, it still has obvious shortcomings when applied in spatial simulations.
In addition, some human-mediated activities such as irrigation and extraction of
groundwater among others can also lead to water imbalance for regions [
22
]. For instance,
some studies proved that irrigation affects the actual runoff and ET in the Aksu and
Yarkand River basins [
12
]. Additionally, it is well known that the two main streams (Aksu
River and Yarkand River) comprise the main agricultural regions in TRB. For future work,
more efforts will be invested into various components of TWS, such as surface water and
groundwater. In addition, a combination of CMIP6 data and an LSTM model will be drawn
to simulate future water storage changes. Lately, this study mainly compares the TWSA
trend of the LSTM model and GRACE dataset to complement the previous researches on
fluxes (e.g., river discharge, ET). Yet, future investigations should take into account the
hydrological process with physical mechanism models for verification. Thus, we relied on
this model since it is the first attempt to be undertaken over the study area of interest, and
its accuracy will be strengthened in the follow-up investigations.
5. Conclusions
The GRACE dataset provides an unprecedented opportunity for studying TWS, includ-
ing changes in surface storage and groundwater storage. From 2002 to 2017, TWSA showed
a significant downward trend (p< 0.001), with an average decline rate of 0.20 mm/month
in the TRB. However, in this study, our goal was to generate a convenient and effective
method for reconstructing total TWSA. The LSTM model using SM, P, T, and ET as predic-
tors was used to generate a longer monthly TWSA. The modeled findings showed that the
LSTM-generated TWSA was largely consistent with GRACE, with a correlation efficient
(r) of 0.922 and an NRMSE of 0.107 (SM, ET, P, and T) during the period 2003–2012. This
finding demonstrated that using the LSTM model can be an effective approach to generate
TWSA. Furthermore, the structure of the model proved to be logical, and the LSTM helped
to prevent overfitting effectively. Finally, TWSA showed a downward trend (p< 0.001),
with an average decline rate of 0.03 mm/month in the TRB in the period 1982–2016.
Author Contributions:
Conceptualization, Y.C. and F.W.; methodology, F.W.; validation, F.W. and
X.W.; investigation, F.W.; data curation, F.W.; writing—original draft preparation, F.W.; writing—
review and editing, Y.C., Z.L., G.F., Y.L., X.W., X.Z. and P.M.K.; project administration, Y.C.; funding
acquisition, Y.C. All authors have read and agreed to the published version of the manuscript.
Funding:
This research was funded by the Strategic Priority Research Program of Chinese Academy
of Sciences, (Grant No. XDA20100303) and the Key Research Program of the Chinese Academy of
Sciences (ZDRWZS–2019–3).
Acknowledgments:
We appreciate the editors and the reviewers for their constructive suggestions
and insightful comments, which helped us greatly to improve this manuscript.
Conflicts of Interest: The authors declare no conflict of interest.
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