**1. Introduction**

Terrestrial water storage (TWS) comprises all of the water stored on the crustal surface and underground, including snow, glaciers, soil water, groundwater, runoff, and biological water components, which is an essential part of the water cycle system [1,2]. However, the TWS is extraordinarily limited, only accounting for 3.47% of the total global water resources [3]. The TWS provides an essential function for industry, agriculture, and human

**Citation:** Shen, Y.; Zheng, W.; Yin, W.; Xu, A.; Zhu, H.; Wang, Q.; Chen, Z. Improving the Inversion Accuracy of Terrestrial Water Storage Anomaly by Combining GNSS and LSTM Algorithm and Its Application in Mainland China. *Remote Sens.* **2022**, *14*, 535. https://doi.org/10.3390/ rs14030535

Academic Editors: Alban Kuriqi and Luis Garrote

Received: 24 November 2021 Accepted: 21 January 2022 Published: 23 January 2022

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life. The freshwater resources of China account for only 6% of the total global water resources [4]. The Chinese per capita freshwater resource is only 2100 cubic meters, which is a quarter of the world's per capita value [5,6]. Moreover, TWS suffers from uneven interannual distribution, apparent conflicts between water supply and demand, and low utilization of water resources [7]. In recent years, a series of natural disasters have occurred frequently, for example, droughts, floods, and soil erosion [8,9]. This phenomenon seriously affects human life and the economic development of society. Thus, it has become an urgent issue to scientifically and effectively manage regional water resources in China [10].

The optimization of hydrological models and advancements in observation techniques have allowed us to accurately monitor the redistribution of TWS at different spatiotemporal scales [11]. Hydrological models are mathematical models of TWS processes, which are widely used in climate change studies and human exploration of global water resources [12]. Unfortunately, hydrological models typically simplify the complex hydrological cycle [13]. Not all hydrological components are included in hydrological models, which results in a tendency to underestimate climate and human-induced changes in the terrestrial water cycle [14]. For example, the Noah model in the Global Land Data Assimilation System (GLDAS) only includes soil moisture, snow water equivalent, and total canopy storage components at 0–2 m depth [15]. The influences of other components are ignored in hydrological models, such as surface water, deep groundwater, and anthropogenic factors [16]. It is essential to find an alternative method for monitoring TWS on a large spatial scale. Correspondingly, the redistribution of substantial water mass will cause changes in the gravity field of the surrounding regions. It is possible to invert the terrestrial water storage anomaly (TWSA) based on gravity anomaly data [17]. Gravity Recovery and Climate Experiment (GRACE) satellites were launched by the National Aeronautics and Space Administration (NASA) in March 2002, which provided an unprecedented method to detect TWSA on a large scale [18]. This observation tool can accurately measure the gravity field and continuously monitor changes in surface mass [19]. In recent years, many researchers have studied the redistribution of the water mass in typical regions based on GRACE, such as the Amazon basin [20], Greenland [21], the North China Plain [22], and Southwest China [23]. However, the orbit radius of GRACE satellites leads to inversion results with a coarser spatiotemporal resolution [24]. Specifically, the temporal resolution is on a monthly scale, and the spatial resolution is about 300–400 km under the harmonic degree of 60–90, which dramatically limits the TWSA inversion in small-scale regions using GRACE [25]. The aging of GRACE satellite elements led to its retirement in 2017 and the launch of its next gravity satellites, namely, GRACE Follow-On (GRACE-FO), in 2018 [7]. There is a gap of nearly one year between the GRACE and GRACE-FO satellites [2]. Hence, it is essential to find an alternative method to continuously monitor TWSA.

The redistribution of water masses will cause the subtle deformation of the surrounding crust [26,27]. It is then possible to invert TWSA by continuously monitoring crustal deformation [28–30]. Crustal deformation can be continuously measured by Global Navigation Satellite System (GNSS) stations. Moreover, there are many advantages with regard to GNSS observations, such as high accuracy and all-weather and real-time measurements [31]. Currently, the GNSS is constantly utilized to derive TWSA in distinct regions around the world, such as California [32,33], the western United States [34,35], southwest China [3,12], and mainland China [8]. In regions with dense GNSS stations, TWSA can be effectively derived using GNSS vertical arrays. GNSS can observe the deformation of the crust caused by TWSA. Correspondingly, the vertical displacement can be utilized to invert the near real-time TWSA in these regions [36]. This inversion strategy has great potential for detecting hydrological signals, which can be employed to establish warning systems for extreme hydrometeorological hazards [37]. In addition, the Crustal Movement Observation Network of China (CMONOC) was established about 10 years ago, which makes it possible to obtain the crustal deformation over mainland China [38,39]. The GNSS datasets provided by CMONOC have been widely utilized to analyze crustal deformation and surface loading [22,40,41]. However, the distribution of GNSS stations is uneven due

to harsh geo-climatic conditions, which dramatically limits the application of GNSS for TWSA inversion [3]. Developing methods to accurately derive TWSA based on sparse GNSS arrays has become a research hotspot.

Unlike previous studies, this study proposes a new deep learning weight loading inversion model (DWLIM) by combining the long short-term memory (LSTM) algorithm, inverse distance weight method, and crustal loading model. Moreover, TWSA was derived for mainland China from 2011 to 2020 using DWLIM, GRACE, and GLDAS. The TWSA results were calculated based on DWLIM, and its variation characteristics were investigated in 10 river basins within China. The organization of this study is as follows: Section 2 describes the materials and methods in this study, and Section 3 presents the TWSA results based on DWLIM, including the inversion of TWSA and validation of DWLIM. Section 4 discusses the variation characteristics of TWSA in the river basins, and this section also analyzes the difference among the TWSA results. Finally, the primary findings of this study are summarized in Section 5.
