**1. Introduction**

As an important component of terrestrial water storage (TWS), groundwater plays a key role in domestic, agriculture and industrial use, as well as ecosystems [1,2]. More than 38% of the world's population lives in arid or semi-arid zones [3], where groundwater is usually the dominant freshwater resource, supplying domestic use and irrigation water [4]. Especially in northwest China, groundwater resources have been facing the risk of depletion, which may lead to the ecological environment of the region losing its ability to self-repair and endangering local ecological security [5]. Therefore, accurate estimation of groundwater storage anomalies (GWSA) is essential for the effective use of local groundwater resources. The traditional method of monitoring groundwater level mainly uses monitoring wells. However, monitoring wells are scarce, and the observation

**Citation:** Su, K.; Zheng, W.; Yin, W.; Hu, L.; Shen, Y. Improving the Accuracy of Groundwater Storage Estimates Based on Groundwater Weighted Fusion Model. *Remote Sens.* **2022**, *14*, 202. https://doi.org/ 10.3390/rs14010202

Academic Editors: Alban Kuriqi and Luis Garrote

Received: 27 October 2021 Accepted: 17 December 2021 Published: 2 January 2022

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**Copyright:** © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

records are short and discontinuous, restricting research related to GWSA [2,6,7]. Therefore, it is important to seek an alternative method to obtain ground-based network data for monitoring of large-scale groundwater storage (GWS) variations.

Since March 2002, Gravity Recovery and Climate Experiment (GRACE) satellites have provided an opportunity to assess global TWS changes, with a resolution of ~300 km [8–10]. Currently, the GRACE gravity satellites are the only way to sense water storage at all levels, including soil moisture (SM), snow-water equivalent (SWE), canopy water storage (CWS), and GWS [10]. To isolate the GWS component from TWS, water storage changes of other components have to be estimated based on hydrological models [11,12]. At present, there are several frequently employed hydrological models and reanalysis datasets, such as the Global Land Data Assimilation System (GLDAS) [13], the WaterGAP Global Hydrology model (WGHM) [14], and the ERA5 reanalysis dataset [15,16]. Furthermore, previous studies have demonstrated the effectiveness of GRACE observations to estimate GWSA in many typically regions of the world, e.g., the Central Valley of California [17,18], northwest India [9,19,20], and the North China Plain [1,21,22].

Currently, most studies mainly rely on a single hydrological model to separate GWS components from GRACE-derived TWS [23–25]. However, the accuracy of these models is restricted by uncertainties in climate forcing (particularly precipitation), model parameters, and deficiencies in model structure [26–31]. Therefore, the effective combination of multiple models can improve the performance of hydrological simulations relative to a single model. For instance, Shamseldin et al. [32] used the method of multi-model ensemble to develop more skillful and reliable probabilistic hydrologic prediction. The results confirmed that better estimates of water storage can be obtained by combining the model outputs of different hydrological models. Long et al. [33] used the Bayesian model-averaging technique, which can merge multiple TWS products to analyze the spatiotemporal variability of TWS. Mehrnegar [27] presented the dynamic model-data-averaging method, which can be used to merge multiple TWS simulations. The result indicated that linear trends and seasonality within global hydrological models can be improved by using the dynamic model-dataaveraging method. These multi-model techniques prove to provide accurate estimates by combining different models according to the different weighting strategies [32,34].

Triple collocation (TC) is a statistical method to estimate the random-error variance of three independent datasets [35]. Currently, the TC method has been used to estimate measurement errors of GRACE data [36]. Specifically, Khaki et al. [37] and Nigatu et al. [38] estimated the changes in key water-storage components by using the GRACE data and soil-moisture data based on the TC analysis method. Yin and Park [39] proposed a simple least-square merging approach using error characteristics quantified from the TC approach to estimate weight. Compared to the classic TC approach, the extended triple collocation (ETC), proposed by McColl [40], can obtain an additional evaluation index, that is, the correlation coefficient relative to the unknown true value. Up to now, there are few studies that have merged datasets from different sources based on the ETC method.

The Hexi Corridor (HC) is one of the most agriculturally rich areas of northwest China, which is characterized as an irrigation district of "no irrigation, no agriculture" [5,41]. Moreover, groundwater resources have been depleted on a large scale in the area due to poor management of groundwater exploitation [42]. The policy of building a water-saving society was introduced in Zhangye City of Gansu Province in 2001 [43]. The government initiated a policy called the Key Governance Planning Project of the Shiyang River Basin in 2007, which aimed to improve the ecological conditions of the area [44,45]. Accurate estimation of GWS is essential for understanding the complex hydrological process and formulating sustainable management policies for groundwater resources in the region.

The purpose of this study is to improve the accuracy of groundwater storage estimates in some regions where in situ groundwater-level measurements are limited and to quantify the impact of climate change and human activities. Specifically, a weighted fusion model is proposed, based on the squared correlation coefficient and error variance calculated by the ETC [40,46] method. The ratio of these two indicators is used to develop the groundwater weighted fusion model (GWFM), which is helpful in merging GWSA based on the GRACE and multiple hydrological models, and compare it with the original results. In addition, a simple and effective method is used to evaluate the contribution of climate factors and human factors to GWS.

#### **2. Materials and Methods**
