2.2.1. GRACE Data

The GRACE RL05 Mascon solutions are utilized to derive TWS anomalies in this study, which are provided by the Center for Space Research (CSR) [52]. Monthly TWS anomalies are provided from April 2002 to June 2017, with a spatial resolution of 0.5 × 0.5◦. The regularization constraint on mascon solutions is derived from original GRACE information with no empirical filtering post-processing [52,53]. Therefore, the product can capture all the signals observed by GRACE within the measurement noise level and be used without

further processing [54]. Missing data in the CSR Mascon are filled by linear interpolation of the nearby monthly mean values [24].

#### 2.2.2. Soil Moisture Datasets

GLDAS was jointly developed by the National Aeronautics and Space Administration and the National Oceanic and Atmospheric Administration, which can obtain land-surface state and flux with high time resolution (https://disc.gsfc.nasa.gov/ (accessed on 1 July 2021)) [13]. In this study, the monthly SM product provided by the GLDAS Noah model with a spatial resolution of 1.0 × 1.0◦ is used to estimate SM over the HC. For consistency of data resolution, the related datasets are interpolated into a spatial resolution of 0.5 × 0.5◦. More details on various soil-moisture data used are summarized in Table 1.

**Table 1.** Summary of soil-moisture products from GLDAS, WGHM, and ERA5-Land.


WGHM [14] was developed by the Institute of Physical Geography at the University of Frankfurt and provides information on spatiotemporal water-storage changes for most hydrological processes. This model accounts for four of the most important terrestrial water-storage components: surface water, snow, soil water, and groundwater storage [55]. The WGHM data were retrieved from https://doi.pangaea.de/10.1594/PANGAEA.918447 (accessed on 1 July 2021). The SM product provided by WGHM is used in this study, which is monthly data from January 2003 to December 2016 at a spatial resolution of 0.5 × 0.5◦.

ERA5-Land [56] is a reanalysis dataset produced by replaying the land component of the ERA5 climate reanalysis (https://cds.climate.copernicus.eu/ (accessed on 1 July 2021)). It is one of the most modern and finest reanalysis datasets produced by the European Centre for Medium-Range Weather Forecasts (ECMWF) within the Copernicus Climate Change Service. In this study, the SM product of ERA5-Land is employed, which is the monthly datasets, with a spatial resolution of 0.1 × 0.1◦ from 2003 to 2016. To maintain the same spatial resolution, the related datasets are interpolated into the 0.5 × 0.5◦ spatial resolution.

#### 2.2.3. Groundwater Level from Wells

Groundwater monitoring data are collected from the groundwater yearbooks compiled by the China Institute of Geological Environment Monitoring (CIGEM), which is published by the Ministry of Land and Resources of the People's Republic of China. Due to the sparse number of stations and a lack of continuous data at individual stations, the measured groundwater-level data of five wells from 2007 to 2014 are selected in the SYRB to verify the performance of GWFM-based GWSA in this study (shown in Figure 1b). The groundwater level can be converted to groundwater storage by multiplying by specific yield values. However, specific yield values are unknown, and the groundwater level is only used to verify the performance of GWFM. Therefore, there is no need to covert the levels to groundwater storage in this study to avoid possible errors associated within unknown specific yield values.

#### 2.2.4. Auxiliary Data

The precipitation dataset is collected from the China Meteorological Data Service Center, based on the precipitation data of high-density ground stations in China (2472 national meteorological observatories). It uses the thin-plate splines method [57] of ANUSPLIN software for spatial interpolation to generate monthly grid data from 1961 to the present, with a spatial resolution of 0.5 × 0.5◦. Additionally, evapotranspiration and temperature

data from the GLDAS and ERA5-Land during 2003–2016 are collected to evaluate the impact of climate factors on GWS.

To evaluate the impact of human factors, the annual groundwater withdrawal data of the HC from 2003 to 2016 are also collected. They are collected from the Water Resources Bulletin of Gansu Province, which is published by the Gansu Provincial Department of Water Resources, China.
