Table 1

2.2 Data

2.2.1 Observed precipitation data

The observed monthly precipitation series was obtained from the Climatic Research Unit (CRU; Harris, Osborn, Jones, & Lister, 2020). There were observed 500 CRU sites within the EIB, of which the longest time series spans from 1820–2021. In this study, 139 precipitation sites spanning a data series of 1967–2020 were selected, and 123 sites with data series from 1961–2021 were used for trend analyses. Missing values were linearly interpolated based on the values in the preceding and subsequent month or the adjacent sites. The CRU gridded precipitation dataset (TS v.4.05) (Harris et al., 2020), with a 0.5º × 0.5º resolution, was also evaluated in this study.

2.2.2 Remote sensing precipitation data

The Global Precipitation Measurement (GPM) Integrated Multi-satellite Retrievals (IMERG) Final run v.06 is a level 3 precipitation product (Huffman, Stocker, Bolvin, Nelkin, & Tan, 2019). This product using multiple precipitation-relevant satellite passive microwave sensors. The algorithm was combined with precipitation gauge analyses, microwave-calibrated infrared satellite estimates, and other precipitation estimators at a finer spatial resolution (0.1°). The data series used in this study spanned from June 2006 to December 2020.

2.2.3 GRACE TWSA data

Several versions of TWSA products have been released by several agencies; this study utilized the RL06 (v.3) GRACE liquid water equivalent thickness anomaly data series (Landerer & Swenson, 2012) from the Center for Space Research (CSR) at the University of Texas (Austin USA), the Geoforschungs Zentrum Potsdam (GFZ), and the Jet Propulsion Laboratory (JPL) in which the spatial resolution was 1º×1º. In addition, the GRACE Mascon solutions from JPL (RL06-v2) (Watkins, Wiese, Yuan, Boening, & Landerer, 2015) and the National Aeronautics and Space Administration Goddard Space Flight Center (GSFC) (RL06-v.1) (Loomis, Luthcke, & Sabaka, 2019) were used; the spatial resolutions of these products were 0.5º×0.5º and 1º×1º, respectively. These five GRACE products were abbreviated as CSR-v3, GFZ-v3, JPL-v3, JPL-v2, and GFSC-v1, and they also include the equivalent water thickness. The monthly series from April 2002 to December 2020 was used in this study. Due to the lack of observational data for validation, it was difficult to determine which product was more suitable for the EIB; as such, all five products were used to derive the TWSA trends. The spherical harmonic coefficients solution was used in three v3 products, while the mascon solution was used in the JPL-v2 and GFSC-v1 products. Post-processing filters were applied to reduce correlated errors. These solutions provide accurate surface-based gridded information, which may be well applied to studies on hydrology (Watkins et al., 2015; Save, Bettadpur, & Tapley, 2016; Loomis et al., 2019). Additional descriptions of data processing are provided in Loomis et al. (2019), Save et al. (2016), and Watkins et al. (2015).

2.3 Methods

2.3.1 Simulation of monthly AET

The hydrological budget method is an effective tool to simulate AET in inland basins. For a closed inland basin, precipitation and AET represent the hydrologic gains and losses, respectively. According to the water balance in the basin, the difference between precipitation and AET is equivalent to water storage changes in the basin; therefore, the monthly AET may be simulated as:
AETi = PiΔSi (1)
where AETi , Pi , andΔSi are the AET, precipitation, and water storage changes within a month for a closed basin, respectively, in which the unit is mm. For the gridded precipitation and TWSA data, the average data series of each closed basin was calculated based on the area weighting of each grid in the basin. For grids covered by the basin boundary, the area weighting of the boundary grid was represented by the proportion of area within the basin boundary.
In simulating the monthly AET, it is necessary to focus the consistency of the time period for each variable. Monthly precipitation and AET are the mean values within a month, computed between the beginning and end of a month. ΔS is the difference between water storage at the end and beginning of the month. However, the TWSA data used in this study represent the mean water storage within a month. Obtaining ΔS from TWSA is key to the simulation; here, ΔS was calculated as:
\({S}_{i}=(\text{TWSA}_{i+1}-\text{TWSA}_{i-1})/2\) (2)
where TWSA(i+1) in the next month andTWSA(i-1) in the previous month represent water storage at the end of the simulated month and the beginning of the simulated month, respectively. The accuracy of this calculation has been validated by Long et al. (2014).

2.3.2 Trend detection and identification of its main attribution methods

The rank-based non-parametric Mann-Kendall (MK) test and trend magnitude method (Hirsch, Slack, & Smith, 1982) were applied to detect long-term monotonic trends and their magnitudes. This test is able to handle non-normality, censoring, data reported as “less-than” values, missing values, and seasonality; it also has high asymptotic efficiency (Fu, Charles, Liu, & Yu, 2009). Further details regarding this test were reported by Xu, Liu, Fu, & Chen (2010). The annual and monthly precipitation trends, AET, and TWSA were detected in each basin or grid.
Based on the water balance principle, the main factors causing changes in the AET and TWSA were identified. According to the water source consumed by the AET, the change in AET was attributed to changes in precipitation and the consumption of other water supply sources. Based on the hydrologic budget within a closed basin, the change in the TWSA was attributed to changes in precipitation and AET. Precipitation and AET have positive and negative effects on the TWSA; this means an increase or decrease in precipitation may prompt an increase or decrease in the TWSA, while an increase or decrease in the AET may trigger a decrease or increase in the TWSA, respectively. Similarly, precipitation and potential evapotranspiration (PET) have positive and negative effects on the AET, respectively. Based on these analyses, the main attribution of AET and TWSA changes was identified at basin scales. The contribution of precipitation and other factors to changes in the AET was semi-quantified by analyzing the magnitude of the trend between AET and precipitation.