*2.1. Study Area*

Nine exorheic catchments were divided from eleven hydrological gauge stations from River Sediment Bulletin of China (RSBC) [35]. The catchment boundaries are derived from the location of gauge stations, Shuttle Radar Topography Mission (SRTM) elevation data (https://www2.jpl. nasa.gov/srtm/), and processed in ArcGIS with Soil and Water Assessment Tool (ArcSWAT) plugin (https://swat.tamu.edu/software/arcswat/). The ArcSWAT is an ArcGIS-ArcView extension and a graphical user input interface for the SWAT (Soil and Water Assessment Tool) model. The Gaoyao, Shijiao, and Boluo hydrological gauge stations are all in the Pearl River Basin (PRB), we merge them into one catchment (Figure 2). The YRB is divided into two sub-basins, based on its two hydrological gauge stations: Yichang and Datong. The information of the nine catchments is listed in Table 1, and the catchments are also presented in Figure 2.

**Figure 2.** Map of exorheic catchments of China. The black curves show the boundaries of the nine exorheic catchments, the black texts with a white background are the abbreviation of catchments names. The magenta stars show the locations of eleven hydrological gauge stations, and the magenta texts present the name of hydrological gauge stations. Their descriptions can be further found in Table 1. The blue curves represent the main rivers and tributaries in China. The country boundary is shown with the dash line.

**Table 1.** Descriptions for the nine exorheic catchments of China (sorted by areas and location). The climate categories are based on annual precipitation and dryness [36].


#### *2.2. Water Balance Equation*

The ET can be estimated from surface water balance on the basin or continental scales, which usually serves as a benchmark for other products. The equation is as follows:

$$\text{ET}\_{\text{WB}} = P - \mathbb{Q} - d\text{s}/dt\tag{1}$$

where ETWB is calculated ET, *P* is precipitation, *Q* is river discharge, and *ds*/*dt* is the change in terrestrial water storage for a specific time period [4,11,15]. TWSC is estimated as the temporal derivative of TWSA from the GRACE products [37,38]. *ET*, *P*, and *Q* are the cumulated amount in a full month [4,39]. Then *ds*/*dt* (TWSC) is the differential of two consecutive months of TWSA at the beginning of a month. To obtain the time point of every beginning of a month of TWSA time series, we interpolate TWSA by an interpolation method. A similar process of calculation can be found in Li et al. [40]. Firstly, seasonal and trend signals are estimated using unweighted least squares and then interpolated for every beginning of a month. Secondly, the residuals removed by TWSA time series subtracting seasonal and trend signals are then interpolated by linear interpolation. Finally, the sum of interpolated residuals, seasonal, and trend signals are the interpolated TWSA time series.

Root mean square error (RMSE) is used to evaluate the deviation between ETWB and other types of ETs. The equation is as follows:

$$RMSE = \sqrt{\frac{1}{N} \sum\_{i=1}^{N} \left(\chi\_i - \chi\_i\right)^2}. \tag{2}$$

where *N* is the data length (time series), X*i* is the ith estimated ET results from other methods, Y*i* is the ith ETWB result.
