*2.4. Methods*

In the above-mentioned data sets, which are provided with different spatial resolutions, are used with regional averages results, the different spatial resolutions have little impact on ET estimates. The grids in the catchments are used to extract regional averages estimates. Their results are computed on a monthly scale. The ET results are shown at monthly mean and annual scales, as the amount of annual ET, interannual changes, and mean annual cycles of ET are the main characteristics of ET. Besides, the difference between the ET estimates can be clearer at monthly mean and annual scales.

We use the TWSC from GRACE (CSR-M), PCMDC, and QRSBC to derive ETWB. To explore the impact of TWSC on ET estimate, we also estimate the ET from precipitation minus runoff directly (expressed as ETPQ) without considering TWSC. The results are shown in Section 3.1.1.

Here we compute TWSC results from different GRACE solutions to evaluate their impact on ET while keeping all other inputs (*P* and *Q*) unchanged (Section 3.1.2). The GRACE products include CSR-M, JPL-M.dsf, CSRT-GSH.sf, and CSR-DDK4. The TWSC used for ET estimates from JPL-M.dsf, CSRT-GSH.sf, and CSR-DDK4 are expressed as ETJPL–M.dsf, ETCSRT–GSH.sf, and ETCSR–DDK4, respectively. They are further discussed in Section 4.1.

We then compare the ET estimates from GLDAS and GLEAM with ETWB (Section 3.2). The discussion of RMSEs between ETWB and other ET estimates are shown in Section 4.2. We attempt to analyze the deviation of precipitation and runoff to the regional ET estimate from a water balance perspective (see Sections 3.3 and 4.3), quantifying the deviations between PCMDC and precipitation forcing data, QRSBC, and QGLDAS estimates. Previous studies demonstrate that the TWSA (or TWSC) from GRACE and GLDAS are comparable [50–52]. Hence, we do not compare the TWSC component in the water balance equation.

We compute the deviations between water balance ET and other ET results, precipitation results, runoff results, and results of precipitation minus runoff (Section 3.3). We assess the impact of deviation of precipitation and runoff on the estimate of ET based on RMSE and the change of RMSE (Section 4.3). The RMSEs are calculated between annual ETWB minus annual PCMDC and other ET estimates minus their precipitation forcing data (expressed as RMSE (ET-P)) from a water balance perspective. Similarly, the RMSE (ET-Q) represents the calculated RMSEs between annual ETWB minus QRSBC and ETGLDAS minus QGLDAS, and the RMSE (ET-(P-Q)) represents the calculated RMSEs between annual ETWB subtracting the result of PCMDC minus QRSBC and annual ETGLDAS subtracting the result of PGLDAS minus QGLDAS from 2003–2015. The proportions of RMSEs changed of RMSE (ET-P), RMSE (ET-Q) and RMSE (ET-(P-Q)) relative to RMSE (ET) are further computed.
