**1. Introduction**

Evapotranspiration (ET) is one of the most important components of the climate system connecting the water, energy, and carbon cycle [1,2]. ET changes can be used as an indicator of climate change, especially in areas where the water cycle is accelerated [3,4]. However, regional ET is often di fficult to estimate. The flux tower observing station network can provide accurate ET observations at each site [5], but it often has too sparse sites for basin scale study. Remote sensing provides an opportunity to monitor spatial-temporal changes in ET [6,7], but regional calibration and uncertainty from vegetation cover data will also lead to large uncertainty in ET [8]. Land surface models (LSMs) can also provide

grid-to-regional scale ET estimates, such as the multiple LSMs simulations using the global land data assimilation system (GLDAS) issued by NASA [9]. Regional ET can be derived from the terrestrial water budget, namely the residual between precipitation (*P*) and the sum of runoff (*Q*) and terrestrial water storage change (*ds*/*dt*), which have been regarded as benchmark estimates for validating ET products or estimates on a regional scale [10,11].

The Gravity Recovery and Climate Experiment (GRACE) satellites mission launched in March 2002 has provided a unique way to monitor terrestrial water storage (TWS) changes on the monthly scale with a ~300 km footprint [12]. As for a given basin, the time series of TWS changes (TWSC) in the basin can be obtained from the differential of TWS anomalies (TWSA) observed by GRACE [1,13,14]. The regional ET can be estimated from TWSC, regional precipitation, and runoff data based on the water balance equation. Rodell et al. [4] discussed the method of calculating ET from GRACE TWSA and suggested that the ET based on the GRACE water balance method can be used to evaluate the ET of the model simulations. Ramillien et al. [15] estimated the ET of 16 globally distributed basins based on the GRACE water balance method, and they are compared to outputs of four global LSMs, which shows good overall agreement. A few studies have applied this method to estimate the regional ET in several global basins, e.g., the Lake Chad basin, Africa [16], continental USA [17], and Amazon Basin [18]. However, the differences among different ET estimates are usually ignored or ascribed to the uncertainty of estimates during data processing [13,15]. Castle et al. [19] and Pan et al. [13] estimated the human-induced ET in the Colorado River Basin (USA) and Haihe River Basin (China) and attributed the differences between GRACE water balance ET and GLDAS ET to the influence of human activities. However, the quality of input precipitation also has a grea<sup>t</sup> influence on the ET outputs [10,20]. Badgley et al. [21] emphasized the significant uncertainty of the regional ET estimate from the choice of input forcing dataset. Liu et al. [11] used a bias-corrected water balance method to calculate annual reference ET from 1983–2006 and evaluated nine ET products in 35 global river basins on the interannual and long-term scale. They determined that different performances among the ET products may result from different forcing datasets. Given the uncertainty of ET products caused by the precipitation forcing data, in this study, we seek to explain the difference among different ET estimates by considering uncertainty from the different precipitation forcing data and modeled runoff from a water balance perspective.

The water balance equation is the classic method to calculate the ET on a regional scale. In China, Mao et al. [22] emphasized the significant impact of water storage due to reservoir construction on calculating ET trends. However, they did not consider other factors that cause the water storage changes, e.g., water withdrawal, lakes change, and glaciers melting [22,23]. Jiang et al. [24] took basin water balance as a benchmark to evaluate the MODIS MOD16 ET products in several exorheic basins. However, the assessment on the uncertainty of GRACE-derived TWSC was limited and was restricted to the Yangtze River Basin (YRB), Yellow River Basin (YeRB), and Songhuajiang River Basin (SRB) on monthly scale. Li et al. [25] used the revised Remote Sensing–Penman Monteith (RS-PM) model [26,27] to produce an ET map in China and derived an estimate of mean annual land–surface ET to 500 mm/yr. The revised RS-PM model predictions did not show a significant systematic error, but they only explained 61% of the ET variations at all the validation sites, which showed the uncertainty of the ET model in the regional estimation. Bai and Liu [10] used water balance-based ET estimates to evaluate the Global Land Evaporation Amsterdam Model (GLEAM), GLDAS and MODIS MOD16 ET products for 22 river basins in China, but the selected basins are restricted in wet basins, most of which are located in the YRB. ET calculated from the water balance equation for some exorheic basins of China are estimated by the above studies. However, little attention is paid to uncertainties from TWSC and precipitation forcing data. Therefore, we conduct a systematic assessment for the ET of exorheic basins from a water balance perspective.

Several studies assume TWSC to be zero on the annual scale due to the lack of data [22], and ET is obtained by precipitation minus runoff directly, as in the studies by Zhang et al. [28], Senay et al. [29] and Xue et al. [30]. However, TWSA can have large variability on seasonal and interannual scales due to human water consumption [31,32] and the building of reservoirs [22,23]. Zeng et al. [33] also acknowledged that ignoring TWSC would bring much bias into ET estimation, especially in regions with low ET. Wang [34] points out the importance of considering interannual TWSC in the estimation of ET. Hence, we compare the difference of ET estimates by considering and not considering TWSC in the water balance equation to explore the impact of TWSC on the ET estimate on interannual and monthly scales.

This study aims to (1) estimate the regional ET of nine exorheic catchments in China using the water balance equation considering TWSC; (2) analyze the impact of not considering TWSC and different TWSC products on the ET estimates; (3) explain the inconsistency between different ET products and regional ET from a water balance perspective. The flowchart of this study is shown in Figure 1.

**Figure 1.** Flowchart of this study. It includes the used data and process of calculation and analysis in this study.

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