**3. Results**

#### *3.1. Impact of TWSC on ET Estimate*

#### 3.1.1. ET Estimated by Ignoring TWSC

Figure 3 shows the monthly mean of ETWB following Equation 1, ETPQ, *P*, *Q*, and TWSC for 2003–2015 in the nine catchments. The negative ETWB values in January and February in the SRB and December in the Haihe River Basin (HRB) may result from the uncertainties of in situ precipitation and TWSC [13,40]. The TWSC has a significant impact on ET estimates in most catchments. The deviation of the monthly mean of ETWB and ETPQ reaches 34.2 mm/month in June (accounting for 52.9% of ETWB) in the Upper Yangtze River Basin (UYRB). The deviations between ETWB and ETPQ range from 6.7 to 37.2 mm/month for twelve months in the Middle Yangtze River Basin (MYRB), and its RMSE accounts for 37.1% of variations of ETWB. The RMSEs are computed following Equation 2. In the YeRB and SRB, the deviations between ETWB and ETPQ are small, with their RMSEs between ETWB and ETPQ reaching only 6.4 and 8.7 mm/month, respectively. In the MRB, the RMSE between ETWB and ETPQ shows the maximum value, i.e., 27.2 mm/month, accounts for 33.5% of variations of monthly mean ETWB.

**Figure 3.** Monthly mean of ETWB (blue curves), ETPQ (red lines), P, Q (purple lines), and TWSC (green lines) for 2003–2015 in the nine exorheic catchments. The histograms represent the monthly precipitation (P). The error bars show the uncertainties of monthly mean ETWB. (**a**)–(**i**) corresponding to the nine exorheic catchments in China. (**a**): UYRB; (**b**): MYRB; (**c**) YeRB; (**d**): SRB; (**e**): PRB; (**f**): LRB; (**g**) HRB; (**h**): HuRB; (**i**): MRB.

The annual ETWB and ETPQ estimates are shown in Figure 4; the mean annual PCMDC, ETWB, and ETPQ results are shown in Table 3. In the UYRB, the largest deviation of annual ET between ETWB and ETPQ is only 27.5 mm/yr in 2014, and the RMSE between ETWB and ETPQ only makes up 2.6% of the mean annual ET. In the SRB, the TWSC has a large impact on annual ET, large deviations between ETWB and ETPQ occur almost all the years, and the proportion of the RMSE accounting for the mean annual ETWB reaches 11.5%. In the Minjiang River Basin (MRB), the RMSE represents 12.7% of the mean annual ET, with the largest deviation (291.8 mm/yr, 39.1% of total ETWB in this year) occurring in 2003.

**Figure 4.** Annual ETWB and ETPQ from 2003–2015. (**a**)–(**i**) corresponding to the nine exorheic catchments in China.

**Table 3.** The mean annual precipitation from CMDC, mean annual ETWB and ETPQ estimation from GRACE in the exorheic catchments of China from 2003–2015, with one standard deviation (unit: mm/yr).


#### 3.1.2. Impact of Different GRACE Solutions on ET Estimate

The monthly mean TWSC from different GRACE solutions is shown in Figure A1, where their mean TWSC is the arithmetical mean from all TWSC estimates for the corresponding calendar month. Note that the TWSC derived from CSR-M compare favorably with the mean TWSC (Figure A1), thus the CSR-M TWSC is used for the estimate of ETWB in this study. The TWSC from CSRT-GSH.sf show significant differences among the four TWSC results, as they exaggerate the monthly mean TWSC in the UYRB, MYRB, YeRB, SRB, and PRB, and the differences may result from the scaling factor derived from CLM4.5 [43]. The spatial distribution of scaling factors is checked in our study (not shown), and the spatial variability of scaling factors varies greatly in the basins, indicating exaggerated TWSC. The maximum deviations are calculated between each two monthly mean TWSC estimates, which range from 10.7 to 35.6 mm/month, the deviations occur in the YeRB (10.7 mm/month) and MRB (35.6 mm/month) (Figure A1c,i), respectively. As the area of MRB is the smallest, and with the most abundant precipitation, it is understandable that the MRB shows the largest deviation of TWSC. The large deviation of TWSC between JPL-M.dsf and other GRACE solutions in the HRB and MRB (Figure A1g,i) may result from the processing strategy and coarse resolution in the spatial of JPL-M since the areas of the two basins are small [54].

The annual ET estimates based on different GRACE solutions are shown in Figure A2. The RMSEs among ETCSR–M (=ETWB), ETJPL–M.dsf, ETCSRT–GSH.sf, and ETCSR–DDK4 are understandably less than those RMSEs between ETWB and ETPQ, and their interannual fluctuations are more consistent than that of ETPQ. We compute the standard deviations (STDs) between the four ET estimates from di fferent GRACE solutions for every single year, and the results show that the max STD is only 51.2 mm/yr, occurring in the MRB. The mean STD for the years from 2003–2015 in the corresponding catchment is also computed, ranging from 9.7 to 27.1 mm/yr (accounting for 1.8–3.9% of annual ETWB), with the least occurring in the YeRB and the largest occurring in the MRB. In three catchments, the max STDs occur in 2003 in the PRB, the Huaihe River Basin (HuRB), and the MRB, which are located in Southeast China. In the other three catchments, the max STDs appear in 2011, which are the YeRB, SRB, and Liaohe River Basin (LRB), in North China.

#### *3.2. Comparison of Di*ff*erent ET Products*

Figure 5 shows the monthly mean of ET estimates from di fferent ET products. Their mean annual cycles are similar among all the catchments. In the humid catchments: in the UYRB, the other three ET products overestimate the ET compared with ETWB for all months except December, the maximum deviation exists in July, which has the most precipitation (Figure 5a). In the MYRB, other ET estimates are bigger than ETWB estimates for all months except November when the ETWB increases to respond to increased precipitation. In the PRB, the mean of ETWB in July is less than that in June and August, and the mean of ETWB in October is also less than September and November (Figure 5e). In the HuRB, ETWB shows a rapid increase response for sharply increased precipitation in July (Figure 5h), while the three other ET results do not catch it. The ETWB also can capture the irregular monthly mean precipitation changes from June to December in the MRB (Figure 5i). In the semihumid and semiarid catchments: the two versions of GLDAS both show the maximum deviation in September with ETWB in the YeRB. Most months of ETGLDAS–2.1 are more than other ET estimates in the LRB. During the intense irrigation period of April and May, the ETWB is significantly greater than other ET estimates in the HRB. From the above, these ET results all show similar annual cycles, while ETWB can capture some irregular variations in monthly precipitation.

**Figure 5.** Monthly mean of ET estimates in the exorheic catchments of China. The error bars show the uncertainties of monthly mean ETWB. (**a**)–(**i**) corresponding to the nine exorheic catchments in China.

The maximum RMSEs between the monthly mean of ETWB and other ET results are in the MRB, which are 27.5 (vs ETGLDAS–1), 26.3 (vs ETGLDAS–2.1), and 24.7 (vs ETGLEAM) mm/month (Table A1). In the YeRB, the RMSEs are the least, which are 7.2, 7.5, and 13.0 mm/month. We also compute the

proportion of the RMSEs accounting for an average of the monthly mean of ETWB. The proportions in the UYRB show the maximum values, which are 50.5% (vs ETGLDAS–1), 43.3% (vs ETGLDAS–2.1), and 43.1% (vs ETGLEAM). The HuRB experienced the minimum proportions, which are 20.4%, 22.3%, and 25.9%, respectively.

The annual ET from different sources is illustrated in Figure 6, which shows huge gaps among different ET estimates. In terms of the humid catchments: In the UYRB and MYRB, it is obvious that other annual ET estimates are all larger than ETWB. Their mean deviations between ETWB and ETGLEAM reaching 144.7 mm/yr (31.3% in mean annual ETWB) and 88.0 mm/yr (12.8% in mean annual ETWB) in the two catchments (Figure 6a,b). In the PRB, ETGLDAS–1 and ETGLEAM both overestimate the annual ET, and ETGLDAS–2.1 shows different interannual variations with respect to ETWB (Figure 6e). In the HuRB, all the ET estimates capture the drop of ET in 2011 due to reduced precipitation (Figure A3h), but there is some discrepancy among mean annual ET. In the MRB, the ET results show large differences in the interannual variations. The ETGLDAS–1 even verges on 1100 mm/yr after 2012. Concerning the semihumid and semiarid catchments: In the YeRB, the ETWB is consistent with ETGLDAS–2.1 except for the years 2006 and 2009, while ETGLEAM underestimates the annual ET for all the years. In the SRB, the ETGLDAS–2.1 is significantly greater than the other annual ET. Nevertheless, the ETGLEAM is close to ETWB. In the LRB, the ETGLDAS–1 is close to ETWB in mean annual ET, and their interannual variations are similar. In the HRB, ETGLDAS–2.1 is closest to ETWB. ETGLEAM somewhat underestimates the annual ET for the other three results. For the two catchments in Northeast China (i.e., SRB and LRB, Figure 6d,f), both ETGLDAS–2.1 results overestimate the annual ET. Additionally, the four ET results show consistent interannual changes in most catchments.

**Figure 6.** Annual ET from different products in the exorheic catchments of China. The dotted lines with different colors corresponding to their mean annual ET. (**a**)–(**i**) corresponding to the nine exorheic catchments in China.

#### *3.3. Comparison of Di*ff*erent Precipitation and Runo*ff *Inputs for ET Estimation*

In all the catchments, the interannual fluctuations of precipitation from different sources show similar patterns (Figure A3), while the mean annual precipitation shows some differences (Figure 7). In the MYRB and YeRB, the PCMDC is higher than PGLDAS–1, which is similar to the comparison from Lv et al. [55] in corresponding regions. In the SRB and LRB (Northeast China), PGLDAS–2.1 is prominently larger than the other three precipitation sources (Figure A3d,f, and Figure 7b). Caution should be taken when using the PGLDAS–2.1 in the two catchments. It should be noted that the annual

PMSWEP is the least for all the catchments (Figure A3), and mean PGLDAS–1 are all less than those of PCMDC (Figure 7a).

**Figure 7.** Deviations of annual ET, precipitation, and runoff between (**a**): WB and GLDAS–1; (**b**): WB and GLDAS–2.1; (**c**): WB and GLEAM. The blue curves with triangles represent the deviations between annual ET and other ET estimates. The red curves with dots represent the deviations between PCMDC minus QRSBC and PGLDAS minus the QGLDAS. The purple lines with rhombus points represent the deviations between PCMDC and other precipitation forcing data. The green lines with square points represent the deviations of runoff between QRSBC and two versions of QGLDAS.

QRSBC, QGLDAS–1, and QGLDAS–2.1 show larger discrepancies than that for precipitation. The comparison of annual runoff from 2003–2015 can be found in Figure A4. Since the runoff is modeled results, it faces more uncertainties than precipitation. As the similar results showed in YRB (UYRB and MYRB) and YeRB in Lv et al. [55], the in situ runoff was significantly larger than that from QGLDAS–1. The interannual variations of runoff from different sources show similar patterns in most catchments except in the YeRB and HRB, which experienced small amounts of runoff. In all the catchments, QGLDAS–2.1 is larger than that from QGLDAS–1, and they are closer to QRSBC in most catchments, presumably due to some modification for GLDAS-2.1 [56].

To explore the impact of precipitation and modeled runoff (GLDAS Noah LSM outputs) on ET estimates, we analyze the difference in both sides of the water balance equation. We first compute the deviation between mean annual ET, precipitation, runoff, and precipitation minus runoff for 2003–2015 (Figure 7). In the UYRB, the mean annual deviation between ETWB and ETGLDAS–1 reaches 200.9 mm/yr, the mean annual deviation between PCMDC minus QRSBC (expressed as P-Q) and PGLDAS–1 minus QGLDAS–1 are close to the deviation of ET (Figure 7a). This deviation is mostly contributed by the deviation of runoff (−241.6 mm/yr). As Figure 7a shows, the deviations of P-Q are close to the deviations of ET in all the catchments. For the water balance (WB) with GLDAS-2.1 (Figure 7b), the deviations of P-Q are close to the deviations of ET in all the catchments except PRB. In the PRB, the deviation of mean annual ET is only 5.3 mm/yr, while the deviation of mean annual precipitation reaches −27.9 mm/yr, and the deviation of mean annual runoff is −4.34 mm/yr (Figure 7b). Based on the water balance method, we only assess the precipitation forcing data variable for GLEAM ET. As Figure 7c shows, in the YeRB, LRB, and HRB, the deviation of precipitation may explain the most differences between annual ETWB and ETGLEAM. In other catchments, it is somewhat opposite between the deviation of annual precipitation and ET.

#### *3.4. Uncertainty Estimation Results*

Uncertainties of TWSC, PCMDC, QRSBC, and ETWB are shown in Table 4. Large uncertainties of TWSC appear in the PRB, HuRB, and MRB, which are more than 30 mm/month. The large uncertainties of TWSC may result from the small study area (HuRB and MRB) and large variations of TWSC caused by abundant precipitation (PRB and MRB). In three catchments (MYRB, PRB, and MRB), their annual precipitation is more than 1300 mm/yr, and their uncertainties of precipitation are also more than 11 mm/month. The uncertainties of runoff are similar to those of precipitation except the YeRB, LRB, and HRB, where the water use is intense and the runoff is little.


**Table 4.** The uncertainties of monthly TWSC, precipitation, runoff, ET, monthly mean ET and annual ET from 2003–2015 (unit: mm/month and mm/yr).

From Table 4, we can conclude that the uncertainties of monthly ET are mainly from TWSC, which is similar to the conclusions in Long et al. [1] and Pan et al. [13]. Almost in all the catchments, the uncertainties of TWSC are two times or even three times larger than the uncertainties of PCMDC, and they are also much larger than the uncertainties of QRSBC. The uncertainties of annual ET are all larger than 45 mm/yr, while the uncertainties are mainly from the uncertainties of annual precipitation.
