*3.2. Evaluation of Interannual Variation in RE*

characteristics.

resolutions.

*3.2. Evaluation of Interannual Variation in RE*  Comparison of annual RE estimated by the 3-hourly, daily, and monthly rainfall data, respectively, is presented in Figure 6. The annual RE derived from the daily gauge data showed a obvious interannual variation, and the RE values ranged from 6893 MJ∙mm/ha∙h in 2007 to 14,637 MJ∙mm/ha∙h in 1998, with the average of 10,134 MJ∙mm/ha∙h during 1998–2012. The RE estimates derived from TRMM daily data showed a similar variability characteristic to the daily gauge data. However, the time series calculated by the TRMM 3-hourly data was obviously low, which ranged between 2557 and 7040 MJ∙mm/ha∙h. In addition, the two RE series based on the MFI approach (derived from the monthly gauge data and the TRMM 3B43 data, respectively) had roughly Comparison of annual RE estimated by the 3-hourly, daily, and monthly rainfall data, respectively, is presented in Figure 6. The annual RE derived from the daily gauge data showed a obvious interannual variation, and the RE values ranged from 6893 MJ·mm/ha·h in 2007 to 14,637 MJ·mm/ha·h in 1998, with the average of 10,134 MJ·mm/ha·h during 1998–2012. The RE estimates derived from TRMM daily data showed a similar variability characteristic to the daily gauge data. However, the time series calculated by the TRMM 3-hourly data was obviously low, which ranged between 2557 and 7040 MJ·mm/ha·h. In addition, the two RE series based on the MFI approach (derived from the monthly gauge data and the TRMM 3B43 data, respectively) had roughly equivalent averages (9951 and 9866 MJ·mm/ha·h) and share similar interannual variation characteristics.

equivalent averages (9951 and 9866 MJ∙mm/ha∙h) and share similar interannual variation

**Figure 6.** Comparison of annual rainfall erosivity estimated by rainfall data with different temporal

At the annual scale, the comparison of the ME, RMSE and BIAS of RE estimation from different TRMM rainfall products and rain gauges data are shown in Table 2, and the scatter plots of the RE characteristics.

RE.

*3.2. Evaluation of Interannual Variation in RE* 

product were closer to the results of the rain gauges data. The TRMM 3-hourly data tended to

**Figure 5.** Distribution of monthly RE values in different categories and their proportion to annual

Comparison of annual RE estimated by the 3-hourly, daily, and monthly rainfall data, respectively, is presented in Figure 6. The annual RE derived from the daily gauge data showed a obvious interannual variation, and the RE values ranged from 6893 MJ∙mm/ha∙h in 2007 to 14,637 MJ∙mm/ha∙h in 1998, with the average of 10,134 MJ∙mm/ha∙h during 1998–2012. The RE estimates derived from TRMM daily data showed a similar variability characteristic to the daily gauge data. However, the time series calculated by the TRMM 3-hourly data was obviously low, which ranged between 2557 and 7040 MJ∙mm/ha∙h. In addition, the two RE series based on the MFI approach (derived from the monthly gauge data and the TRMM 3B43 data, respectively) had roughly

overestimate the low values but underestimate the high values of monthly RE.

**Figure 6.** Comparison of annual rainfall erosivity estimated by rainfall data with different temporal resolutions. **Figure 6.** Comparison of annual rainfall erosivity estimated by rainfall data with different temporal resolutions.

At the annual scale, the comparison of the ME, RMSE and BIAS of RE estimation from different TRMM rainfall products and rain gauges data are shown in Table 2, and the scatter plots of the RE At the annual scale, the comparison of the ME, RMSE and BIAS of RE estimation from different TRMM rainfall products and rain gauges data are shown in Table 2, and the scatter plots of the RE estimates from TRMM rainfall products and the rain gauge data are shown in Figure 7. The TRMM 3-hourly data presented large errors for annual RE estimation, with an ME value of −5516 MJ·mm/ha·h, RMSE value of 5686 MJ·mm/ha·h and BIAS value of −54.4%. Moreover, the low slope value (0.49) of scatter fitting curve further revealed that the TRMM 3-hourly rainfall product significantly underestimated the annual RE. Comparatively, the TRMM daily and 3B43 products performed better for the annual RE estimation, with ME values of 1858 and −85 MJ·mm/ha·h, RMSE values of 2114 and 1336 MJ·mm/ha·h, and BIAS values of 18.3% and −0.85%, respectively (Table 2). Moreover, the R<sup>2</sup> values of the scatter fitting curve between the TRMM RE and rain gauge RE were as high as 0.86 and 0.92 for the TRMM daily and 3B43 data, respectively. Figure 7b also reveals that the TRMM 3B43 product tended to overestimate the low values but underestimate the high values of annual RE.


**Table 2.** Results of bias analysis for annual rainfall erosivity from the TRMM 3h, daily and 3B43 rainfall data.

rainfall data.

Mean

ME

RMSE

annual RE.

estimates from TRMM rainfall products and the rain gauge data are shown in Figure 7. The TRMM 3-hourly data presented large errors for annual RE estimation, with an ME value of −5516 MJ∙mm/ha∙h, RMSE value of 5686 MJ∙mm/ha∙h and BIAS value of −54.4%. Moreover, the low slope value (0.49) of scatter fitting curve further revealed that the TRMM 3-hourly rainfall product significantly underestimated the annual RE. Comparatively, the TRMM daily and 3B43 products performed better for the annual RE estimation, with ME values of 1858 and −85 MJ∙mm/ha∙h, RMSE values of 2114 and 1336 MJ∙mm/ha∙h, and BIAS values of 18.3% and −0.85%, respectively (Table 2). Moreover, the R2 values of the scatter fitting curve between the TRMM RE and rain gauge RE were as high as 0.86 and 0.92 for the TRMM daily and 3B43 data, respectively. Figure 7b also reveals that the TRMM 3B43 product tended to overestimate the low values but underestimate the high values of

**Table 2.** Results of bias analysis for annual rainfall erosivity from the TRMM 3h, daily and 3B43

(MJ∙mm/ha∙h) 4618 11992 10134 9866 9951

(MJ∙mm/ha∙h) −5516 1858 / −85 /

 **TRMM 3h TRMM Daily Gauge Daily TRMM 3B43 Gauge Monthly** 

**Figure 7.** Scatter plots of annual rainfall erosivity from (**a**) TRMM 3h and daily products and (**b**) Table 3. B43. **Figure 7.** Scatter plots of annual rainfall erosivity from (**a**) TRMM 3 h and daily products and (**b**) TRMM 3B43.

Furthermore, the assessment of TRMM rainfall products for annual RE estimation was extended to utilize the indicators of FBI, FAR, POD and ETS, which were analyzed at different RE thresholds of 2000, 4000, 6000, 8000, 10,000, 12,000 and 14,000 MJ∙mm/ha∙h, respectively. As shown in Figure 8, TRMM 3-hourly product tended to underestimate the annual RE, with the decreasing FBI values, especially for heavy RE; however, there was a systematic overestimation of annual RE by the TRMM daily data. The POD of the TRMM daily data kept changing around 1.0, which indicated a good performance for RE detection; however, its FAR values increased from 0 to 0.46 as the RE threshold increased, which meant that the proportion of miscalculated values increased. The TRMM 3-hourly data performed poorly, with low POD and high FAR values, especially for heavy RE. Overall, the TRMM 3B43 product performed best in terms of estimating light and heavy RE among the three TRMM rainfall datasets with the highest ETS scores. Furthermore, the assessment of TRMM rainfall products for annual RE estimation was extended to utilize the indicators of FBI, FAR, POD and ETS, which were analyzed at different RE thresholds of 2000, 4000, 6000, 8000, 10,000, 12,000 and 14,000 MJ·mm/ha·h, respectively. As shown in Figure 8, TRMM 3-hourly product tended to underestimate the annual RE, with the decreasing FBI values, especially for heavy RE; however, there was a systematic overestimation of annual RE by the TRMM daily data. The POD of the TRMM daily data kept changing around 1.0, which indicated a good performance for RE detection; however, its FAR values increased from 0 to 0.46 as the RE threshold increased, which meant that the proportion of miscalculated values increased. The TRMM 3-hourly data performed poorly, with low POD and high FAR values, especially for heavy RE. Overall, the TRMM 3B43 product performed best in terms of estimating light and heavy RE among the three TRMM rainfall datasets with the highest ETS scores. *Remote Sens.* **2020**, *12*, x FOR PEER REVIEW 11 of 20

**Figure 8.** Changes in the frequency bias index (**a**), the false alarm ratio (**b**), the probability of detection (**c**) and the equitable threat score (**d**) at different rainfall erosivity thresholds. **Figure 8.** Changes in the frequency bias index (**a**), the false alarm ratio (**b**), the probability of detection (**c**) and the equitable threat score (**d**) at different rainfall erosivity thresholds.

*3.3. Performance of Spatial Pattern of RE* 

of annual RE.

Figure 9. The distribution of annual gauge RE, both from daily and monthly gauge rainfall data, in different areas was quite different. The high RE was mainly distributed in the northeast (with annual RE over 12,000 MJ∙mm/ha∙h) and the low RE values in the southwest of the Poyang Lake basin (approximately 6000–7000 MJ∙mm/ha∙h) (Figure 9a,d). Additionally, the annual RE from TRMM 3-hourly, daily and 3B43 rainfall products had good spatial consistency with that from the rain gauges data, although the high RE values obtained from the TRMM 3-hourly data covered the wider area than that from rain gauges data. This spatial consistency was further validated by the high coefficient of determination (R2) (0.63 for TRMM 3-hourly data, 0.72 for TRMM daily data, and 0.71 for TRMM 3B43 data) between the satellite pixels and the rain gauges within the grids (Figure 10). However, the slope values of the regression lines were 0.49 and 1.24, respectively, for TRMM 3-hourly and TRMM daily estimates. These values indicated that TRMM 3-hourly rainfall product significantly underestimated the annual RE, while TRMM daily rainfall product overestimated it. Comparatively, the TRMM 3B43 data performed best in terms of depicting the spatial characteristics

The spatial patterns of the average annual RE estimated from TRMM 3-hourly, daily and 3B43
