*3.3. Performance of Spatial Pattern of RE*

The spatial patterns of the average annual RE estimated from TRMM 3-hourly, daily and 3B43 rainfall data are shown in Figure 9. As a reference case for comparative purposes, the spatial distributions of RE from rain gauges data (both daily and monthly data), which were obtained by a interpolation method of inverse distance weighting (IDW) with a power of 2, are also shown in 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 (R<sup>2</sup> ) (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 of annual RE. *Remote Sens.* **2020**, *12*, x FOR PEER REVIEW 12 of 20

**Figure 9.** Spatial patterns of average annual RE estimated by rainfall data with different temporal resolutions. **Figure 9.** Spatial patterns of average annual RE estimated by rainfall data with different temporal resolutions.

**Figure 10.** Scatter plots of annual rainfall erosivity at rain gauges against their nearest satellite pixel.

Figure 11 shows the spatial distributions of four evaluating indices values (R, ME, RMSE, and BIAS) of annual RE estimation from TRMM rainfall products for every rain station. The statistical distributions of stations in different categories of evaluation indices were summarized in Table 3. The annual RE from the TRMM daily and 3B43 data correlated well with that from the rain gauges data, and their R values exceeded 0.8 at 45 (59.2%) and 46 (60.5%) of the 76 stations, respectively. The number of stations with R > 0.8 was only 20 (26.3%) for the TRMM 3-hourly data. However, all three

**Figure 10.** Scatter plots of annual rainfall erosivity at rain gauges against their nearest satellite pixel. **Figure 10.** Scatter plots of annual rainfall erosivity at rain gauges against their nearest satellite pixel.

Figure 11 shows the spatial distributions of four evaluating indices values (R, ME, RMSE, and BIAS) of annual RE estimation from TRMM rainfall products for every rain station. The statistical distributions of stations in different categories of evaluation indices were summarized in Table 3. The annual RE from the TRMM daily and 3B43 data correlated well with that from the rain gauges data, and their R values exceeded 0.8 at 45 (59.2%) and 46 (60.5%) of the 76 stations, respectively. The number of stations with R > 0.8 was only 20 (26.3%) for the TRMM 3-hourly data. However, all three Figure 11 shows the spatial distributions of four evaluating indices values (R, ME, RMSE, and BIAS) of annual RE estimation from TRMM rainfall products for every rain station. The statistical distributions of stations in different categories of evaluation indices were summarized in Table 3. The annual RE from the TRMM daily and 3B43 data correlated well with that from the rain gauges data, and their R values exceeded 0.8 at 45 (59.2%) and 46 (60.5%) of the 76 stations, respectively. The number of stations with R > 0.8 was only 20 (26.3%) for the TRMM 3-hourly data. However, all three TRMM rainfall products reflected similar spatial patterns of R, i.e., the most stations with large R located in the northeast of the Poyang Lake basin.


**Table 3.** Statistical distribution of bias of annual rainfall erosivity from TRMM 3h, daily and 3B43 rainfall data.

*Remote Sens.* **2020**, *12*, x FOR PEER REVIEW 14 of 20

**Figure 11.** Spatial distributions of R (**a**,**b**,**c**), ME (**d**,**e**,**f**), RMSE (**g**,**h**,**i**) and BIAS (**j**,**k**,**l**) of annual RE estimation from TRMM 3h (**a**,**d**,**g**,**j**), daily (**b**,**e**,**h**,**k**) and 3B43 (**c**,**f**,**i**,**l**) products. **Figure 11.** Spatial distributions of R (**a**–**c**), ME (**d**–**f**), RMSE (**g**–**i**) and BIAS (**j**–**l**) of annual RE estimation from TRMM 3h (**a**,**d**,**g**,**j**), daily (**b**,**e**,**h**,**k**) and 3B43 (**c**,**f**,**i**,**l**) products.

The ME values varied considerably in three TRMM data estimates. TRMM 3-hourly data showed negative MEs in all examined pixels in the basin, with the ME falling into the class of −3000–0 MJ·mm/ha·h at 6 (7.9%) stations and <−3000 MJ·mm/ha·h at 70 (92.1%) stations. However, the ME in the TRMM daily data showed positive errors at 71 (93.4%) of the 76 stations, 25 (32.9%) of which were larger than 3000 MJ·mm/ha·h. Moreover, the stations with a large ME (both negative in the TRMM 3-hourly and positive in the TRMM daily estimates) were primarily located in northern parts of the basin. TRMM 3B43 generally presented a small error, with MEs ranging between −3000 and 3000 MJ·mm/ha·h, and the stations with positive MEs (35 stations and accounting for 46.1%) were mainly located in middle and southern areas; furthermore, stations with negative MEs (41 stations and accounting for 53.9%) were distributed in the northern parts of the basin. The RMSE of TRMM 3-hourly data for more than 60% of stations (46 stations) was greater than 5000 MJ·mm/ha·h, and 39.5% of stations (30 stations) had RMSEs between 2000 and 5000 MJ·mm/ha·h. The number of stations with RMSE > 5000 MJ·mm/ha·h greatly decreased to 6 (7.9%) and 12 (15.8%) in the TRMM daily and 3B43 estimates, respectively; moreover, 7 (9.2%) stations and 14 (18.4%) stations had RMSE values smaller than 2000 MJ·mm/ha·h. As for the BIAS, its spatial distribution was almost the same as that of ME; that is, all examined pixels had negative BIAS values in the TRMM 3-hourly estimates, and more than 93% of stations (71 stations) showed positive BIAS values in the TRMM daily estimates. TRMM 3B43 generally presented a small BIAS, and positive values (33 stations and accounting for 43.4%) were mainly found in the middle and southern areas, while negative values (41 stations and accounting for 53.9%) were distributed in the north area of the basin.

#### **4. Discussion**

Previous results revealed that the largest monthly RE values were mainly concentrated in June, followed by that in May, and the smallest RE typically presented in December. The intra-annual distribution characteristics of RE corresponded to changes of precipitation in which more than 45% of the annual rainfall was concentrated during April–June. Both the TRMM 3B42 3-hourly and daily products depicted the intra-annual distribution characteristic correctly, i.e., greater than 70% of RE occurred during summer and spring, and only approximately 10% was concentrated in winter. However, the TRMM daily data performed better in summer, with a small BIAS (3.0%), and performed worse in winter, with a BIAS of 68.5%. This result was mainly associated with the seasonality of accuracy in TRMM rainfall products. Many researches have testified that the accuracy of TRMM rainfall products was influenced by season, rain type and climatological factors [79–82]. For example, the study of Han et al. [83] in urban areas revealed that TRMM precipitation had the higher accuracy during the warm seasons and there was a good correlation between the increasing temperature and the increasing accuracy of TRMM data. Wang et al. [45] noted that, compared with other satellite-based rainfall estimates, the TRMM performed best during the wet season. Ward et al. [84] also pointed out that TRMM 3B42 products may underestimated the rainfall in the dry season. For the TRMM 3-hourly data, this study revealed that it had the significant underestimation of monthly RE values, especially both the frequency and the contribution rates of high values of monthly RE were obviously underestimated. This result was principally associated with the underestimating of TRMM 3-hourly estimates for larger rainfall events, such as high-intensity storm events or heavy rainfall events [83]. On the other hand, the estimated RE from the TRMM 3-hourly data was compared with the results derived from the daily gauges data in this study. Differences in estimation methods of RE may inevitably resulted in systematic bias, as has been mentioned in many previous studies [85,86].

At the annual scale, this study found that TRMM 3B43 data performed best in terms of estimating annual RE, with the ME of −85 MJ·mm/ha·h, the RMSE of 1336 MJ·mm/ha·h, and the BIAS of −0.85%. This result was consistent with many previous studies on the accuracy of TRMM products. Dinku et al. [87] compared and evaluated the TRMM 3B43 data over Ethiopia with other satellite-based rainfall products and revealed that the TRMM 3B43 had the highest accuracy with the small BIAS (<10%) and RMSE (about 25%). Guo and Liu [88] pointed out that the accuracy of TRMM 3B43 was

higher than that of TRMM 3B42 and 3B42RT in Poyang Lake basin. Fleming et al. [89] found that, in Australia, the TRMM 3B43 data was highly correlated (with R of higher than 0.80) with gridded rain gauges data during 1998–2007, especially the correlation was strongest in summer. Cao et al. [36] reported that the TRMM 3B43 product performed best in the Yangtze River Delta of China, with the BIAS values ranging between −10% and 10% and the R of 0.88 at an annual scale. The study by Semire et al. [90] in Malaysia also received similar results.

Spatially, this study revealed that all three TRMM rainfall products generally captured the overall spatial pattern of annual RE, which had good spatial consistency with results from rain gauges data. However, TRMM 3-hourly data significantly underestimated the RE, while the TRMM daily data overestimated the RE. The TRMM 3B43 data performed best in terms of depicting the spatial characteristics of annual RE. The spatial biases may be related to the weak ability of the TRMM 3-hourly and daily rainfall products to detect heavy or extreme precipitation, which occurred frequently in the northern regions of the Poyang Lake basin [91–93].

## **5. Conclusions**

This work quantified the RE in the Poyang Lake basin based on three TRMM rainfall products and investigated their suitability for RE estimation compared with the results obtained from the traditional gauges rainfall. The results showed that TRMM 3B42 3-hourly product had a significant systematic underestimation of monthly RE, especially during the period of April–June for the large values. The TRMM 3B42 daily product seem to have better performance, especially in the summer, with a small BIAS (3.0%). At the annual scale, the TRMM 3-hourly data presented large errors in estimating the annual RE, with an ME of −5516 MJ·mm/ha·h, an RMSE of 5686 MJ·mm/ha·h and a BIAS of −54.4%. Comparatively, the TRMM 3B42 daily and 3B43 data had smaller errors, with the ME values of 1858 and −85 MJ·mm/ha·h, the RMSE values of 2114 and 1336 MJ·mm/ha·h, and the BIAS values of 18.3% and <sup>−</sup>0.85%, respectively. 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. A spatial performance analysis showed that the TRMM 3B42 3-hourly, daily and 3B43 rainfall products could correctly reflect the spatial patterns of the average annual RE, with spatial correlation coefficients of 0.63 for TRMM 3-hourly, 0.72 for TRMM daily, and 0.71 for TRMM 3B43 data. The slopes of the regression lines showed that TRMM 3-hourly product significantly underestimated the annual RE but overestimated the annual RE when using the TRMM daily data.

Finally, it is also important to recognize that this study is only an attempt at evaluating the suitability of TRMM products with different temporal resolution for RE estimation quantitatively. The outcomes of this study help in enhancing the understanding of the accuracy of use TRMM rainfall products to estimate RE. However, the study needs further deeper analyses and investigations; the above preliminary conclusions are derived only based on the given period and the characteristics of the region. Applying the conclusions drawn in this study to other regions should be considered with caution.

**Author Contributions:** Conceptualization, X.L. and Z.L.; Data curation, Z.L. and Y.L.; Formal analysis, X.L. and Z.L.; Funding acquisition, X.L. and Y.L.; Investigation, X.L.; Methodology, X.L.; Project administration, X.L.; Resources, X.L.; Software, X.L.; Validation, Z.L.; Visualization, Y.L.; Writing—original draft, X.L.; Writing—review & editing, Z.L. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by the National Key Research and Development Project, grant number 2018YFE0206400, and the National Natural Science Foundation of China, grant number 41871093.

**Conflicts of Interest:** The authors declare no conflict of interest.
