**1. Introduction**

Rainfall erosivity (RE) is a significant indicator of erosion capacity [1–3]. RE combines the effects of rainfall amount, duration, and intensity [4,5] and measures the potential ability of rainfall to erode soils [6,7]. Thus, RE is widely used in many models for the quantitative assessment of soil erosion and soil loss [6,8], such as the world famous and widely used model, the Universal Soil Loss Equation (USLE) [6] and its improved versions, RUSLE [9] and RUSLE2 [10], the Water Erosion Prediction Project model (WEPP) [11], the Soil Erosion Model for Mediterranean regions (SEMMED) [12], the European Soil Erosion Model (EUROSEM) [13], the Unit Stream Power-based Erosion Deposition model (USPED) [14], and so on. Accurate RE is critical in risk assessment of soil erosion and soil loss in the large-scale catchment, and it is also of great significance for agricultural management and sustainable land use planning [15–17].

The RE is conventionally calculated by a storm's kinetic energy and the maximum intensity of rainfall during a short time period (at least 30 min) [6]. Since such detailed information is difficult to obtain at standard meteorological stations [18], the traditional rainfall observations from rain gauges (i.e., daily, monthly, or annual rainfall data) have often been used to estimate the RE [19–25]. On the other hand, the rapid development of remote sensing technology improved the temporal and spatial resolutions and the accuracy of satellite-based rainfall products [26–28], which also greatly improved their applicability [28]. Currently, several global and regional satellite-based rainfall products with good temporal and spatial resolutions have been considered as a possible alternative to the traditional rain gauge observations in present and foreseeable future [29], which are also accepted as promising strategies for RE estimation.

The TRMM (Tropical Rainfall Measuring Mission) satellite was designed by America and Japan to measure the tropical and sub-tropical rainfall [30], which was the first satellite mission dedicated to increasing the understanding of distribution and variability of precipitation. TRMM carried multiple rain sensors, including one active sensor (precipitation radar, PR) and two passive sensors (the visible and infrared scanner, VIRS, and TRMM microwave imager, TMI) [31,32]. Multiple rainfall products are available from those individual sensors at varying spatial resolutions. Moreover, TRMM Multi-satellite Precipitation Analysis (TMPA) combined the data from TRMM-PR, VIRS, TMI with passive microwave, infrared and visible measurements available from national and international satellites, and could provide rainfall data series with the temporal resolution of 3-hourly and spatial resolution of 0.25◦ × 0.25◦ at the coverage area of global 50◦ S to 50◦ N [28,29]. Numerous studies have validated that TRMM products have acceptable accuracy [28,29,33–38], and good performance has been achieved using TRMM rainfall data in many research fields, including hydrological modeling [33,39–45],rainfall characteristics [35,46,47], weather processes [48,49], latent heat flux [50–52], extreme precipitation [53,54], and drought/flood monitoring [55–60].

Recently, several studies also have attempted to use TRMM rainfall products, as complementary rainfall data, for RE estimation and evaluated its performance. For example, the authors in [61] presented a new method which merged the daily rain gauges observations with the TRMM 3B42 data to estimate the RE across China, and their results indicated that a combination of TRMM and gauge data provided the RE estimates with the best accuracy when compared with block kriging gauges and TRMM alone. The research in [62] examined the suitability of TRMM precipitation data for mapping RE in Africa and revealed that the spatial estimates of mean annual RE can be well characterized by monthly satellite-based precipitation. Authors in [63] also developed a new method for calculating RE using 3-hourly TRMM precipitation data. However, these previous attempts and preliminary studies mainly focused on the estimation of RE using one product of TRMM rainfall and lacked a comparative assessment of RE results based on TRMM data with different temporal resolutions. It is not clear which temporal resolutions of TRMM rainfall products, i.e., 3-hourly, daily or monthly, is most suitable for calculating RE. This situation has hampered the extensive application of TRMM rainfall products for mapping RE, and also affected soil loss prediction and risk assessment of soil erosion to a certain extent.

Therefore, this study extends the previous studies and quantifies the seasonal distribution and annual change of RE in Poyang Lake basin, China based on three TRMM rainfall products (TRMM 3B42 3-hourly, daily, and 3B43 monthly products) and rain gauges data, respectively. Subsequently, the suitability of those TRMM rainfall products for RE estimation is assessed and evaluated by several different evaluation indices of bias of RE. The outcomes of this study are expected to provide some useful references for the further application of TRMM products in calculating and mapping RE, and it is also valuable for the soil loss prediction, risk assessment of soil erosion, as well as land use management.

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

#### *2.1. Study Area*

In this study, the Poyang Lake basin was selected as the study area, which is located on the south bank of the middle and lower reaches of the Yangtze River, China (28◦220–29◦450 N and <sup>115</sup>◦470–116◦45<sup>0</sup> E) (Figure 1). The basin covers an area of 1.62 <sup>×</sup> <sup>10</sup><sup>5</sup> km<sup>2</sup> , and is one of the regions in South China with the most serious soil erosion problems [64]. The lake mainly receives the inflow of Ganjiang River, Fuhe River, Xiushui River, Xinjiang River, Raohe River, as well as runoff from the alluvial plains around the lake, and flows into the Yangtze River. In which, the Ganjiang River is the

largest tributary of Poyang Lake water system and contributes about 55% of the total discharge into the lake [65]. The elevation of the basin vary from 30 m in the alluvial plains to more than 2200 m in the mountain area. The Poyang Lake basin is characterized by subtropical humid climate, with an average annual precipitation of 1626 mm and average temperature of 17.6 ◦C during 1960–2012. Generally, precipitation is mainly concentrated in the rainy season (during April–June), and the streamflow in rainy season accounts for more than 50% of total annual streamflow, but about only 13.7% during from October to the following January [66]. The spatial distribution of precipitation in the basin is also uneven, with the ratio of maximum to minimum ranging from 1.65 to 2.51. The highest annual rainfall was observed at Wuyuan station (3036 mm) in 1998 and the lowest was at Hukou station (776 mm) in 1978. The land use in the basin is mainly woodland, accounting for 46%, followed by shrubland and cropland, accounting for 25% and 24%, respectively (Figure 2). The area of grassland, town and open water is generally small [67]. largest tributary of Poyang Lake water system and contributes about 55% of the total discharge into the lake [65]. The elevation of the basin vary from 30 m in the alluvial plains to more than 2200 m in the mountain area. The Poyang Lake basin is characterized by subtropical humid climate, with an average annual precipitation of 1626 mm and average temperature of 17.6 °C during 1960–2012. Generally, precipitation is mainly concentrated in the rainy season (during April–June), and the streamflow in rainy season accounts for more than 50% of total annual streamflow, but about only 13.7% during from October to the following January [66]. The spatial distribution of precipitation in the basin is also uneven, with the ratio of maximum to minimum ranging from 1.65 to 2.51. The highest annual rainfall was observed at Wuyuan station (3036 mm) in 1998 and the lowest was at Hukou station (776 mm) in 1978. The land use in the basin is mainly woodland, accounting for 46%, followed by shrubland and cropland, accounting for 25% and 24%, respectively (Figure 2). The area of grassland, town and open water is generally small [67].

*Remote Sens.* **2020**, *12*, x FOR PEER REVIEW 3 of 20

**Figure 1. Figure 1.** The study area and the distribution The study area and the distribution of the rain gauges in the basin. of the rain gauges in the basin.

*Remote Sens.* **2020**, *12*, x FOR PEER REVIEW 4 of 20

**Figure 2.** The land use map of Poyang Lake basin. **Figure 2.** The land use map of Poyang Lake basin.

#### *2.2. Date 2.2. Date*

TRMM rainfall products used in this paper are the TRMM 3B42 3-hourly data, daily data and the 3B43 monthly data, respectively, which were derived from the National Aeronautics and Space Administration (NASA) Goddard Earth Sciences (GES) Data and Information Services Center (DISC) (https://disc.gsfc.nasa.gov/datasets). The ranges of these data cover the time period from 1 January 1998 to 31 December 2012, and the spatial resolutions are all 0.25° × 0.25°. According to statistics, there are about 270 grids (0.25° × 0.25°) in the study area. And for the comparison and evaluation of RE results based on TRMM rainfall data with different temporal resolutions, the observed daily rainfall data of 76 traditional ground-based rainfall stations in the basin covering the same period were obtained from the National Meteorological Information Center, China (NMIC) (http://data.cma.cn). The monthly gauged rainfall was also aggregated from these daily values. The spatial distribution of these rainfall stations is shown in Figure 1. TRMM rainfall products used in this paper are the TRMM 3B42 3-hourly data, daily data and the 3B43 monthly data, respectively, which were derived from the National Aeronautics and Space Administration (NASA) Goddard Earth Sciences (GES) Data and Information Services Center (DISC) (https://disc.gsfc.nasa.gov/datasets). The ranges of these data cover the time period from 1 January 1998 to 31 December 2012, and the spatial resolutions are all 0.25◦ × 0.25◦ . According to statistics, there are about 270 grids (0.25◦ × 0.25◦ ) in the study area. And for the comparison and evaluation of RE results based on TRMM rainfall data with different temporal resolutions, the observed daily rainfall data of 76 traditional ground-based rainfall stations in the basin covering the same period were obtained from the National Meteorological Information Center, China (NMIC) (http://data.cma.cn). The monthly gauged rainfall was also aggregated from these daily values. The spatial distribution of these rainfall stations is shown in Figure 1.

#### *2.3. Methods 2.3. Methods*

#### 2.3.1. Estimation of RE 2.3.1. Estimation of RE

Due to the difficult collection of kinetic energy and intensity of rainfall with a time resolution of 30 min, several alternative methods using the routine meteorological records of rainfall have been Due to the difficult collection of kinetic energy and intensity of rainfall with a time resolution of 30 min, several alternative methods using the routine meteorological records of rainfall have been

proposed to calculate RE. In this study, three different quantitative models based on 3-hourly, daily, and monthly rainfall were used to estimate monthly and annual RE, respectively.

The model based on the TRMM 3B42 3-hourly rainfall product was a model developed by Zhu et al. [63], which improved the basic formula of RE and made it suitable for TRMM data. TRMM products can be directly used as data sources for RE calculation. This improvement has been applied in many areas in China, such as Daling River basin, Liaoning Province, and achieved good performance. The model equation is [63]:

$$RE\_k = 0.29[1 - 0.72 \exp(-0.082i\_{wvr})] \cdot \Delta V \cdot I\_{180} \tag{1}$$

where *RE<sup>k</sup>* is a event-based rainfall erosivity; *iavr* is 3-hour average rainfall intensity from TRMM 3B42 3-hourly product; ∆*V* is the rainfall and *I*<sup>180</sup> is the maximum 180-min rainfall intensity.

The monthly RE was obtained by summing up all erosion events in a month:

$$RE\_m = \sum\_{k=1}^{m} RE\_k \tag{2}$$

The annual RE was the sum of monthly RE values in a year.

The model based on daily rainfall (TRMM 3B42 daily product and the daily gauged rainfall) used in this study was improved and developed by Zhang et al. [68]. The model was validated and widely applied in many regions in China [69,70] and was also recommended to calculate the soil loss in the first general suvey of soil and water conservation in China [71]. The model equations are [68]:

$$RE\_i = a \sum\_{j=1}^{k} \left( P\_j \right)^{\beta} \tag{3}$$

$$\beta = 0.8363 + \frac{18.177}{\overline{P}\_{d12}} + \frac{24.455}{\overline{P}\_{y12}} \tag{4}$$

$$
\alpha = 21.586 \beta^{-7.1891} \tag{5}
$$

where *RE<sup>i</sup>* is the RE value of half-month; *P<sup>j</sup>* is the erosive rainfall, according to the analysis results of observational data of China's rainfall and surface runoff, a daily rainfall amount that exceeds 12 mm is the standard for China's erosive rainfall (*P<sup>j</sup>* is the actual daily rainfall when rainfall ≥12 mm, otherwise, *Pj* is 0) [72]; α and β are coefficients to reflect the rainfall characteristics; *Pd*<sup>12</sup> and *Py*<sup>12</sup> are average daily and annual rainfall when daily rainfall ≥12 mm, respectively.

The monthly RE was obtained by summing up the *RE<sup>i</sup>* in a month, and the annual RE was the sum of monthly RE values in a year.

The model based on monthly rainfall (TRMM 3B43 product and the monthly gauged rainfall) was the Modified Fourier Index (MFI) approach. Several studies have shown that RE and the rate of erosion are strongly correlated with the MFI [19,73]. Therefore, the MFI has often been applied in the estimation of annual RE and in the development of soil loss maps in regional-scale erosion models [74]. Additionally, the MFI-based model was also recommended to establish erosion risk areas by Food and Agriculture Organization (FAO). Annual RE is estimated by the following equations [74]:

$$MFI = \sum\_{i=1}^{12} \frac{r\_i^2}{P} \tag{6}$$

$$RE = 0.3598MFI^{1.9462} \tag{7}$$

where *r<sup>i</sup>* is the monthly rainfall; *P* is the average annual rainfall. The coefficients 0.3598 and 1.9462 were obtained from the study of Zhang and Fu [69], which was suitable for Jiangxi Province (Poyang Lake basin), China.

In addition, the spatial distribution of RE from rain gauges data was interpolated by the inverse distance weighted (IDW) technique with a power of 2.

#### 2.3.2. Evaluating Index

To quantitatively evaluate the suitability of TRMM 3B42 3-hourly, daily and 3B43 products for estimating RE, several evaluating indices, including the correlation coefficient (R), the mean error (ME), the root mean squared error (RMSE), and the relative bias (BIAS), were selected to assess the systematic bias of RE estimation compared with the results from the rain gauges data. The Equations for R, ME, RMSE, and BIAS were as follow:

$$R = \frac{\sum\_{i=1}^{n} \left( \overline{\text{RE}\_{\text{TRMM}i} - \overline{\text{RE}\_{\text{TRMM}}}} \right) \left( \text{RE}\_{\text{gauge}} - \overline{\text{RE}\_{\text{gauge}}} \right)}{\sqrt{\sum\_{i=1}^{n} \left( \overline{\text{RE}\_{\text{TRMM}i}} - \overline{\text{RE}\_{\text{TRMM}}} \right)^{2}} \cdot \sqrt{\sum\_{i=1}^{n} \left( \overline{\text{RE}\_{\text{gauge}}} - \overline{\text{RE}\_{\text{gauge}}} \right)^{2}}} \tag{8}$$

$$ME = \frac{1}{n} \sum\_{i=1}^{n} \left( RE\_{TRMMi} - RE\_{gauge\\_i} \right) \tag{9}$$

$$RMSE = \sqrt{\frac{1}{n} \sum\_{i=1}^{n} \left(RE\_{TRMMi} - RE\_{gauge\\_i}\right)^2} \tag{10}$$

$$BIAS = \frac{\sum\_{i=1}^{n} (RE\_{TRMMi} - RE\_{gauge\\_i})}{\sum\_{i=1}^{n} RE\_{gauge\\_i}} \times 100\% \tag{11}$$

where *RETRMM i* is the value of RE obtained by TRMM products; *RE*gauge *<sup>i</sup>* is the value of RE obtained by rain gauges data; and *RETRMM* and *REgauge* are the average values of their respective series; *n* is the total number of data.

In addition, the accuracy of annual RE based on TRMM rainfall products were further assessed by four statistical indicators: (1) the frequency bias index (FBI), which indicates whether the TRMM rainfall products underestimate (FBI < 1) or overestimate (FBI > 1) the RE values, (2) the false alarm ratio (FAR), which measures the fraction of RE that is actually false alarms, (3) the probability of detection (POD), which provides the proportion of RE that is correctly estimated, and (4) the equitable threat score (ETS), which provides the fraction of RE that is correctly detected, adjusted for the number of hits He that could be expected due purely to random chance [75–77]. Further information on these indicators and their implications can be found in the studies of Li et al. [34], Koo et al. [77] and Getirana et al. [78]. Their values were calculated using Equations (12)–(16), respectively:

$$FBI = \frac{a+b}{a+c} \tag{12}$$

$$FAR = \frac{b}{a+b} \tag{13}$$

$$POD = \frac{a}{a+c} \tag{14}$$

$$ETS = \frac{a - He}{a + b + c - He} \tag{15}$$

$$He = \frac{(a+b)(a+c)}{N} \tag{16}$$

where *N* is the total number of the rainfall series; *a* is the number of REs that are correctly estimated by the TRMM rainfall products; *b* is the number of false signal (RE is detected by the TRMM rainfall products but not presented in gauges data); and *c* represents the number of REs that are not detected by the TRMM rainfall products. *Remote Sens.* **2020**, *12*, x FOR PEER REVIEW 7 of 20 products but not presented in gauges data); and *c* represents the number of REs that are not detected by the TRMM rainfall products.

Moreover, in order to quantify the ability of each dataset in predicting light and heavy RE, the FBI, POD, FAR, and ETS were calculated at different RE thresholds of 2000, 4000, 6000, 8000, 10,000, 12,000 and 14,000 MJ·mm/ha·h, respectively. Moreover, in order to quantify the ability of each dataset in predicting light and heavy RE, the FBI, POD, FAR, and ETS were calculated at different RE thresholds of 2000, 4000, 6000, 8000, 10,000, 12,000 and 14,000 MJ∙mm/ha∙h, respectively.

#### **3. Results 3. Results**

winter.

#### *3.1. Evaluation of the Intra-Annual Distribution of RE 3.1. Evaluation of the Intra-Annual Distribution of RE*

The comparison of monthly RE from the TRMM 3B42 3-hourly and daily products and the gauges daily rainfall is summarized in Figure 3. The rain gauges RE showed a clear seasonal variation. Specifically, the RE values during the period of April–June was the highest in the whole year, especially in June, with the maximum value up to 5000 MJ·mm/ha·h and an average of 2324 MJ·mm/ha·h. This period was also the main rainy season of the Poyang Lake Basin, the heavy rainfall or rainstorm events usually occurred in this period, which may lead to a high risk of soil erosion. The lowest value of RE mainly presented during December–January, with the average of less than 200 MJ·mm/ha·h. Figure 3 also shows that TRMM 3-hourly product had a significant systematic underestimation of monthly RE, especially during the period of April–June. The comparison of monthly RE from the TRMM 3B42 3-hourly and daily products and the gauges daily rainfall is summarized in Figure 3. The rain gauges RE showed a clear seasonal variation. Specifically, the RE values during the period of April–June was the highest in the whole year, especially in June, with the maximum value up to 5000 MJ∙mm/ha∙h and an average of 2324 MJ∙mm/ha∙h. This period was also the main rainy season of the Poyang Lake Basin, the heavy rainfall or rainstorm events usually occurred in this period, which may lead to a high risk of soil erosion. The lowest value of RE mainly presented during December–January, with the average of less than 200 MJ∙mm/ha∙h. Figure 3 also shows that TRMM 3-hourly product had a significant systematic underestimation of monthly RE, especially during the period of April–June.

**Figure 3.** Comparison of monthly rainfall erosivity (RE) from different rainfall data. **Figure 3.** Comparison of monthly rainfall erosivity (RE) from different rainfall data.

The changes of R, ME, RMSE, and BIAS of monthly RE from the TRMM 3B42 3-hourly and daily products are shown in Figure 4 and Table 1. The correlation coefficients had high variability in different months, the R values of TRMM 3B42 3-hourly data ranged from 0.72 to 0.93, while that of TRMM 3B42 daily data ranged from 0.76 to 0.95 (Figure 4d). The high values of R indicated that the RE estimates using TRMM rainfall products, regardless of 3-hourly or daily data, captured the change characteristics of RE. However, large errors were found in the TRMM 3-hourly data, with the ME ranging from −83 to −900 MJ∙mm/ha∙h, especially during the spring (−587 MJ∙mm/ha∙h) and summer months (−707 MJ∙mm/ha∙h). Positive errors were mainly found in the TRMM daily data, with the ME ranging between 233 and 308 MJ∙mm/ha∙h in spring and less than 109 MJ∙mm/ha∙h during second half of the year. This temporal pattern of errors could be presented more clearly The changes of R, ME, RMSE, and BIAS of monthly RE from the TRMM 3B42 3-hourly and daily products are shown in Figure 4 and Table 1. The correlation coefficients had high variability in different months, the R values of TRMM 3B42 3-hourly data ranged from 0.72 to 0.93, while that of TRMM 3B42 daily data ranged from 0.76 to 0.95 (Figure 4d). The high values of R indicated that the RE estimates using TRMM rainfall products, regardless of 3-hourly or daily data, captured the change characteristics of RE. However, large errors were found in the TRMM 3-hourly data, with the ME ranging from −83 to −900 MJ·mm/ha·h, especially during the spring (−587 MJ·mm/ha·h) and summer months (−707 MJ·mm/ha·h). Positive errors were mainly found in the TRMM daily data, with the ME ranging between 233 and 308 MJ·mm/ha·h in spring and less than 109 MJ·mm/ha·h during second half of the year. This temporal pattern of errors could be presented more clearly through the changes

performed better in summer, with a BIAS of only 3.0%; however, these data performed worse in

in the RMSE (Figure 4b), which was larger for the TRMM 3-hourly data than for the TRMM daily data. In addition, the changes in the relative errors of the TRMM 3-hourly data were weak in different months, with a BIAS of approximately −49%. The TRMM daily data performed better in summer, with a BIAS of only 3.0%; however, these data performed worse in winter. *Remote Sens.* **2020**, *12*, x FOR PEER REVIEW 8 of 20

**Figure 4.** Monthly changes in (**a**) the mean error (ME), (**b**) the root mean squared error (RMSE), (**c**) the relative bias (BIAS) and (**d**) the correlation coefficient (R). **Figure 4.** Monthly changes in (**a**) the mean error (ME), (**b**) the root mean squared error (RMSE), (**c**) the relative bias (BIAS) and (**d**) the correlation coefficient (R).

**Table 1.** Seasonal changes in bias between Tropical Rainfall Measuring Mission products (TRMM) and rain gauges data. **Index Spring Summer Autumn Winter TRMM 3h TRMM Daily Gauge Daily TRMM 3h TRMM daily Gauge Daily TRMM 3h TRMM Daily Gauge Daily TRMM 3h TRMM Daily Gauge Daily**  Mean (MJ∙mm/ha∙h) 619 1475 1206 741 1492 1448 173 502 409 179 526 312 ME (MJ∙mm/ha∙h) −587 269 / −707 44 / −236 93 / −133 214 / RMSE (MJ∙mm/ha∙h) 616 317 / 734 170 / 277 106 / 171 258 / BIAS (%) −48.6 22.3 / −48.8 3.0 / −57.7 22.7 / −42.6 68.5 / R 0.84 0.91 / 0.92 0.91 / 0.92 0.97 / 0.81 0.84 / Figure 5 shows the distribution of monthly RE values in different categories and their proportion to annual RE. The small RE category (0−500 MJ∙mm/ha∙h) had the largest frequency, occurring in 41% of all months, and this category contributed to approximately 11% of the total annual RE in the rain gauges data. The RE estimates from the TRMM 3-hourly data were much larger than that from the rain gauges data. Its frequency was over 71% for the small RE category, and Figure 5 shows the distribution of monthly RE values in different categories and their proportion to annual RE. The small RE category (0−500 MJ·mm/ha·h) had the largest frequency, occurring in 41% of all months, and this category contributed to approximately 11% of the total annual RE in the rain gauges data. The RE estimates from the TRMM 3-hourly data were much larger than that from the rain gauges data. Its frequency was over 71% for the small RE category, and the corresponding contribution rate was as high as 37% of the total annual RE. The statistics for the TRMM daily data were slightly smaller than those from rainfall gauge data, regardless of frequency and contribution rate. The second largest category was 500 < RE < 1000 MJ·mm/ha·h, with approximately 25% occurrence and 20.5% of the contribution to the total annual RE in the rain gauges data. Although the frequency estimated by the TRMM 3-hourly data was almost consistent with that of the gauge data, its contribution rate was large, accounting for as much as 41.1% of the total annual RE. For the TRMM daily data, the frequency and contribution were close to the results of the rain gauges data. It is found that both frequency and contribution estimated by the TRMM daily data generally became equivalent to that from the rain gauges data for middle and large RE categories (RE > 1000 MJ·mm/ha·h). However, both frequency and contribution rates from the TRMM 3-hourly data were grossly underestimated, especially in the categories of RE > 2000 MJ·mm/ha·h. Figure 5 indicates that the estimates of monthly RE using the TRMM 3B42 daily product were closer to the results of the rain gauges data. The TRMM 3-hourly data tended to overestimate the low values but underestimate the high values of monthly RE.

daily data generally became equivalent to that from the rain gauges data for middle and large RE categories (RE > 1000 MJ∙mm/ha∙h). However, both frequency and contribution rates from the TRMM 3-hourly data were grossly underestimated, especially in the categories of RE > 2000 MJ∙mm/ha∙h. Figure 5 indicates that the estimates of monthly RE using the TRMM 3B42 daily

the corresponding contribution rate was as high as 37% of the total annual RE. The statistics for the TRMM daily data were slightly smaller than those from rainfall gauge data, regardless of frequency and contribution rate. The second largest category was 500 < RE < 1000 MJ∙mm/ha∙h, with approximately 25% occurrence and 20.5% of the contribution to the total annual RE in the rain gauges data. Although the frequency estimated by the TRMM 3-hourly data was almost consistent


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

**Table 1.** Seasonal changes in bias between Tropical Rainfall Measuring Mission products (TRMM) and rain gauges data.

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