# Spatial Distribution and Temporal Trends of Rainfall Erosivity in Three Gorges Reservoir Area of China

Authors: Huiying Liu; Guanhua Zhang; Pingcang Zhang; Shengnan Zhu
Journal: Mathematical Problems in Engineering
 (2020)

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## Abstract

Rainfall erosivity is a key factor to predict soil erosion rate in universal soil loss equation (USLE) and revised USLE (RUSLE). Understanding rainfall erosivity characteristics, especially its spatial distribution and temporal trends, is essential for soil erosion risk assessment and soil conservation planning. In this study, the spatial-temporal variation of rainfall erosivity in the Three Gorges Reservoir Area (TGRA) of China during 1960–2010, at annual and seasonal scales, was explored based on daily rainfall data from 40 stations (26 meteorological stations and 14 hydrologic stations). The Mann–Kendall test and Co–kriging interpolation method were applied to detect the temporal trends and spatial patterns. The results showed that TGRA’s annual rainfall erosivity increased from west, south, and east to the north-central, ranging from 3647.0 to 10884.8 MJ·mm·ha−1·h−1 with an average value of 6108.1 MJ·mm·ha−1·h−1. The spatial distribution of summer and autumn rainfall erosivity was similar to the pattern of annual rainfall erosivity. Summer is the most erosive season among four seasons, accounting for 53% of the total annual rainfall erosivity, and winter is the least erosive season. July is the most erosive month with an average of 1327.3 MJ·mm·ha−1·h−1, and January is the least erosive month. Mean rainfall erosivity was 5969.2 MJ·mm·ha−1·h−1 during 1960–2010, with the lowest value of 3361.0 MJ·mm·ha−1·h−1 in 1966 and highest value of 8896.0 MJ·mm·ha−1·h−1 in 1982. Mann–Kendall test showed that the annual rainfall erosivity did not change significantly across TGRA. Seasonal rainfall erosivity showed a significant decrease in autumn and insignificant decrease in summer and winter. Monthly rainfall erosivity in TGRA showed insignificant increases from Jun to Jul and then underwent decreases from Aug to Nov. and from Dec to Feb and it rose again in Feb reaching a 0.01 level significance. The daily rainfall data of supplemental stations is very useful to interpolate rainfall erosivity map, which could help to find the credible maximum and minimum value of TGRA. In total, the findings could provide useful information both for soil erosion prediction, land management practices, and sediment control project of TGRA.


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## Body

## 1. Introduction

Soil erosion is recognized as a serious eco-environmental problem of world-wide [1]. Universal soil loss equation (USLE) and its revised version (RUSLE and RUSLE2) [2, 3] were commonly used to predict soil erosion, then to assess soil erosion risk, and evaluate the effectiveness of soil conservation measures [4, 5]. Rainfall erosivity (R factor) is one of the important factors influencing soil erosion [6, 7]. It represents the ability of rainfall to detach soil particles and erode the landscape and is determined by rainfall maximum 30-min intensity (I30) and its kinetic energy (E), classically expressed as EI30 in USLE and RUSLE [3, 6]. Wischmeier and Smith [6] developed the first iteration of the modern rainfall erosivity index used today [2, 6, 7] and has also proved EI30’s applicability in the Loess Plateau of China during the 1980s [8, 9]. However, EI30 is difficult to determine and the basic data involved are not readily available in many parts of the world as it relies much more on long-term rainfall data of high temporal resolution [3, 6, 10]. Consequently, some simple algorithms were developed to calculate R-factor relying on daily rainfall [11–13] or monthly rainfall [14], among which, half-month [15] and month models [13, 14] were the most widely used ones [11, 15]. Furthermore, this simplified model was adopted by the Chinese government in First National Census for Water [16]. Nowadays, this simplified model has been used worldwide [11, 17–20] to explore the spatial distribution and temporal trends of R factor, including China, both on the national [19] and regional scales [21–26].Due to the rapid growth of population, coupling with the widespread deforestation and expansion of agricultural land during the last century [5], Three Gorges Reservoir Area (TGRA) has become one of the most severely erosive areas in the Yangtze River basin [21]. It is thus very necessary to explore both the temporal (when) and spatial (where) characteristics of rainfall erosivity in for making soil conservation and sediment control strategies. However, the spatial and temporal coverage of pluviograph data are usually very scarce because of limited data span and expensive cost. Lacking of long-term rainfall intensity data makes the USLE and RUSLE difficult to be applied rationally in this region. Although some researchers had used this simplified model in some tributaries of Yangtze River basin [27–31], evaluation of R factor has not been well documented in TGRA. There are still some different opinions on the spatial-temporal variations among them [30–33]. The analysis about spatial distribution of R factor in their studies has not been well demonstrated and was insufficient to answer the spatial and temporal distribution characteristics of rainfall erosivity in TGRA. Furthermore, different data sources and time series of rainfall records resulted in significant differences in spatial distribution and annual value of R in TGRA [27–30]. Daily rainfall data, downloaded from China Meteorological Data Sharing Service System, is the most popular choice for most scholars studying R factor in TGRA [29, 30]. Daily rainfall data from hydrological gauging station also are the primary choice of other researchers [32, 34]. The diverse spans of rainfall records impose restriction on spatial-temporal variations of R factor when the previous researches were compared and analyzed. Nevertheless, the length of rainfall records does influence the confidence level for annual R factor, as the data series should have more than 20 years of record in order to include dry and wet climate periods [2, 3, 33]. It is well known that limited or scarce stations also restrict the generalization and application of research findings [29, 30]. More importantly, the previous studies indicated an insignificant decreasing trend in annual precipitation accompanied by an increasing R factor in sub-basin of TGRA during 2001–2010 [31, 32, 34], which potentially results in a higher water erosion risk in TGRA. The features of R factor are closely related to soil erosion and sediment yield which flows into the Three Gorges Reservoir.Although Wu et al. and Wang [29, 30] constructed the spatial distribution of R factor in TGRA, the analysis about sub-basins in their study was too weak to answer the spatial and temporal distribution of R factor. There remains a need, therefore, to provide an assessment of R factor and guide the watershed planning of soil conservation measures in subregions of TGRA. It is very critical to analyze systematical the spatial distribution and temporal trends of R factor in TGRA based on the same data span, data sources, and calculating method.Therefore, the specific objectives of this study are as follows: (1) to examine the spatial distribution of annual and seasonalR factors of TGRA combined meteorological stations with hydrological rain gauging stations and (2) to characterize the temporal trends of R factor for different time-scales in the light of the same data span of 1960–2010. The results in this study offer a relatively reliable R value on the soil erosion prediction in TGRA and provide an applicable spatial distribution of R factor for the evaluation of the effectiveness of soil conservation measures.


## 2. Materials and Methods

### 2.1. Study Area

TGRA is located at the end of the upper Yangtze River (106°16′–111°28′E, 28°56′–31°44′N) (Figure1) and consists of 22 counties (cities) or districts of Chongqing municipality and Hubei province with an area of 58000 km2 [29, 30, 35]. It is characterized by a humid subtropical monsoon climate with an obvious seasonality. The annual precipitation ranges from 755.0 to 1786.0 mm with 60% of falling between June and September during 1960–2010. TGRA has an altitude ranging from -22 to 3096 m a.s.l. and the mean altitude is nearly 800 m a.s.l. with a mean temperature of 15–18°C. Mountainous terrain occupies over 90% of the total region [35]. The main soil types are purple, yellow, yellow brown, and so on. Erodible purple soil is the dominant soil type. Highly erodible bedrock, including purple sandstone and shale, crops out throughout much of the area. The total eroded area was 38800 km2, accounting for 66.8% of the study region in the mid-1980’s (Water Resources Ministry, 2003). Consequently, in 1989, this area was selected for the testing zone of measures designed for soil erosion control, and it has in subsequent years been the subject of a succession of conservation projects. The China Bulletin of Soil and Water Conservation (2017) showed that soil erosion area of the TGRA was about 23000 km2, in which moderate erosion and strong erosion were 41.27% and 10.27%, and the extremely strong erosion and severe erosion were 4.20% and 1.14%, respectively.Figure 1
Geographical location of Three Gorges Reservoir Area and rain gauge stations.In order to deeply analyze the rainfall erosivity distribution characteristics, the study region was divided into seven subregions as shown in Figure1. Subregion A includes the Dong River and the Longxi River Basin, subregion B the Mudong River and part of Wujiang River Basin, subregion C the Xiaojiang River Basin, subregion D the Long River Basin, subregion E the Tangxi and Daning River Basin, subregion F the Modaoxi and Daxi River Basin, and subregion G the Hubei province section of TGRA. In Yangtze River Basin, the seasons were divided as follows: spring was from March to May, summer June to August, autumn September to November, and winter December to February of the following year.


### 2.2. Precipitation Data Collection

Rainfall data of 1960–2010 were collected from 40 stations (Figure1). Two data sources were employed: one is daily rainfall data, downloaded from China Meteorological Data Sharing Service System (http://cdc.cma.gov.cn), which includes 51 years’ (1960–2010) data of 26 continuous series precipitation stations; another one is excerpted from China Hydrological Almanac issued by Yangtze River Water Resources Committee of China which contains 41 years’ (1960–1990, 2001–2010) data of 14 discontinuous series precipitation stations. During 1991–2000, the precipitation records from China Hydrological Almanac are not available because of the changed policy and expensive cost. The precipitation records from China Meteorological Data Sharing Service System include 17 rain gauge stations within the TGRA and 9 stations from surrounding areas (Figure 1). All 40 stations were selected to ensure reliability, continuity, and availability of long-term data series in the study region.


### 2.3. Methods

#### 2.3.1. Rainfall Erosivity Calculation

As mentioned above, continuous rainfall data series with a high time resolution for classical algorithm ofR factor (USLE R factor) are rarely available and daily rainfall data have been widely used worldwide to estimate R factor. Zhang and Fu [15] compared five simple models for estimating R factor based on average annual rainfall, average monthly rainfall, and daily rainfall data, respectively and then proposed a new daily rainfall model to estimate R factor which was subsequently widely used in China. The daily rainfall model was expressed as(1)Rk=α∑i=1jPikβ,where Rk is the rainfall erosivity of the kth half-month, MJ·mm·ha−1·h−1; k = 1, 2, …, 24; Pik is the effective rainfall for day i of the kth half-month, and it is the actual rainfall when the actual rainfall is higher than 12 mm, otherwise, it is considered to be 0 [36]; j is the number of days in the kth half-month, j = 13, 14, 15, 16; α and β are parameters determined by the following formulas:(2)β=0.8363+18.144Pd12+24.455Py12,(3)α=21.586β−7.1891,where Pd12 is the average daily rainfall which is greater than 12 mm and Py12 is the annual average of erosive rainfall. The monthly, seasonal, and annual mean R values were successively computed based on equations (1)–(3).


#### 2.3.2. Trend Analysis of Rainfall Erosivity

The Mann–Kendall trend test [37, 38] has been widely applied to meteorological time series because it could identify monotonic trends of a time-series [21, 39, 40]. It is based on two useful indexes S and Z in the Mann–Kendall test to determine whether a time series of n data points has a significant trend. A positive Z indicates an upward trend and negative Z indicates a downward trend. The trend is statistically significant at α = 0.05 and 0.01 significance level when Z>1.96 and 2.58, respectively. The detailed procedure of the Mann–Kendall trend test is presented [40]and [39]. We used it to identify the trend of annual R factor at 26 sites spanning 51 years in the current study.


#### 2.3.3. Spatial Interpolation of Rainfall Erosivity

To understand the spatial distribution and temporal changes ofR factor, the mean annual, seasonal, and multiperiod R factors were interpolated through the Geostatistical Analyst module of the ArcGIS 10.2 (ESRI, America). The Co–kriging method was selected to interpolate the spatial distribution of R factor, because it can incorporate the neighboring primary data and make best prediction compared with other methods [21, 41]. Additionally, the Co-kriging method has been proved to be the most suitable interpolation method for rainfall erosivity in mainland China [24].


## 2.1. Study Area

TGRA is located at the end of the upper Yangtze River (106°16′–111°28′E, 28°56′–31°44′N) (Figure1) and consists of 22 counties (cities) or districts of Chongqing municipality and Hubei province with an area of 58000 km2 [29, 30, 35]. It is characterized by a humid subtropical monsoon climate with an obvious seasonality. The annual precipitation ranges from 755.0 to 1786.0 mm with 60% of falling between June and September during 1960–2010. TGRA has an altitude ranging from -22 to 3096 m a.s.l. and the mean altitude is nearly 800 m a.s.l. with a mean temperature of 15–18°C. Mountainous terrain occupies over 90% of the total region [35]. The main soil types are purple, yellow, yellow brown, and so on. Erodible purple soil is the dominant soil type. Highly erodible bedrock, including purple sandstone and shale, crops out throughout much of the area. The total eroded area was 38800 km2, accounting for 66.8% of the study region in the mid-1980’s (Water Resources Ministry, 2003). Consequently, in 1989, this area was selected for the testing zone of measures designed for soil erosion control, and it has in subsequent years been the subject of a succession of conservation projects. The China Bulletin of Soil and Water Conservation (2017) showed that soil erosion area of the TGRA was about 23000 km2, in which moderate erosion and strong erosion were 41.27% and 10.27%, and the extremely strong erosion and severe erosion were 4.20% and 1.14%, respectively.Figure 1
Geographical location of Three Gorges Reservoir Area and rain gauge stations.In order to deeply analyze the rainfall erosivity distribution characteristics, the study region was divided into seven subregions as shown in Figure1. Subregion A includes the Dong River and the Longxi River Basin, subregion B the Mudong River and part of Wujiang River Basin, subregion C the Xiaojiang River Basin, subregion D the Long River Basin, subregion E the Tangxi and Daning River Basin, subregion F the Modaoxi and Daxi River Basin, and subregion G the Hubei province section of TGRA. In Yangtze River Basin, the seasons were divided as follows: spring was from March to May, summer June to August, autumn September to November, and winter December to February of the following year.


## 2.2. Precipitation Data Collection

Rainfall data of 1960–2010 were collected from 40 stations (Figure1). Two data sources were employed: one is daily rainfall data, downloaded from China Meteorological Data Sharing Service System (http://cdc.cma.gov.cn), which includes 51 years’ (1960–2010) data of 26 continuous series precipitation stations; another one is excerpted from China Hydrological Almanac issued by Yangtze River Water Resources Committee of China which contains 41 years’ (1960–1990, 2001–2010) data of 14 discontinuous series precipitation stations. During 1991–2000, the precipitation records from China Hydrological Almanac are not available because of the changed policy and expensive cost. The precipitation records from China Meteorological Data Sharing Service System include 17 rain gauge stations within the TGRA and 9 stations from surrounding areas (Figure 1). All 40 stations were selected to ensure reliability, continuity, and availability of long-term data series in the study region.


## 2.3. Methods

### 2.3.1. Rainfall Erosivity Calculation

As mentioned above, continuous rainfall data series with a high time resolution for classical algorithm ofR factor (USLE R factor) are rarely available and daily rainfall data have been widely used worldwide to estimate R factor. Zhang and Fu [15] compared five simple models for estimating R factor based on average annual rainfall, average monthly rainfall, and daily rainfall data, respectively and then proposed a new daily rainfall model to estimate R factor which was subsequently widely used in China. The daily rainfall model was expressed as(1)Rk=α∑i=1jPikβ,where Rk is the rainfall erosivity of the kth half-month, MJ·mm·ha−1·h−1; k = 1, 2, …, 24; Pik is the effective rainfall for day i of the kth half-month, and it is the actual rainfall when the actual rainfall is higher than 12 mm, otherwise, it is considered to be 0 [36]; j is the number of days in the kth half-month, j = 13, 14, 15, 16; α and β are parameters determined by the following formulas:(2)β=0.8363+18.144Pd12+24.455Py12,(3)α=21.586β−7.1891,where Pd12 is the average daily rainfall which is greater than 12 mm and Py12 is the annual average of erosive rainfall. The monthly, seasonal, and annual mean R values were successively computed based on equations (1)–(3).


### 2.3.2. Trend Analysis of Rainfall Erosivity

The Mann–Kendall trend test [37, 38] has been widely applied to meteorological time series because it could identify monotonic trends of a time-series [21, 39, 40]. It is based on two useful indexes S and Z in the Mann–Kendall test to determine whether a time series of n data points has a significant trend. A positive Z indicates an upward trend and negative Z indicates a downward trend. The trend is statistically significant at α = 0.05 and 0.01 significance level when Z>1.96 and 2.58, respectively. The detailed procedure of the Mann–Kendall trend test is presented [40]and [39]. We used it to identify the trend of annual R factor at 26 sites spanning 51 years in the current study.


### 2.3.3. Spatial Interpolation of Rainfall Erosivity

To understand the spatial distribution and temporal changes ofR factor, the mean annual, seasonal, and multiperiod R factors were interpolated through the Geostatistical Analyst module of the ArcGIS 10.2 (ESRI, America). The Co–kriging method was selected to interpolate the spatial distribution of R factor, because it can incorporate the neighboring primary data and make best prediction compared with other methods [21, 41]. Additionally, the Co-kriging method has been proved to be the most suitable interpolation method for rainfall erosivity in mainland China [24].


## 2.3.1. Rainfall Erosivity Calculation

As mentioned above, continuous rainfall data series with a high time resolution for classical algorithm ofR factor (USLE R factor) are rarely available and daily rainfall data have been widely used worldwide to estimate R factor. Zhang and Fu [15] compared five simple models for estimating R factor based on average annual rainfall, average monthly rainfall, and daily rainfall data, respectively and then proposed a new daily rainfall model to estimate R factor which was subsequently widely used in China. The daily rainfall model was expressed as(1)Rk=α∑i=1jPikβ,where Rk is the rainfall erosivity of the kth half-month, MJ·mm·ha−1·h−1; k = 1, 2, …, 24; Pik is the effective rainfall for day i of the kth half-month, and it is the actual rainfall when the actual rainfall is higher than 12 mm, otherwise, it is considered to be 0 [36]; j is the number of days in the kth half-month, j = 13, 14, 15, 16; α and β are parameters determined by the following formulas:(2)β=0.8363+18.144Pd12+24.455Py12,(3)α=21.586β−7.1891,where Pd12 is the average daily rainfall which is greater than 12 mm and Py12 is the annual average of erosive rainfall. The monthly, seasonal, and annual mean R values were successively computed based on equations (1)–(3).


## 2.3.2. Trend Analysis of Rainfall Erosivity

The Mann–Kendall trend test [37, 38] has been widely applied to meteorological time series because it could identify monotonic trends of a time-series [21, 39, 40]. It is based on two useful indexes S and Z in the Mann–Kendall test to determine whether a time series of n data points has a significant trend. A positive Z indicates an upward trend and negative Z indicates a downward trend. The trend is statistically significant at α = 0.05 and 0.01 significance level when Z>1.96 and 2.58, respectively. The detailed procedure of the Mann–Kendall trend test is presented [40]and [39]. We used it to identify the trend of annual R factor at 26 sites spanning 51 years in the current study.


## 2.3.3. Spatial Interpolation of Rainfall Erosivity

To understand the spatial distribution and temporal changes ofR factor, the mean annual, seasonal, and multiperiod R factors were interpolated through the Geostatistical Analyst module of the ArcGIS 10.2 (ESRI, America). The Co–kriging method was selected to interpolate the spatial distribution of R factor, because it can incorporate the neighboring primary data and make best prediction compared with other methods [21, 41]. Additionally, the Co-kriging method has been proved to be the most suitable interpolation method for rainfall erosivity in mainland China [24].


## 3. Results

### 3.1. Spatial Distribution of Rainfall Erosivity in TGRA

The spatial distribution of annualR factor for 1960–2010 and different decades (1960–1990, 1991–2000, and 2001–2010) in TGRA is presented in Figure 2. It is noted that the spatial distribution of 51-year annual R factor showed a strong variability (Figure 2(a)). It generally increased from west, south, and east to the north-central area, respectively, ranging from 3647.0 to 10884.8 MJ·mm·ha−1·h−1·yr−1 with a mean value of 6108.1 MJ·mm·ha−1·h−1·yr−1. The spatial characteristics indicated that the annual R factor of was characterized by a low on both sides and high in the middle in TGRA. The highest annual R factor was found in the subregion E and the lowest was in the subregion B. The annual R factor of the seven geographical subregions in the TGRA showed an order of subregion E > subregion C > subregion F > subregion D > subregion G > subregion A > subregion B (Table 1). The annual R factor in the subregion C, subregion E, and subregion F showed significant differences with other subregions (Table 1). For different decades (Figures 2(b)–2(d)), the spatial distribution of R factor in 1960–1990 and 2001–2010 displayed similar patterns to that of 1960–2010: the relative higher values were distributed in subregion C (Xiaojiang River basin) and subregion E (Daning River basin) while the subregion B possessed a lower level (Mudong River basin). It was noticed that the spatial distribution of annual R factor in 1991–2000 demonstrated a different pattern that increases from west and east to the central area, respectively, and high erosivity area slightly moving to the southwest (Figure 2(c)). In this decade, the annual R factor ranged from 3848.0 to 7286.0 MJ·mm·ha−1·h−1·yr−1, with an average of 5641.9 MJ·mm·ha−1·h−1·yr−1. However, the mean R values were 6134.5 MJ·mm·ha−1·h−1·yr−1 during 1960–1990 and 5937.0 MJ·mm·ha−1·h−1·yr−1 in 2001–2010, respectively (Table 1 and Table 2). The spatial mean R factor of 1991–2000 was 29% lower than that of 1960–1990 in the subregion E, 10% lower than in the subregion B, subregion C, and subregion G. The spatial mean R factor of 1991–2000 was 32% lower than that of 2001–2010 in subregion E. More differences could be found about maximum, minimum and standard deviation in subregion E (Figure 3). Rainfall erosivity exhibited a strong seasonal variability which was roughly consistent with the corresponding precipitation in this region (Figure 4). Generally, summer was the most erosive season, followed by spring and autumn, and winter was the least erosive season.Figure 2
Spatial distribution of mean annualR factor for 51-year and different decades in TGRA.
(a)
(b)
(c)
(d)Table 1
Statistical characteristics of average rainfall erosivity (MJ·mm·ha−1·h−1) for each subregion in the TGRA during 1960–2010.
Subregion
Annual
Spring
Summer
Autumn
Winter
Mean
Stdev
Mean
Stdev
Mean
Stdev
Mean
Stdev
Mean
Stdev
Region A
5315.0
504.0
1418.3
144.5
2772.3
288.5
1103.2
185.7
38.4
3.7
Region B
4687.1
57.0
1191.4
45.2
2499.6
98.0
924.4
25.5
31.0
4.0
Region C
7132.0
769.0
1551.0
62.5
3837.2
437.9
1729.3
238.1
53.7
8.3
Region D
5406.0
455.0
1367.0
74.8
2834.5
327.1
1115.7
113.9
44.8
3.6
Region E
8146.0
1515.7
1736.9
399.7
4289.3
908.2
2016.8
416.1
94.6
15.2
Region F
6529.0
293.0
1451.0
92.0
3399.8
170.6
1495.8
125.3
74.8
17.1
Region G
5401.0
777.9
1199.1
199.6
3014.7
428.9
1143.2
252.7
86.7
15.2
TGRA
6108.1
1455.7
1414.6
287.3
3253.3
789.6
1366.6
457.0
63.7
26.7Table 2
Annual average rainfall erosivity (MJ·mm·ha−1·h−1), Z of MK test, and precipitation (mm) for different periods in each subregion.
Subregions
Elevation (a.s.l)
1960–1990
1991–2000
2001–2010
1960–2010
R
Z
P
R
Z
P
R
Z
P
R
Z
P
Region A
447
5484.7
0.41
1146.5
5484.4
0.21
1157.1
5115.4
0.29
1119.8
5315.0
−0.16
1140.0
Region B
726
5074.0
0.29
1166.9
4615.8
0.24
1165.0
4422.4
0.36
1091.6
4687.1
−0.14
1143.2
Region C
556
6988.5
0.61
1205.7
6367.7
0.44
1188.4
6182.4
0.21
1131.9
7132.0
−0.32
1192.1
Region D
896
5401.1
0.60
1201.2
5771.3
0.35
1186.4
4786.8
0.30
1082.7
5406.0
−0.27
1178.4
Region E
1017
7641.7
0.50
1348.0
5920.0
0.56
1152.6
7828.1
0.08
1303.5
8146.0
−0.22
1343.6
Region F
948
6288.2
0.49
1270.0
6527.3
0.53
1169.2
5958.2
0.16
1151.7
6529.0
−0.23
1233.9
Region G
971
5827.8
0.60
1119.3
5262.4
0.59
1081.9
5595.6
0.69
1092.6
5401.0
0
1102.1
TGRA
800
6134.5
0.50
1204.9
5641.9
0.43
1148.4
5937.0
0.32
1147.4
6108.1
−0.17
1190.2Figure 3
Statistics characteristics ofR for different periods in each subregion.
(a)
(b)
(c)
(d)Figure 4
Spatial distribution of seasonal (a)R factor and (b) precipitation during 1960–2010.
(a)
(b)The springR factor ranged from 895.4 to 2917.3 MJ·mm·ha−1·h−1 with an average of 1414.6 MJ·mm·ha−1·h−1 that accounts for 23.6% of the total annual R factor. The spring R factor for the seven subregions showed an order of subregion E > subregion C > subregion F > subregion D > subregion G > subregion A > subregion B (Table 1).The highest spring R factor was also found in subregion C (Xiaojiang River basin) and subregion E (Daning River basin) and the lowest was in subregion B (Mudong River basin). The highest season R factor was found in summer, accounting for 53.3% of the total annual R factor in TGRA, which ranged from 1997.5 to 5887.3 MJ·mm·ha−1·h−1 with the average value of 3253.3 MJ·mm·ha−1·h−1. The highest R factor of summer also appeared in the upstream of Daning River basin (subregion E) and the lowest was in Mudong River basin (subregion B). The summer R for the seven subregions showed an order of subregion E > subregion C > subregion F > subregion G > subregion D > subregion A > subregion B (Table 1). The summer order is different from annual order and spring order in subregion D and subregion G. The spatial distribution of summer R factor was similar to annual R factor, which was higher in subregion C, subregion E, and subregion F (Figure 4). The autumn R factor varied from 684.3 to 2782.7 MJ·mm·ha−1·h−1 with an average of 1366.6 MJ·mm·ha−1·h−1 accounting for 22.2% of the total annual R factor. The spatial distribution of autumn R factor was similar to the pattern of annual and summer R factor, which increased from west, south, and east to the north-central. The autumn R factor percentages of the seven geographical subregions showed a same order as those of summer. The lowest seasonal R factor was found in winter, only accounting for 1.0% of the total annual R factor and ranging from 23.0 to 138.4 MJ·mm·ha−1·h−1. In most of the 40 stations, the winter R factor was lower than 100 MJ·mm·ha−1·h−1, indicating a very low R factor level. The spatial distribution of winter R factor was different from that of the other three seasons; higher winter R factor appeared in most of the east-central TGRA. In conclusion, subregion E held the highest R value and subregion B possessed the lowest R value in TGRA.The monthlyR factor varied greatly within one year because rainfall including high-intensity storms was not evenly distributed (Figure 5). July is the most erosive month with an average R factor of 1327.3 MJ·mm·ha−1·h−1, followed by June of 1034 MJ·mm·ha−1·h−1. January is the least erosive month with the lowest R factor being only 11.7 MJ·mm·ha−1·h−1. The mean monthly R factor of May–Sep occupied 82.5%. The monthly R factor during the flood season (Apr–Oct) was almost 18 times of that in dry season (Nov–Mar).Figure 5
Mean monthlyR factor and precipitation.


### 3.2. Temporal Variation of Rainfall Erosivity

R factor of each station was calculated based on average daily precipitation from 1960 to 2010 (Table 3). It can be seen from Table 3 that the coefficient of variance was 0.20 for TGRA and 0.25–0.46 for all the stations, indicating a moderate variability of 51-year annual R factor in both TGRA and each station. For the whole study region, the annual mean R factor from 1960 to 2010 was 5969.17 MJ·mm·ha−1·h−1·yr−1, with the lowest value of 3361.08 MJ·mm·ha−1·h−1·yr−1 in 1966 and highest value of 8896.84 MJ·mm·ha−1·h−1·yr−1 in 1982 (Figure 6). For the specific station, Cuntan station was located in the boundary of subregion A and subregion B held the minimum R factor of 1112 MJ·mm·ha−1·h−1·yr−1 in 2001, and Jianlou station seated in the subregion E of TGRA held the maximum R factor >23000 MJ·mm·ha−1·h−1·yr−1 in 1967 (Table 3). However, different decades had different temporal mean annual R value that decreases in the order of 1960–1990 > 2001–2010 > 1991–2000.Table 3
AnnualR factor of 51 year and different decades in TGRA and each station (MJ·mm·ha−1·h−1·yr−1).
No.
Station
Altitude (m)
Data source
1960–1990
1991–2000
2001–2010
1960–2010
Mean
Max
Min
Mean
Std.
Cv
1
Suining
355
CMAS
4919.74
4514.43
5493.68
8388.27
1844.93
4970.67
1667.07
0.34
2
Shapingba
259
CMAS
5118.33
5756.41
5691.59
10669.18
2393.02
5318.64
1809.32
0.34
3
Cuntan
210
CMAS
4391.01
4662.95
5065.85
11015.84
1111.88
4576.66
1862.26
0.41
4
Qingxichang
212
CMAS
4758.47
4501.44
3800.91
7895.39
2067.71
4520.32
1266.13
0.28
5
Daxian
345
CMAS
6693.96
5933.33
7662.95
13260.98
1943.77
6766.98
2255.83
0.33
6
Liangping
455
CMAS
7494.76
6880.68
5777.34
14915.13
2379.90
7037.75
2302.40
0.33
7
Wanyuan
674
CMAS
6908.07
6962.32
5838.47
19027.57
3280.52
9020.30
3211.40
0.36
8
Zhongxian
270
CMAS
5921.87
6039.74
4912.29
10661.88
2704.90
5747.02
1752.94
0.31
9
Shizhu
580
CMAS
4416.42
5060.38
4082.04
11186.78
1673.11
4477.12
1571.49
0.35
10
Wanxian
188
CMAS
6908.07
6962.32
5838.47
12914.70
3648.34
6707.28
2041.47
0.30
11
Longjiao
1500
CMAS
5490.48
5617.68
6261.35
13670.90
2830.15
5666.57
2001.13
0.35
12
Banqiao
1100
CMAS
8078.16
4573.13
6784.92
12362.13
2283.49
7035.06
2457.61
0.35
13
Lvcongpo
1820
CMAS
10428.42
8979.02
8424.96
16675.65
5917.31
10324.68
2792.60
0.27
14
Enshi
457
CMAS
8813.33
8554.49
7376.80
13597.67
3443.28
8434.31
2602.92
0.31
15
Fengjie
188
CMAS
5838.07
5996.24
5406.67
10089.92
3083.50
5670.66
1558.84
0.27
16
Badong
109
CMAS
5412.25
5576.08
5468.37
11123.61
2391.74
5455.38
1785.43
0.33
17
Wuxi
300
CMAS
5489.63
5203.64
5309.12
9177.43
1834.11
5398.16
1636.68
0.30
18
Zigui
151
CMAS
4711.67
4403.30
5344.48
8934.55
2545.27
4790.81
1629.04
0.34
19
Wufeng
620
CMAS
7764.11
7699.31
6454.02
13935.53
3716.33
7442.06
2374.10
0.32
20
Xingshan
210
CMAS
4224.27
4522.98
4710.55
8856.24
1849.96
4378.19
1543.16
0.35
21
Fangxian
427
CMAS
2985.06
2556.35
2979.62
5615.30
1176.67
2913.63
962.43
0.33
22
Sandouping
800
CMAS
6439.26
5611.81
6329.44
12021.94
3086.47
6333.13
1780.58
0.28
23
Yichang
133
CMAS
6126.22
5566.38
6359.33
12825.72
2320.96
6012.67
2020.79
0.34
24
Laohekou
90
CMAS
3598.05
3320.42
4160.95
8954.83
1033.34
3576.28
1577.55
0.44
25
Jingzhou
32
CMAS
5745.72
5691.50
5626.56
11362.58
2093.81
5812.22
2069.19
0.36
26
Jinfoshan
1906
CMAS
4873.23
4077.01
5344.48
11902.95
2496.49
4865.67
1674.26
0.34
27
Metan
270
CHA
4209.18
4546.32
6510.41
1604.60
4291.41
1329.78
0.31
28
Shuanghe
440
CHA
5452.64
5385.90
12334.15
2817.51
5436.36
1632.52
0.30
29
Gaotan
285
CHA
5617.08
4927.16
9449.45
1991.04
5617.08
1713.72
0.31
30
Jiannan
640
CHA
5771.95
5061.60
9915.53
2965.75
5594.36
1551.95
0.28
31
Moudao
1380
CHA
6480.31
5570.94
12355.14
3319.26
6258.51
1594.34
0.25
32
Gaolou
1100
CHA
11018.92
11904.79
18792.42
5746.04
11304.69
3002.74
0.27
33
Tuxiang
840
CHA
5824.89
5539.94
10292.67
3387.06
5755.39
1533.88
0.27
34
Jianlou
260
CHA
13158.45
14993.26
23046.65
6142.71
13605.96
4314.90
0.32
35
Tangfang
230
CHA
9124.60
8408.03
15297.45
4566.68
8949.83
2453.17
0.27
36
Xiangshuihe
600
CHA
5876.79
4749.04
10085.41
2422.05
5601.73
1870.74
0.33
37
Dachang
155
CHA
5084.65
6126.28
14291.06
2083.19
5338.71
2465.70
0.46
38
Wushan
271
CHA
5019.37
4489.53
8299.70
2154.98
4890.14
1357.59
0.28
39
Zhengjiaping
259
CHA
3932.62
4012.37
7334.61
1450.66
3952.07
1406.44
0.36
40
Yanglinqiao
500
CHA
5215.29
4976.50
8203.06
3011.73
5155.59
1305.26
0.25
TGRA
6134.46
5641.46
5799.27
8896.84
3361.08
5969.17
1189.32
0.20
CMAS: China Meteorological Data Sharing Service System; CHA: China Hydrological Almanac; Cv: coefficient of variation.Figure 6
Temporal changes of annualR factor in TGRA from 1960 to 2010.The trend variations were also analyzed for each station, subregions, and the entire basin using the Mann–Kendall test at monthly, seasonal, and yearly scales, respectively (Tables2 and 4). The critical value of Mann-–Kendall test is 1.96 at significance level α = 0.05 (95% confidence level). According to Table 2, except subregion G, R values for the other six subregions showed an insignificant decreasing trend during 1960–2010; but for 1960–1990, 1991–2000, and 2001–2010, all subregions over various time scales showed an insignificant increasing trend. The trend line slope of annual R factor showed a linearly decreasing trend over entire basin of 51 years (Figure 6).Table 4
Temporal trends of annual, seasonal, and monthlyR factors for TGRA and each station.
Station
Jan
Feb
Mar
Apr
May
Jun
Jul
Aug
Sep
Oct
Nov
Dec
Spring
Summer
Autumn
Winter
Annual
TGRA
1.49
2.58
∗
∗
−0.70
0.71
−0.15
1.61
1.35
−0.05
−1.90
−0.60
−0.70
0.12
−0.55
1.28
−2.03
∗
1.72
0.06
Suining
−0.68
0.03
−1.80
−2.00
∗
0.17
3.41
∗
∗
1.01
1.85
−2.40
∗
−3.60
∗
∗
−0.31
0.50
−2.75
∗
∗
2.44
∗
−2.07
∗
−0.62
1.04
Shapingba
−0.21
1.77
0.05
1.46
0.36
2.84
∗
∗
1.14
−0.60
−3.80
∗
∗
−0.65
1.93
−1.53
0.65
1.38
−2.18
∗
0.61
0.00
Cuntan
−0.37
−0.32
−0.18
0.78
0.70
1.85
0.68
1.92
−2.50
∗
−0.49
−0.24
0.32
0.18
1.88
−1.30
0.36
0.31
Qingxichang
−0.80
−0.18
−2.50
∗
−0.31
−0.88
−1.48
2.94
∗
∗
−3.00
∗
∗
−4.20
∗
∗
−1.58
−2.10
∗
0.26
−0.94
−0.07
−2.61
∗
∗
−0.18
−1.61
Daxian
0.03
0.32
−0.05
−2.00
∗
3.57
∗
∗
2.16
∗
2.57
∗
1.43
−3.50
∗
∗
0.99
1.07
1.19
1.01
1.61
−1.19
0.22
0.41
Liangping
0.84
0.19
−1.69
−1.28
−0.32
2.63
∗
∗
−1.12
0.44
−2.50
∗
−0.11
−0.50
−1.51
−0.81
0.34
−1.46
−0.74
−0.93
Wanyuaun
0.00
−1.10
−1.07
−2.30
∗
2.83
∗
∗
2.65
∗
∗
4.78
∗
∗
1.07
−2.30
∗
0.39
−2.10
∗
0.39
0.42
2.66
∗
∗
−0.99
−0.28
−0.67
Zhongxian
0.08
−0.91
−2.60
∗
∗
1.74
−0.05
0.60
−1.09
0.70
−1.93
−1.74
−1.74
−1.33
−0.54
−0.13
−0.95
−1.45
−0.62
Shizhu
1.98
∗
0.84
−3.80
∗
∗
2.31
∗
0.23
−0.16
0.63
1.80
−3.70
∗
∗
0.16
1.61
0.65
−0.05
0.94
−1.12
0.69
0.41
Wanxian
−0.28
0.78
−4.50
∗
∗
−1.58
−1.33
2.96
∗
∗
−2.50
∗
1.64
−1.06
1.02
−0.28
−1.43
−1.22
0.13
−0.44
−0.42
−0.67
Longjiao
−0.26
1.45
−2.00
∗
0.68
−0.62
4.26
∗
∗
−1.43
4.19
∗
∗
−1.38
3.33
∗
∗
0.44
1.32
−0.16
2.10
∗
−0.19
0.60
1.61
Banqiao
−2.00
∗
0.08
−1.16
−0.06
−2.20
∗
0.98
0.15
−1.78
−5.30
∗
∗
−3.80
∗
∗
−1.70
−2.70
∗
∗
−1.00
0.21
−3.65
∗
∗
0.60
−1.55
Lvcongpo
3.38
∗
∗
2.86
∗
∗
2.27
∗
1.48
−5.30
∗
∗
−2.50
∗
−0.03
−0.41
−4.80
∗
∗
−3.30
∗
∗
−3.20
∗
∗
3.14
∗
∗
−1.25
−0.47
−2.87
∗
∗
4.29
∗
∗
−1.56
Enshi
2.52
∗
0.89
−1.82
0.88
2.05
∗
−0.52
0.49
−1.33
−3.60
∗
∗
−0.57
−0.73
−0.05
0.26
−0.54
−1.56
0.31
−1.09
Fengjie
0.21
−0.08
−2.50
∗
−0.80
−3.10
∗
∗
2.70
∗
∗
3.64
∗
∗
0.00
−1.82
−1.40
−0.97
0.26
−1.85
−0.54
−1.07
−0.16
0.08
Badong
0.42
3.78
∗
∗
−1.19
2.42
∗
−0.62
−1.07
0.10
1.43
−2.20
∗
−0.68
−2.30
∗
−0.23
−0.24
−0.54
−1.12
1.65
−0.13
Wuxi
−0.06
0.68
−1.80
1.58
−1.04
2.75
∗
∗
0.16
−2.10
∗
−1.45
−0.68
1.01
−1.51
0.28
0.32
−0.49
−0.74
0.10
Zigui
−0.22
2.81
∗
∗
0.27
0.74
1.28
−0.65
4.34
∗
∗
3.98
∗
∗
−1.95
−0.45
0.63
0.00
0.39
1.94
−0.42
0.62
1.40
Wufeng
0.52
4.95
∗
∗
−0.11
1.54
0.68
−1.49
1.28
−0.16
−3.20
∗
∗
−1.09
0.36
1.40
0.58
0.32
−2.00
2.92
∗
∗
0.05
Xingshan
1.33
2.79
∗
∗
0.00
3.44
∗
∗
0.65
1.85
0.97
3.36
∗
∗
−3.30
∗
∗
−0.65
−1.80
−2.20
∗
1.06
1.27
−1.32
0.94
1.09
Fangxian
0.58
1.51
−1.53
0.31
2.60
∗
∗
0.70
1.75
−0.75
−1.25
−1.58
−0.29
0.00
1.20
0.55
−1.22
0.97
0.23
Sandouping
0.26
0.76
−0.39
−0.85
−0.38
0.28
0.72
0.87
0.13
0.24
−1.87
−1.44
−1.75
0.03
0.73
−0.82
−0.31
Yichang
0.99
3.36
∗
∗
−0.23
−0.39
0.29
0.81
0.52
1.14
1.72
−0.42
−0.29
−0.24
0.02
0.45
0.63
1.67
0.42
Laohekou
2.10
∗
1.17
2.05
∗
−1.92
1.62
4.04
∗
∗
3.12
∗
∗
2.49
∗
−3.00
∗
∗
−0.67
−2.60
∗
∗
1.45
0.32
2.05
∗
−2.18
∗
1.38
0.68
∗
∗
,
∗Statistically significant at 0.01 and 0.05 significance levels, respectively.The Mann–Kendall test of each station was performed to analyze the temporal changes ofR factor across TGRA. Insignificant increasing trends were reported for 51-year R factor and three periods (1961–1990, 1991–2000, and 2001–2010) (Figure 7). The spatial distribution of long-term annual Z was generally negative in subregion A and subregion B and positive in subregion G (Figure 7(d)), indicating that the annual R factor decreased in the western TGRA while it increased in the eastern TGRA in the past 51 years. It is also noted that the spatial distribution of temporal trends differed substantially for different periods due to its numbers of stations. The highest Z = 0.89 was observed in the decade of 1991–2000, and the lowest Z = 0.18 was during 2001–2010. Temporal changes of annual R for most of the stations were similar to the changes in TGRA; only Zigui station and Jinfoshan station had significant increasing trends (0.05 level) that probably substantially contributed to the increasing trend in 2001–2010.Figure 7
Spatial distribution ofR factor variation trends in different periods. (a) 1960–1990. (b) 1991–2000. (c) 2001–2010. (d) 1960–2010.
(a)
(b)
(c)
(d)Table4 displayed the temporal trends of annual, seasonal, and monthly R factor for TGRA and each station. Mean Z of spring R factor for TGRA was -0.05, indicating a decrease in spring R factor that was probably attributed to the significant decreasing trend at the 0.01 level in Suining station. Though half of the stations showed an increase in spring R factor over the time series, none of them reached a significant level. The summer R factor in TGRA showed an insignificant increase during 1960–2010, as might be considerably contributed by the significant increasing trends in Suining, Wanyuan, Longjiao, and Laohekou stations. Significant decreasing trend at the 0.05 level was detected for the autumn R factor in TGRA. Most of the stations indicated a decrease in autumn from 1960 to 2010 and the significant decreasing trends of Qingxichang, Banqiao, and Lvcongpo stations (α = 0.01) and Suining, Shapingba, and Laohekou stations (α = 0.05) substantially contributed to the total decreasing trend. Similar to the temporal trend of summer R factor, the winter R factor in TGRA also showed an insignificant increase during 1960–2010, as probably devoted by the significant increasing trends at 0.01 level in Lvcongpo, Wufeng, and Jingzhou stations.The monthlyR factor in TGRA showed insignificant increases from Jun to Jul and then underwent decreases from Aug to Nov (Table 4). From Dec to Feb, monthly R rose again with Feb reaching a 0.01 level significance, which might mainly contribute to the increasing trend of winter R. Furthermore, there were 7 stations in Feb indicating significant increasing trends (0.01 level), greatly leading to the increasing trend in this month. It is noticeable that there were 11 and 7 stations showing significant increasing trends in Jun and Jul, respectively, which probably substantially contributed to the increasing trends in these two months. A similar situation also occurred in Sep when 16 stations showed significant decreases, which was more likely to contribute the decreasing trend of this month.


## 3.1. Spatial Distribution of Rainfall Erosivity in TGRA

The spatial distribution of annualR factor for 1960–2010 and different decades (1960–1990, 1991–2000, and 2001–2010) in TGRA is presented in Figure 2. It is noted that the spatial distribution of 51-year annual R factor showed a strong variability (Figure 2(a)). It generally increased from west, south, and east to the north-central area, respectively, ranging from 3647.0 to 10884.8 MJ·mm·ha−1·h−1·yr−1 with a mean value of 6108.1 MJ·mm·ha−1·h−1·yr−1. The spatial characteristics indicated that the annual R factor of was characterized by a low on both sides and high in the middle in TGRA. The highest annual R factor was found in the subregion E and the lowest was in the subregion B. The annual R factor of the seven geographical subregions in the TGRA showed an order of subregion E > subregion C > subregion F > subregion D > subregion G > subregion A > subregion B (Table 1). The annual R factor in the subregion C, subregion E, and subregion F showed significant differences with other subregions (Table 1). For different decades (Figures 2(b)–2(d)), the spatial distribution of R factor in 1960–1990 and 2001–2010 displayed similar patterns to that of 1960–2010: the relative higher values were distributed in subregion C (Xiaojiang River basin) and subregion E (Daning River basin) while the subregion B possessed a lower level (Mudong River basin). It was noticed that the spatial distribution of annual R factor in 1991–2000 demonstrated a different pattern that increases from west and east to the central area, respectively, and high erosivity area slightly moving to the southwest (Figure 2(c)). In this decade, the annual R factor ranged from 3848.0 to 7286.0 MJ·mm·ha−1·h−1·yr−1, with an average of 5641.9 MJ·mm·ha−1·h−1·yr−1. However, the mean R values were 6134.5 MJ·mm·ha−1·h−1·yr−1 during 1960–1990 and 5937.0 MJ·mm·ha−1·h−1·yr−1 in 2001–2010, respectively (Table 1 and Table 2). The spatial mean R factor of 1991–2000 was 29% lower than that of 1960–1990 in the subregion E, 10% lower than in the subregion B, subregion C, and subregion G. The spatial mean R factor of 1991–2000 was 32% lower than that of 2001–2010 in subregion E. More differences could be found about maximum, minimum and standard deviation in subregion E (Figure 3). Rainfall erosivity exhibited a strong seasonal variability which was roughly consistent with the corresponding precipitation in this region (Figure 4). Generally, summer was the most erosive season, followed by spring and autumn, and winter was the least erosive season.Figure 2
Spatial distribution of mean annualR factor for 51-year and different decades in TGRA.
(a)
(b)
(c)
(d)Table 1
Statistical characteristics of average rainfall erosivity (MJ·mm·ha−1·h−1) for each subregion in the TGRA during 1960–2010.
Subregion
Annual
Spring
Summer
Autumn
Winter
Mean
Stdev
Mean
Stdev
Mean
Stdev
Mean
Stdev
Mean
Stdev
Region A
5315.0
504.0
1418.3
144.5
2772.3
288.5
1103.2
185.7
38.4
3.7
Region B
4687.1
57.0
1191.4
45.2
2499.6
98.0
924.4
25.5
31.0
4.0
Region C
7132.0
769.0
1551.0
62.5
3837.2
437.9
1729.3
238.1
53.7
8.3
Region D
5406.0
455.0
1367.0
74.8
2834.5
327.1
1115.7
113.9
44.8
3.6
Region E
8146.0
1515.7
1736.9
399.7
4289.3
908.2
2016.8
416.1
94.6
15.2
Region F
6529.0
293.0
1451.0
92.0
3399.8
170.6
1495.8
125.3
74.8
17.1
Region G
5401.0
777.9
1199.1
199.6
3014.7
428.9
1143.2
252.7
86.7
15.2
TGRA
6108.1
1455.7
1414.6
287.3
3253.3
789.6
1366.6
457.0
63.7
26.7Table 2
Annual average rainfall erosivity (MJ·mm·ha−1·h−1), Z of MK test, and precipitation (mm) for different periods in each subregion.
Subregions
Elevation (a.s.l)
1960–1990
1991–2000
2001–2010
1960–2010
R
Z
P
R
Z
P
R
Z
P
R
Z
P
Region A
447
5484.7
0.41
1146.5
5484.4
0.21
1157.1
5115.4
0.29
1119.8
5315.0
−0.16
1140.0
Region B
726
5074.0
0.29
1166.9
4615.8
0.24
1165.0
4422.4
0.36
1091.6
4687.1
−0.14
1143.2
Region C
556
6988.5
0.61
1205.7
6367.7
0.44
1188.4
6182.4
0.21
1131.9
7132.0
−0.32
1192.1
Region D
896
5401.1
0.60
1201.2
5771.3
0.35
1186.4
4786.8
0.30
1082.7
5406.0
−0.27
1178.4
Region E
1017
7641.7
0.50
1348.0
5920.0
0.56
1152.6
7828.1
0.08
1303.5
8146.0
−0.22
1343.6
Region F
948
6288.2
0.49
1270.0
6527.3
0.53
1169.2
5958.2
0.16
1151.7
6529.0
−0.23
1233.9
Region G
971
5827.8
0.60
1119.3
5262.4
0.59
1081.9
5595.6
0.69
1092.6
5401.0
0
1102.1
TGRA
800
6134.5
0.50
1204.9
5641.9
0.43
1148.4
5937.0
0.32
1147.4
6108.1
−0.17
1190.2Figure 3
Statistics characteristics ofR for different periods in each subregion.
(a)
(b)
(c)
(d)Figure 4
Spatial distribution of seasonal (a)R factor and (b) precipitation during 1960–2010.
(a)
(b)The springR factor ranged from 895.4 to 2917.3 MJ·mm·ha−1·h−1 with an average of 1414.6 MJ·mm·ha−1·h−1 that accounts for 23.6% of the total annual R factor. The spring R factor for the seven subregions showed an order of subregion E > subregion C > subregion F > subregion D > subregion G > subregion A > subregion B (Table 1).The highest spring R factor was also found in subregion C (Xiaojiang River basin) and subregion E (Daning River basin) and the lowest was in subregion B (Mudong River basin). The highest season R factor was found in summer, accounting for 53.3% of the total annual R factor in TGRA, which ranged from 1997.5 to 5887.3 MJ·mm·ha−1·h−1 with the average value of 3253.3 MJ·mm·ha−1·h−1. The highest R factor of summer also appeared in the upstream of Daning River basin (subregion E) and the lowest was in Mudong River basin (subregion B). The summer R for the seven subregions showed an order of subregion E > subregion C > subregion F > subregion G > subregion D > subregion A > subregion B (Table 1). The summer order is different from annual order and spring order in subregion D and subregion G. The spatial distribution of summer R factor was similar to annual R factor, which was higher in subregion C, subregion E, and subregion F (Figure 4). The autumn R factor varied from 684.3 to 2782.7 MJ·mm·ha−1·h−1 with an average of 1366.6 MJ·mm·ha−1·h−1 accounting for 22.2% of the total annual R factor. The spatial distribution of autumn R factor was similar to the pattern of annual and summer R factor, which increased from west, south, and east to the north-central. The autumn R factor percentages of the seven geographical subregions showed a same order as those of summer. The lowest seasonal R factor was found in winter, only accounting for 1.0% of the total annual R factor and ranging from 23.0 to 138.4 MJ·mm·ha−1·h−1. In most of the 40 stations, the winter R factor was lower than 100 MJ·mm·ha−1·h−1, indicating a very low R factor level. The spatial distribution of winter R factor was different from that of the other three seasons; higher winter R factor appeared in most of the east-central TGRA. In conclusion, subregion E held the highest R value and subregion B possessed the lowest R value in TGRA.The monthlyR factor varied greatly within one year because rainfall including high-intensity storms was not evenly distributed (Figure 5). July is the most erosive month with an average R factor of 1327.3 MJ·mm·ha−1·h−1, followed by June of 1034 MJ·mm·ha−1·h−1. January is the least erosive month with the lowest R factor being only 11.7 MJ·mm·ha−1·h−1. The mean monthly R factor of May–Sep occupied 82.5%. The monthly R factor during the flood season (Apr–Oct) was almost 18 times of that in dry season (Nov–Mar).Figure 5
Mean monthlyR factor and precipitation.


## 3.2. Temporal Variation of Rainfall Erosivity

R factor of each station was calculated based on average daily precipitation from 1960 to 2010 (Table 3). It can be seen from Table 3 that the coefficient of variance was 0.20 for TGRA and 0.25–0.46 for all the stations, indicating a moderate variability of 51-year annual R factor in both TGRA and each station. For the whole study region, the annual mean R factor from 1960 to 2010 was 5969.17 MJ·mm·ha−1·h−1·yr−1, with the lowest value of 3361.08 MJ·mm·ha−1·h−1·yr−1 in 1966 and highest value of 8896.84 MJ·mm·ha−1·h−1·yr−1 in 1982 (Figure 6). For the specific station, Cuntan station was located in the boundary of subregion A and subregion B held the minimum R factor of 1112 MJ·mm·ha−1·h−1·yr−1 in 2001, and Jianlou station seated in the subregion E of TGRA held the maximum R factor >23000 MJ·mm·ha−1·h−1·yr−1 in 1967 (Table 3). However, different decades had different temporal mean annual R value that decreases in the order of 1960–1990 > 2001–2010 > 1991–2000.Table 3
AnnualR factor of 51 year and different decades in TGRA and each station (MJ·mm·ha−1·h−1·yr−1).
No.
Station
Altitude (m)
Data source
1960–1990
1991–2000
2001–2010
1960–2010
Mean
Max
Min
Mean
Std.
Cv
1
Suining
355
CMAS
4919.74
4514.43
5493.68
8388.27
1844.93
4970.67
1667.07
0.34
2
Shapingba
259
CMAS
5118.33
5756.41
5691.59
10669.18
2393.02
5318.64
1809.32
0.34
3
Cuntan
210
CMAS
4391.01
4662.95
5065.85
11015.84
1111.88
4576.66
1862.26
0.41
4
Qingxichang
212
CMAS
4758.47
4501.44
3800.91
7895.39
2067.71
4520.32
1266.13
0.28
5
Daxian
345
CMAS
6693.96
5933.33
7662.95
13260.98
1943.77
6766.98
2255.83
0.33
6
Liangping
455
CMAS
7494.76
6880.68
5777.34
14915.13
2379.90
7037.75
2302.40
0.33
7
Wanyuan
674
CMAS
6908.07
6962.32
5838.47
19027.57
3280.52
9020.30
3211.40
0.36
8
Zhongxian
270
CMAS
5921.87
6039.74
4912.29
10661.88
2704.90
5747.02
1752.94
0.31
9
Shizhu
580
CMAS
4416.42
5060.38
4082.04
11186.78
1673.11
4477.12
1571.49
0.35
10
Wanxian
188
CMAS
6908.07
6962.32
5838.47
12914.70
3648.34
6707.28
2041.47
0.30
11
Longjiao
1500
CMAS
5490.48
5617.68
6261.35
13670.90
2830.15
5666.57
2001.13
0.35
12
Banqiao
1100
CMAS
8078.16
4573.13
6784.92
12362.13
2283.49
7035.06
2457.61
0.35
13
Lvcongpo
1820
CMAS
10428.42
8979.02
8424.96
16675.65
5917.31
10324.68
2792.60
0.27
14
Enshi
457
CMAS
8813.33
8554.49
7376.80
13597.67
3443.28
8434.31
2602.92
0.31
15
Fengjie
188
CMAS
5838.07
5996.24
5406.67
10089.92
3083.50
5670.66
1558.84
0.27
16
Badong
109
CMAS
5412.25
5576.08
5468.37
11123.61
2391.74
5455.38
1785.43
0.33
17
Wuxi
300
CMAS
5489.63
5203.64
5309.12
9177.43
1834.11
5398.16
1636.68
0.30
18
Zigui
151
CMAS
4711.67
4403.30
5344.48
8934.55
2545.27
4790.81
1629.04
0.34
19
Wufeng
620
CMAS
7764.11
7699.31
6454.02
13935.53
3716.33
7442.06
2374.10
0.32
20
Xingshan
210
CMAS
4224.27
4522.98
4710.55
8856.24
1849.96
4378.19
1543.16
0.35
21
Fangxian
427
CMAS
2985.06
2556.35
2979.62
5615.30
1176.67
2913.63
962.43
0.33
22
Sandouping
800
CMAS
6439.26
5611.81
6329.44
12021.94
3086.47
6333.13
1780.58
0.28
23
Yichang
133
CMAS
6126.22
5566.38
6359.33
12825.72
2320.96
6012.67
2020.79
0.34
24
Laohekou
90
CMAS
3598.05
3320.42
4160.95
8954.83
1033.34
3576.28
1577.55
0.44
25
Jingzhou
32
CMAS
5745.72
5691.50
5626.56
11362.58
2093.81
5812.22
2069.19
0.36
26
Jinfoshan
1906
CMAS
4873.23
4077.01
5344.48
11902.95
2496.49
4865.67
1674.26
0.34
27
Metan
270
CHA
4209.18
4546.32
6510.41
1604.60
4291.41
1329.78
0.31
28
Shuanghe
440
CHA
5452.64
5385.90
12334.15
2817.51
5436.36
1632.52
0.30
29
Gaotan
285
CHA
5617.08
4927.16
9449.45
1991.04
5617.08
1713.72
0.31
30
Jiannan
640
CHA
5771.95
5061.60
9915.53
2965.75
5594.36
1551.95
0.28
31
Moudao
1380
CHA
6480.31
5570.94
12355.14
3319.26
6258.51
1594.34
0.25
32
Gaolou
1100
CHA
11018.92
11904.79
18792.42
5746.04
11304.69
3002.74
0.27
33
Tuxiang
840
CHA
5824.89
5539.94
10292.67
3387.06
5755.39
1533.88
0.27
34
Jianlou
260
CHA
13158.45
14993.26
23046.65
6142.71
13605.96
4314.90
0.32
35
Tangfang
230
CHA
9124.60
8408.03
15297.45
4566.68
8949.83
2453.17
0.27
36
Xiangshuihe
600
CHA
5876.79
4749.04
10085.41
2422.05
5601.73
1870.74
0.33
37
Dachang
155
CHA
5084.65
6126.28
14291.06
2083.19
5338.71
2465.70
0.46
38
Wushan
271
CHA
5019.37
4489.53
8299.70
2154.98
4890.14
1357.59
0.28
39
Zhengjiaping
259
CHA
3932.62
4012.37
7334.61
1450.66
3952.07
1406.44
0.36
40
Yanglinqiao
500
CHA
5215.29
4976.50
8203.06
3011.73
5155.59
1305.26
0.25
TGRA
6134.46
5641.46
5799.27
8896.84
3361.08
5969.17
1189.32
0.20
CMAS: China Meteorological Data Sharing Service System; CHA: China Hydrological Almanac; Cv: coefficient of variation.Figure 6
Temporal changes of annualR factor in TGRA from 1960 to 2010.The trend variations were also analyzed for each station, subregions, and the entire basin using the Mann–Kendall test at monthly, seasonal, and yearly scales, respectively (Tables2 and 4). The critical value of Mann-–Kendall test is 1.96 at significance level α = 0.05 (95% confidence level). According to Table 2, except subregion G, R values for the other six subregions showed an insignificant decreasing trend during 1960–2010; but for 1960–1990, 1991–2000, and 2001–2010, all subregions over various time scales showed an insignificant increasing trend. The trend line slope of annual R factor showed a linearly decreasing trend over entire basin of 51 years (Figure 6).Table 4
Temporal trends of annual, seasonal, and monthlyR factors for TGRA and each station.
Station
Jan
Feb
Mar
Apr
May
Jun
Jul
Aug
Sep
Oct
Nov
Dec
Spring
Summer
Autumn
Winter
Annual
TGRA
1.49
2.58
∗
∗
−0.70
0.71
−0.15
1.61
1.35
−0.05
−1.90
−0.60
−0.70
0.12
−0.55
1.28
−2.03
∗
1.72
0.06
Suining
−0.68
0.03
−1.80
−2.00
∗
0.17
3.41
∗
∗
1.01
1.85
−2.40
∗
−3.60
∗
∗
−0.31
0.50
−2.75
∗
∗
2.44
∗
−2.07
∗
−0.62
1.04
Shapingba
−0.21
1.77
0.05
1.46
0.36
2.84
∗
∗
1.14
−0.60
−3.80
∗
∗
−0.65
1.93
−1.53
0.65
1.38
−2.18
∗
0.61
0.00
Cuntan
−0.37
−0.32
−0.18
0.78
0.70
1.85
0.68
1.92
−2.50
∗
−0.49
−0.24
0.32
0.18
1.88
−1.30
0.36
0.31
Qingxichang
−0.80
−0.18
−2.50
∗
−0.31
−0.88
−1.48
2.94
∗
∗
−3.00
∗
∗
−4.20
∗
∗
−1.58
−2.10
∗
0.26
−0.94
−0.07
−2.61
∗
∗
−0.18
−1.61
Daxian
0.03
0.32
−0.05
−2.00
∗
3.57
∗
∗
2.16
∗
2.57
∗
1.43
−3.50
∗
∗
0.99
1.07
1.19
1.01
1.61
−1.19
0.22
0.41
Liangping
0.84
0.19
−1.69
−1.28
−0.32
2.63
∗
∗
−1.12
0.44
−2.50
∗
−0.11
−0.50
−1.51
−0.81
0.34
−1.46
−0.74
−0.93
Wanyuaun
0.00
−1.10
−1.07
−2.30
∗
2.83
∗
∗
2.65
∗
∗
4.78
∗
∗
1.07
−2.30
∗
0.39
−2.10
∗
0.39
0.42
2.66
∗
∗
−0.99
−0.28
−0.67
Zhongxian
0.08
−0.91
−2.60
∗
∗
1.74
−0.05
0.60
−1.09
0.70
−1.93
−1.74
−1.74
−1.33
−0.54
−0.13
−0.95
−1.45
−0.62
Shizhu
1.98
∗
0.84
−3.80
∗
∗
2.31
∗
0.23
−0.16
0.63
1.80
−3.70
∗
∗
0.16
1.61
0.65
−0.05
0.94
−1.12
0.69
0.41
Wanxian
−0.28
0.78
−4.50
∗
∗
−1.58
−1.33
2.96
∗
∗
−2.50
∗
1.64
−1.06
1.02
−0.28
−1.43
−1.22
0.13
−0.44
−0.42
−0.67
Longjiao
−0.26
1.45
−2.00
∗
0.68
−0.62
4.26
∗
∗
−1.43
4.19
∗
∗
−1.38
3.33
∗
∗
0.44
1.32
−0.16
2.10
∗
−0.19
0.60
1.61
Banqiao
−2.00
∗
0.08
−1.16
−0.06
−2.20
∗
0.98
0.15
−1.78
−5.30
∗
∗
−3.80
∗
∗
−1.70
−2.70
∗
∗
−1.00
0.21
−3.65
∗
∗
0.60
−1.55
Lvcongpo
3.38
∗
∗
2.86
∗
∗
2.27
∗
1.48
−5.30
∗
∗
−2.50
∗
−0.03
−0.41
−4.80
∗
∗
−3.30
∗
∗
−3.20
∗
∗
3.14
∗
∗
−1.25
−0.47
−2.87
∗
∗
4.29
∗
∗
−1.56
Enshi
2.52
∗
0.89
−1.82
0.88
2.05
∗
−0.52
0.49
−1.33
−3.60
∗
∗
−0.57
−0.73
−0.05
0.26
−0.54
−1.56
0.31
−1.09
Fengjie
0.21
−0.08
−2.50
∗
−0.80
−3.10
∗
∗
2.70
∗
∗
3.64
∗
∗
0.00
−1.82
−1.40
−0.97
0.26
−1.85
−0.54
−1.07
−0.16
0.08
Badong
0.42
3.78
∗
∗
−1.19
2.42
∗
−0.62
−1.07
0.10
1.43
−2.20
∗
−0.68
−2.30
∗
−0.23
−0.24
−0.54
−1.12
1.65
−0.13
Wuxi
−0.06
0.68
−1.80
1.58
−1.04
2.75
∗
∗
0.16
−2.10
∗
−1.45
−0.68
1.01
−1.51
0.28
0.32
−0.49
−0.74
0.10
Zigui
−0.22
2.81
∗
∗
0.27
0.74
1.28
−0.65
4.34
∗
∗
3.98
∗
∗
−1.95
−0.45
0.63
0.00
0.39
1.94
−0.42
0.62
1.40
Wufeng
0.52
4.95
∗
∗
−0.11
1.54
0.68
−1.49
1.28
−0.16
−3.20
∗
∗
−1.09
0.36
1.40
0.58
0.32
−2.00
2.92
∗
∗
0.05
Xingshan
1.33
2.79
∗
∗
0.00
3.44
∗
∗
0.65
1.85
0.97
3.36
∗
∗
−3.30
∗
∗
−0.65
−1.80
−2.20
∗
1.06
1.27
−1.32
0.94
1.09
Fangxian
0.58
1.51
−1.53
0.31
2.60
∗
∗
0.70
1.75
−0.75
−1.25
−1.58
−0.29
0.00
1.20
0.55
−1.22
0.97
0.23
Sandouping
0.26
0.76
−0.39
−0.85
−0.38
0.28
0.72
0.87
0.13
0.24
−1.87
−1.44
−1.75
0.03
0.73
−0.82
−0.31
Yichang
0.99
3.36
∗
∗
−0.23
−0.39
0.29
0.81
0.52
1.14
1.72
−0.42
−0.29
−0.24
0.02
0.45
0.63
1.67
0.42
Laohekou
2.10
∗
1.17
2.05
∗
−1.92
1.62
4.04
∗
∗
3.12
∗
∗
2.49
∗
−3.00
∗
∗
−0.67
−2.60
∗
∗
1.45
0.32
2.05
∗
−2.18
∗
1.38
0.68
∗
∗
,
∗Statistically significant at 0.01 and 0.05 significance levels, respectively.The Mann–Kendall test of each station was performed to analyze the temporal changes ofR factor across TGRA. Insignificant increasing trends were reported for 51-year R factor and three periods (1961–1990, 1991–2000, and 2001–2010) (Figure 7). The spatial distribution of long-term annual Z was generally negative in subregion A and subregion B and positive in subregion G (Figure 7(d)), indicating that the annual R factor decreased in the western TGRA while it increased in the eastern TGRA in the past 51 years. It is also noted that the spatial distribution of temporal trends differed substantially for different periods due to its numbers of stations. The highest Z = 0.89 was observed in the decade of 1991–2000, and the lowest Z = 0.18 was during 2001–2010. Temporal changes of annual R for most of the stations were similar to the changes in TGRA; only Zigui station and Jinfoshan station had significant increasing trends (0.05 level) that probably substantially contributed to the increasing trend in 2001–2010.Figure 7
Spatial distribution ofR factor variation trends in different periods. (a) 1960–1990. (b) 1991–2000. (c) 2001–2010. (d) 1960–2010.
(a)
(b)
(c)
(d)Table4 displayed the temporal trends of annual, seasonal, and monthly R factor for TGRA and each station. Mean Z of spring R factor for TGRA was -0.05, indicating a decrease in spring R factor that was probably attributed to the significant decreasing trend at the 0.01 level in Suining station. Though half of the stations showed an increase in spring R factor over the time series, none of them reached a significant level. The summer R factor in TGRA showed an insignificant increase during 1960–2010, as might be considerably contributed by the significant increasing trends in Suining, Wanyuan, Longjiao, and Laohekou stations. Significant decreasing trend at the 0.05 level was detected for the autumn R factor in TGRA. Most of the stations indicated a decrease in autumn from 1960 to 2010 and the significant decreasing trends of Qingxichang, Banqiao, and Lvcongpo stations (α = 0.01) and Suining, Shapingba, and Laohekou stations (α = 0.05) substantially contributed to the total decreasing trend. Similar to the temporal trend of summer R factor, the winter R factor in TGRA also showed an insignificant increase during 1960–2010, as probably devoted by the significant increasing trends at 0.01 level in Lvcongpo, Wufeng, and Jingzhou stations.The monthlyR factor in TGRA showed insignificant increases from Jun to Jul and then underwent decreases from Aug to Nov (Table 4). From Dec to Feb, monthly R rose again with Feb reaching a 0.01 level significance, which might mainly contribute to the increasing trend of winter R. Furthermore, there were 7 stations in Feb indicating significant increasing trends (0.01 level), greatly leading to the increasing trend in this month. It is noticeable that there were 11 and 7 stations showing significant increasing trends in Jun and Jul, respectively, which probably substantially contributed to the increasing trends in these two months. A similar situation also occurred in Sep when 16 stations showed significant decreases, which was more likely to contribute the decreasing trend of this month.


## 4. Discussion

### 4.1. Spatial Distribution of Rainfall Erosivity

Zhang’s semimonth model was developed in China and is favored for its high-quality results [15, 20, 21]. Annual rainfall erosivity was calculated, and its spatial distribution was obtained using the Co–kriging interpolation technique. As mentioned above, the annual rainfall erosivity spatially ranged from 3647.0 to 10,884.8 MJ·mm·ha−1·h−1 with an average value of 6108.1 MJ·mm·ha−1·h−1 and standard deviation of 1455.6 MJ·mm·ha−1·h−1. According the criterion of Huang et al. [41], TGRA was classified as medium rainfall erosivity. Therefore, the quantitative relationship was discussed between the rainfall erosivity and the rainfall in TGRA. The distribution map of seasonal precipitation (Figure 4) was generated based on the average daily rainfall. From Figure 4, although some differences exist in parts of the region, the spatial distribution of seasonal rainfall erosivity visually agrees well with that of seasonal precipitation, which indicates that the precipitation almost determines the rainfall erosivity both in amount and spatial distribution. To analyze the influence of geographic location and elevation on R factor, the linear relationships between average annual R factor and longitude, latitude, elevation, and mean annual rainfall of each station were performed (Figure 8). The critical value of correlation coefficient test R0.05, 40 = 0.312. According to Figure 8, the correlation coefficients between R factor and longitude, latitude, and elevation were not significant. Only the relationship between annual R-factor and annual precipitation reached a significant level. Figure 8(d) indicats that the correlation between areal rainfall erosivity and areal rainfall during 1960–2010 reached a significant level (α < 0.05). Rainfall is the main external factor contributing to rainfall erosivity. Intra-annually, the proportion of R factor was higher than that of precipitation in summer, indicating that erosive rainfall occurred mostly in summer compared with other seasons (Figure 5).Figure 8
Relationship between annual rainfall erosivity, longitude, latitude, and precipitation.
(a)
(b)
(c)
(d)Compared with the previous studies in TGRA, the results concerning the spatial-temporal distribution ofR factor were inconsistent and some important differences could be discovered, primarily in subregion C and subregion F. Fan et al. [27] and Wang et al. [28] found the mean annual R factor in upper Yangtze River basin was 3000.0–4000.0 MJ·mm·ha−1·h−1·yr−1. However, they did not detect the highest R factor area of Daning River basin and underestimated approximately 40% of the R factor in TGRA as their stations are not located in subregion E. The Daning River basin of subregion E held the highest R factor in TGRA and also has the most precipitation [32, 34]. The R value of the current study was consistent with the results of Fan et al. [27] and Wang et al. [28] in subregion G. Wu et al. [29] and Wang [30] both studied the TGRA supported by meteorological stations and showed a similar annual R factor of 3500.0–7500.0 MJ·mm·ha−1·h−1·yr−1 but a higher R factor located in southwest of subregion G. However, there is over 20% difference between Wu et al. [29] and Wang [30] in subregion E. The mean annual R factor of subregion E in the present study is consistent with the results of Hua et al. [34] and Ren and Liu [32]. The small differences of R factor in the subregion E came from the impact of data series length in determining rainfall erosivity. The R value fluctuates by the short span of rainfall data series because of climatic change in the previous researches.A long series of rainfall records from sufficient stations is the premise of studies on spatial distribution and temporal trends ofR factor. This study collected the daily precipitation data from the China Meteorological Data Sharing Service System (1960–2010) and China Hydrological Almanac (1960–1990 and 2001–2010) to investigate the spatial-temporal distribution of R factor. Spatial interpolation was conducted to predict R factor distribution for the three periods of 1960–1990, 1991–2000, and 2001–2010 (Figure 2).Figures2(b) and 2(d) show the spatial distribution of mean annual R factor during 1960–1990 and 2001–2010 containing 40 stations (26 continuous series precipitation stations and 14 discontinuous series precipitation stations), respectively. Figure 2(c) show the spatial distribution of mean annual R factor during 1991–2000 based on 26 continuous series precipitation stations. Figures 2(b) and 2(d) have similar spatial characteristics in TGRA except the extreme value. The reason was that the short length of rainfall data resulted in fluctuation of R factor during 2001–2010. However, Figure 2(c) is different from Figures 2(b) and 2(d). The highest R value could not be detected in Figure 2(c) due to the lack of rainfall stations during 1991–2000. Figure 2(c) demonstrates the same results as those of the previous studies [27, 28]. Therefore, only Figure 2(b) appears to have a similar spatial distribution to Figure 2(a). Furthermore, the daily rainfall data of supplemental stations in this study were very helpful to interpolate R factor, which improved the spatial interpolation accuracy and strengthened the spatial-temporal distribution reliability of R factor. The distribution map could provide a relatively reliable R factor for USLE and RUSLE of regional erosion. It also provided a scientific basis to investigate soil erosion and evaluate the effects of soil conservation measures and ecological restoration projects.


### 4.2. Parameters of the Calculated Method

It is important to recognize that, although the method used in this study has its inherent advantages in depicting the changing characteristics ofR factor, several uncertainties still exist regarding the application of the method. First, α and β are the important parameters in the calculation formula of R factor, and their values are closely related to the zonal climate characteristics and the underlying surface of the basin. The same amount of rainfall in summer can generate a totally different erosivity than that in the winter, because the summer rains tended to be more intense than winter rains. Even though values of α and β were calculated by the same way in different basins of China, the R value need more evidences to prove. According to its definition, the R factor is directly related to the rainfall’s kinetic energy and intensity. In this study, the R factor is calculated from the daily erosive rainfall whether the actual daily rainfall is higher than 12 mm or not; this may also have introduced uncertainties into the estimation of the R factor. Future studies would be improved by investigating the relationship of parameters α and β and the climate and catchment characteristics to reduce or eliminate parameter value uncertainties. Moreover, it is necessary to take more factors into account when estimating the R factor in the future studies.


## 4.1. Spatial Distribution of Rainfall Erosivity

Zhang’s semimonth model was developed in China and is favored for its high-quality results [15, 20, 21]. Annual rainfall erosivity was calculated, and its spatial distribution was obtained using the Co–kriging interpolation technique. As mentioned above, the annual rainfall erosivity spatially ranged from 3647.0 to 10,884.8 MJ·mm·ha−1·h−1 with an average value of 6108.1 MJ·mm·ha−1·h−1 and standard deviation of 1455.6 MJ·mm·ha−1·h−1. According the criterion of Huang et al. [41], TGRA was classified as medium rainfall erosivity. Therefore, the quantitative relationship was discussed between the rainfall erosivity and the rainfall in TGRA. The distribution map of seasonal precipitation (Figure 4) was generated based on the average daily rainfall. From Figure 4, although some differences exist in parts of the region, the spatial distribution of seasonal rainfall erosivity visually agrees well with that of seasonal precipitation, which indicates that the precipitation almost determines the rainfall erosivity both in amount and spatial distribution. To analyze the influence of geographic location and elevation on R factor, the linear relationships between average annual R factor and longitude, latitude, elevation, and mean annual rainfall of each station were performed (Figure 8). The critical value of correlation coefficient test R0.05, 40 = 0.312. According to Figure 8, the correlation coefficients between R factor and longitude, latitude, and elevation were not significant. Only the relationship between annual R-factor and annual precipitation reached a significant level. Figure 8(d) indicats that the correlation between areal rainfall erosivity and areal rainfall during 1960–2010 reached a significant level (α < 0.05). Rainfall is the main external factor contributing to rainfall erosivity. Intra-annually, the proportion of R factor was higher than that of precipitation in summer, indicating that erosive rainfall occurred mostly in summer compared with other seasons (Figure 5).Figure 8
Relationship between annual rainfall erosivity, longitude, latitude, and precipitation.
(a)
(b)
(c)
(d)Compared with the previous studies in TGRA, the results concerning the spatial-temporal distribution ofR factor were inconsistent and some important differences could be discovered, primarily in subregion C and subregion F. Fan et al. [27] and Wang et al. [28] found the mean annual R factor in upper Yangtze River basin was 3000.0–4000.0 MJ·mm·ha−1·h−1·yr−1. However, they did not detect the highest R factor area of Daning River basin and underestimated approximately 40% of the R factor in TGRA as their stations are not located in subregion E. The Daning River basin of subregion E held the highest R factor in TGRA and also has the most precipitation [32, 34]. The R value of the current study was consistent with the results of Fan et al. [27] and Wang et al. [28] in subregion G. Wu et al. [29] and Wang [30] both studied the TGRA supported by meteorological stations and showed a similar annual R factor of 3500.0–7500.0 MJ·mm·ha−1·h−1·yr−1 but a higher R factor located in southwest of subregion G. However, there is over 20% difference between Wu et al. [29] and Wang [30] in subregion E. The mean annual R factor of subregion E in the present study is consistent with the results of Hua et al. [34] and Ren and Liu [32]. The small differences of R factor in the subregion E came from the impact of data series length in determining rainfall erosivity. The R value fluctuates by the short span of rainfall data series because of climatic change in the previous researches.A long series of rainfall records from sufficient stations is the premise of studies on spatial distribution and temporal trends ofR factor. This study collected the daily precipitation data from the China Meteorological Data Sharing Service System (1960–2010) and China Hydrological Almanac (1960–1990 and 2001–2010) to investigate the spatial-temporal distribution of R factor. Spatial interpolation was conducted to predict R factor distribution for the three periods of 1960–1990, 1991–2000, and 2001–2010 (Figure 2).Figures2(b) and 2(d) show the spatial distribution of mean annual R factor during 1960–1990 and 2001–2010 containing 40 stations (26 continuous series precipitation stations and 14 discontinuous series precipitation stations), respectively. Figure 2(c) show the spatial distribution of mean annual R factor during 1991–2000 based on 26 continuous series precipitation stations. Figures 2(b) and 2(d) have similar spatial characteristics in TGRA except the extreme value. The reason was that the short length of rainfall data resulted in fluctuation of R factor during 2001–2010. However, Figure 2(c) is different from Figures 2(b) and 2(d). The highest R value could not be detected in Figure 2(c) due to the lack of rainfall stations during 1991–2000. Figure 2(c) demonstrates the same results as those of the previous studies [27, 28]. Therefore, only Figure 2(b) appears to have a similar spatial distribution to Figure 2(a). Furthermore, the daily rainfall data of supplemental stations in this study were very helpful to interpolate R factor, which improved the spatial interpolation accuracy and strengthened the spatial-temporal distribution reliability of R factor. The distribution map could provide a relatively reliable R factor for USLE and RUSLE of regional erosion. It also provided a scientific basis to investigate soil erosion and evaluate the effects of soil conservation measures and ecological restoration projects.


## 4.2. Parameters of the Calculated Method

It is important to recognize that, although the method used in this study has its inherent advantages in depicting the changing characteristics ofR factor, several uncertainties still exist regarding the application of the method. First, α and β are the important parameters in the calculation formula of R factor, and their values are closely related to the zonal climate characteristics and the underlying surface of the basin. The same amount of rainfall in summer can generate a totally different erosivity than that in the winter, because the summer rains tended to be more intense than winter rains. Even though values of α and β were calculated by the same way in different basins of China, the R value need more evidences to prove. According to its definition, the R factor is directly related to the rainfall’s kinetic energy and intensity. In this study, the R factor is calculated from the daily erosive rainfall whether the actual daily rainfall is higher than 12 mm or not; this may also have introduced uncertainties into the estimation of the R factor. Future studies would be improved by investigating the relationship of parameters α and β and the climate and catchment characteristics to reduce or eliminate parameter value uncertainties. Moreover, it is necessary to take more factors into account when estimating the R factor in the future studies.


## 5. Conclusions

The spatial distribution and temporal trend of annual, seasonal, and monthlyR factors in TGRA of China from 1960 to 2010 were analyzed using daily rainfall data from 40 stations. The main findings are summarized as follows.Spatially, the annualR factor varied from 3647.0 to 10884.8 MJ·mm·ha−1·h−1 with an average value of 6108.1 MJ·mm·ha−1·h−1. The spatial distribution of summer and autumn R factors was similar to the pattern of annual R factor, which increased from west, south, and east to the north-central. The highest seasonal R factor was found in summer, accounting for 53% of the total annual R factor, and winter is the least erosive season. July is the most erosive month with an average of 1327.3 MJ·mm·ha−1·h−1, and January is the least erosive month.Temporally, the mean annualR factor was 5969.2 MJ·mm·ha−1·h−1, with the lowest value of 3361.0 MJ·mm·ha−1·h−1 in 1966 and highest value of 8896.0 MJ·mm·ha−1·h−1 in 1982. The M-K test showed that the annual R factor did not change significantly across TGRA. The seasonal R factor showed a significant decrease in autumn and insignificant decrease in summer and winter. The monthly R factor in TGRA showed insignificant increases from Jun to Jul and then underwent decreases from Aug to Nov. From Dec to Feb; monthly R rose again with Feb reaching a = 0.01-level significance which was probably attributed to the significant increasing trends (α = 0.01) of 7 stations.Future studies should relate the trends ofR factor detected from this study to sediment loading in major rivers across Yangtze River Basin or China to further evaluate the usefulness of the R factor in evaluating potential soil erosion at the large basin to regional scale.



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*Source: 5302679-2020-01-30.xml*