Spatiotemporal variation and tendency analysis on rainfall erosivity in the Loess Plateau of China

Rainfall erosivity is an important factor to be considered when predicting soil erosion. Precipitation data for 1971 – 2010 from 39 stations located in the Loess Plateau of China were collected to calculate the spatiotemporal variability of rainfall erosivity, and the long-term tendency of the erosivity was predicted using data from the HadGEM2-ES model. Statistical analyses were done using Mann – Kendall statistic tests and ordinary Kriging interpolation. The results showed that the annual mean rainfall erosivity in the Loess Plateau decreased from 1,286.02 MJ mm hm (cid:1) 2 h (cid:1) 1 a (cid:1) 1 in 1971 – 1990 to 1,201.46 MJ mm hm (cid:1) 2 h (cid:1) 1 a (cid:1) 1 in 1991 – 2010 and mainly occurred in July to August. The rainfall erosivity decreased from the southeast to the northwest of the Loess Plateau and was closely related to the annual precipitation amount. However, the effect of annual precipitation on rainfall erosivity weakened under climate change: the annual precipitation increased and the rainfall erosivity decreased. Climate change, however, had little in ﬂ uence on the spatial variation in rainfall erosivity in the Loess Plateau. The results obtained can facilitate the prediction of spatial and temporal variations in soil erosion in the Loess Plateau.


GRAPHICAL ABSTRACT INTRODUCTION
Soil erosion is one of the most important ecological problems in the world. Nearly a third of arable land has been exposed to soil erosion, which has increased at a rate of 1.0 × 10 7 hm 2 per year (Pimentel et al. ). Soil erosion removes fertile soil and seriously threatens agricultural production and food security.
The eroded soil usually enters rivers, causing siltation and water eutrophication, and thus endangers water safety and affects normal production and life. Predicting and protecting against soil erosion are of great significance to the construction of an ecological civilization and to the sustainable development of the economy and society. Consequently, mechanisms of soil erosion and measures to control it have been hot research topics (Lal ; Pimentel ).
Rainfall is the driving force and prerequisite for soil erosion (Zhang et al. ). The Universal Soil Loss Equation (USLE) devised by Wischmeier & Smith () and the Revised Universal Soil Loss Equation (RUSLE) proposed by Renard & Freimund () and Renard et al. () for the United States are widely used to predict soil erosion (Anees et al. ). The rainfall erosivity (R-factor) in these models indicates the ability of rainfall to cause soil erosion and is considered the best factor for studying the response of soil erosion to rainfall changes (Nearing et al. ). Meusburger et al. MJ mm hm À2 h À1 (Panagos et al. ). Due to the difficulty in obtaining rainfall data with a high temporal resolution, Vrieling et al. () used satellite data and combined rainfall intensity and rainfall erosivity to establish a method for forecasting rainfall erosivity, thereby demonstrating a potential tool for soil erosion prediction in data-poor areas. Previous studies have enhanced our understanding of spatiotemporal variations in rainfall erosivity, but these studies were constrained by the limited availability of daily rainfall data and by the length of rainfall data. Studying available long-term rainfall data and estimating rainfall erosivity could provide information on the potential trends of soil erosion, especially in areas that are lacking data.
In the Loess Plateau of China, intensive rainfall and sparse vegetation can lead to relatively serious soil erosion.
A large amount of sediment enters the Yellow River and causes many problems, including river channel siltation and the deterioration of aquatic ecosystems (Liu & Liu ). using GIS based on regional data from the Yanhe watershed and concluded that the annual soil loss was 0.5-2.0 × 10 7 kg km À2 . Sun et al. () analyzed the effects of topography and land-use patterns on soil erosion in the Loess Plateau and suggested that 'Grain-to-Green Program' is effective for preventing soil erosion. Xu () carried out a quantitative analysis of the correlations between vegetation coverage (C f ), annual rainfall erosivity (R e ), and annual precipitation (P m ). Xu's results indicated that R e will increase rapidly when P m > 300 mm, and that when P m > 530 mm, the rate at which R e increases with P m becomes higher. Current research generally focuses on specific watersheds where daily rainfall data are easily available. Consequently, there are relatively few papers addressing the long-term spatiotemporal variation of rainfall erosivity in the Loess Plateau. More analysis is needed for the region as a whole based on available long-term daily rainfall data. The results of the analysis could form the basis for soil loss prediction in the region. Moreover, the impact of climate change on soil erosion needs to be understood (Almagro et al. ). Few studies, however, have been carried out that have made predictions and analyses of variations in rainfall erosivity under projected climate change in the Loess Plateau of China. Consequently, a climate change perspective and decision basis cannot be provided for decision makers.
The overall aim of this study was to address these knowledge gaps. Precipitation data from 1971 to 2010 were collected from 39 representative stations in the Loess Plateau of China to analyze the spatiotemporal variability of rainfall erosivity. The main objectives of this study are as follows: (1) to determine the spatial and temporal variability of annual rainfall erosivity in the Loess Plateau; (2) to predict the change tendency of future rainfall erosivity using a typical global circulation model (GCM).

Study area
The Loess Plateau is located between 100 52 0 -114 31 0 E and 33 37 0 -41 25 0 N, including most or part of Shanxi, Shaanxi, Gansu, Qinghai, and Henan Provinces and the Inner Mongolia and Ningxia Regions. The total area is about 63.5 × 10 4 km 2 . Most areas of the plateau have semi-humid or semi-arid climates, and the climates in different areas are quite different. The annual mean temperature is 3.6-14.3 C, and the annual evaporation is 1,400-2,000 mm.
The main crops grown are wheat, corn, soybeans, and sorghum. The study area is characterized by complex landforms and deep soil layers (mainly loose and easily eroded dark loessial soil and loessal soil). The annual precipitation ranges from 200 to 750 mm, with large interannual and seasonal variations. There are frequent storms, which are the main driving force of soil erosion. The annual mean soil erosion modulus of the Loess Plateau is 0.5-1.0 × 10 7 kg km À2 a À1 , and the thickness of the soil layer lost every year is about 1 cm.

Data
We used data from the 39 representative meteorological

Calculation of the rainfall erosivity values
The USLE and the RUSLE models use an algorithm and daily precipitation to determine rainfall erosivity in half-months. In this study, half-monthly rainfall erosivity estimates were obtained using the model proposed by Zhang et al. (). The model has been shown to be suitable for the prediction of rainfall erosivity for the Loess Plateau (Wu et al. ). Rainfall erosivity was calculated as follows: where R i is the rainfall erosivity index in the ith half-month period (MJ·mm·hm À2 ·h À1 ); k is the number of days in the half-month period; P j is the erosive rainfall (mm) on the jth day in the half-month period. Daily precipitation is required to be greater than or equal to 12 mm, otherwise calculated as 0, and the threshold of 12 mm is consistent with the Chinese standard for erosive rainfall. The parameters α, β need to be determined for the model and are calculated from the following formulae: β ¼ 0:8363 þ 18:177 P d12 þ 24:455 P y 12 (3) where P d 12 is the average daily precipitation (mm) with a daily rainfall of 12 mm or more; P y 12 represents the annual mean precipitation (mm) with a daily rainfall of 12 mm or more. During the calculation, the half-month period is defined as the 15th day of each month: the 1st to 15th day of each month is one half month, and the rest of the month is calculated as another half month. The whole year is divided into 24 half-month periods, and the monthly, annual rainfall erosivity, and annual mean rainfall erosivity are obtained.
In the present study, the average rainfall erosivity refers to the average of data from different meteorological stations over a given time, while the annual mean rainfall erosivity refers to the average of data over a period of time for a specific location. insignificant and changeable, which indicates that erosive rainfall is not only affected by the precipitation amount but also reflects the annual changes in precipitation.

Temporal variation of rainfall erosivity
The intra-annual distribution of rainfall erosivity for the years from 1971 to 2010 is shown in Figure 3(a) and 3(b).
The rainfall erosivity during the year formed a single-peak distribution, first increasing and then decreasing. The annual precipitation distribution and the rainfall erosivity followed a similar pattern: in January and February, the rainfall erosivity was almost zero, it then gradually increased, reaching a peak in July and August, and then gradually decreased to zero in November. The total rainfall erosivity in July to August accounted for 61.5% (1971)(1972)(1973)(1974)(1975)(1976)(1977)(1978)(1979)(1980)(1981)(1982)(1983)(1984)(1985)(1986)(1987)(1988)(1989)(1990) Figure 4(b)). Overall, rainfall erosivity fluctuated with the increases and decreases in annual precipitation, but there were some years where the correlation between rainfall erosivity and precipitation was not strong. Taking 1989 and 1990 as an example, the rainfall erosivity was basically the same, but the difference in precipitation was 17.5%. This shows that rainfall erosivity is also affected by rainfall distribution and other factors. The Mann-Kendall tests showed that, in general, the inter-annual changes in rainfall erosivity increased from 1975 to 1981 and decreased from 1982 to 2010. This is similar to the trends for erosive rainfall, but, as shown in Figure 4(a) and 4(b), the annual decrease rate in rainfall erosivity during 1991-2010 was slightly slower than that during 1971-1990, and eventually stabilized.

Spatial distribution of rainfall erosivity
As shown in Figure 5, the annual mean rainfall erosivity decreased from southeast to northwest. For the area as a whole, the annual mean rainfall erosivity was 1,286.02 and   Under the RCP4.5 scenario, the annual mean precipitation from 2020 to 2100 would be 505.12 ± 130.02 mm a À1 , which is 26.8 and 34.1% higher than the  From historical data (   The rainfall erosivity in different periods was divided into two parts according to the length of the series, after the annual mean rainfall erosivity was interpolated by ordinary Kriging in ArcGIS in every parts, and the rainfall erosivity variation figure (Figure 6) was obtained using raster calculation. The variation in the rainfall erosivity from 1971-1980 to 1981-1990

DISCUSSIONS Temporal changes in rainfall erosivity
The mean precipitation on the Loess Plateau was In terms of inter-annual changes, the annual mean rainfall erosivity from 1971 to 1990 was 1,139.75 ± 487.57 MJ mm hm À2 h À1 a À1 , with an insignificant decreasing rate of 1.83 MJ mm hm À2 h À1 a À1 (Figure 4). When To improve the analysis of the relationship between rainfall erosivity and precipitation over various time scales, the present study made use of the Standardized Precipitation Index (SPI) and used the SPI PROGRAM to  Table 3.
It can be seen from Figure 7 that the monthly rainfall erosivity has a good corresponding relationship with precipitation. However, the precipitation amount is not the determining condition for the variation in rainfall erosivity. Spatial variation of rainfall erosivity and its response to precipitation In the 1980s, rainfall erosivity decreased in southern Gansu, central Shaanxi, and northern Shanxi and increased slightly pairs of data were generated in the RCP4.5 and RCP8.5 scenarios, respectively.) The fitting results are shown in Figure 8.
In the historical data, the annual precipitation was mainly concentrated between 200 and 600 mm. Initially, rainfall erosivity increased at a small rate. The rate of increase then gradually increased before gradually decreasing. The annual rainfall erosivity was generally below 2,500 MJ mm hm À2 h À1 . The logistic function provided a good fitting effect with the historical data (R 2 ¼ 0.77, P < 0.01). The formula is as follows:  (4) where R y is the annual rainfall erosivity (MJ·mm·hm À2 ·h À1 ), and P y is the annual precipitation (mm). When the annual precipitation was 200-600 mm, the annual rainfall erosivity was about 316.68-2,163.19 MJ mm hm À2 h À1 .
When compared with the historical data, it was evident that the annual precipitation in the RCP4.5 scenario was mainly concentrated in the 300-900 mm range, and the annual rainfall erosivity was generally below 2,500 MJ mm hm À2 h À1 . In contrast to the RCP4.5 scenario, the annual rainfall erosivity in the RCP8.5 scenario was mainly concentrated below 3,000 MJ mm hm À2 h À1 . The logistic function fits the RCP4.5 data well (R 2 ¼ 0.49, P < 0.05), but the function does not converge with the RCP8.5 data. The Allometric1 function in ORIGIN 2020 was used to do the fitting, and a good fitting effect was also obtained for the RCP8.5 data (R 2 ¼ 0.55 (P < 0.05), Figure 8(c)). For the same rainfall amount, when P < 442.51 mm, the rainfall erosivity of the RCP4.5 scenario is greater than that of RCP8.5, and vice versa. Under the future climate modes, the annual rainfall erosivity gradually increases and becomes more discrete with an increase in precipitation, which indicates that the rainfall data generated by the HadGEM2-ES model are complex. However, as Figure 8 shows, when the annual precipitation is less than 1,000.0 mm, the 95% confidence band is narrow, which indicates that two functions are applicable for the prediction of rainfall erosivity using data from HadGEM2-ES. It is clear, therefore, that the detailed changes of future rainfall erosivity require further quantitative research.

CONCLUSIONS
Rainfall data from 1971 to 2010 for 39 typical meteorological stations in the Loess Plateau were collected to calculate the spatiotemporal variation of rainfall erosivity. Additionally, future trends in rainfall erosivity were predicted using the RCP4.5 and RCP8.5 scenarios. The main conclusions are as follows: (1) From 1971 to 2010, the mean rainfall erosivity on the Loess Plateau was 1,239.64 MJ mm hm À2 h À1 . Overall, annual rainfall erosivity exhibited a slightly decreasing trend. On a monthly basis, rainfall erosivity appeared as a unimodal distribution throughout the year and was mainly concentrated in July to August. There were some differences, however, in the distribution during different hydrological years.
(2) The change in annual mean rainfall erosivity was different for different time series, while the spatial distribution of rainfall erosivity showed an overall decrease from the southeast to the northwest. The province with the highest rainfall erosivity was Shanxi, while Ningxia had the lowest.
Southern Shanxi, and central and southern Shaanxi were areas susceptible to rainfall erosion in the Loess Plateau.
(3) Rainfall erosivity obtained from future climate scenarios is lower than that obtained from historical data. While the precipitation amount increased in future scenarios, the relationship between precipitation and rainfall erosivity was relatively discrete. Future rainfall erosivity presents a relatively regular spatial distribution pattern: high in the southeast and low in the northwest. Areas with intense rainfall erosion on the Loess Plateau were concentrated in the south (RCP4.5) and southeast (RCP8.5).