Identification and classification of rainfall erosivity variation based on Hurst and correlation coefficient

Abstract: The spatial distributions and temporal trends of rainfall erosivity are critical for accurately assessing soil erosion rates, especially under the circumstances of climate change. Temporal trends of rainfall erosivity have been noted by researchers. However, reports on the methods for temporal changes of rainfall erosivity, especially the comprehensive comparison of its components (trend, jump, periodicity, and so on), are still lacking, which reduces the accuracy of assessing soil erosion risk. The single test method of rainfall erosivity series showed large uncertainties. Through the comprehensive test methods, the most reliable components could be extracted, which was an effective way to reduce the uncertainty. In this study, a joint analysis method for rainfall erosivity series based on Hurst and correlation coefficient was proposed. Firstly, the Hurst coefficient of rainfall erosivity series was calculated, and the variation was divided into 3 intervals: no variation, weak variation and strong variation. The variation components were analyzed by a variety of test methods, and correlation analysis was conducted between the variation components and the original rainfall erosivity series to extract the variation component with the largest correlation coefficient. Then this component was eliminated, and the above steps were repeated, until all the variation components were removed from the series. Finally, the original rainfall erosivity series would be a combination of random series and the variation components. In practical applications, long-term daily rainfall data from 1961 to 2013 or 2014 in 174 national weather stations were assembled to characterize the spatial and temporal patterns of annual rainfall erosivity across the Yangtze River basin. Kendall rank correlation test and Spearman rank correlation test were employed to detect the temporal trends. Sliding run test, Mann-Kendall test and Bayes test were employed to detect the jump variations. Fourier (cumulative variance chart), power spectral density and simple partial wave method were employed to detect the periodic variations. The results showed that: 1) A total of 130 stations in the 174 meteorological stations were not affected by human activities, and there was no significant variation. There were 31 stations with weak variation, and 13 stations with strong variation. Stations with rainfall erosivity variation increased from southwest to northeast, which was consistent with the trend of precipitation, and these stations were mainly located in middle and lower reaches of the Yangtze River. 2) The average annual rainfall erosivity in the Yangtze River basin was 6041.2 MJ·mm/(hm2·h). Long-term average annual rainfall erosivity decreased from east to west, ranging from 110.7 to 15 799.9 MJ·mm/(hm2·h). The value of average annual rainfall erosivity increased with the increase of longitude. There was no significant relationship between rainfall erosivity and latitude. 3) A representative weather station (Fengjie, Chongqing) was selected for a comprehensive test. Results of the test verified the feasibility of the proposed method, and also showed that the results calculated from the single test method were uncertain. Based on Hurst and correlation coefficient analysis, the variation degree of annual rainfall erosivity series in Fengjie was strong, and the variation forms were periodic and jump variations, in which the compound period was 5 and 16 a, and the downward jump point was in 2011. This method was derived from Hurst coefficient and the relationship between correlation coefficient and variation components, and could grade the levels of variation in rainfall erosivity series. The results provide valuable information for soil erosion prediction.