基于Hurst指数与相关系数的降雨侵蚀力变异识别与分级方法

变化环境下区域降雨侵蚀力的时空变化问题对区域水土流失防治工作提出了新的挑战。降雨侵蚀力序列不再是纯随机序列,往往存在趋势、跳跃或者周期的变化,在对降雨侵蚀力序列分析与计算时,现有研究往往采用单一的检验方法,缺乏对降雨侵蚀力序列各类成分的综合比较,所得到的结果可信度及其程度如何无法判断。该研究提出了基于Hurst系数和相关系数的降雨侵蚀力序列联合分析方法。该方法首先计算降雨侵蚀力序列的Hurst系数,引用水文序列变异的概念,从统计学角度将降雨侵蚀力序列确定性成分分为三级(无变异、弱变异和强变异)。然后通过多种检验方法综合检验,将得到的结果与原序列进行相关性分析提取相关系数最大的确定性成分(趋势、跳跃和周期),对其进行剔除,重复上述步骤,将降雨侵蚀力序列中的确定性成分进行一一分解,最终得出的降雨侵蚀力序列将是一个随机序列与确定性序列的组合。实际应用中,根据长江流域174个气象站点1961—2014年逐日降雨资料,对流域内各气象站点年降雨侵蚀力序列进行确定性成分分析与分级结果表明:长江流域174个气象站点中有130个站点降雨侵蚀力序列无明显变异,有31个站点降雨侵蚀力序列出现弱变异,有13个站点降雨侵蚀力序列出现强变异。以重庆奉节站为例进行综合检验,分析结果为整体强变异,该站年降雨侵蚀力序列存在复合周期和跳跃成分,其中复合周期为5 a和16 a,向下的跳跃点为2011年。该研究为变化环境下区域降雨侵蚀力预测提供理论依据。

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.