基于敏感性分析的最优降雨阈值选择

THE OPTIMAL RAINFALL THRESHOLDS SELECTION BASED ON SENSITIVITY ANALYSIS

降雨变量的选择对于降雨阈值模型精度至关重要。以秦巴山区2001~2020年2760个降雨型滑坡和日值降雨数据为例,首先对降雨站构建泰森多边形,实现滑坡与致灾降雨相对应,共获得1053例致灾降雨和283,446例非致灾降雨,以此为基础,通过当日降雨量(R)和前期有效降雨量(EAR)构建降雨阈值模型;其次,为选择恰当的变量EAR,使用5种有效降雨量模型在不同参数k下生成201种待选的EAR,通过构建直方图获得EAR在致灾和非致灾降雨序列中的概率:P(EAR|L),P(EAR|NL),通过贝叶斯公式计算得到降雨致灾的条件概率和先验概率:P(L|EAR),P(L);之后分别使用4种降雨变量选择方法确定最优的EAR,其中:基于散度的和基于信息增益的敏感性分析(DGSA,GGSA)通过计算P(EAR|L)和P(EAR|NL)之间的散度和信息增益进行变量选择,基于条件概率的相关性分析通过计算P(L|EAR)和P(L)的曲线下面积差进行降雨变量选择,Pearson相关性分析通过计算EAR和P(L|EAR)之间的相关性系数进行降雨变量选择;为验证4种降雨变量选择方式的合理性,同时使用两种线性分类器和两种非线性分类器直接构建R-EAR型降雨阈值,以平均正确率对降雨变量选择方法进行验证。分析和统计结果表明:(1)研究区92.15%的滑坡由降雨诱发,46.59%的降雨型滑坡由暴雨直接诱发,68.95%的降雨型滑坡由暴雨直接或间接诱发,表明暴雨是降雨型滑坡的主要诱因;(2)通过DGSA和GGSA计算得到的降雨变量重要性系数与阈值模型的性能之间存在显著的线性递增关系,线性相关性在0.98以上,表明可以通过敏感性分析进行降雨变量选择,达到构建最优降雨阈值模型的目的;(3)相较于Pearson相关性分析,在降雨变量与灾害发生频率呈非线性的情况仍可以使用DGSA和GGSA进行降雨变量的选择。

The choice of rainfall variables is critical for the accuracy of the rainfall threshold model.At the base of 2760 rainfall-induced landslides and daily rainfall data in the study area from 2001 to 2020,a Thiessen polygon was constructed to identify the rainfall that triggered and did not trigger landslides,a total of 1,053 and 283,446 respectively.Based on this data,a rainfall threshold model is planned to be constructed by the daily rainfall(R)and the previous effective rainfall(EAR).Second,to select the appropriate variable EAR,five effective antecedent rainfall(EAR)models are used to generate 201 candidate rainfall variables under different parameters k.Probability distribution of rainfall variables in triggered and did not trigger landslide rainfall:P(EAR|L),P(EAR|NL),are obtained by histogram.The conditional probability and prior probability of rainfall-induced landslide:P(L|EAR),P(L)are obtained by the Bayesian formula.Then,four rainfall variable selection methods were used to determine the optimal EAR.Among which:DGSA,GGSA performs variable selection by computing the divergence and information gain between P(L|EAR)and P(EAR|NL).Conditional probability-based correlation analysis performs variable selection by computing the difference in the area under the curve of P(L|EAR)and P(L).The Pearson correlation method performs variable selection by computing the correlation between EAR and P(L|EAR).Finally,we use two linear classifiers and two nonlinear classifiers to obtain the R-EAR rainfall threshold and use the average correct rate to verify the variable selection methods.The results show that:92.15%of landslides in the study area were induced by rainfall,among which,46.59%were directly induced by heavy rain,68.95%were directly or indirectly induced by heavy rain,indicating that heavy rain was the main cause of rainfall-type landslides;2)There is a significant linear increasing relationship between the importance coefficient calculated by DGSA and GGSA and the performance of the rainfall threshold,the linear correlation is above 0.98,indicating that sensitivity analysis can be used to identify rainfall variables associated with the optimal rainfall threshold;3)Compared with the Pearson correlation method,DGSA and GGSA are still applicable when the rainfall variable is nonlinear with the frequency of landslides.