滑坡概率分析中降雨的联合概率结构

Joint Probabilistic Structure of Rainfall in Analysis of Landslides Probability

降雨是降雨型滑坡概率分析和预测的主要输入,以日降雨量和累计降雨量为重庆市降雨的控制参量,建立两者的联合概率模型,为后续分析提供基础。沿用滑坡分析中常用的处理方式,将日降雨量划分等级转化为离散变量,将累计降雨量视为连续随机变量。然后,导出了离散变量和连续变量的联合概率模型,并发展了条件密度变换解及其Diracδ函数序列逼近。将之用于重庆市累计降雨量的条件密度函数计算,并验证了计算结果的合理性。由于累计降雨量条件密度函数的复杂性,引入混合分布模型对其进行数学建模,形式不太复杂且精度比较理想。最后,结合日降雨等级频度函数与累计降雨量条件概率密度模型建立了联合概率模型。

Rainfall is the main input for probabilistic analysis and prediction of rainfall-triggered landslide.The joint probabilistic structure of daily rainfall（DR） and cumulative rainfall（CR）,which are dominant parameters of rainfall related on landslide in Chongqing region,was analyzed.Following the traditional technology,daily rainfall was translated into discrete variable by rainfall grade and cumulative rainfall became continuous variable if records with very small cumulative rainfall were ignored.Then joint probabilistic model of discrete variable and continuous one was derived,and transiting solution of conditional density function was put forward,together with its approximation via a family of Dirac δ sequences.Naturally,the proposed method was used to analyze conditional density function of cumulative rainfall in Chongqing region,and the numerical results were verified by comparison.However,most of the conditional density functions were irregular and not modeled by simple probability density function,thus the finite mixture distribution was introduced,which is of uncomplicated format and relatively high precision.At last,the joint probabilistic model of daily rainfall and cumulative rainfall was built up by combining frequency function of grade of daily rainfall with conditional density model of cumulative rainfall.