Function applicability to class conditional probability density of hourly rainfall

Abstract

暴雨强度公式在水文、气象、工程设计等各领域都是非常关注的问题,而常用降雨概率分布函数的适用性欠缺,理论分布函数一直处于争鸣之中。从逐时降雨概率密度函数的适用性分析入手,有利于发现普适且恰当的理论密度函数。本文从我国暴雨洪涝灾害易发区中沿30°N选取4个经纬度长方形区域(雅安附近、鄂西南、江汉平原南部、杭州湾西),并在其南、北各选一对比分区(海南岛、郑州),对6个分区内降雨资料直接采用全样本,统计逐时降雨的三类概率密度经验函数,对照这些函数的特性,从理论上分析了众多分布函数的适用性,筛选适用函数并进行拟合试验,优选出理论密度函数。研究结果表明:三参广义伽玛函数拟合误差最小,而两参广义正态函数更恰当、被首推为理论密度函数;拟合参数寻优时的目标函数综合了乘性与加性误差模型,能使拟合曲线兼顾头尾;本研究有别于极值降雨概率分布中仅采用极少部分样本的方法,采用降雨概率密度方法替代传统的年极值法,使重现期计算更准确有效,能提高暴雨强度公式的科学性,拟合的高精度与函数的普适性有望解决降雨概率分布模型统一的问题。;Due to the deficiency of international-unified theoretical function for rainfall probability distribution, it is necessary to analyze the applicability, appropriateness and universality of commonly used probability density function(PDF). On the basis of summarizing the characteristics of three kinds of class conditional probability density of hourly rainfall, the applicability of 20 kinds of functions is theoretically analyzed and compared. The generalized Gamma distribution(GΓD), generalized normal distribution(GND) and Weibull distributions are selected as reference functions, and the genetic algorithm and genetic algorithms are used to carry out fitting experiments. When the fitting deviation is equivalent to the observation error, a necessary condition for the appropriateness of the theoretical distribution function is used for discriminant analysis. The fitting results show that the Weibull distribution performs worst, the GΓD has the smallest fitting deviation, and the GND performs best. Therefore the GND is recommended for theoretical distribution fitting. In addition, the genetic algorithm can directly obtain the optimal approximate solution through multi-objective parameter optimization, which can simplify the derivation and calculation steps. The multiplicative and additive deviation models are both used as objective functions, which can take the beginning and the end of fitting curves, as well as the absolute and relative deviations into account.