年降水量概率分布的贝叶斯推断及其数值求解  

Bayesian Inference of Annual Precipitation Probability Distribution and Its Numerical Solution

作　　者：孔强 KONG Qiang(Shijiazhuang Hutuo River Ecological Engineering Operation and Maintenance Service Center,Shijiazhuang 050000,China)

机构地区：[1]石家庄市滹沱河生态工程运维服务中心,河北石家庄050000

出　　处：《水资源开发与管理》2023年第12期6-13,共8页Water Resources Development and Management

摘　　要：本文对43个城市年降水量系列和5个径流系列样本进行了W、D统计量正态性检验,结果显示,年降水量有41个样本系列通过了95%置信水平下正态性假设检验;对水文系列总体均值和方差进行了区间估计,分析了在置信区间边缘,水文样本可能的正态总体组合。同时,以贝叶斯理论为基础,将可能存在的正态总体分布组合作为先验分布,以样本的P-Ⅲ频率曲线作为似然函数,采用蒙特卡罗(MC)方法,计算了贝叶斯后验概率分布的密度函数,从而得出了给定概率的降水量值置信区间。多地区长序列年降水量正态性检验表明,区域多年降水量数值满足正态性条件。提出了基于给定样本估计可能正态分布范围的方法,以贝叶斯公式推断得出的频率计算结果,能够解释现有频率计算方法存在的预测结果不稳定的问题,可为水文频率计算方法改进提供参考和依据。The normality test of W and D statistics is carried out on 43 urban annual precipitation series and 5 runoff series samples.The results show that 41 sample series of annual precipitation passed the normality hypothesis test at 95% confidence level.The mean and variance of the hydrological series are estimated,and the hydrological samples are analyzed from the possible normal population combinations at the edge of the confidence interval.Based on Bayesian theory,the density function of Bayesian posterior probability distribution is calculated by using the probability function of P-Ⅲ frequency curve of the sample,and the confidence interval of precipitation value is obtained by using Monte Carlo(MC)method.The normality test of annual precipitation for long series in many regions shows that the regional annual precipitation meets the normal condition.This paper proposes a method to estimate the possible normal distribution range based on a given sample,and the frequency calculation results inferred by Bayesian formula can explain the instability of the prediction results of the existing frequency calculation methods,and provide reference and basis for the improvement of hydrological frequency calculation methods.

关 键 词：水文频率计算 正态性检验 贝叶斯推断 P-Ⅲ分布 置信区间 

分 类 号：TV124[水利工程—水文学及水资源]