绘点公式在线性矩参数估计中对稀遇频率估计值的影响探讨  

Influence of Plotting Position Formulas on Quantile Estimates in L-moments Analysis

作　　者：苏小玲[1,2] 林炳章[1,2] 吴俊梅 

机构地区：[1]南京信息工程大学水文气象学院,江苏南京210044 [2]南京信息工程大学大气科学学院,江苏南京210044 [3]昆山市气象局,江苏昆山215300

出　　处：《水文》2016年第2期17-22,共6页Journal of China Hydrology

基　　金：水利部公益性行业科研专项(201001047);江苏省高校自然科学研究面上项目(13KJB170017);淮河流域气象开放研究基金项目(HRM201205)

摘　　要：根据太湖流域96个雨量站年最大日雨量资料进行分析计算,在线性矩中当采用绘点公式Pi∶n=(i+A)/(n+B),B>A>-1时,选取不同参数A和B的值,通过蒙特卡洛模拟方法 ,计算实际资料频率估计值与生成资料频率估计值的平均值的均方根误差来探讨不同绘点公式对频率估计值的影响。一般认为A=0,B=0时,线性矩估算是无偏的。重点讨论当估计稀遇频率事件时,A=0,B=0是否仍然恰当;如若不是,A和B取什么值是最佳的组合。结果表明:在线性矩参数估计中对常遇频率估计值采用无偏绘点公式时频率估计值不确定性很小,而对稀遇频率估计值采用无偏绘点公式计算存在较大的不确定性。比较了不同绘点公式对太湖流域年最大日雨量100-y,1 000-y,10 000-y频率估计值的影响,发现在线性矩参数估计中对稀遇频率估计值稳健性表现最好的绘点公式是Pi∶n=(i-0.35)/n,即A=-0.35,B=0。Based on annual maximum daily precipitation data series at 96 gauging stations in the Taihu Lake Basin in East China,via L-Moment Analysis in combination with Monte Carlo Simulation method, the influence of different A and B in the plotting po-sition formula Pi∶n=（i ＋A）/（n ＋B）,B A -1 on quantile estimates has been discussed and assessed. The criterion of RMSE between the actual data frequency estimates and the average of quantiles obtained based on the generated data was applied to computation and analysis in the assessment, focusing on the influence on quantiles for rare frequencies such as 100- y, 1 000-y and 10 000-y events. It is found out that the unbiased estimator of Pi∶n=i/n, i.e. A=0 and B=0 in the plotting formula, has a little influence on frequency estimates in terms of uncertainties for frequent estimates such as 2- y, 5-y and 10-y events in the L-moments analysis,but a considerable influence for rare frequency estimates such as 100-y, 1 000-y and 10 000-y events. It is recommended that the plotting position formula of Pi∶n=（i-0.35）/n, i.e. A=-0.35 and B=0, is good for quantile estimates for all frequencies, particularly for the rare frequencies events though the unbiased estimator of Pi∶n=i/n is also suitable to the frequent events.

关 键 词：绘点公式 线性矩法 蒙特卡罗模拟方法 稀遇频率估计值 

分 类 号：P333.6[天文地球—水文科学] P349[水利工程—水文学及水资源]