季節性を持つ水文時系列に基づくPDS法とAMS法の比較

Abstract

本研究は, わが国における豪雨と洪水を対象に, これらの発生過程が季節性を持つことを示す。このような水文事象に対して, 毎年最大値系列(AMS)を抽出し, 一般化極値(GEV)分布により確率水文量を推定する場合, 過大な確率水文量が求められることを示している。ただし, 水文事象の一年間の平均生起個数が4個程度以上であるか, AMS解析とPDS解析による確率水文量が一致する場合に, GEV分布は精度の良い確率水文量を与える。

This paper compares AMS (Annual Maximum Series) method with PDS (Partial Duration Series) method in hydrologic frequency analysis through a Monte Carlo experiment. The numerical experiment takes into account the seasonality inherent in hydrologic processes. Based on 174 two-day areal rainfall series in 43 years and 117 flood peak discharge series in 47 years, statistical analysis has revealed the difference between the actual occurrence process and the Poisson process that holds for rare events.For two series of two-day rainfalls and peak discharges, the Monte Carlo experiment deals with distribution of occurrence interval and distribution of extreme rainfalls and discharges. The exponential distribution for inter event time is used for the Poisson process, while the empirical distributions obtained by the statistical analysis are used for seasonal rainfall and discharge series.The experiment has revealed the importance of the effect of seasonality. When applying the GEV (Generalized Extreme Value) distribution to AMS, one would overestimate 100-year quantile because of ignoring the seasonality.However, if the quantile estimate obtained by the GP (Generalized Pareto) distribution for PDS is almost the same as the one by GEV-AMS approach, the use of GEV can be justified. It was also concluded that the average number of PDS elements in a year should be four or more to avoid the overestimation by the GEV-AMS approach.