利用區域化法推估台灣地區未設站地點年最大ㄧ日雨量之頻率

Frequency Analysis of Annual Maximum 1-Day Rainfall for Ungauged Sites in Taiwan Using Regionalization Approach

黃亮芸(Liang-Yun Huang)

指導教授 ： 蕭政宗

淡江大學/工學院/水資源及環境工程學系碩士班/碩士(2007年)

https://doi.org/10.6846/TKU.2007.00011

摘要

本文研究目的在於應用區域化方法以推估台灣地區未設站地點不同頻率之年最大一日雨量，本文首先利用指數洪水法(index flood method)配合由線性動差所推估之參數來建立區域頻率模式，並以克利金法(kriging)推估未設站地點之平均年最大一日雨量，以進行該地點之頻率分析。區域頻率模式的建立是以均勻區域為單元，本文將以集群分析(cluster analysis)依各測站之座標與年最大一日雨量之平均值及變異係數來劃分均勻區域，並以線性動差為基礎的不一致及異質性估量來檢定所劃分區域內資料的一致性及均勻性，其次再以適合度估量選取最佳區域頻率模式。本文以台灣地區77個雨量站的年最大一日雨量為分析基礎，經以集群分析判定最佳均勻區域劃分數為三區，各區域之最佳頻率分佈除一區為通用帕雷托分佈(generalized Pareto distribution)外，其餘二區均為皮爾遜第Ⅲ型分佈Pearson type Ⅲ distribution)。至於未設站地點之頻率分析，本文將先以克利金法建立年最大一日雨量平均值及變異係數之空間變異量(variogram)模式，未設站地點即可據以推估其年最大一日雨量平均值及變異係數，其次計算未設站地點座標與年最大一日雨量平均值及變異係數至各均勻區域中心之距離，以最小距離來判定未設站地點所歸屬的區域，之後即可利用該區域所建立之區域頻率模式及該地點推估之平均年最大一日雨量進行該地點之頻率分析。

關鍵字

區域頻率分析 ； 指數洪水法 ； 線性動差 ； 克利金 ； 年最大一日雨量

並列摘要

The purpose of the study aims to estimate frequencies of annual maximum 1-day rainfall for ungauged sites in Taiwan using regionalization approach. The index flood method with parameters estimated by L-moments is used to establish the regional frequency model. Kriging is then employed to estimate the mean annual maximum 1-day rainfall of ungauged sites in order to analyze the rainfall magnitudes of various frequencies. Delineation of homogeneous regions is determined by cluster analysis in this study based on the coordinates of the rainfall gauge stations, the means and coefficient of variation of the annual maximum 1-day rainfall. The L-moment based discordancy, heterogeneity, and goodness-of-fit measures are then used to detect unusual sites and select the optimal regional probability models. In this study, a total of 77 rainfall gauge stations are used as the basis to estimate the frequencies of the annual maximum 1-day rainfall for ungauged sites. The number of homogeneous regions derived by cluster analysis is 3. The best regional probability model for one region is Pearson type Ⅲ distribution, and generalized Pareto distribution is the best model for the other two regions. Frequency analysis for ungauged sites needs to establish the variogram models of the mean and coefficient of variation of the annual maximum 1-day rainfall first. The obtained variogram models is then used to estimate the mean annual maximum 1-day rainfall for the ungauged sites. The ungauged sites belong to which homogeneous region depend on the minimum distance to the centroid of the homogeneous regions. Combined with the derived regional frequency model and estimated mean annual maximum 1-day rainfall, the computing procedures of frequency analysis for ungauged sites are identical with the procedures of gauged sites.

並列關鍵字

Regional frequency analysis ； Index flood method ； L-moment ； Kriging ； Annual maximum 1-day rainfall

參考文獻

蕭政宗、楊志傑，2006，台灣地區之區域乾旱頻率分析，農業工程學報，第50卷，第2期，第83-101頁。

Kendall, M. G., 1975, Rank Correlation Measures, 1stEd., Charles Griffin, London.

Atiem, I. A., and Harmancioglu, N. B., 2006, Assessment of regional floods using L-moments: The case of the River Nile, Water Resources Management, 20(5), 723-747.

Belle, G. V., and Hughes, J. P., 1984, Nonparametric tests for trend in water quality, Water Resources Research, 20(1), 127-136.

Burn, D. H., 1989, Cluster analysis as applied to regional flood frequency, Journal of Water Resources Planning and Management, 115(5), 567-582.