降雨強度延時頻率分析（Intensity-Duration-Frequency, IDF）為從事水文設計與分析重要且基本之工作，其分析結果將直接作為後續防災與水工結構物設計之基準。其分析結果之精確性及依此推估未設站地區之降雨等值線為應用兩項重要課題。本研究搜集臺灣南投縣國立臺灣大學實驗林管理處轄區鄰近之中央氣象局及水利署紀錄超過30年之11個測站，以二參數及三參數對數常態分佈、皮爾森第三類分佈及對數皮爾森第三類分佈及極端值第一類分佈等五種機率分布對6種重現期距年及8種延時進行分析，經卡方及K-S適合度檢定後並由最小標準差法（SE）選取最佳機率分布，並由該11測站IDF分析結果以克利金法進行各延時及重現期距之降雨等值線繪製。研究結果顯示五種機率分布差異並不大，但海拔較高之測站較符合極端值第一類分布，海拔較低者較符合皮爾森第三類分佈。以IDF分析結果進行不同延時及重現期距等值線之繪製，在長延時及長重現期距之組合可發現實驗林轄區之降雨有呈現由北往南增加，由東往西增加之趨勢，並於阿里山附近形成明顯之降雨中心，較短延時及重現期距之空間分佈趨勢較不明顯。
Rainfall Intensity-Duration-Frequency (IDF) analysis is a basic and crucial task for hydrologic analysis and design. It provides a key reference for disaster prevention and hydraulic design. The precision of the analysis and estimated rainfall contour are two important issues. Data of eleven rain stations recorded over 30 years from Central Weather Bureau and Water Resources Agency in Nantou County, Taiwan, were analyzed in this study. Five probability distributions including 2-parameter (LN-2) and 3-paramter log-normal (LN-3), Pearson Type III (PT-III), log-Pearson Type III (LPT-III) and Extreme Value Type I (EV-I) were applied and tested by goodness of fit of Chi-square and K-S test. Authors further selected the optimal distribution of 6 return period and 8 duration using minimum Standard Error (SE) and therefore delineate the rainfall contours of different combination of return period and duration using Kriging method. The result shows that there is no significant difference among the five probability distributions, however the data of rain stations in higher elevation fits EV-I distribution and in lower elevation fits LPT-III distribution. The rainfall contours indicates that the rainfall increase from north to south, east to west in longer return period and duration; however the rainfall reveals no significant trend in shorter return period and duration.
