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。

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.

誌謝	I
中文摘要	II
Abstract	III
目錄	V
表目錄	VIII
圖目錄	IX
符號表	X
第一章、緒論	1
1.1研究動機及目的	1
1.2文獻回顧	2
1.3本文架構	4
第二章、研究方法	5
2.1雨量資料趨勢檢定	5
2.2區域頻率模式的建立	6
2.2.1 均勻區域的劃分	7
2.2.2指數洪水法	11
2.2.3線性動差法推估參數	13
2.2.4資料不一致性檢定	15
2.2.5資料均勻性檢定	16
2.2.6機率分佈適合度檢定	17
2.3無因次區域年最大一日雨量機率分佈	18
2.4 區域頻率分析	23
2.4.1設站地點之頻率分析	23
2.4.2未設站地點之頻率分析	24
第三章、雨量資料概述	34
第四章、結果與討論	35
4.1年最大一日雨量趨勢檢定	35
4.2均勻區域劃分結果	35
4.3均勻區域內年最大一日雨量檢定	43
4.3.1一致性檢定	43
4.3.2均勻性檢定	43
4.4均勻區域內頻率模式建立	44
4.5設站地點之頻率分析	47
4.6未設站地點之頻率分析	54
4.7區域頻率模式驗證	60
五、結論	62
參考文獻	63
表目錄
                                                          
表2- 1不一致估量的刪除標準	16
表3- 1本文所選用雨量站基本資料	29
表3- 2本文所選用各雨量站之年最大一日雨量特性	31
表4- 1各區域各雨量站動差比及不一致估量	37
表4- 2各區域異質性估量	44
表4- 3各區域適合度估量	45
表4- 4各區域所選定之機率分佈函數及其參數值	45
表4- 5各區域各站不同復現期之年最大一日雨量	52
表4- 6未設站地點之頻率分析	59
表4- 7各均勻區域刪除站頻率分析誤差	60
圖目錄
                                                       
圖3- 1本文所選用雨量站相關位置圖	28
圖3- 2各雨量站年最大ㄧ日雨量平均值之等值線圖	33
圖3- 3各雨量站年最大ㄧ日雨量變異係數之等值線圖	34
圖4- 1不同分群數目之側影圖	39
圖4-2各均勻區域分區結果	42
圖4-3各區域之無因次年最大一日雨量機率分佈函數	46
圖4-4各區域之無因次年最大一日雨量分位數	47
圖4-5各區域不同復現期與無因次年最大一日雨量關係圖	48
圖4- 6第Ⅰ區各站不同復現期之年最大一日雨量關係圖	50
圖4- 7第Ⅱ區各站不同復現期之年最大一日雨量關係圖	50
圖4- 8第Ⅲ區各站不同復現期之年最大一日雨量關係圖	51
圖4- 9理論變異量模式與實測變異量之比較	55
圖4- 10假設未設站地點之位置圖	57

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