本文研究目的在於探討台灣地區北部、中部、南部及東部區域之區域乾旱頻率，本文主要應用指數洪水法(index flood method)之概念並配合線性動差(L-moment)推估參數以建立各區域之乾旱機率分佈並推估不同迴歸期之乾旱量及乾旱延時。本文以標準化降雨指數(standardized precipitation index，SPI)定義乾旱，首先選定能代表各雨量站年雨量資料的機率分佈，而後將年雨量轉換為SPI值，本文定義SPI小於0為乾旱的開始，至大於0為止為一乾旱事件，其間連續負值SPI的時段為乾旱延時，乾旱事件之累積SPI值稱為乾旱量，此二乾旱特性為本文分析區域乾旱頻率的基礎。其次利用以線性動差為基礎的不一致(discordancy)、異質性(heterogeneity)及適合度(goodness-of-fit)估量評估同一區域之乾旱資料是否一致及均勻，並選取一合適的區域乾旱量及乾旱延時機率分佈函數。本文以台灣地區共35個紀錄年限超過30年的雨量站之年雨量紀錄，經以前述步驟分析得北、中、南、東各區域最適合代表區域無因次乾旱量的分佈分別為皮爾遜第III型分佈(Pearson type III distribution)、三參數對數常態分佈(three-parameter lognormal distribution)、通用帕雷托分佈(generalized Pareto distribution)及皮爾遜第III型分佈，而最適合代表區域無因次乾旱延時的分佈在北區及中區皆為皮爾遜第III型分佈，南區及東區皆為通用帕雷托分佈。決定最佳的區域乾旱頻率模式後，即可建立區域內各站乾旱量及乾旱延時與迴歸期之關係，並可推估各站發生不同頻率之乾旱量及乾旱延時，因此各區域各站曾發生過之歷史乾旱事件之迴歸期即可據以推估。

This study aims to investigate the regional drought frequency for the north, central, south, and east regions in Taiwan. Index flood method associated with L-moment estimation are employed to establish the regional drought frequency distribution for each region and to estimate the return periods for various drought magnitudes and drought duration. In this study, standardized precipitation index (SPI) is used to define droughts. Probability distribution for annual rainfall data is determined first, then followed by transforming the annual rainfall data into SPI. A drought event is defined as the period during which the SPI is below zero. The continuous period of negative SPIs is considered as the drought duration and the cumulative SPIs during the drought duration is considered as the drought magnitude. These two drought characteristics are considered for regional drought frequency analysis in this study. The L-moment based discordancy, heterogeneity, and goodness-of-fit measures are used to detect the unusual sites and select the regional probability distributions of droughts. A total of thirty-five annual rainfall data with record length exceeding 30 years from different regions in Taiwan are selected to illustrate the proposed methodology. The results show that the best data fitted dimensionless regional drought magnitude probability distributions for north, central, south, and east regions are Pearson type III, three-parameter lognormal distribution, generalized Pareto, and Pearson type III distributions, respectively. The best fitted dimensionless regional drought duration probability distributions for north and central regions are Pearson type III distribution, while the generalized Pareto distribution is the best data fitted model for drought duration in south and east regions. The at-site frequencies of drought duration and magnitude for each region can then be determined by the index flood method and used to estimate the return periods of drought duration and magnitude for historical drought events.

目錄
                                                                 頁次                                                       
謝誌	I
中文摘要	II
Abstract	III
目錄	V
圖目錄	VII
表目錄	IX
符號表	X
第一章 前言	1
1.1 研究動機	1
1.2 章節架構	2
第二章 文獻回顧	4
2.1 乾旱定義及標準化降雨指數	4
2.2 區域頻率分析	6
第三章 研究方法	8
3.1乾旱定義及標準化降雨指數	8
3.2區域頻率分析(regional frequency analysis)	12
3.2.1 指數洪水法(index flood method)	12
3.2.2 線性動差法推估參數	14
3.2.3 區域頻率分析之步驟	16
3.2.4 不一致估量(discordancy measure)	17
3.2.5 異質性估量(heterogeneity measure)	19
3.2.6 適合度估量(goodness-of-fit measure)	20
3.2.7 機率分佈及參數推估	21
3.2.8 頻率分析	27
第四章 乾旱資料	29
4.1 雨量資料概述	29
4.2年雨量機率分佈及SPI	33
第五章 結果與討論	40
5.1 乾旱資料特性	40
5.2 乾旱資料一致性及均勻性檢定	45
5.3 適合度檢定及區域乾旱機率分佈	49
5.4 區域頻率分析	57
5.5 歷史乾旱事件之探討	66
第六章 結論與建議	70
6.1 結論	70
6.2 建議	71
參考文獻	73
 
圖目錄
頁次
圖3-1 SPI計算示意圖	9
圖3-2 SPI乾濕程度分級圖	11
圖3-3 乾旱事件、乾旱延時、乾旱量及乾旱間距定義示意圖	11
圖4-1 各區域雨量站相關位置圖	32
圖4-2 北部區域太閣南站(01D100)年雨量理論分佈與觀測值比較圖	35
圖4-3 中部區域珊珠湖站(01E240)年雨量理論分佈與觀測值比較圖	35
圖4-4 南部區域大湖山站(01L390)年雨量理論分佈與觀測值比較圖	36
圖4-5 東部區域銅門站(01T070)年雨量理論分佈與觀測值比較圖	36
圖4-6 北部區域太閣南站(01D100)歷年SPI變化情形	37
圖4-7 中部區域珊珠湖站(01E240)歷年SPI變化情形	37
圖4-8 南部區域大湖山站(01L390)歷年SPI變化情形	38
圖4-9 東部區域銅門站(01T070)歷年SPI變化情形	38
圖4-10 各區域各站發生乾旱之年份(      ：無紀錄之年份)	39
圖5-1 乾旱事件頻率與平均乾旱量之關係圖	44
圖5-2 乾旱事件頻率與平均乾旱間距之關係圖	44
圖5-3 乾旱事件頻率與平均乾旱延時之關係圖	45
圖5-4 各區域之無因次乾旱量機率分佈函數	54
圖5-5 各區域之無因次乾旱量分位數	55
圖5-6 各區域之無因次乾旱延時機率分佈函數	55
圖5-7 各區域之無因次乾旱延時分位數	56
圖5-8 北部區域各站迴歸期與乾旱量之關係圖	60
圖5-9 中部區域各站迴歸期與乾旱量之關係圖	60
圖5-10 南部區域各站迴歸期與乾旱量之關係圖	61
圖5-11 東部區域各站迴歸期與乾旱量之關係圖	61
圖5-12 北部區域各站迴歸期與乾旱延時之關係圖	62
圖5-13 中部區域各站迴歸期與乾旱延時之關係圖	62
圖5-14 南部區域各站迴歸期與乾旱延時之關係圖	63
圖5-15 東部區域各站迴歸期與乾旱延時之關係圖	63
 
表目錄
                                      頁次
表3-1 SPI乾溼程度分級表	10
表3-2 不一致估量標準值	18
表4-1 各區域雨量站基本資料	30
表4-2 各區雨量站的年平均雨量及gamma分佈參數	31
表5-1 各區域各站之乾旱資料特性	43
表5-2 各區域各站乾旱量之線性動差比及不一致估量( )	47
表5-3 各區域各站乾旱延時之線性動差比及不一致估量( )	48
表5-4 各區域異質性估量( )	49
表5-5 各區域適合度估量( )	50
表5-6 各區域所選用的機率分佈函數及其參數值	51
表5-7 各區域不同機率之無因次乾旱量和乾旱延時	56
表5-8 各區域各站不同迴歸期之乾旱量	64
表5-9 各區域各站不同迴歸期之乾旱延時	65
表5-10 1954年、1980年、1993年及2002-2003年乾旱量與乾旱延時迴歸期	68
表5-10(續) 1954年、1980年、1993年及2002-2003年乾旱量與乾旱延時迴歸期	69

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