臺灣博碩士論文加值系統

極端降雨事件之發生頻率在近年來不斷提升且造成的巨大的災害，因此區域頻率分析常被用來推估災害洪水發生之回歸週期。然而許多的研究大多給定強烈的假設，如忽略各測站間之降雨相關性。研究指出宜蘭地區降雨被季風所影響，且因為身處三角口袋型，儘管沒有颱風的影響還是出現極端降雨事件。
本研究中主要是應用聯結函數(Copula)於時空降雨分布模式且探討區域性的頻率分析在宜蘭地區，研究期間為1960-2011年。本模型主要是依照以下的三個步驟進行。首先應用聯結函數建立各測站間之降雨相關性在不被邊際分配需要相同的假設影響下，接著配對聯結函數將用來把多變量聯結函數拆解成多個雙變量聯結函數。第二，條件機率分配將用來分析研究區域不同情境下的降雨情形。最後應用聯結函數之區域頻率分析將與過去的傳統方法做比較且同時模擬在相同回歸週期下的降雨情形。
建立測站間相關性結構後，聯合機率密度函數用來模擬複雜的降雨型態和區域頻率分析。在固定中游的降雨大小後，模擬的結果顯示上下游有著不同的降雨型態，且下游的測站之降雨都多於上游的測站；而考慮相關性之區域頻率分析的結果顯示，在考慮測站結構關係可以更加推估出貼近真實的極限降雨。對於單一測站的回歸週期模擬結果中，在較小的回歸週期中，降雨強度的變異較大；在較高的回歸週期中，變異則不大。因此考慮相關性的頻率分析除了可以模擬更多的降雨型態之外還可以得到區域真實的極限降雨事件，並且證實在區域分析中相關性的重要性。

Extreme rainfall events occur increasingly and cause enormous loss; consequently, regional frequency analysis has become more important and widely used to estimate the return period of floods. However, the dependence among stations was not considered in the past. Studies have shown that the variation of rainfall patterns was affected by monsoon, especially during winter, in I-Lan area, i.e. the northeast corner of Taiwan. The most important factor that affects the precipitation in I-Lan is the local circulation caused by the triangle-shaped terrain. Therefore, without the influence of strong weather systems, e.g. typhoon, extreme rainfall events still occur.
The purpose of this study is applying techniques of copula to analyze the multisite stochastic hourly rainfall patterns and regional frequency considering the dependence among surrounding rainfall stations during the period of 1960-2011. This model is following three steps to analyze the rainfall patterns and return periods. First, we use copulas to model the dependence among rainfall stations without the influence of marginal distributions, and then pair-copula structures are applied to separate the multivariate copula into several of bivariate copulas. Second, conditional probability density function is used to realize the major space-time pattern of local precipitation with different scenarios. Finally, copula-based regional frequency analysis is compared with the index flood methods with L-moments, and the return period simulation
IV
considering dependence among stations is also exhibited in this part.
After constructing the dependent structure, the joint density function can be used to simulate the complicate regional rainfall patterns and regional return periods. In a specific scenario, the rainfall in downstream is more than in upstream when the extreme rainfall event occurs in midstream. Furthermore, copula-based return periods considering dependence are more accord with the real events than the index flood methods with L-moments. Considering dependent structure by copula can not only simulate the complex rainfall patterns but also reduce the possibility of underestimated or overestimated situation.

謝誌 .................................................................................................................................. I
中文摘要 .......................................................................................................................... II
Abstract ........................................................................................................................... III
Table of Contents ............................................................................................................. V
List of Figures ............................................................................................................... VIII
List of Tables .................................................................................................................... X
Chapter 1 Introduction .................................................................................................. 1
1. Motivation and Objectives.................................................................................... 2
2. Chapter Description .............................................................................................. 3
3. Flow Chart ............................................................................................................ 5
Chapter 2 Literature Review ......................................................................................... 6
1. Regional Frequency Analysis ............................................................................... 6
2. L-moments ............................................................................................................ 8
3. Copulas ................................................................................................................. 9
Chapter 3 Materials and Methods ............................................................................... 11
1. Study Area .......................................................................................................... 11
VI
2. Copula Functions ................................................................................................ 13
2.1 Copulas ........................................................................................................... 13
2.2 Copula Family ................................................................................................ 14
2.3 Pair Copula ..................................................................................................... 17
3. L-Moments ......................................................................................................... 20
3.1 Introduction to L-Moments ............................................................................ 20
3.2 Parameter Estimation Using L-Moments ....................................................... 23
3.3 Choice of a frequency distribution ................................................................. 29
4. Regional Frequency Analysis ............................................................................. 31
4.1 Multi-site frequency analysis ......................................................................... 31
4.2 Index flood method ......................................................................................... 32
5. Statistic Model Analysis Tool ............................................................................ 33
5.1 Rank correlation - Kendall’s ...................................................................... 33
5.2 Akaike Information Criterion ......................................................................... 33
Chapter 4 Result and Discussion ................................................................................. 34
1. Data selection ..................................................................................................... 34
1.1 Data integrity .................................................................................................. 34
VII
1.2 Extreme rainfall event thresholds ................................................................... 36
2. Copula functions ................................................................................................. 39
2.1 Marginal distributions .................................................................................... 39
2.2 Vines structure-pair copulas ........................................................................... 41
2.3 Copula selection ............................................................................................. 43
2.4 Rainfall Scenario ............................................................................................ 45
3. L-moment ........................................................................................................... 53
3.1 Sample L-moments and Identification of homogeneous regions ................... 53
3.2 Choice of a frequency distribution ................................................................. 57
4. Regional frequency analysis ............................................................................... 60
4.1 Copulas versus L-moments ............................................................................ 60
4.2 Simulation for return periods .......................................................................... 64
Chapter 5 Conclusion and Recommendation .............................................................. 70
1. Conclusion .......................................................................................................... 70
2. Recommendation ................................................................................................ 71
References ...................................................................................................................... 73

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