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系統識別號 U0026-1210201114593600
論文名稱(中文) 以聯結函數建立不同重現期距之設計暴雨歷線
論文名稱(英文) Copula-based Design Hyetographs for Various Recurrence Intervals
校院名稱 成功大學
系所名稱(中) 水利及海洋工程學系碩博士班
系所名稱(英) Department of Hydraulics & Ocean Engineering
學年度 100
學期 1
出版年 100
研究生(中文) 王心怡
研究生(英文) Hsin-Yi Wang
學號 n8891102
學位類別 博士
語文別 中文
論文頁數 117頁
口試委員 指導教授-蔡長泰
指導教授-蕭政宗
召集委員-林國峰
口試委員-吳瑞賢
口試委員-周乃昉
口試委員-游保杉
中文關鍵字 聯結函數  雙變量頻率分析  聯合重現期  集群分析  設計歷線 
英文關鍵字 Copulas  Bivariate frequency Analysis  Join recurrence intervals  Cluster analysis  Design hyetographs 
學科別分類
中文摘要 在防洪及排水工程設計中,設計歷線(design hyetograph)為不可或缺之基本水文資料,其大多利用降雨強度(或深度)等單變量的特性,作為工程設計的標準,且假設歷線不因不同重現期而異。然而歷線的描述除了需要降雨強度(intensity)、尖峰時間(time to peak)、延時(duration)和總降雨量(rainfall depth)等變數之關係外,更需了解其雨量在時間上之分佈情形。僅以單變量的頻率分析不能完整描述水文事件之特性與其時間歷程。基於歷線的重要性及前述的問題,本文將提出一推導不同重現期設計歷線之理論方法。
本文建議直接由實測降雨資料推求不同重現期之設計歷線。首先藉由聯結函數(copula)建立降雨深度–延時聯合機率分佈,並推導出降雨深度–延時–頻率(depth-duration-frequency, DDF)之關係式。再利用降雨事件之特性以集群分析(cluster analysis)法將降雨事件分類。最後依據各分類事件利用累積降雨曲線與累積分佈函數(cumulative distribution function, CDF)形狀相似之關係,以機率密度函數(probability density function, PDF)代表降雨歷線,即可得到不同重現期之設計降雨歷程。
文末則以高雄氣象站之47年(1960-2006)實測降雨資料說明本文建議之方法,並推導該站不同重現期在不同降雨延時下之設計降雨歷線。研究結果可知高雄氣象站之颱風降雨事件,其降雨深度為gamma分佈,降雨延時為Gumbel分佈,聯合分佈是以Plackett copulas表示,並建立DDF關係式。在設計降雨歷線上,可將颱風降雨歷線分為形狀左偏型、中間型和右偏型等三類,分別以Beta、Weibull、和lognormal PDF描述各群之代表歷線。最後結合DDF關係式與代表歷線之PDF,可得到不同重現期下,不同降雨延時之設計歷線。此結果可提供防洪排水工程規劃在水文事件設計風險上之參考,亦使水文頻率分析有更進一步的發展。
英文摘要 Hyetograph design is essential for hydrologic modeling and stormwater drainage design, especially for hydrologic processes which have made water resources engineering employing some hydrologic characteristics as planning and design criteria of flood-mitigaiton facilities, such as rainfall intensity for rainfall frequency analysis. However, the traditional method to derive the design hyetograph is using the empirical method to design rainfall hyetograph and have fixed shapes for hypothesis. Besides, to describe a complete hydrological time distribution function needs several variables, such as intensity, time to peak, duration and rainfall depth. The univariate frequency analysis can not give the hyetograph of any specific recurrence intervals. This study thus aims to propose a methodology to derive the design hyetographs for various recurrence intervals.
Firstly, we analyze bivariate frequency of storm events, copulas are then employed to model the dependence between rainfall depth and duration in storm events. Then we derive the depth-duration-frequency (DDF) formula based on using copulas to represent the joint distribution of rainfall depth and duration. In hyetograph design, using cluster analysis to divide typhoon events, and using probability density functions (PDFs) to fit the shapes of hyetographs. Lastly, we link up DDF with PDFs to represent design hyetographs.
Typhoon data recorded at Kaohsiung Weather Station are used as an example to illustrate the proposed methodology. The marginal distributions for rainfall depth and duration are fitted as the three-parameter gamma and Gumbel distributions, respectively. The Plackett copula is selected to construct the DDF formula.The DDF allows rainfall depth for a specific rainfall duration and recurrence interval to be estimated. In hyetograph design, typhoon events are dived for three groups, such as negative skew type, middle type and positive skew type. The best fitting to the observed hyetographs are Beta, Weibull and lognormal probability density function, respectively. These results of storm frequency analysis could give the hyetograph of any specific recurrence intervals. The design hyetographs for various recurrence intervals are achieved through combining DDF and PDFs. Results obtained from this study can improve understanding of complex hydrologic processes and enhance design safety criterion of hydraulic structures.
論文目次 中文摘要 I
ABSTRACT II
誌 謝 IV
目 錄 V
表目錄 VIII
圖目錄 IX
符號說明 XI
第一章 緒 論 1
1.1研究緣起 1
1.2研究動機與目的 2
1.3本文組織 3
第二章 文獻回顧 5
2.1歷線設計方法 5
2.2單變量頻率分析 6
2.3雙變數聯合機率分佈 7
2.4聯結函數在水利工程之應用 8
第三章 研究方法 11
3.1歷線函數建立 11
3.1.1機率密度函數 13
3.1.2形狀參數推估方法 15
3.2多變量統計分析方法 17
3.2.1主成份分析 17
3.2.2 K-Means集群分析法 21
3.3頻率分析 22
3.3.1雙變量頻率分析 23
3.3.2聯結函數(copula) 25
3.4適合度檢定方法 30
第四章 降雨深度–延時–頻率分析 33
4.1雨場切割與資料統計特性 33
4.1.1暴雨事件選取標準 33
4.1.2降雨深度和延時之分佈特性 36
4.2雙變量分佈之聯合分析 39
4.2.1參數推估方法 39
4.2.2聯結函數之選取 41
4.2.3條件式分佈特性 44
4.3降雨深度-延時-頻率理論關係式之建立 45
4.3.1聯合重現期 45
4.3.2條件式重現期 47
4.4小結 48
第五章 不同重現期之設計暴雨歷線 50
5.1歷線形狀之機率密度模式 50
5.1.1降雨統計特性與無因次分析 50
5.1.2主成份分析與集群分析 52
5.1.3代表歷線之建立與選取 63
5.2不同重現期距之降雨歷線設計 67
5.2.1雙變量降雨歷線設計 68
5.2.2常用經驗式設計歷線比較 71
5.3小結 76
第六章 結論與建議 77
6.1結論 77
6.2建議 78
參考文獻 79
附錄一 最大概似法推求參數 87
附錄二 原始資料矩陣 90
附錄三 不同重現期下一日和二日設計暴雨歷線 102
附錄四 經驗式與機率密度模式之歷線比較 106
自 述 115
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