淹水事件是世界上最頻繁發生的自然災害之一，可能導致嚴重的的社會經濟影響。近年來，台灣的降雨型態在氣候變遷影響下出現了時間和空間分佈極端化，造成許多地區的淹水頻率提高，淹水風險分析成了水利工程師設計防洪構造物與排水系統至關重要的考量因素；因此，如何量化淹水風險是評估淹水潛勢的關鍵。本研究採用多變數聯結函數，探討雨型變化對三爺溪淹水風險的影響。首先，採用三變數聯結函數耦合臺南雨量站歷史降雨事件的尖峰時刻、總延時及總雨量三者特徵；其次，透過聯結函數蒙地卡羅取樣法隨機生成1000筆降雨的特徵變數值，將隨機降雨特徵資料經均勻雨型法、三角雨型法及簡單尺度不變性馬可夫雨型分配降雨場次；接者，藉由二維水動力模型模擬演算研究區域的平均淹水深度；最後，利用累積分佈函數定義三種雨型條件下的平均淹水深，以作為真實的淹水機率。為了驗證三變數聯結函數對於降雨的模擬能力，本研究另以雙變數聯結函數結果作為對照組，僅考慮總延時及總雨量二者特徵的耦合關係，探討兩者所產製出的降雨變數於推估淹水風險的正確性。研究結果顯示，三變數聯結函數之蒙地卡羅法產製的變數結果比使用雙變數的產製結果更適合描述受到氣候變遷影響的極端降雨狀況；此外，三種雨型當中又以馬可夫雨型方法的淹水機率最符合歷史降雨紀錄的淹水機率趨勢，這些結果不僅證明了三變數聯結函數應用於氣象水文領域的分析可行性，更說明了選擇雨型對於淹水模擬的重要程度。故本研究之方法可應用於多數台灣易淹水地區，更準確的預測未來多變降雨型態產生的淹水風險。

In recent years, extreme rainfalls have increased the flood risk in urban areas without adequate drainage systems. In this study, a new approach has been proposed to analyze the influence of rainfall hyetographs on flood risk using hydraulic simulation and multivariate copulas. First, a joint probability distribution function (PDF) was established using trivariate copula theory to account for the correlation among rainfall depth, duration, and peak time based on historical events in Sanye river basin, Taiwan. Second, the Monte Carlo simulation was adopted based on the established PDF to generate 1,000 random rainfall events. Third, the random events were translated into rainfall hytegraphs with uniform, triangle, and Gauss-marlov shapes based on the characteristics of rainfall depth, duration, and peak time. Finally, the 1,000 rainfall events were input into a two-dimensional hydrodynamic model to simulated the average flood depths for cumulative distribution function (CDF) estimation. In addition to the trivariate copulas, bivariate copulas using rainfall depth and duration as variables were adopted in this research for comparison following the same procedure. The results show that the simulation rainfall data of trivariate copula is more suitable for describing extreme rainfall hyetographs. The flood risks calculated by Gauss-marlov rainfall pattern have the best matches with historical flood risks. This study highlighted the importance of considering correlation among rain variables in flood risk estimation. In the future, this method can be applied in flood-prone areas for disaster management based on frequency analysis.

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