雙變數迦瑪分布頻率因子序率模擬法及其應用於評估氣候變遷對年颱風降雨量影響之研究

Abstract

序率模擬近年來被廣泛應用發展於水文模式、洪水風險分析及環境影響評估等方面，研究皆顯示序率模擬不但可以使變量具有概率意義且可將其不確定性予以量化。氣候變遷對降雨特性之影響，多年以降雨量及季節降雨量為研究對象。對事件降雨量及延時之降雨特性而受氣候變遷之影響，則因為記錄較少且不連續，而少有研究成果。但從排水設計與水庫供水線上調度而言，則事件降雨之特性至關重要。因此，本研究主要目的在於建立降雨歷程序率模擬之模式，分析暴雨事件之特性及氣候變遷對各種暴雨參數特性之影響，並建立參數化之序率暴雨連續模擬模式，以提供模擬氣候變遷對集水區年颱風降雨之影響，並建立該影響之機率評估方法。 本文雙變數迦瑪分布頻率因子序率模擬法及其應用於評估氣候變遷對颱風降雨量影響之研究分為三個部分，首先進行不同降雨類型之事件切割分析，並針對不同類型降雨之延時、總降雨量及降雨間隔時間進行不同分佈之K-S檢定、卡方檢定、分佈模式選取及Mardia等適合度檢定。第二部分研究提出一以頻率因子為基礎之雙變數伽瑪分布，以成功地進行延時與總降雨量雙水文量之序率模擬。模擬模式中首先推導出雙變量常態分布相關係數與雙變量伽瑪分布相關係數之互相對應關係式。即可透過水文頻率分析之一般方程式，將雙變量常態分布樣本轉換為雙變量伽瑪分布樣本。研究結果顯示本研究利用頻率因子進行雙變量伽瑪模擬之隨機樣本配對不僅具有欲模擬邊際密度函數之成分隨機變數且可掌握兩者間之相關係數。由模擬之雙變數樣本配對散佈圖亦顯示出兩變數呈現適當的線性型態(獨立結構)且此特性可常見於水文應用上。本模式亦改善前人雙變數伽瑪分布模擬模式之參數較為複雜且繁衍不易之問題。最後利用所提出之參數化序率暴雨模擬模式以進行連續降雨之模擬，且結合不同氣候情境條件假設，將之應用於評估氣候變遷對集水區年颱風降雨之影響;例如假設氣候變遷導致某地颱風降雨事件次數增加，則可用以評估其對集水區年颱風降雨之影響。

Many studies related to climate change focused on global, continental or regional scale effect in space and annual or seasonal scale effect in time. However, for practical planning and engineering design, it is necessary to deal with local (spatial) and event (temporal) scales. However, the mathematical expressions of many previous stochastic simulation models are complex with a large number of parameters to be calibrated from the observed rainfall data and have computational limitations. In this dissertation, a continuous stochastic storm-rainfall simulation model (SRSM) is presented to accommodate the aforementioned scales and provide quantitative assessment of the impact on annual typhoon rainfall under given scenarios of climate change. The SRSM is a parametric stochastic simulation model which considers random processes of four major storm types: frontal rainfall, Mei-Yu, convective storms and typhoons occurring annually in Taiwan. Random process of a storm rainfall event is characterized by (1) inter-arrival time of storm events and (2) joint probability distribution of storm duration and total rainfall depth. Occurrences of storm events of a certain storm type can be modeled as a Poisson process and the inter-arrival time is modeled as a random variable with exponential distribution. A frequency-factor based bivariate gamma distribution model is proposed for generating random sample pairs (duration and total depth), which have not only the desired marginal densities of component random variables but also their correlation coefficient. Under certain scenarios of climate change, i.e. when the average number of typhoon events for the study site increases or decreases, we can assess the impact of climate change on annual typhoon rainfall from a stochastic point of view.