序率模擬應用於氣候變遷衝擊評估與線性動差機率分布適合度檢定

Assessment of Climate Change Impact and L-moments-based Goodness-of-fit Tests by Stochastic Simulation

吳宜珍(Yii-Chen Wu)

指導教授 ： 鄭克聲

國立臺灣大學/生物資源暨農學院/生物環境系統工程學研究所/博士(2011年)

https://doi.org/10.6342/NTU.2011.02775

摘要

水文在大自然界為一個隨機過程，利用序率模擬的技術，若能掌握歷史資料的特性決定重要變數，反應變數間的相互關係，藉由序率模擬可模仿所欲研究水文系統的面貌，近年來已被廣泛應用於水文模式，文中針對過去利用序率模擬建立水文模式所遭遇到的問題，提出二種方法解決；其一為合適機率分布的選擇，研究中利用序率模擬，提出在水文分析上，常用的三參數機率分布線性動差比圖適合度檢定接受域的方法，提昇線性動差比圖適合度檢定在水文分析上實用性。其二為考量空間相關性建立颱風降雨模式，提出一多雨量站颱風事件降雨量之序率模擬，評估不同的氣候變遷情境對颱風降雨量的影響。其結果分述如下：

使用序率模擬建立線性動差比圖適合度檢定之建立
近來線性動差比圖(LMRD)已成為適合度檢定機率分布的重要工具，建立與樣本大小有關的接受域，可顯示出隨機樣本的參數推估不確定性，在線性動差比圖適合度檢定是很有幫助的。二參數機率分布(常態分佈與甘保分布)的線性動差比圖之接受域已建立完成，然而許多水文參數較適合三參數機率分布(如：皮爾遜第三型分布、極端值分布)。由於二參數分布在線性動差比圖上的理論值為一點，而三參數分布的線性動差比理論值為一曲線，所以在接受域的建立上三參數分布比二參數分布困難。
文中利用序率模擬提出一個建立三參數分布線性動差比圖適合度檢定接受域的方法，以皮爾遜第三型分布為例，建立了與樣本有關的95%線性動差比圖適合度檢定接受域，驗證結果非常良好，該接受域可應用在樣本大小20-300，樣本偏態係數不超過3的適合度檢定。

多雨量測站事件降雨量之聯合序率模擬
欲對氣候變遷提出的調適策略、制定合理政策，評估氣候變遷對颱風降雨量的影響是必要工作。氣候模式種類甚多，且不同模式對相同未來情境下之模擬結果亦未必相同。氣候模式之空間尺度無論對水資源管理或水利工程設計而言均不適當。為能顧及氣候變遷之序率特性，透過序率模擬，假設之情境與水文過程之重要變數能直接關連。並可評估各種設定情境下，水文模式之可能變化。
文中以石門水庫集水區為例，考量集水區雨量站的空間相關特性，提出一多雨量站颱風事件降雨量之序率模擬，評估不同的氣候變遷情境對集水區年颱風事件降雨量(BATR)的影響。考量多個雨量站共變異結構，則BATRs的改變更加明顯。由於水文和環境變數上具有顯著的空間相關性，因此氣候變遷針對水文和環境變數上的影響評估，需要考慮多個雨量站共變異結構。

關鍵字

序率模擬 ； 頻率分析 ； 適合度檢定 ； 皮爾遜第三型分布 ； 線性動差 ； 氣候變遷

並列摘要

The dissertation presents two innovative stochastic simulation approaches (1) L-moment based goodness-of-fit (GOF) test, (2) Assessing the impact of climate change.

Through stochastic simulation we established sample-size-dependent 95% acceptance regions for the Pearson type Ⅲ distribution. The proposed approach involves two key elements―the conditional distribution of population L-skewness given a sample L-skewness and the conditional distribution of sample L-kurtosis given a sample L-skewness. The established 95% acceptance regions of the Pearson type Ⅲdistribution were further validated through four types of validity check, and were found to be applicable for goodness-of-fit tests for random samples of any sample size between 20 and 300 and coefficient of skewness not exceeding 3.0.
The other stochastic simulation approach is proposed for assessing the impact of climate changes on basin-average annual typhoon rainfalls (BATRs) under certain synthesized climate change scenarios. Number of typhoon events and event-total rainfalls are considered as random variables characterized by the Poisson and gamma distributions, respectively. The correlation structure of event-total rainfalls at different rainfall stations is found to be significant (higher than 0.8) and plays a crucial role n the proposed stochastic simulation approach. Basin-average annual typhoon rainfalls were simulated for the Shihmen Reservoir watershed in northem Taiwan by considering changes in the mean values of annual number of typhoon events and event-total rainfalls, while assuming the correlation structure of multisite typhoon rainfalls to remain unchanged. The simulation results indicate that changes in expected values of BATR can be easily projected with simpler models; however, changes in extreme properties of BATR are more complicated. Comparing to changes in expected values of BATRs, lesser changes in more extreme events can be observed. This is due to the reduction in coefficient of skewness of gamma distribution BATR under different climate change scenarios. With consideration of the multisite correlation structure, changes in BATRs become more significant. Thus, in assessing the impacts of climate change on many hydrological and environmental variables which exhibit significant spatial correlation pattern, the multisite correlation structure needs to be taken into consideration.

並列關鍵字

Stochastic simulation ； Frequency analysis ； Goodness-of-fit test ； Pearson type Ⅲdistribution

參考文獻

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