採用廣義極值分布對馬來半島極端降雨進行統計模擬

A Statistical Modeling of Extreme Rainfall in Peninsular Malaysia Using the Generalized Extreme Value (Gev) Distribution

本研究採用時間序列為1971-2007年，馬來西亞水利灌溉局22個自動降雨測站之日降水資料，取年最大值及季最大值對馬來半島極端降雨的變化進行分析，進一步擬合廣義極值分布模式（GEV），計算出極端降雨的重現水平。根據研究結果顯示，半島東部地區的年最大降雨強度最高，而半島中部地區為低強度的極端降雨，但是在近年來有上升的趨勢，表示此區在未來可能面臨過去所未曾遭遇到的極端洪災事件。在季節分析上，中部地區春秋二季在未來可能遭受更頻繁的水患事件，而北部地區在秋季時則可能面臨乾旱的災害。本研究以GEV分布模式推估出50年和100年極端降雨的重現水平。在參數估計上，根據最佳配適度檢定結果顯示最大似然估計法（MLE）的配適度優於線性動差估計（LM）。我們發現半島西部和東部極端降雨重現水平的推估值具有明顯的空間差異，其中東岸地區重現水平的變化明顯高於半島西部地區，表示西部地區極端降雨實際觀測值很容易就超越了百年重現水平。上述的研究結果也透露出GEV分布模式對於半島西部地區極端降雨的重現水平估計依然難以掌握，雖然在配適度上得到了不錯的配適成效，這值得讓我們做進一步地思考。在極端降雨的空間分布特徵上，這樣的結果也暗示了近年馬來半島極端降雨的趨勢在空間分布上的轉變。

In this study, we have used the maximum daily rainfall data from a total of 22 automatic rainfall stations obtained from Department of Irrigation and Drainage Malaysia (DIDM) during 1971-2007. We have made use of the annual and seasonal maximum daily rainfall data to analyze extreme rainfall in Malaysia. We have also applied the generalized extreme value (GEV) distribution to model the occurrence probability of extreme rainfall in Peninsular Malaysia. The results showed that the greatest rainfall intensity was found in the east coast of Malaysia, while the lowest extreme rainfall intensity was found in the west central areas. Besides, our study also highlights a positive trend of extreme rainfall event that occurred at west central region in recent year. This result also suggests a likely increase of extreme flooding events in Malaysia in the coming years. For seasonal analysis, it is suggested that a rising flood disaster would possibly be affecting west central areas during the spring (MAM) and autumn (SON), while the northern part of Peninsula would probably suffered from the drought disaster during SON. We have also used the GEV distribution to calculate the return value for the 50-year and 100-year return periods. The maximum likelihood estimation (MLE) is suggested to be the best estimation in this study based on the result of goodness-of-fit. In this study, we have also noticed an apparent difference between the western and eastern parts of Peninsular Malaysia on the variation scale of return level, in which the variation recorded in the eastern region was greater than that of the western region. In addition, the observed rainfall level in the western region had exceeded the 100-year return level estimation. Our results suggest that deliberation is needed in the use of the GEV distribution for the estimation of the return levels of extreme rainfall in the western part of Peninsular Malaysia. For the spatial pattern of the extreme rainfall, our results also suggest that there is a shift in the spatial distribution of the extreme rainfall in recent years.