- 學位論文
混合式群集演算法之研究及其於洪峰流量區域頻率分析之應用
A Study on the Hybrid-cluster Algorithm for Regional Frequency Analysis of Flood Discharge
摘要
臺灣常遭逢季風、梅雨以及颱風之侵襲，高強度降雨事件使得防洪設施之排洪能力面臨相當嚴峻之考驗。2009年，莫拉克颱風對南臺灣造成重大災害，驚人之降雨量超過排洪系統負荷，使得二仁溪、荖濃溪及旗山溪等河川發生多處溢堤及潰堤現象，釀成相當嚴重之水患災情。本研究之目的係探討在面對未設置站地點或水文資料不足區域，如何改善及提升過去以臺灣全區採用單一機率分布而造成之精確度問題，研究中利用有限測站之觀測資料及其上游集水區之地文因子，並藉由劃分出具有水文特性之均一性區域，以進行區域洪水頻率分析及推估洪峰流量，進而篩選出區域之最適機率分布，也期冀可提供未來區域重新檢視防洪設施保護能力之參考。 本研究選擇臺灣南部地區包括：朴子溪流域、八掌溪流域、急水溪流域、曾文溪流域、鹽水溪流域、二仁溪流域與高屏溪流域等共七個流域作為研究區域，並以區域內之22個流量站之歷年年最大流量資料與測站地文因子為分析對象。研究中，分別以凝聚式層次群集演算法(agglomerative hierarchical clustering algorithm)、K-均值演算法(K-means algorithm)與結合上述兩方法之混合式群集分析法(hybrid-cluster algorithm)進行區域劃分，進而擇定一最佳方法，劃分出具有地理及水文特性之均一性區域。再以線性動差法為基礎之兩種區域度量，非調和度量(discordance measure)與均質性估量(homogeneous measure)，檢定區域內水文特性之均一性，接著利用適合度估量(goodness-of-fit measure)，判斷各區域內適合之機率分布，最後推估其洪峰流量，找出區域最適合之機率分布。 研究結果顯示，以混合式群集分析法中華德法(Ward’s method)加K-均值演算法分析之結果為最佳，且將南部地區由七個流域劃分為四個區域，其各區結果不僅滿足水文特性之均一性，亦符合測站間在地理位置上相互緊鄰之空間分布特性。此外，本研究亦顯示南部地區區域頻率分析在第一區及第二區最適機率分布為對數皮爾遜第III型分布；第三區及第四區最適機率分布為通用極端值分布。
並列摘要
Because of the monsoon climate and typhoon event, the drainage capacity of the flood control facilities in Taiwan were strictly tested by the extreme precipitation events. In 2009, Typhoon Morakot caused serious disaster in southern Taiwan. The extreme rainfall lead to flooding at many places because of the exceeding capacity of drainage system. The purpose of this study is to improve the accuracy of using the single probability distribution at the region lacking of hydrological information. In this study, by using the limited information from the gauged stations and the physiographic factor of upstream catchment area, we classify the area which has the similar hydrological characteristics so that we can analysis the flood frequency and estimate the peak flow more precisely, and select the most appropriate probability distribution for the area. In this study, the seven basins in southern Taiwan as the research area, 22 stations within the region with annual maximum flow data and station physiographic factor are the analysis objects. In this study, agglomerative hierarchical clustering algorithm, K-means algorithm and the hybrid-cluster algorithm which combined the above two methods were used to regionalized the area. In each determined region, it’s will have the homogeneity of geographical and hydrological characteristics. Then using discordance measure and homogeneous measure which based on the L-moments to verify the homogeneity of hydrological characteristics. In the end, using the goodness-of-fit measure to determine the appropriate probability distribution for each region and then estimate the peak flow to find the best probability distributions for the region. The results indicated that the Ward's method and K-Means algorithm of hybrid-cluster algorithm is the best choice, and the seven basins in southern Taiwan were divided into four regions. The result not only meet the homogeneity of hydrological characteristics but also in line with the stations on the spatial distribution characteristics of geographical location. Moreover, the optimal probability distribution for the first and second region is Log Pearson Type III Distribution (LPT3) and the optimal probability distribution for the third and fourth region is Generalized Extreme-Value Distribution (GEV).
參考文獻
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