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    Title: 修正型低尾端線性動差統計方法之衍導及其於枯旱極端事件之應用
    Other Titles: Deriving LL-moments for Low Tail Statistical Analysis and Its Application to Drought Events
    Authors: 虞國興;王鵬瑞;鄭思蘋;張宗烜
    Contributors: 淡江大學水資源及環境工程學系
    Keywords: 線性動差;高尾端線性動差;低尾端線性動差;通用極端值分布;L-moment;LH-moment;LL-moment;Generalized extreme value (GEV)
    Date: 2008-10
    Issue Date: 2014-02-12 20:48:21 (UTC+8)
    Abstract: 線性動差法在諸多機率分布函數之參數推估方法中,受離群值(outlier)之影響較小、近似無偏估及推估高效率等方面之優點已廣為所知;惟在極端事件上不論是洪水之高值端(higher-tail)或枯水之低值端(lower-tail)的部分,由於該方法之觀測資料線性組合與給定極端值部分過小之權重,致容易發生傳統L-moments方法在極端值推估上之妥適性問題。本研究以高尾端1997年Wang發展之LH-moments為基礎,進一步針對低值端之部分衍導「修正型低尾端線性動差法(LL-moments)」之各階動差計算式,以提供枯旱極端事件方面之應用。本研究以三參數之通用極端值分布(the generalized extreme value, GEV)為例,依序推導其1至4階之LL-moments。研究中,一方面利用數值方法探討不同形狀參數(shape)下,LL-moments方法於枯旱事件之適用性;另一方面,選取高屏溪流域之六龜、荖濃兩處流量站歷年最低旬流量資料進行實務分析及應用。希冀藉由低尾端線性動差相關方法之探究及實務上之驗證,提供台灣地區乾旱頻率分析及水資源經營管理之參考。
    L-moments have the advantage of providing parameters estimates that are nearly unbiased, highly efficient and not much influenced by outliers in the data. Because of L-moments are linear combinations of the observed data values. Besides, extreme sample values are given little weight in the estimation, the sample information about the higher-tails or lower-tail of the distribution may not be adequately evaluated. In this paper, LL-moments are derived, which is modified L-moments. It is adopted to characterize the lower part of extreme events, such as drought. Meanwhile, it also referred and based on LH-moments algorithm. The generalized extreme value (GEV) distribution, all with three parameters, are illustrated to derive the forms of estimation of LL-moments. The first order to forth order forms of moments are expressed in this study. First of all, the numerical algorithm is adopted, giving different shape parameters, to explore how suitable is LL-moment applied to evaluate the severity of drought events. Furthermore, the 10-day annual minimum flows of two stations in Kao-Pin River, Liu-kwei and Lao-nong, are selected to apply for estimating low flow quantiles. It should be useful for getting evaluation drought severity to adjust water resources management tactic at the right time and lower the risk of regional water supply.
    Relation: 2008農業工程研討會論文集,12頁
    Appears in Collections:[水資源及環境工程學系暨研究所] 會議論文

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