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題 名 | 臺灣地區時雨量與日雨量之多重碎形分析=Multifractal Analysis for Hourly and Daily Rainfall in Taiwan |
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作 者 | 林旭信; 劉長齡; 張德鑫; | 書刊名 | 臺灣水利 |
卷 期 | 58:3=231 2010.09[民99.09] |
頁 次 | 頁17-25 |
分類號 | 328.63 |
關鍵詞 | 多重碎形; 測度; 機率分佈多重尺度法; 餘維度函數; 軌跡動差法; Multifractal; Measure; Probability distribution multiple scaling technique; Codimension function; Trace moment; |
語 文 | 中文(Chinese) |
中文摘要 | 自然界許多物理現象均為非線性與隨機性。傳統使用統計方法加以分析(如ARMA、ARIMA模式),這些方法有其適用範圍。自1970年Mandelbrot提出碎形理論之後,碎形理論即被廣泛地應用在各個領域,其後的學者亦致力於這方面之研究,水文領域亦有大量之研究成果,其中以降雨量為主要研究對象。碎形理論被視為分析雨量時空特性強有力之工具。 過去十幾年多重碎形理論已受到重視。Schertzer和Lovejoy利用倍增瀑布(multiplicativecascade)的概念建構雨量變異性模式。一測度(measure)是否具有多重碎形結構常用之解析法有機率分佈多重尺度法(probability distribution multiple scalingtechnique,簡稱PDMS),與軌跡動差法(trace moment method,簡稱TM)。機率分佈多重尺度法可以餘維度函數(codimension function)、軌跡動差法可以經驗動差尺度指數函數(empirical moment scaling exponent function)描述多重碎形測度,Legendre轉換描述了餘維度函數與經驗動差尺度指數函數之關係。國外學者已將多重碎形理論應用至各個領域,降雨量的時空特性是否具多重碎形結構亦是被研究的重要一環。 本文的主要目的為分析台灣地區北、中、南與東部24個雨量站之時雨量、日雨量記錄是否具有多重碎形結構,資料長度平均為30年,經實際分析之結果顯示:此24個雨量站均存在餘維度函數與經驗動差尺度指數函數,意味著台灣地區之降雨量具多重碎形結構。另外由Legendre轉換檢核計算之結果。其差異並不大,由Lavalle等人在1993年提出之計算式,檢核頻譜分析法與軌跡動差法之計算結果,發現其結果差異亦不大。 |
英文摘要 | The phenomena of nature are all nonlinear. These physical processes are all random.Traditionally, we analysed the properties of them by using statistical methods such likeARMA or ARAMA model. Statistical methods were applied in suitable application areas. Since1970 Mandelbrot proposed fractal theory, it was widely applied in many domains. The scholarswere absorbed in the study of fractal theory after 1970. There is a lot of research effort in thefield of hydrology. The rainfall is a substantial set of the study of fractal theory in hydrology.Fractal theory can be viewed as powerful tool of analyzing the temporal-spatial peculiarities. In the last decade, multifractals have been given considerable attention. Schertzerand Lovejoy modeled the variability of rainfall by a multiplicative cascade. The methods,probability distribution multiple scaling technique (PDMS) and trace moment (TM), usually used to determine whether a measure to be or not to be multifractals. To describe multifractalmeasure, it can be employed codimension function with PDMS method and empirical momentscaling exponent function with TM method. The relationship between codimension functionand empirical moment scaling exponent function can be constructed by Legendre transform.The foreign scholars have applied multifractal theory to many application areas especially inthe study of the temporal-spatial properties of rainfall that to be or not to be multifractals. The main objective of this paper is to study the behavior of the rainfall data, collectedat 24 rainfall stations in Taiwan area, over periods up to 30 years. The results show that allrainfall data exist codimension function and empirical moment scaling exponent function. Thisimplies that the rainfall in Taiwan is multifractals. The deviation of using Legendre transformand power spectrum are not significant. |
本系統中英文摘要資訊取自各篇刊載內容。