具隨機碎形特性之設計暴雨雨型

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Title:	具隨機碎形特性之設計暴雨雨型 A Random Fractal Model for Design Storm Hyetographs
Authors:	鄭克聲許恩菁葉惠中
Contributors:	土資系
Keywords:	雨型碎形設計暴雨高斯馬可夫歷程尺度不變性 Hyetograph Fractal Design storm Gauss-markov process Scale invariant
Date:	1999-09
Issue Date:	2017-01-04 14:28:23 (UTC+8)
Abstract:	本研究以隨機碎形特性與高斯馬可夫歷程，建立設計暴雨之無因次雨型。研究中首先選取較長設計延時（≧ 6 小時）所對應之年最大值事件，並針對其降雨延時及總降雨量予以無因次化。基於隨機碎形中簡單尺度不變之特性，經無因次化後的各次降雨事件，可被視為相同隨機歷程之各次表現值，而可據以推估該隨機歷程之各項參數。其次，本研究以非定常性之一階高斯馬可夫歷程，模擬無因次降雨歷程；並利用拉格朗茲法與條件聯合機率密度函數，計算滿足尖峰降雨百分比之統計特性下之最可能雨型。我們所提出之雨型具有五項特點：（１）符合尖峰降雨百分比之統計特性、（２）降雨量之時間分佈與年最大暴雨事件之歷程特性一致、（３）雨型因暴雨類型而異、（４）經適當之尺度轉換後，雨型可適用於不同延時之設計暴雨、（５）建立雨型所使用之降雨事件與建立降雨強度－延時－頻率曲線所使用之降雨事件大致相同 We propose a dimensionless model for design storm hyetographs based on the characteristics of random fractal and Gauss-Markov process. Annual maximum events corresponding on longer design storm durations (≧ 6 hrs) were collected and dimensionalized with respect to their event durations and total rainfall depths. We prove that under simple scaling property dimensionless rainfall events are realizations of a common random process and therefore can be used for parameter estimation of the random process. Next, by using the Lagrange technique and the conditional joint probability density function, we show that the rainfall process can be modeled as a nonstationary first-order Gauss-Markov process, and obtain the hyetograph that is most likely to occur and also preserves the statistical characteristics of the peak rainrate. The proposed hyetograph model has the following properties: (1) It preserves the peak rainfall property. (2) It represents the time distribution of the annual maximum events. (3) The hyetograph is storm-type specific. (4) By appropriate scale transformation, the same hyetograph can be used for design storms of various durations. (5) The hyetograph is developed using almost the same data (storm events) as the development of intensity-duration-frequency curves.
Relation:	臺灣水利 47:3=187 民88.09 頁43-54
Appears in Collections:	[Department of Natural Resources ] journal articles

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