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.
