事件基礎之降雨非定常性分析及簡型投影月雨量模擬

Abstract

在過去，我們假設降雨的統計特徵為非時變性，這個概念稱為定常性。但近年來由於氣候變化，我們現在面臨更加激烈和頻繁的極端水文事件，故定常性的假設已經不能符合實際的情況。因此，非定常性的概念就顯得越來越重要，並且需要仔細地重新相應的評估方法。 本研究分為水文頻率分析和降水模擬兩部分，兩者均利用非定常性概念來做進一步的探討。在第一部分中，本研究定義了每個單一事件及其相對應的特性，來分析台灣九個具代表性的氣象測站（基隆、臺北、新竹、臺中、臺南、高雄、恆春、花蓮以及臺東）的降水數據。基於分配與趨勢鑑定（Identification of Distribution and Trend, IDT）原則，採用總和經驗模態分解（Ensemble Empirical Mode Decomposition, EEMD）方法研究時間序列平均和變異性的值隨時間變化的趨勢。在第二部分中，以建立時間點和它們的時間延滯的多維空間來模擬未來的月降雨量，這個概念稱為簡型投影（Simplex projection）方法。此外，利用增加變異數來預測未來值並增加可變異性。 通過對第一部分的分析，我們發現總和經驗模態分解方法計算得到的趨勢充分證明了「短延時、強降雨」的特徵，並且幾乎所有測站都表現出明顯的非定常性；對於第二部分，增加變異數後的模擬值結果也顯示出較好的模擬結果。因此，通過頻率分析和預測降雨量，我們可以應用在水文風險的避免和施政方針、審查當前的管理政策和工程標準，並在水利工程中有更好的長期規劃。

In the past, we assume that the statistical characteristics of rainfall no matter in the past or in the future were the same, this concept is called stationarity. However, because of climate change, we face more intense and frequent extreme hydrological events nowadays, the stationarity assumption may be inappropriate. Consequently, non-stationary situation becomes increasingly popular and corresponding assessment approaches need to be re-evaluated carefully. This study is divided into two parts, hydrological frequency analysis and precipitation simulation, and both of which make use of the concept of non-stationary. For the first part, this study determines each single event and their properties to analyze the precipitation data from nine major stations in Taiwan. Based on the scheme of Identification of Distribution and Trend (IDT), the method of Ensemble Empirical Mode Decomposition (EEMD) is applied to explore the time variation of first and second statistical moments of time series. For the second part, multi-dimensional space of time points and their time lags are established to simulate the future monthly simulation, this concept is referred to as Simplex projection. Besides, by adding variables getting by modified K-NN method, we hope to increase the variability of exactly forecasting the future values. From the analysis of the first part, we find that the trends calculated by EEMD sufficiently demonstrate the characteristic of “short duration but high rainfall intensity”, and nearly all stations show obvious non-stationarity. For the second part, the combination usage of Simplex projection and modified K-NN method shows a better-fitting than the usage of Simplex projection alone. As a result, from the frequency analysis and future forecast, we can determine the hydrological risks, review the current management policies and engineering standards, and have a better long-term planning in hydraulic engineering.