以模糊理論分析降雨空間變異性推估流量及非點源污染量

Abstract

在模擬非點源污染的過程中，降雨是相當重要的資訊，採用一個降雨代表值來描述整個集水區之降雨情況，往往會造成流量及非點源污染推估極大的誤差，故近年來已有學者針對此問題進行探討，考慮降雨空間變異性對水質及水量推估的影響。但多數研究在各雨量站降雨資料之權重分配上較不具有彈性，在降雨分區劃分的過程中，描述集水區內各分區之降雨特性時仍稍顯粗糙，且對於各雨量站權重的表現並無一套有系統且合理之給定方式，故勢必造成模擬推估結果與實際情況間之誤差。為減少此誤差且讓流量及非點源污染量推估與實際情況更相符，本研究由傳統反距離指數法的概念出發，發展一套模糊化修正式反距離指數法，應用模糊理論(Fuzzy theory)中隸屬度的概念，分析降雨在集水區中之空間變異性。並採用WinVAST模式進行流量及非點源污染量之模擬與推估，將整個集水區依據地形再劃分為數個子流域，以各子流域區塊為各別輸入的單位，透過更詳盡地輸入資料，且運用模糊化的屬性特性，解決傳統降雨資料分析之限制，以期更完整地描述各子流域區塊之實際降雨特性，進而提高流量及非點源污染量推估之準確性。具有空間變異性之分析結果，即可應用在集水區分區管制優先順序之決策上，以及發展非點源污染最佳管制作業之經濟有效配置。 由結果可知，模糊化修正式反距離指數法，透過調整模糊化隸屬函數來表現周圍雨量站相對之權重，確實可以提高降雨推估的彈性及準確度；特別是在地形較為崎嶇的案例區，此方法具有其相對之優勢。值得注意的是，在模糊化修正式反距離法優化最佳水平距離指數”m”，及優化最佳垂直高程差距離指數”n”，在多數情況下，m值均大於n值；此結果說明，周圍各雨量站相對重要性遞減之速率，受到水平間距因子的影響甚於垂直高程差因子。在流量及非點源污染模擬應用的部分，降雨在空間的變異性與高程為正向關係或降雨地區化集中之暴雨，採用模糊化修正式反距離指數法，均能有效地降低降雨推估誤差，及提高流量及非點源污染模擬結果之準確性，尤其是與高程具有絕對相關之設計暴雨，此方法之改善更為明顯。而隨機空間變異之降雨，採用模糊化修正式反距離指數法，對於降雨推估及流量模擬之準確性，提升效果較不明顯。在自然環境下，降雨通常會與空間高程具有密切的正相關，因某些因素造成地區性集中之暴雨亦較為常見，隨機空間變異之暴雨較不合理，因此，可以證實，模糊化修正式反距離指數法在降雨具有空間變異的情況下，具有極佳之彈性，且推估結果可信度相當高。

A watershed management program is usually based on the results of watershed modeling. Accurate modeling results are decided by the appropriate parameters and input data. Rainfall is the most important input for watershed modeling. Precipitation characteristics, such as rainfall intensity and duration, usually exhibit significant spatial variation, even within small watersheds. Therefore, properly describing the spatial variation of rainfall is essential for predicting the water movement in a watershed. Varied circumstances require a variety of suitable methods for interpolating and estimating precipitation. In this study, a modified method, combining the inverse distance method and fuzzy theory, was applied to precipitation interpolation. Meanwhile, genetic algorithm (GA) was used to determine the parameters of fuzzy membership functions, which represent the relationship between the location without rainfall records and its surrounding rainfall gauges. The objective in the optimization process was to minimize the estimated error of precipitation. The results show that the estimated error is usually reduced by this method. Particularly, when there are large and irregular elevation differences between the interpolated area and its vicinal rainfall gauging stations, it is important to consider the effect of elevation differences, in addition to the effect of horizontal distances. Reliable modeling results can substantially lower the cost for the watershed management strategy. The modeling results with spatial differences characteristics can also be used for deciding the sequence of precedence management in a watershed, and developing the optimal allocation of Best management practices (BMPs).