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題 名 | 碎形河川網路之寬度函數通式推導及其於計劃集水區逕流推估上之應用=Generalized Derivation of the Width Function in a Fractal River Network and Its Application to Runoff Estimation of a Project Watershed |
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作 者 | 王如意; 王鵬瑞; 高銘佐; | 書刊名 | 農業工程學報 |
卷 期 | 47:4 2001.12[民90.12] |
頁 次 | 頁1-19 |
分類號 | 436.124 |
關鍵詞 | 碎形生成單元; 寬度函數; 信息熵; Fractal generator; Width function; Informational entropy; |
語 文 | 中文(Chinese) |
中文摘要 | 本研究之目的為建立一種機制,期使碎形之理論能實際應用於集水區之逕流推估上。一般自我相似(self-similar)碎形河川網路生成之方法係利用碎形生成單元(fractal generator)經遞迴疊代(recursive replacement)之過程所繁衍而成,然而面對臺灣集水區特殊之水文及地文條件下,此種僅以單一碎形生成單元繁衍模擬之方式實不易反應出臺灣集水區內河川網路之高度變異特性。本研究深入將碎形生成單元細分為內部河段(interior link)與外部河段(exterior link)等碎形生成單元,並引用寬度函數(width function)以詮釋集水區之河川網路結構,進而應用歸納方式推導出適合各種碎形生成單元類型之寬度函數通式以合成碎形河川網路,並代入寬度函數為主軸之地貌型瞬時單位歷線(width-function based geomorphologic instantaneous unit hydrograph, WF-GIUH)模式以進行集水區之降雨—逕流推估。 本研究採用河川網路信息熵(informational entropy)與累積寬度函數(cumulative width function, CWF)作為選擇合適碎形生成單元之判別標準。文中選用臺灣北部淡水河流域之寶橋及三峽等兩個集水區共16場颱洪事件作為模式檢定與驗證,以評估模式之適用性。由研究結果顯示,本研究已成功地將碎形理論實際應用於集水區之逕流推估應用上,且該機制可進一步加以研析,俾供臺灣集水區防洪規劃及水土保持研析之參考應用。 |
英文摘要 | An approach by applying the fractal concept to estimate hydrologic response is proposed in this study by matching suitable self-similar networks (SSNs) to a specific watershed and modeling the runoff with a width-function based geomorphologic instantaneous unit hydrograph (WF-GIUH). In order to work out the identification between a specific basin and SSNs that are generated by generators, a generalized width function is derived. Generally, only one fractal generator is used in the generation process. Simulating the various patterns of natural river networks, however, may not be simple. An new algorithm is thus proposed to generate the SSNs by an exterior generator cooperating with an interior generator, and subsequently the corresponding generalized width function with respect to any time of generation is obtained. Additionally, cumulative width functions (CWF) on the basis of the derived function, as well as the informational entropies are used as criteria to obtain the best pattern of the generator for the specific watershed. The WF-GIUH model is then applied to calculate the runoff of the project watershed as an outcome of the estimation. To assess the adaptability of the estimation model, several watersheds of northern Taiwan are selected as study areas. The analytical results of the outflow estimation indicate that the fractal algorithm can be implemented successfully for the calculation of hydrologic responses in a project watershed. |
本系統中英文摘要資訊取自各篇刊載內容。