分區式隨機碎形圖形編碼及其於河川網路模擬之應用

The Coding of Separately Random Fractal Patterns and Its Applications to River Network Simulations

洪君伯(Chun-Po Hung)

指導教授 ： 王如意

國立臺灣大學/生物資源暨農學院/生物環境系統工程學研究所/博士(2004年)

https://doi.org/10.6342/NTU.2004.00125

摘要

本研究針對颱洪暴雨時期河川網路變化之高度複雜性建立一套完整之隨機碎形河網編碼方法(coding method)及推衍相關之拓樸距離(topological distance)與幾何距離(geometric distance)計算公式，以提供隨機碎形河網於降雨－逕流歷程之模擬與應用。研究中將所研析之隨機碎形圖形編碼方式應用於河川網路(river network)之生成模擬中，並選用台灣北部淡水河流域寶橋上游集水區為主要研析流域，以隨機碎形圖形編碼方式進行河川網路模擬。文中利用上述之距離推求公式計算生成河川網路之寬度函數(width function)，再根據以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)進行河川流量之模擬，以探討隨機碎形圖形於水文模擬之適用性。研究結果顯示，以隨機碎形模擬之河川網路進行之流量模擬結果確實比一般碎形之河川網路及DEM河川網路所獲致之流量模擬結果為佳，由此可以證明隨機碎形河網較接近實際河網降雨－逕流歷程之特性，且適用於不同自然型態之隨機碎形河網模擬。

關鍵字

自相似 ； 隨機碎形 ； 編碼 ； 河網 ； 寬度函數

並列摘要

This study proposes an analytical method for coding random self-similar river networks as a series of numbers, and investigates the corresponding algorithm that calculates the topological and the geometric distances from the code series. A process for generating fractal patterns, with various probabilities of generating particular pattern links, as in separately random self-similar generation or separately random fractals, is proposed, based on the wide range of stochastic characteristics of natural patterns. The coding method is applied to generate random self-similar river networks and the corresponding algorithm for calculating the geometric distances of the links is employed to determine the width function of the river networks, and thus evaluates the adaptability of the process. The width-function based geomorphologic instantaneous unit hydrograph (WF-GIUH) model is then applied to estimate the runoff of the Po-bridge watershed in northern Taiwan. The results imply that the separately random self-similar generating algorithm can be used successfully to calculate hydrological responses in a river basin.

並列關鍵字

Self-similar ； Width function ； Random fractals ； River network ； Coding method

參考文獻

7.王如意、洪君伯、王鵬瑞、鄭士仁：「分區式隨機碎形河川網路編碼及其幾何距離計算」，農業工程學報，第50卷第3期，pp.1-18，民國93年9月。

15.陳樹群、陳聯光：「隨機河系網之建構模擬」，農業工程研討會論文集，民國84年。

18.Agnese, C., “Scale Invariance Properties of the Peak of the Width Function in Topologically Random Networks,” Water Resources Research, 34(6), pp.1571-1583, 1998.

20.Claps, P., and G. Oliveto, “Reexamining the Determination of the Fractal Dimension of River Networks,” Water Resources Research, 32(10), pp.3123-3135, 1996.

21.Claps, P., M. Fiorentino, and G. Oliveto, “Informational Entropy of Fractal River Networks,” J. Hydrology, 187, pp.145-156, 1996.