與尺度無關之河川蜿蜒量化指標－蜿蜒碎形維度

Quantitative Index of River Meandering with Scale Invariance: Sinuosity Fractal Dimension

李宗仰(TZONG-YEANG LEE) ； 林淑真(SHU-CHEN LIN) ； 劉長齡(CHANG-LING LIU)

《台灣水利》 42卷3期 (1994/09) Pp. 12-21

https://doi.org/10.6937/TWC.199409_42(3).0004

摘要

蜿蜒度是衡量河川彎曲程度的重要指標，然蜿蜒度之定義有多種方式，且不同尺度間之結果亦往往不同，此造成在應用上之困擾，特別是不易建立蜿蜒之地形與環境變數間之相依關係。爲能克服此等困擾並找尋更合適的河川蜿蜒量化指標，本文使用碎形理論來加以解析，經由該法求得蜿蜒碎形維度。研究中以兩種方式模擬河川流路並輔以真實河川之計算，依此驗證蜿蜒碎形維度可替代傳統之蜿蜒度，而且蜿蜒碎形維度亦能提供河川間不同彎曲程度之比較。因此，使用蜿蜒碎形維度來解釋及分析河川之平面型態特性，或可提供更客觀且更趨一致性的結果。

關鍵字

河川蜿蜒 ； 蜿蜒度 ； 碎形維度

並列摘要

Sinuosity is an important index of measuring the winding of a river, however it has many definitions and various results with different measuring scales. These cause troubles for their applications, especially, not easy to establish the relation between sinuosity and environmental variables. To overcome these difficulties and find a more adequate quantitative index to describe the river meandering, this paper presents the concept of fractal geometry to analyze the bending of a river and calculates its sinuosity fractal dimension. Two different simulations and real rivers are used to show that the sinuosity fractal dimension can substitute for the traditional sinuosity index. Comparison can be made among sinuosity fractal dimensions. The results indicate that the sinuosity fractal dimension can be used to explain and analyze the planform pattern of a river and obtain more objective and consistent conclusions.

並列關鍵字

River meandering ； Sinuosity index ； Fractal dimension