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題 名 | 以Cantor集觀念解析水文變量在時間尺度上之行為=The Behaviour of Hydrologic Variables in Time-Scale by Cantor Set Concept |
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作 者 | 林淑真; | 書刊名 | 臺灣水利 |
卷 期 | 46:2=182 1998.06[民87.06] |
頁 次 | 頁85-96 |
分類號 | 443.046 |
關鍵詞 | 碎形理論; Cantor集; 碎形維度; 門限值; Fractal theory; Cantor set; Fractal dimension; Threshold; |
語 文 | 中文(Chinese) |
中文摘要 | 本研究以隨機的 Cantor 集合觀念為基礎,引入碎形理論來解析臺灣北、中、南 三區之降雨觀測資料在時間尺度上的行為變化。由實際案例的計算結果,證明得該等水文量 具有時間的尺度不變性及隨門限值升高而導致群集性的下降,同時亦驗證得在不同的門限值 變動下,其所推估得之一致的尺度不變區最大值是相同的。除此之外,利用超越門限值所得 之機率 -- 尺度律,進而建立起飽和尺度(重現期)與門限值(設計水文量)之相依關係, 該方法是有別於傳統的水文頻率分析法,兩者相較可得:前者並不需導入機率密度分佈及救 解或檢定其參數之外,同時可獲致相近的結果,因此本研究提供了一種替代性的計算方法。 最後,文中亦針對實際工程上之應用考量,給予討論及建議。 |
英文摘要 | Based on the concept of the random Cantor set, this paper used the fractal theory to analyze the behaviour of rainfall data on time-scale variability in the north, central and south of Taiwan. One data set in each region is selected for the study. Both the scale invariance in time and the decreasing in clustering with increasing the threshold are proved. With the function of probability-scale law on different levels of threshold, the relation can be established between the saturation scale (return period) and the threshold (design hydrologic variate). The methodology is not the same as the traditional method, i.e., frequency analysis method. Both are compared, the result shows that the former needs not the information of probability density function and estimation or testing of parameters. Moreover both methods can reach the similar results, so the proposed method is an alternative one for modeling the hydrologic process. For practical consideration in engineering, discussion and suggestion are also submitted. |
本系統中英文摘要資訊取自各篇刊載內容。