中国旱涝灾害的分形结构

基于分形理论在中国旱涝灾害研究方面所存在的问题,首先系统地分析了中国华北区、西北区等不同区域和松花江、长江等不同流域旱涝灾害的分形结构,其次以唐山市为例系统分析了同一地点不同等级旱涝灾害分维的时序变化及其关系,进而探讨了以分维为中介参数在旱涝灾害与其影响因素之间建立定量化经验关系的可能。研究结果表明,中国旱涝灾害具有客观的分形结构,分维是表征中国旱涝灾害发生特征的良好参数;在此基础上,系统地计算出了中国旱涝灾害的分维值、分析了唐山市不同等级旱涝灾害分维的时序变化关系,并建立了辽河、长江等流域水系空间维数与流域洪涝分维之间的定量关系式DF=3．6179DR-4．0242(式中DR为流域水系空间维数,DF为流域洪涝分维)。

ON FRACTAL CHARACTERS OF DROUGHT AND FLOOD OF CHINA

Mandelbrot enunciated the uncertainty of the length of a coastline in his paper “How long is the coastline of Britain？” published in “Science” in 1967. The fractal concept was presented for the first time in that paper and has been applied to many fields ever since. Although fractal dimensions of lots of phenomena were calculated, related studies on fractal character of drought and flood of China are seldom. Based on the fractal theory, issues of drought and flood were preliminarily discussed in this paper. Firstly, fractal structures of drought and flood were systemically analyzed to different regions and river basins; Secondly, changes of fractal dimensions of drought and flood with different grades and their relationships were also discussed as a case study of Tangshan city. Furthermore, quantitative experiential relationship between drought or flood and the influenced factor was established by use of the fractal dimension as a parameter. Some significant conclusions were drawn as follows：Fractal structure existed objectively in drought and flood of China, fractal dimension is a good parameter as a token of drought and flood. Moreover, the fractal dimensions of drought and flood of China were systematically calculated, and the change of fractal dimensions of drought and flood with different grades was analyzed, and the quantitative formula between the fractal dimensions of river basins and those of flood was established as D_F＝3.6179D_R－4.0242（where：D_R is the fractal dimension of river basin, D_F is the fractal dimension of flood）.