吉林省水系构成的分形研究

doi:10.11867/j.issn.1001-8166.2003.02.0178

根据对分形水系的新近认识探讨了吉林省水系结构的自相似规律。Horton-Strahler的水系标度定律隐含着水系的位序-规模法则和河流长度-流域面积的异速生长关系，这暗示着α＝ lnR_b／lnR_l是一种等级结构的维数，不能将之与空间结构维数混同；Hack模型的标度因子b＝lnR_l／lnR_a是一种广义的空间维数之比，不能据之确定主河道的分维。基于上述思想，对吉林省10个主要水系的等级结构进行考察，发现气候相对湿润的山区水系的α值高于气候相对干燥的平原地区水系的α值，而平原-干燥区水系的b值高于山地-湿润区水系的b值。从河流发育的地质、地貌背景和气候-水文关系等角度对上述现象进行了的初步解释，并根据洮儿河的异常α值修正了LaBabera-Rosso的水系分维定义。

关键词: 水系, 分维, Horton定律, Hack定律, 吉林省河流

Fractal river networks and the relationship between mainstream length and drainage area of Jilin Province are researched in the paper by means of new theoretical progress in fractal geomorphology. It has been proved that the parameter (α) based on Horton’s law, which is always expressed as α=lnR_b/lnR_l, is a fractal dimension in hierarchical sense instead of spatial sense, and the double of the scaling factor(b) based on Hack's model,L=μA^b, which can be written as b=lnR_l/lnR_a, is not fractal dimension of river courses, but a ratio of generalized dimension of mainstream to that of corresponding catchment (the latter is not always equal to 2). A discovery is made that the α values of river networks in mountainous areas or rainy places are greater than those in flatlands or the areas with less rainfall, and the b values to the contrary. The contributing factors of the spatial patterns of α- and b- values of river systems distributing in Jilin's map are directed to the configuration of land surface, property of rocks, and precipitation, etc. One of the definition on fractal dimensions of river networks given by LaBarbera and Rosso,D=min(2,2logR_b/logR_a), has been revised as D=min［2,max(1,2logR_b/logR_a)］, according to the calculated results from the data of Jilin's rivers.

Key words: River network, Relation of mainstream length to catchment area, Fract.

中图分类号:

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摘要

STUDIES OF THE FRACTAL NETWORK COMPOSITION OF RIVERS IN JILIN PROVINCE,CHINA