黄土高原流域水系的HORTON级比数和分形特性

Horton's Order Ratios of Water Course Network of Drainage Basin and their Fractal Characters in the Loess Plateau

研究沟道长度与江水面积关系 ,并将Hortoh定律和水路网分形理论应用于黄土高原的流域水系。 2 4个流域(面积 140km2 ～ 734 1km2 )沟道长度与汇水面积 ,幂函数关系最好 (L =aAb)。Horton级比参数与水道级别无关 ,近于常数。采用几种模型计算分维值 ,比较国外的研究结果。不同公式计算的分维 ,意义不同。公式d =lnRL/lnRB 表示长度分维 ,D =2LnRB/LnRA 代表面积分维。这些分维值 ,在一定程度上 ,可认为是常数 ,但并不是精确的固定值 ,它们都与沟谷密度无关 。

This paper studies the relationship of the length of water course network and the area of the drainage basin,Horton's law of composition for the water course network and fractal characters drainage basin in the Loess Plateau.The results from 24 catchments(140 km 2～7 341km 2)show that the power function(L=aA b)is the best fitted expression of the length and the area Horton's order ratio is approximate to a constant and independent of order level of channel.It is to be compared that the results calculated by sever models of fractal with foreign data.The different formula should be different meaning.The length-area fractal dimension d=2lnR B/lnR A.In some extent the value of fractal dimension is approximate to a constant,but not fixed and exact,independent of density of channel.There is not quite clear relationship between the fractal dimension and the length of water course network,and the area of the drainage basin as well.