黄土高原重点流域河网分形特征研究

Analysis on fractal characteristics of river networks of key watersheds in the Loess Plateau

分形理论为流域地貌形态特征的定量描述开辟了新的思路。本文采用盒维数计算原理和方法,计算黄土高原20条重点流域的河网分维值,探讨其分维值与流域面积、径流模数、产沙模数的相关关系,结果表明:黄土高原地貌形态在其无标度区间内表现出很好的分形特征,根据计算出的各流域分维值发现,黄土高原大多数流域可能处于侵蚀发育的幼年期;流域干流长度与流域面积的幂函数关系式拟合较好,符合Hack提出的主河道长度与流域面积的关系;径流模数与河网分维存在很好的线性关系,其相关系数通过了显著性水平为0.01的检验;河网分维与流域面积、产沙模数都呈正相关性,但难以用某一种简单函数描述。最后通过多元回归分析,建立了产沙模数模型,验证结果表明,该模型具有较高精度,可以对流域产沙模数进行估算。

The theory of fractal provides a new method to describe the characteristics of physiognomy. The theory and method of Box dimension were used to calculate the fractal dimensions of 20 watersheds in Loess Plateau, and the relationships between fractal dimensions and watershed areas, runoff modulus, sediment modulus were studied at the same time. The results showed that： only Kuye River and Gushanehuan River basins are in old phase of geomorphologie erosion and most watersheds in Loess Plateau are in juvenile phased which means that the sediment yield in loess Plateau would increase in the future. The relation between river network fraetal dimension and watershed area could not be described by a simple function which means that networks density could not reveal the distributed situation of fiver channel in their watersheds, and river network fraetal dimension also could not reveal the non-uniformity of river channel. The power relation between main stream length and runoff area fits well and obeys the Hack relation. The linear relationship between fractal dimension and sediment modulus is good and passes the test of correlation coefficient test table. The sediment yield model was established by multiple regression analysis among sediment modulus and runoff, fractal dimension and watershed area. The verified results by measured data from 20 watersheds indicated the model has a good accuracy to estimate sediment yield in watersheds.