中文摘要：

目的探讨在GIS支持下河网分维数的计算方法以及不同分维的意义。方法应用数字高程模型，在GIS支持下提取陕北黄土高原韭园沟流域的河网，利用空间分析方法、分形理论以及统计学知识进行计算、模拟。结果基于霍顿水系定律得到韭园沟流域河网分维数是1．662，基于分形基本定义得出的是1．589。结论①利用GIS计算河网分维数与传统方法相比，具有高效、简捷、检验性好的优点；②对同一河网，使用不同方法得到的分维数不同，表明河网分形性质丰富多彩；③分形维数对比时一般应满足计算方法一致，且在同一个无标度域内。

英文摘要：

Aim Based on the digital elevation model, to find the method of drainage network fractal dimension figured out by GIS and analyze the meaning of different fractal dimensions. Methods Drainage network is derived from the digital elevation model of JiuYuangou watershed, Northern Shaanxi, whose fractal dimension is figured out by special analysis method, fractal theory and statistical principles. Results The drainage network fractal dimensions of JiuYuangou watersheds based on Horton Law and basic definition of fractal theory are figured out 1. 662 and 1. 589 respectively. Conclusion ①The method of drainage networks fractal dimension calculated by GIS is very effective, concise and more objective compared to the traditional methods.②For the same drainage network, different calculating methods lead to different fractal dimensions, which indicates the fractal character of drainage network is colorful. ③The comparison of fractal dimensions should be based on the same calculating method and the same scale-free region.