中文摘要：

实现具有三维立体特征的流域地貌分形维数直接准确计算，是目前分形地貌学研究所面临的主要问题之一。依据变分法求解三维表面分形维数的基本原理．以DEM栅格数据为基础，利用ArcGIS9．2中的窗口分析功能．对所建立的小流域模型不同发育阶段的三维地貌闵可夫斯基维数进行研究。结果表明，变分法和GIS的有机结合使三维地貌分形维数的直接计算成为可能，小流域模型不同发育阶段的三维地貌在各自无标度区内呈显著的分形特征，三维地貌闵可夫斯基维数不仅能有效表达小流域模型不同发育阶段地貌的差异性（变化范围达0．452），还可准确表达地貌动态变化特征，将其作为小流域模型三维地貌分形特征定量描述指标是可行的。

英文摘要：

Direct and accurate calculation on three-dimension watershed geomorphology is one of key issues in current fractal geomorphology. Based on the Fundamental principle of variational method, the three-dimension surface fractal dimensions of a indoor small watershed model were calculated. And based on DEM data of the watershed model under different development periods as well ad the function of windows analysis in ArcGIS 9.2, the three-dimension geomorphology minkowski dimension of the watershed model under different development periods were calculated and studied. The results indicated that： the organic combination of variational method and GIS makes it possible to calculate directly the three-dimension geomorphology fractal dimension, and the three-dimension geomorphology of the small watershed model under different development periods possess good fractal characteristics in non-scale range respectively. In addition,three-dimension geomorphology minkowski dimension not only indicates effectively the variations of the geomorphology of the indoor watershed model under different development periods, but also reflects accurately the dynamic characteristics of watershed geomorphology,as a result,it is feasible to make three-dimension geomorphology minkowski dimension as a quantitative index of the three-dimension geomorphology fractal character of the small watershed model.