中文摘要：

针对现有地貌形态三维分形模型结构存在的不足,构建一个新的地貌形态三维分形维数测算模型。基于该模型对砒砂岩区274个小流域的地貌形态三维分形维数进行计算并分析其空间变异规律。研究表明：1基于该模型计算的分形维数能更准确地反映地貌形态复杂度信息;2砒砂岩区小流域地貌形态三维分形维数介于1.683 6~1.948 6之间;3地貌形态三维分形维数整体上覆土砒砂岩区（均值为1.765 9）〈裸露砒砂岩强度侵蚀区（均值为1.785 4）和剧烈侵蚀区（均值为1.774 8）〈覆沙砒砂岩区（均值为1.796 6）。由于地表覆盖物、砒砂岩裸露程度和土壤侵蚀机理的差异而形成的不同地貌特征是该区地貌形态分形特征空间变异的主要原因。

英文摘要：

This article focuses on constructing a three-dimensional fractal model to quantify topographic features and analyzes its spatial variation in arsenic rock area. Topographical complexity is commonly described by the fractal dimension, which is a comprehensive index for topography, and a significant parameter for the soil erosion model at the watershed scale. Although lots of fractal models describing topographic features have been built by domestic and overseas scholars, mostare flawed on the model structure. To solve this problem, the article proposes a new index describing relief volume, and designs a new 3D fractal model for arsenic rock area. Based on the fractal model, ESRI ARCENGINE was used to develop the software computing fractal dimension of topographic features. The fractal dimensions of 274 small watersheds were calculated by this software,and their statistical values, such as average value, maximum value, minimum value, standard deviation and coefficient of differentiation,were obtained using zonal statistical tool.The thematic map showing spatial variation was produced using Arc GIS software based on classification statistical method. Finally, the reasons causing the spatial variation of 274 small watershedsfractal dimensions were analyzed in aspects of landform genesis and internal differences in arsenic rock area. The results show that： 1） The 3D fractal dimensions computed by the developed software which was designed in this article can accurately describe the topographical complexity,and the new index is very effective; 2） The 3D fractal dimensions of all small watersheds are between 1.683 6and 1.948 6 in arsenic rock area; 3） On the whole, the 3D fractal dimensions is largest in the arsenic rock area covered by sands（the average value is 1.796 6）, the second is the serious and severesoil erosion area in the arsenic rock area covered by the bare sandstone（the average values are 1.785 4 and 1.774 8, respectively）, and the last one is arsenic rock area covered by loess（the average