基于分形的中低分辨率坡度降尺度变换方法研究

Research on method of re-scaling coarser resolution slope based on fractal analysis approach

【目的】针对中低分辨率数字高程模型(DEM)提取坡度的尺度效应问题,建立一种能够对中低分辨率坡度进行降尺度变换的方法。【方法】利用地形分形特性和半变异函数理论,可知坡度是分辨率和分维数的函数,从而对县南沟流域设立的建模区和检验区的坡度进行降尺度变换,并对变换结果进行精度评价。【结果】在0.2～1.0倍的原始分辨率坡度范围内,100,50和25m分辨率坡度分形变换后,与目标较高分辨率坡度在统计意义上相似,并且空间分布格局基本一致,其中0.2～0.25倍的原始分辨率坡度为最佳变换范围。【结论】分形变换可以为坡度的降尺度变换问题提供理论支持,对坡度变换方法的完善有重要意义。

【Objective】 In view of the scale effect problem resulted from the slope extraction based on low resolution Digital Elevation Model（DEM）,this paper introduced a method which can rationally re-scale the low resolution slopes.【Method】 The fractal property of the topography and the theory of variogram demonstrate that slope is a function of the spatial resolution and the fractal dimension of a DEM,and by re-scaling the slopes we obtained a low resolution DEM based on the model experiments in Xiannangou Basin,and evaluated the accuracy of the re-scaled slope.【Result】 This paper concludes that within 0.2-1.0 times original resolution slope range,the re-scaling results of 100 m,50 m and 25 m resolution slope are similar to the slopes based on high resolution DEMs,in both slope value and slope spatial distribution,and the best re-scaling slope extent is 0.2-0.25 times of original resolution slope.【Conclusion】 It is shown that the method provides theoretical support for slope scale problems,and has a significant meaning in perfecting slope transform methods.