Research On Method Of Re-scaling Coarser Resolution Slope Based On Fractal Analysis Approach

Slope as an important terrain index is a significant parameters in soil erosionmodel and hydrological model. Slope is often extracted based on moderate or lowresolution DEM at basin and regional scale in soil erosion assessment. With reductionof DEM resolution, however, the slope values extracted from DEM result in seriousdecay. Therefore, it is significant to down-scaling the decayed slope.This paper divided the envelope rectangle area of Xiannangou basin in loess hillyarea into four district parts, i.e. Ⅰ, Ⅱ, Ⅲ and Ⅳ respectively from small to large,and established the analysis area for model construction and model verificationaccording to slope re-scaling theme. Firstly, we created multi-resolution DEM withsame location basis for each district part by digitalizing the line graph of every districtarea with ANUDEM software, and re-sampled the high resolution Hc-DEM withbilinear method with ArcGIS software to generate a set of DEM (Hc-DEMb) with aseries of resolution corresponding to that of Hc-DEM. At the same time, we extractedslope values from Hc-DEM and Hc-DEMb respectively following by re-scalingprocess. Fractal property of their topography and analysis based on their variogramdemonstrate that slope is a function of spatial resolution and fractal dimension for aDEM, and one can obtain a low resolution DEM by slope re-scaling based on thefunction of slope transformation. The conclusions of this paper are as follows.(1) Calculation of fractal dimension thematic layer based on DEMAs the resolution of a DEM becomes coarser, slopes extracted from the DEM willbe flattened. Using the fractal property of their topography and the theory ofvariogram, we demonstrated that slope is a function of spatial resolution and fractaldimension for a DEM. We divided original low resolution DEM into sub-areas withsizes of3×3,5×5and7×7, and calculated the fractal dimension and standarddeviation of the higher resolution DEM data dropped into these sub-areas. We finallyfound that a certain degree of correlation exists between the fractal dimension and thestandard deviation which leads to a regression function between them. The standarddeviations of DEMs with different resolutions are stable in same sub-area extent. We calculated the fractal dimension value of every cell of the low resolution DEM basedon neighborhood analysis with3×3,5×5and7×7windows, and obtained the fractaldimension thematic layer.(2) Fractal dimension analysisBased on the sub-areas of the low resolution DEM with sizes of3×3,5×5and7×7respectively, we calculated the fractal dimension of the higher resolution DEMelevation data dropped into these sub-areas, then calculated the fractal dimension D ofevery cell of the low resolution DEM according to the relation between fractaldimension and standard deviation. The results show that the window of5×5achievesbetter fractal dimension surface for Hc-DEMb data, and that of7×7achieves betterfractal dimension surface for Hc-DEM data.(3) Analysis on the application area suitable to slope re-scalingWe analyzed the statistics of the re-scaling results with adjacent and acrossresolutions, calculated the determination coefficient between the transformed (anduntransformed as well) results and reference slope data, and analyzed the changes ofthe slope value of feature points resulted from the transform and the resulted effectsaround slope edge-line. The results above indicate that within the range of transformscale factor suitable to the re-scaling method (0.2~1.0times of original resolution),the re-scaling results with100m,50m and25m resolution can obtain slopes similar tothe that from high resolution DEMs, in both slope value and slope spatial distribution,and the best re-scaling scale factor ranges between0.2and0.25times of originalresolution slope.It is shown that the proposed method provides theoretical and technical supportfor slope scale problems, and has a significant meaning in perfecting slope transformsystems.