Effective Scale of Slope and Aspect Derived from Grid-based Digital Elevation Model

Terrain parameters,such as slope and aspect,are the most frequently surface geomorphic parameters in terrain analysis,hydrological modeling,environmental studies and other geosciences fields.Currently,these terrain parameters are often estimated by 3×3 local moving window at grid-based digital elevation model(DEM);and the estimated value is set to the centre cell in 3×3 window.In other words,the slope/aspect map derived from DEM is the same resolution as the DEM.There exists a question in this observation whether the resolution of slope/aspect map is the same as the DEM resolution or not? Based on the vector algebra and real DEM,it demonstrates that the slope/aspect estimated by 3×3 window is larger than a grid cell of DEM,which is 1.7 to 2.7 times of DEM resolution.