I would like to ask a question to experts on spatial statistics:
I have a gridded Digital Elevation Model (DEM) which provides terrain elevation (z) at cartesian coordinates (x,y). Together with the DEM I know the RMS of the elevations. As far as I understand the RMS can be applied to any point in the DEM and the standard deviation of the elevations is stationary.
Now, if I take two points from the DEM, the elevations at these points are not independent, but are auto-correlated if the distance between the points is below a certain range. I can build a variogram from the DEM elevation data which provides the function of elevation variation as a function of distance. For distances beyond the range the elevation variation is independent and just the mean of all elevations in the terrain.
However, what I really want to know is the uncertainty of the elevation at different close distances. I would assume that the uncertainty is equal to the RMS at large range, but apporaches zero if the distance apporaches zero. What I need is the function vor values between zero-distance and the range. I would just apply the variogram function of the elevation to the uncertainty and scale it from the mean elevation to the RMS, but I guess this is a pretty much simplified approach.
Any thoughts and comments are welcome