Downscaling climate data using DEM

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I have gridded climate data (temperature and precipitation) at 0,1° resolution and I want to downscale it into a finer scale using digital elevation model. The relationship between the climate variables and altitude is very strong, but not spatially constant. Thus, I applied geographically weighted regression (GWR) instead of ordinary least square regression to get more precise results. Then I tested the spatial autocorrelation of GWR residuals using Moran's I statistics to determine if it is possible to extend the model to the residual kriging form. But according to the test, the GWR residuals are not spatially autocorrelated and therefore, the GWR alone should be used in the model. Nevertheless, without interpolating the residuals, the model will deviate from the grid point values. But I want to have accurate values at grid point locations.

Is there any way to solve this problem? Is it correct to use some of the deterministic interpolation methods to interpolate the residuals, for example IDW or natural neighbor? Or is there a completely different and better way to figure out the problem than the above?

Thank you very much for any ideas



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