Dear Lorenzo Bottaccioli ,

I think you can use geostatistical interpolation methods like Kriging method, but you must select the suitable values of range, sill and Nugget of semivariogram parameters to get the representative interpolation, then you can assign the rainfall value for each DEM pixel (cell).

I agree with Dr. A.A.F. Beg. Using Geostatistical Analysis in ArcMap you can interpolate using a variety of methods such as Linear Polynomial Interpolation, Inverse Distance Weighted Method or Bayesian Krigging. I have used this tool for other applications in ArcGIS (see under my profile).

The success of spatial interpolation varies according to the type of model chosen, its mode of geographical management and the resolution used. The quality of a result is determined by the quality of the continuous spatial rainfall, which ensues from the interpolation method used.

Best Tool will be MATLAB,ArcGIS

There are several methods available for interpolation in ArcMap. You can try kriging technique if the variogram of your data fits with a model.

If your data points (rain gauges) are densely and evenly spaced, then you may try IDW interpolation technique.

Dear Lorenzo Bottaccioli ,

The best tool i have used is SAGA GIS , toolbox : spatial ans geostatistics, or raster creation tools, or kriegging.

To know the different method, please have à quick look to this link :

https://www.int-arch-photogramm-remote-sens-spatial-inf-sci.net/XL-5-W3/139/2013/isprsarchives-XL-5-W3-139-2013.pdf.

Sincerly,

HP

You can try resample up or downscalling method, B-spline interpolation in SAGA GIS too.