I have a point data set will a fairly low sample density and a raster that should loosely correlate with the values of the points. For example, this could be elevation and temperature readings. I want to create a surface that interpolates the points, preserving the values at the points where I have data, but in between follows the trend from the existing raster. A bit like is this very bad drawing.enter image description here

Has anyone done this before and know how to do it. I suppose I could interpolate the points to start with (spline will preserve my values so I'll use that. then add/multiply version of my raster that has been normalized so that its 1 at each point then + or - the size of difference from the average at each point. I'm not sure if this would work, if it would be the best method, or how to produce the normalized raster. Does anyone have any ideas?

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