Is there a way to interpolate anomaly directly? I have a set of temperature anomaly (difference between actual and normal temperature) and I want to interpolate the anomaly directly.


Yes you can, your surface would be something from -5 to +5 or similar, no problem with that. You can use IDW for example.

If you take into account elevation, for example using a dem, you can calculate the expected temperature surface, for example: (elev/100)*0.4 assuming temperature decreases 0.4 degrees Celsius every 100m (which I don't know. If it is true, just as an example). Add that expression to the raster calculator and then, you will be able to compare or subtract your temperature anomaly to the elevation temperature anomaly.

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