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I have information of minimum and maximum mean monthly temperatures Tmin and Tmax, respectively), from more than 300 weather gauges and now I require to create interpolated surfaces of temperatures using cokriging or similar.

These weather gauges are located within a wide elevation gradient, in a wide geographic area (much of South America).

When I compare the observed temperatures (Tmin and Tmax from gauges) against the respective elevations (the one obtained from GMTED2010, as the elevation of a given pixel corresponding the geographic coordinates of a given gauge), I find that correlation is high and significant as expected. However, in the case of Tmin, I find an even stronger correlation with latitude.

Now, I plan to create the required surfaces of interpolated temperatures through a formula that defines the Tmin (dependent variable) as a linear model of independent variables: Tmin ~ elevation + latitude.

Does it make any sense?

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