I want to give you some hints about the differences in the methods.
More information can also be found on the esri help pages An overview of the Interpolation toolset
Because your variable (sunshine) depends on a second variable (level of pollution) Kriging may be a good method. You can use your second variable as an “external drift”. Kriging requires very deep knowledge of geostatistic.
If you start with interpolation analysis I would start with simpler methods: IDW, Spline (with barriers ) or Natural Neighbor.
Natural Neighbor does not support barriers. I believe that barriers are important for you.
So let's look at some differences between IDW and Spline with barriers:
- using a two-dimensional minimum curvature spline technique
- creates a smooth surface
- The resulting surface passes exactly through the input points. But: Usually some values of the resulting surface can be higher than the maximum of the input values (and lower than the minimum of the input values). You have to decide if that is possible for you. I think that it's good for you because your stations are probably not right there where in reality the minimum or maximum values occurs. Try it and see if the calculated minima and maxima are meaningful.
- less smooth surface than spline
- best result when our station distribution is dense (regard to the local variation of sunshine)
- The maximum value of the resulting surface is never higher than the maximum of the input value. The minimum value of the resulting surface is never lower than the minimum of the imput value.
- The resulting raster is a convex hull. Therefore, the border of your area of interest may not be entire covered by the resulting raster.
I would start with Spline with barriers. You can use Spatial Analyst for this. The profile tool of 3D Analyst can help to examine the results.