I wanted to interpolate the trend values (trend of sunshine hour calculated over 20 years) throughout the study area from the available station points. My confusion is in the selection of interpolation tools I shall use in ArcGIS to do that (IDM, Kriging, Natural Neighbor, spline and all that).
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:
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.