The author has recently shown that rainfall interstation correlation functions can be derived analytically from mathematically described storm models. In this paper the formal derivation of such correlation functions is improved. The terminology has been made more general to furnish a basis for further developments in deriving and interpreting correlation functions. One of the storm models that can be treated analytically is the exponential model, which contains a shape parameter measuring the steepness of the storm profile. Varying this parameter from zero to infinity, a family of storm profiles is obtained ranging from a flat (rectangular) type to extremely peaked types with vanishing storm width. This paper investigates how the analytical interstation correlation function behaves when varying the storm profile parameter. The results given as families of correlation curves complete the collection of the graphical representation of rainfall interstation correlation functions derived thus far. They are required in interpreting and calibrating empirically found correlation functions. Storm diameter, the length of the cross section in the gauged area across which storms pass, and the proportion of completely dry days over the gauged area, are used as further parameters.