Separate modeling of the spatial mean field, the spatial variance field, and the space-time residual fields can give a more detailed and possibly more accurate representation of spatial interpolation errors when we have repeated observations on a fixed monitoring network. This article gives expressions for the spatial interpolation errors in terms of the statistics of the component fields, which enable us to assess the relative importance of different kinds of uncertainty. This modeling approach is applied to data of sulfur dioxide concentrations in Europe, and a comparison with neighborhood kriging is done by means of cross-validation.