The above discussion of a general interface also applies to schemes which consider a mosaic of surfaces within the grid-box of the GCM or use a delocalized physics [Vintzileos and Sadourny, 1997], as all tiles only view one set of atmospheric conditions. In the special case where the surface scheme uses a grid different from the one of the GCM, it will have to do the disaggregation, as it holds all the information needed.
More complex is the issue of the sub-grid scale variability of atmospheric forcings provided by the GCM. The special case of precipitation is discussed here as some models already take this aspect into account by distinguishing between stratiform and convective precipitation. This distinction is problematic, as it relies on distinctions between parameterizations of GCMs rather than physical quantities. Some GCMs do not produce these two types of precipitation but have a single parameterization which covers all cases.
A more physical solution would be to provide with precipitation an extra variable which for each grid box describes its distribution. This could be either the spatial variance of the field within the grid-box or the parameter to a spatial distribution function. In the case of variance we would have zero for the stratiform precipitation and some small value for convective rainfall. This choice has the advantage that the GCM has a finer control over the sub-grid scale variability assumed in the LSS. This approach could also be extended to other variables if needed. In the present situation we will choose the variance as it is the simplest description of the second momentum of the sub-grid scale distribution.