Pincus, Robert, and Stephen A. Klein, 2000: Unresolved spatial variability and microphysical process rates in large-scale models.  Journal of Geophysical Research, 105(D22), 27,059-27,066.

Abstract:  Prognostic cloud schemes in large scale models are typically formulated in terms of grid-cell average values of cloud condensate concentration q, although variability in q at spatial scales smaller than the grid cell is known to exist.  Because the source and sink processes modifying q are nonlinear, the process rates computed using the mean value of q are biased relative to process rates which account for sub-grid scale variability.  A preliminary assessment shows that these biases can modify instantaneous process rates by as much as a factor of two.  Observations of q at a continental site suggest that the bias is avoided in current practice through the arbitrary tuning of model parameters. Models might be improved if sub-grid scale variability in q were explicitly considered; several approaches to this goal are suggested.