A critique of one- and two-dimensional models of boundary layer clouds with a binned representations of drop microphysics

A variety of models of boundary layer turbulence are increasingly being coupled to binned representation of cloud-drop spectra for the purpose of studying cloudy boundary layers and aerosol-cloud-drop interactions. A critique of one dimensional models shows that extant methods of coupling bin-microphysical models to the turbulence model omit important terms involving covariances of perturbation quantities. Errors incurred from the omission of these terms are significant: cloud-drop activation is not properly represented, and the initial stages of precipitation growth may be retarded in horizontally inhomogeneous boundary layers. If the promise of one-dimensional models is ever to be realized, some means of accurately representing these terms must be developed. Because large-scale models often have grid-spacings much larger than typical cloud-eddy-scale circulations, attempts to couple them to more detailed microphysical representations will also suffer from the problems discussed in the context of one-dimensional models. This should provide added motivation for improving the representation of microphysical processes on the sub-grid scale. An analysis of two-dimensional eddy-resolving models closed on the basis of energy inertial range arguments illustrates that the lack of an energy cascade in two dimensions results in increasingly vigorous circulations as the modelʹs grid-mesh is refined. Two-dimensional model simulations can display significant variability to vanishingly small differences in the initial conditions, and drizzle rates vary by as much as 30% when total water concentrations are increased by only 1%. Such sensitivities make it difficult to constrain the models given the degree of uncertainty that characterizes measurements of state variables in clouds. Despite some inconsistencies in the formulation of their closure terms, two-dimensional models are at least able to qualitatively represent the interaction of the large-eddies and microphysical processes in boundary layer flows. For this reason they appear to be useful, not as surrogates for reality, but rather as a means for further refining hypotheses about the physical system thereby increasing the chances that such hypotheses can be tested observationally.