Another Look at Stochastic Condensation for Subgrid Cloud Modeling: Adiabatic Evolution and Effects

Abstract

The theory of stochastic condensation, which models the impact of an ensemble of unresolved supersaturation fluctuations S′ on the volume-averaged droplet-size distribution f (r), is revisited in the modern context of subgrid cloud parameterization. The exact transition probability density for droplet radius driven by independent, Gaussian S′ fluctuations that are periodically renewed is derived and shown to be continuous but not smooth. The Fokker–Planck model follows naturally as the smooth-in-time approximation to this discrete-in-time process. Evolution equations for the moments of f (r) that include a contribution from subgrid S′ fluctuations are presented; these new terms are easily implemented in moment-based cloud schemes that resolve supersaturation. New, self-consistent expressions for the evolution of f (r) and mean supersaturation S in a closed, adiabatic volume are derived without approximation; quite appropriately, these coupled equations exactly conserve total water mass. The behavior of this adiabatic system, which serves as a surrogate for a closed model grid column, is analyzed in detail. In particular, a new nondimensional number is derived that determines the relative impact of S′ fluctuations on droplet spectral evolution, and the contribution of fluctuations to S is shown to be negative definite and maximal near the accommodation length and has a direct correspondence to the analysis of Cooper. Observational support for the theory of stochastic condensation is found in cloud droplet spectra from cumulus cloud fields measured during the Rain in the Cumulus over the Ocean (RICO) and Small Cumulus Microphysics Study (SCMS) campaigns. Increasing spectral broadening with increasing spatial scale is discovered and compares well with theoretical predictions. However, the observed spectra show evidence of non-Gaussian S′ fluctuations and inhomogeneous mixing, processes neglected in the current theory.