Formulation of Microphysical Inhomogeneity in Cumulus Clouds Using 1D Variability Factor

Neglecting subgrid-scale (SGS) variability can lead to substantial bias in calculations of microphysical process rates. The solution to the SGS variability bias problem lies in representing the variability using joint probability distribution functions (JPDFs) for the different microphysical variables.

Different formulations of JPDFs based on Large Eddy Simulation (LES) studies of shallow cumulus and cumulus congestus clouds were evaluated. It was shown that inhomogeneity in both cloud types can be quantified by their respective JPDFs calculated using datasets from the entire simulation time period (“generic” JPDFs). The generic JPDF can be a-priory integrated and yield a one-dimensional variability factor (V-factor) specific for each cloud type. A quite accurate approximation of V-factors by an analytical function in the form of a 3^rd order polynomial was obtained and can be easily implemented in mesoscale models.

The effect of accounting for cloud inhomogeneity on precipitation was also evaluated. Over the 24 h simulation the surface precipitation in the shallow Cu case increased by 38% when inhomogeneity was accounted. In the congestus Cu case the increase in precipitation was even more significant: by more than 75% over only 8 hours since rain first appeared at the surface. The sensitivity experiments revealed that most of the increase resulted from the augmented autoconversion process. The effect of modified by V-factor accretion rates was much less significant, primarily, because of the nearly linear dependence of accretion on its parameters. This fact shows importance of the most accurate formulation of the autoconversion process.