A PDF-Based Microphysics Parameterization for Shallow Cumulus Clouds

Abstract

Unbiased calculations of microphysical process rates such as autoconversion and accretion in mesoscale numerical weather prediction models require that subgrid-scale (SGS) variability over the model grid volume be taken into account. This variability can be expressed as probability distribution functions (PDFs) of microphysical variables.Using dynamically balanced large-eddy simulation (LES)model results froma case ofmarine trade cumulus, the authors develop PDFs of the cloud water, droplet concentration, and rainwater variables (qc, Nc, andqr). Both 1Dand 2Djoint PDFs (JPDFs) are presented. The authors demonstrate that accounting for the JPDFs results inmore accurate process rates for a regional-model grid size. Bias in autoconversion and accretion rates are presented, assuming different formulations of the JPDFs. Approximating the 2D PDF using a product of individual 1D PDFs overestimates the autoconversion rates by an order of magnitude, whereas neglecting the SGS variability altogether results in a drastic underestimate of the grid-mean autoconversion rate. PDF assumptions have a much smaller impact on accretion, largely because of the near-linear dependence of the variables in the accretion rate formula and the relatively weak correlation between qc and qr over the small LES grid volumes. The latter is attributed to the spatial decorrelation in the vertical between the two fields. Although the full PDFs are both height and time dependent, results suggest that fixed-in-time and fixed-in-height PDFs give an acceptable level of accuracy, especially for the crucial autoconversion calculation.