Upscaling microphysical process rates to the grid box size

Microphysical calculations in large-scale models can be degraded by the neglect of subgrid variability in moisture and temperature. That is, a local microphysics formula, which accurately computes microphysical processes at a point in space, will still yield inaccurate results if it is driven by inaccurate distributions of moisture and temperature. Inaccuracy occurs when microphysical processes are non-linear, and the variability in moisture and temperature within a grid box is large.

To avoid this inaccuracy, local microphysical formulas may be upscaled to an extensive grid box. Spatial variability within a grid box may be represented by a probability density function (PDF). Then the upscaling may be done by analytically integrating the local microphysical formula over the PDF. In this paper, we analytically upscale the local microphysical formulas of Khairoutdinov and Kogan, which collectively constitute a double-moment scheme for drizzle in marine stratocumulus. Then we implement the upscaled formulas interactively in a single-column model and test the model for a drizzling marine stratocumulus case, namely research flight two (RF02) of the DYCOMS-II field experiment.

Compared to the local microphysics solution, the upscaled microphysics exhibits increased autoconversion of cloud droplets to raindrops and increased accretion of cloud droplets onto raindrops (i.e. increased collection). Furthermore, the upscaled microphysics evaporates a smaller percentage of rainwater, particularly just below the exactly saturated altitude at cloud base. The combined result of the aforementioned effects is a significant increase in rainwater at the ocean surface, in closer agreement to a benchmark large-eddy simulation.