Analytic upscaling of a local microphysics scheme. Part I: Derivation
Article first published online: 7 JUN 2012
Copyright © 2012 Royal Meteorological Society
Quarterly Journal of the Royal Meteorological Society
Volume 139, Issue 670, pages 46–57, January 2013 Part A
How to Cite
Larson, V. E. and Griffin, B. M. (2013), Analytic upscaling of a local microphysics scheme. Part I: Derivation. Q.J.R. Meteorol. Soc., 139: 46–57. doi: 10.1002/qj.1967
- Issue published online: 5 FEB 2013
- Article first published online: 7 JUN 2012
- Manuscript Accepted: 30 MAR 2012
- Manuscript Revised: 29 FEB 2012
- Manuscript Received: 13 MAY 2010
- probability density function;
In large-scale simulations of the atmosphere, microphysical processes occur on smaller scales than the grid-box size. If the processes are nonlinear, and the variability within a grid box is large, then ignoring the subgrid variability leads to inaccuracy. To avoid this inaccuracy, local microphysical formulas, valid at a point in space, may be upscaled to a large grid box.
This may be done by integrating the local microphysical formula over the probability density function (PDF) that represents spatial subgrid variability. This paper will upscale local formulas proposed by Khairoutdinov and Kogan, which constitute a complete microphysics scheme for drizzle in marine stratocumulus. It is tractable to upscale this scheme because all formulas in it are power laws. The marginal PDFs will be assumed to have either a normal mixture or log-normal functional form.
In Part II of this pair of papers, the upscaled formulas are implemented interactively in a single-column model and tested for a drizzling marine stratocumulus case. Copyright © 2012 Royal Meteorological Society