Journal cover Journal topic
Geoscientific Model Development An interactive open-access journal of the European Geosciences Union
Geosci. Model Dev., 9, 4273-4295, 2016
https://doi.org/10.5194/gmd-9-4273-2016
© Author(s) 2016. This work is distributed under
the Creative Commons Attribution 3.0 License.
Model description paper
25 Nov 2016
Parameterizing microphysical effects on variances and covariances of moisture and heat content using a multivariate probability density function: a study with CLUBB (tag MVCS)
Brian M. Griffin and Vincent E. Larson University of Wisconsin – Milwaukee, Department of Mathematical Sciences, Milwaukee, WI, USA
Abstract. Microphysical processes, such as the formation, growth, and evaporation of precipitation, interact with variability and covariances (e.g., fluxes) in moisture and heat content. For instance, evaporation of rain may produce cold pools, which in turn may trigger fresh convection and precipitation. These effects are usually omitted or else crudely parameterized at subgrid scales in weather and climate models.

A more formal approach is pursued here, based on predictive, horizontally averaged equations for the variances, covariances, and fluxes of moisture and heat content. These higher-order moment equations contain microphysical source terms. The microphysics terms can be integrated analytically, given a suitably simple warm-rain microphysics scheme and an approximate assumption about the multivariate distribution of cloud-related and precipitation-related variables. Performing the integrations provides exact expressions within an idealized context.

A large-eddy simulation (LES) of a shallow precipitating cumulus case is performed here, and it indicates that the microphysical effects on (co)variances and fluxes can be large. In some budgets and altitude ranges, they are dominant terms. The analytic expressions for the integrals are implemented in a single-column, higher-order closure model. Interactive single-column simulations agree qualitatively with the LES. The analytic integrations form a parameterization of microphysical effects in their own right, and they also serve as benchmark solutions that can be compared to non-analytic integration methods.


Citation: Griffin, B. M. and Larson, V. E.: Parameterizing microphysical effects on variances and covariances of moisture and heat content using a multivariate probability density function: a study with CLUBB (tag MVCS), Geosci. Model Dev., 9, 4273-4295, https://doi.org/10.5194/gmd-9-4273-2016, 2016.
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Short summary
Microphysical process rates, such as the formation, growth, and evaporation of precipitation, affect the variances, covariances, and fluxes of moisture and heat content. These effects appear as covariance terms within the Reynolds-averaged predictive equations for the scalar (co)variances and fluxes. Using a multivariate probability density function (PDF) and a simple warm-rain microphysics scheme, these microphysical covariance terms can be obtained by analytic integration over the PDF.
Microphysical process rates, such as the formation, growth, and evaporation of precipitation,...
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