The Subgrid Importance Latin Hypercube Sampler (SILHS): a multivariate subcolumn generator

Coarse-resolution climate and weather forecast models cannot accurately parameterize small-scale, non-linear processes without accounting for subgrid-scale variability. To do so, some models integrate over the subgrid variability analytically. Although analytic integration methods are attractive, they can be used only with physical parameterizations that have a sufficiently simple functional form. Instead, this paper introduces a method to integrate subgrid variability using a type of Monte-Carlo integration. The method generates subcolumns with suitable vertical correlations and feeds them into a microphysics parameterization. The subcolumn methodology is non-intrusive and can be used with a wide variety of physical parameterizations. Our subcolumn generator is multivariate, which is important for physical processes that involve two or more hydrometeor species, such as accretion of cloud droplets by rain drops. In order to reduce sampling noise in the integrations, our subcolumn generator employs two variance reduction methods, namely importance and stratified (Latin hypercube) sampling. For this reason, we name the subcolumn generator the Subgrid Importance Latin Hypercube Sampler (SILHS). This paper tests SILHS in interactive, single-column simulations of a marine stratocumulus case and a shallow cumulus case. The paper then compares simulations that use SILHS with those that use analytic integration. Although the SILHS solutions exhibit considerable noise from time step to time step, the noise is greatly damped in most of the time-averaged profiles.