Multivariate quadrature for representing cloud condensation nuclei activity of aerosol populations

Atmospheric aerosol is comprised of distinct multicomponent particles that are continuously modified as they are transported in the atmosphere. Resolving variability in particle physical and chemical properties requires tracking high-dimensional probability density functions, which is not practical in large-scale atmospheric simulations. Reduced representations of atmospheric aerosols are needed for efficient regional- and global-scale chemical transport models. Although the aerosol size-composition distribution is described by a high-dimensional probability density function, here we show that cloud condensation nuclei (CCN) activity of aerosol populations can be represented with high accuracy using an optimized set of representative particles. The sparse representation of the aerosol mixing state, designed for use in quadrature-based moment models, is constructed from a linear program that is combined with an entropy-inspired cost function. Unlike reduced representations common to large-scale atmospheric models, such as modal and sectional schemes, the maximum-entropy approach described here is not confined to pre-determined size bins or assumed distribution shapes. This study is a first step toward a quadrature-based aerosol scheme that will track multivariate aerosol distributions with sufficient computational efficiency for large-scale simulations.