  Sparse representations of atmospheric aerosols are needed for efficient
regional- and global-scale chemical transport models. Here we introduce a new
framework for representing aerosol distributions, based on the quadrature
method of moments. Given a set of moment constraints, we show how linear
programming, combined with an entropy-inspired cost function, can be used to
construct optimized quadrature representations of aerosol distributions. The
sparse representations derived from this approach accurately reproduce cloud
condensation nuclei (CCN) activity for realistically complex distributions
simulated by a particle-resolved model. Additionally, the linear programming
techniques described in this study can be used to bound key aerosol properties,
such as the number concentration of CCN. Unlike the commonly used sparse
representations, such as modal and sectional schemes, the maximum-entropy
approach described here is not constrained to pre-determined size bins or
assumed distribution shapes. This study is a first step toward a particle-based
aerosol scheme that will track multivariate aerosol distributions with
sufficient computational efficiency for large-scale simulations.
