Numerical advection of correlated tracers: preserving particle size/composition moment sequences during transport of aerosol mixtures

Nonlinear transport algorithms designed to reduce numerical diffusion fail to preserve correlations between moments, isotope abundances, etc. when these scalar densities are transported in models as separate tracers. In case of the particle size/composition coordinates of an aerosol, such loss can give rise to unphysical moment sets. New statistical approaches to aerosol dynamics, which involve tracking moments directly, offer highly efficient alternatives to sectional and modal methods for representing aerosols in climate models, but it is essential that moment set integrity be preserved throughout a simulation. In this paper we review the problem and weaknesses of previous attempts at solution, including vector transport – a scheme in which the moments, as internal aerosol coordinates, are transported together with a single lead tracer such as number or mass. A non-negative least squares (NNLS) solution that finally eliminates the problem without requiring modification of the transport algorithm itself is presented. Following each transport step, new moment sets are resolved into sums of previously validated sets with non-negative coefficients using NNLS Transport errors are removed and the now guaranteed-to-be-valid moment sets are ready for passage to the aerosol dynamics module. In addition to moment set validation, the new scheme reduces numerical diffusion during transport and provides greater accuracy for the source apportionment of aerosol mixtures. The method is not limited to moment transport – similar improvements in accuracy are expected using NNLS in conjunction with modal and sectional methods.