Preserving tracer correlations in atmospheric transport models

Abstract

A linear non-diffusive algorithm for advective transport is developed that greatly improves the level of detail at which aerosols and clouds can be represented in atmospheric models. Linear advection schemes preserve tracer correlations but the basic linear scheme, employing zeroth-order finite differencing, is rarely used by atmospheric modelers on account of its excessive numerical diffusion. Higher-order schemes are in widespread use, but these present new problems as nonlinear adjustments are required to avoid occurrences of negative concentrations, spurious oscillations, and other non-physical effects. Generally successful at reducing numerical diffusion during the advection of individual tracers, e.g. particle number or mass, the higher-order schemes fail to preserve even the simplest correlations between interrelated tracers. As a result, important tracer attributes of aerosol and cloud populations including radial moments of particle size distributions, molecular precursors related through chemical equilibria, aerosol mixing state, and distribution of cloud phase are all poorly represented in models. We introduce a new scheme, minVAR, that is both non-diffusive and preservative of tracer correlations, thereby combining the best features of the basic and higher-order schemes while enabling new features such as the tracking of sub-grid information at arbitrarily fine scales with high computational efficiency. Plain Language Summary:In this paper we resolve a long-standing bottleneck to the representation of aerosols and clouds in atmospheric models beyond the two-moment microphysical schemes currently in use. The bottleneck is caused by the failure of higherorder advection schemes to preserve correlations between interrelated tracers during transport -a task for which they were never designed. The paper was motivated in part by our recent convective cloud chamber study [Yang et al., 2022], which employed a second-order advection scheme and a two-moment cloud microphysical scheme limited to tracking particle number and mass. The new approach introduces a diffusion limiter, under the idea that achieving minimal spatial variance on an Eulerian model grid implies maximal resolution and elimination of numerical diffusion. By preserving tracer correlations and eliminating numerical diffusion, minVAR -short for minimum variance -includes the best features of the basic linear and higher-order schemes. This innovation resolves the twomoment bottleneck, a necessary step for high-fidelity, multi-moment representation of aerosols and clouds in atmospheric models.