| Abstrakt: |
A linear non‐diffusive algorithm for advective transport is developed that greatly improves the detail at which aerosols and clouds can be represented in atmospheric models. Linear advection schemes preserve tracer correlations but the most basic linear scheme 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, for example, particle number or mass, the higher‐order schemes fail to preserve even the simplest of correlations between interrelated tracers. As a result, important 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 poorly represented. We introduce a new transport 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: A long‐standing challenge for the representation of aerosols and clouds in atmospheric models is to properly transport particles in space using higher‐order advection schemes. These schemes have less numerical diffusion than the simple basic scheme, but cannot maintain the physical relationship between particle number and mass that needs to be simulated correctly for better understanding of aerosol‐cloud‐turbulence interactions either in a laboratory‐scale cloud chamber or at larger atmospheric scales. The present advection scheme (minVAR, short for minimum variance) introduces a diffusion limiter, under the idea that achieving minimal spatial variance on an Eulerian grid implies maximal resolution and—it turns out ‐ complete elimination of numerical diffusion. By preserving tracer correlations and eliminating numerical diffusion, minVAR includes the best features of the simple basic and higher‐order schemes. This innovation resolves the two‐moment limitation, a necessary first step toward the high‐fidelity, multi‐moment, multi‐scale representation of aerosols and clouds in atmospheric models. Moments, because they are so strongly and nonlinearly correlated, provide an excellent example of correlation failure and serve to focus the present study. That said, there is no reason to suggest that the methods developed here would be inapplicable to other correlated tracer sets. Key Points: A diffusion limiter—minVAR—was added to the linear basic advection scheme and found to eliminate numerical diffusion completelyThe minimum variance property of minVAR makes the new method optimal for advection of independent tracers as well as correlated onesminVAR establishes a unique one‐to‐one correspondence between points along a Lagrangian trajectory and their mapping to the Eulerian grid [ABSTRACT FROM AUTHOR] |
