Entropy-based and static stability-based lagrangian model grids

Abstract

Lagrangian transport modeling has gained increasing popularity in the last few decades not only within the atmospheric community. The chance to avoid, or at least to minimize, the numerical diffusion ever present in the Eulerian numerical schemes is the strongest motivation for the Lagrangian formulation of transport. By considering transport of chemically passive species in the atmosphere extending between the Earth's surface and the mesosphere, we show how horizontal and vertical scales of a numerical grid can be realized in a physically consistent way. Focusing on the Lagrangian (irregular) grid, we derive such consistent horizontal and vertical resolutions from the assumption that their ratio, the so-called aspect ratio, is controlled by the static stability and from the assumption that the entropy of the system is uniformly distributed over all air parcels. We also show how numerical diffusion can be used to parametrize physical mixing instead of disturbing the numerical solutions of transport equations. © 2012. American Geophysical Union. All Rights Reserved.