A doubly blended model for multiscale atmospheric dynamics

Abstract

The compressible flow equations for a moist, multi-component fluid constitute the most comprehensive description of atmospheric dynamics used in meteorological practice. Yet, compressibility effects are weak and acoustic waves outright unimportant in the atmosphere. This has led to the development of ``soundproof'' models which suppress sound waves entirely and provide good approximations for small- to meso-scale motions. Most global flow models are based instead on the hydrostatic primitive equations which only suppress vertically propagating acoustic modes and are applicable to relatively large-scale motions. Generalized models have been proposed that combine the advantages of the hydrostatic primitive and the soundproof equation sets. In this note we reveal close relationships between the compressible, pseudo-incompressible (soundproof), hydrostatic primitive, and the Arakawa & Konor unified model equations by introducing a continuous two-parameter family of models that default to either of these limiting cases for particular parameter constellations.