A doubly blended model for multiscale atmospheric dynamics

The compressible flow equations for a moist, multicomponent fluid constitute the most comprehensive description of atmospheric dynamics used in meteorological practice. Yet, compressibility effects are often considered weak and acoustic waves outright unimportant in the atmosphere, except possibly for Lamb waves on very large scales. This has led to the development of "soundproof" models, which suppress sound waves entirely and provide good approximations for small-scale to mesoscale motions. Most global flow models are based instead on the hydrostatic primitive equations that 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, the authors reveal close relationships between the compressible, pseudoincompressible (soundproof), hydrostatic primitive, and the Arakawa and Konor unified model equations by introducing a continuous two-parameter (i.e., "doubly blended") family of models that defaults to either of these limiting cases for particular parameter constellations.