A Unified Framework for Discrete Integrations of Compressible and Soundproof Equations of All-Scale Atmospheric Dynamics

Piotr K. Smolarkiewicz
European Center for Medium-Range Weather Forecasting
Reading, United Kingdom

A unified forward-in-time framework is developed for consistent integrations of soundproof (either anelastic or pseudo-incompressible) and fully compressible (either explicit acoustic, or amenable for semi-implicit soundproof-like time stepping) nonhydrostatic equations of motion for rotating stratified fluids under gravity. A characteristic aspect of the framework, revealed in time-dependent geometry, is a special role of the mass continuity equation combining soundproof and compressible systems into a common conservative form, while defining advecting momenta for all prognosed fluid properties expressed per unit of mass; hereafter, specific fluid variables, such as specific momenta (i.e., velocity components). In this unified framework all specific dependent variables in all variants of governing PDEs are evolved with the same numerics, closed by distinct pressure equations (either thermodynamic or elliptic) representative of each system. This allows for direct comparison of various theoretical formulations of the governing PDEs and facilitates exchanging specific variables predicted by different models. The numerical advancements are illustrated with canonical simulations of planetary baroclinic instability, an archetype of global weather. The results shed new light on the role of soundproof systems in modeling all-scale weather and climate.  

Thursday, 1 August 2013, 3:30 PM
Refreshments 3:15 PM
NCAR-Foothills Laboratory
3450 Mitchell Lane
Bldg 2 Main Auditorium, Room 1022

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Piotr K. Smolarkiewicz

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Thursday, August 1, 2013 - 3:30pm