A Blended Soundproof-to-Compressible Numerical Model for Small- to Mesoscale Atmospheric Dynamics

A blended model for atmospheric flow simulations is introduced that enables seamless transition from semi-implicit fully compressible to pseudo-incompressible dynamics. The model equations are written in non-perturbational form and integrated using a wellbalanced second-order finite volume discretization. The scheme combines an explicit predictor for advection with elliptic corrections for the pressure field. Compressibility is implemented through a diagonal term in the elliptic equation. The compressible/soundproof transition is realized by weighting this term appropriately and it provides a mechanism for removing unwanted acoustic imbalances in compressible runs, with potential ramifications for data assimilation. As the thermodynamic pressure gradient is used in the momentum equation, the influence of perturbation pressure on buoyancy is included for thermodynamic consistency. This model is equivalent to Durran's original pseudo- incompressible model, which uses the Exner pressure. Numerical experiments demonstrate quadratic convergence and competitive solution quality for several benchmarks. With the thermodynamically consistent buoyancy correction the "p-\rho-formulation" of the sound-proof model closely reproduces the compressible results. The proposed approach offers a framework for model comparison largely free of biases due to different discretizations. With data assimilation applications in mind, the seamless compressible-sound-proof transition mechanism is also shown to enable the removal of acoustic imbalances in initial data for which balanced pressure distributions are unknown.

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