A comparison of compressible and anelastic models of deep dry convection

The atmosphere is nonhydrostatic when convection is present. Thunderstorms are one example. For numerical weather prediction models to reproduce convection accurately, they must be nonhydrostatic, nonlinear, and must utilize either compressible or anelastic models. Here we examine the response to an initial warm bubble that results in hydrostatic adjustment using compressible and anelastic models. The comparison of the models includes examining the perturbation flow field initial conditions, time evolution, potential vorticity perturbations, and the computational efficiency within isothermal and standard atmosphere base states. In addition to these parameters, both the traditional and available energetics are examined. The broad structure of the flow fields is qualitatively and quantitatively similar between the anelastic and compressible models and their base states. For example, the potential vorticity perturbations in both models are comparable. However, some differences exist in the perturbation fields. This is demonstrated in the compressible model that contains vertically propagating acoustic waves and horizontally propagating Lamb waves. The acoustic waves distort the pressure, density, and vertical velocity perturbation fields within the compressible model. The structural differences between the isothermal and standard atmosphere base states are induced by the advection of potential temperature into the stratospheric portion of the atmosphere in the standard atmosphere base state. Traditional and available energetics are both conserved within the model domain with a 10-5% error. Kinetic, potential, internal, available elastic and potential energies are altered by the adjustment process. The compressible model contains an oscillatory mode in its energetics. There is no available elastic energy within the anelastic model because acoustic waves are filtered out. Filtration of the acoustic modes allows the anelastic model run time to be less than that of the compressible model. However, time-differencing techniques can be implemented to improve the compressible model run time. Hence, the objective of the entire study is to confirm if this implementation is just as effective as using the anelastic model.