A Multiscale Anelastic Model for Meteorological Research

Wojciech W. Grabowski National Center for Atmospheric Research, Boulder, Colorado

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Piotr K. Smolarkiewicz National Center for Atmospheric Research, Boulder, Colorado

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Abstract

The recently reported nonhydrostatic anelastic numerical model for simulating a range of atmospheric processes on scales from micro to planetary is extended to moist processes. A theoretical formulation of moist precipitating thermodynamics follows the standard cloud models; that is, it explicitly treats the formation of cloud condensate and the subsequent development and fallout of precipitation. In order to accommodate a broad range of temporal scales, the customized numerical algorithm merges the explicit scheme for the thermodynamics with the semi-implicit scheme for the dynamics, where the latter is essential for the computational efficiency of the global model. The coarse spatial resolutions used in present global models result in a disparity between the timescales of the fluid flow and the much shorter timescales associated with phase-change processes and precipitation fallout. To overcome this difficulty the approach based on the method of averages is employed, where fast processes are evaluated with adequately small time steps (and lower accuracy) over the large time step of the model, to provide an accurate approximation to the large time step integral of fast forcings in the stiff system. This approach allows for stable integrations when cloud processes are poorly resolved and it converges to the formulation standard in cloud models as the resolution increases. The theoretical developments are tested in simulations of small-, meso-, and planetary-scale idealized moist atmospheric flows. Results from the small-scale simulations demonstrate that the proposed approach compares favorably with traditional explicit techniques used in cloud models. Planetary simulations, on the other hand, illustrate an ability to capture moist processes in low-resolution large-scale flows.

Corresponding author address: Dr. Wojciech W. Grabowski, NCAR, P.O. Box 3000, Boulder, CO 80307-3000. Email: grabow@ncar.ucar.edu

Abstract

The recently reported nonhydrostatic anelastic numerical model for simulating a range of atmospheric processes on scales from micro to planetary is extended to moist processes. A theoretical formulation of moist precipitating thermodynamics follows the standard cloud models; that is, it explicitly treats the formation of cloud condensate and the subsequent development and fallout of precipitation. In order to accommodate a broad range of temporal scales, the customized numerical algorithm merges the explicit scheme for the thermodynamics with the semi-implicit scheme for the dynamics, where the latter is essential for the computational efficiency of the global model. The coarse spatial resolutions used in present global models result in a disparity between the timescales of the fluid flow and the much shorter timescales associated with phase-change processes and precipitation fallout. To overcome this difficulty the approach based on the method of averages is employed, where fast processes are evaluated with adequately small time steps (and lower accuracy) over the large time step of the model, to provide an accurate approximation to the large time step integral of fast forcings in the stiff system. This approach allows for stable integrations when cloud processes are poorly resolved and it converges to the formulation standard in cloud models as the resolution increases. The theoretical developments are tested in simulations of small-, meso-, and planetary-scale idealized moist atmospheric flows. Results from the small-scale simulations demonstrate that the proposed approach compares favorably with traditional explicit techniques used in cloud models. Planetary simulations, on the other hand, illustrate an ability to capture moist processes in low-resolution large-scale flows.

Corresponding author address: Dr. Wojciech W. Grabowski, NCAR, P.O. Box 3000, Boulder, CO 80307-3000. Email: grabow@ncar.ucar.edu

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