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A Fully Compressible Nonhydrostatic Deep-Atmosphere Equations Solver for MPAS

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  • 1 National Center for Atmospheric Research, Boulder, Colorado
  • 2 University of California, Davis, Davis, California
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Abstract

A solver for the nonhydrostatic deep-atmosphere equations of motion is described that extends the capabilities of the Model for Prediction Across Scales-Atmosphere (MPAS-A) beyond the existing shallow-atmosphere equations solver. The discretization and additional terms within this extension maintain the C-grid staggering, hybrid height vertical coordinate, and spherical centroidal Voronoi mesh used by MPAS, and also preserve the solver’s conservation properties. Idealized baroclinic wave test results, using Earth-radius and reduced-radius sphere configurations, verify the correctness of the solver and compare well with published results from other models. For these test cases, the time evolution of the maximum horizontal wind speed, and the total energy and its components, are presented as additional solution metrics that may allow for further discrimination in model comparisons. The test case solutions are found to be sensitive to the configuration of dissipation mechanisms in MPAS-A, and many of the differences among models in previously published test case solutions appear to arise because of their differing dissipation configurations. For the deep-atmosphere reduced-radius sphere test case, small-scale noise in the numerical solution was found to arise from the analytic initialization that contains unstable lapse rates in the tropical lower troposphere. By adjusting a parameter in this initialization, the instability is removed and the unphysical large-scale overturning no longer occurs. Inclusion of the deep-atmosphere capability in the MPAS-A solver increases the dry dynamics cost by less than 5% on CPU-based architectures, and configuration of either the shallow- or deep-atmosphere equations is controlled by a simple switch.

© 2021 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: William C. Skamarock, skamaroc@ucar.edu

Abstract

A solver for the nonhydrostatic deep-atmosphere equations of motion is described that extends the capabilities of the Model for Prediction Across Scales-Atmosphere (MPAS-A) beyond the existing shallow-atmosphere equations solver. The discretization and additional terms within this extension maintain the C-grid staggering, hybrid height vertical coordinate, and spherical centroidal Voronoi mesh used by MPAS, and also preserve the solver’s conservation properties. Idealized baroclinic wave test results, using Earth-radius and reduced-radius sphere configurations, verify the correctness of the solver and compare well with published results from other models. For these test cases, the time evolution of the maximum horizontal wind speed, and the total energy and its components, are presented as additional solution metrics that may allow for further discrimination in model comparisons. The test case solutions are found to be sensitive to the configuration of dissipation mechanisms in MPAS-A, and many of the differences among models in previously published test case solutions appear to arise because of their differing dissipation configurations. For the deep-atmosphere reduced-radius sphere test case, small-scale noise in the numerical solution was found to arise from the analytic initialization that contains unstable lapse rates in the tropical lower troposphere. By adjusting a parameter in this initialization, the instability is removed and the unphysical large-scale overturning no longer occurs. Inclusion of the deep-atmosphere capability in the MPAS-A solver increases the dry dynamics cost by less than 5% on CPU-based architectures, and configuration of either the shallow- or deep-atmosphere equations is controlled by a simple switch.

© 2021 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: William C. Skamarock, skamaroc@ucar.edu
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