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Hing Ong

Abstract

This comment on Hitchman and Rowe first deepens their introduction by distinguishing adiabatic and diabatic tilting of vorticity. Then, it strengthens their interpretation by emphasizing that momentum must be vertically transported with reference to isentropic levels to yield the potential vorticity (PV) dipoles. Moreover, it points out a flaw in their PV budget analysis and proposes a remedy for the flaw. Their convective momentum transport paradigm and the vorticity tilting paradigm reinterpret the same physical process. However, they counted one physical process twice by associating the two paradigms with two different terms. As an attempt to remedy the flaw, this comment associates the reinterpretation of the two paradigms with a transformation of the PV equation; their paradigm corresponds to a flux form. With the proposed remedy, their paradigm can be more easily translated to advances in convective parameterization because of its horizontal locality.

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Hing Ong and Paul E. Roundy

Abstract

This study derives a complete set of equatorially confined wave solutions from an anelastic equation set with the complete Coriolis terms, which include both the vertical and meridional planetary vorticity. The propagation mechanism can change with the effective static stability. When the effective static stability reduces to neutral, buoyancy ceases, but the role of buoyancy as an eastward-propagation mechanism is replaced by the compressional beta effect (i.e., vertical density-weighted advection of the meridional planetary vorticity). For example, the Kelvin mode becomes a compressional Rossby mode. Compressional Rossby waves are meridional vorticity disturbances that propagate eastward owing to the compressional beta effect. The compressional Rossby wave solutions can serve as a benchmark to validate the implementation of the nontraditional Coriolis terms (NCTs) in numerical models; with an effectively neutral condition and initial large-scale disturbances given a half vertical wavelength spanning the troposphere on Earth, compressional Rossby waves are expected to propagate eastward at a phase speed of 0.24 m s−1. The phase speed increases with the planetary rotation rate and the vertical wavelength and also changes with the density scale height. Besides, the compressional beta effect and the meridional vorticity tendency are reconstructed using reanalysis data and regressed upon tropical precipitation filtered for the Madden–Julian oscillation (MJO). The results suggest that the compressional beta effect contributes 10.8% of the meridional vorticity tendency associated with the MJO in terms of the ratio of the minimum values.

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William C. Skamarock, Hing Ong, and Joseph B. Klemp

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.

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