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.

This article promotes a measure to validate the hydrostatic approximation via scaling the nontraditional Coriolis term (NCT) in the zonal momentum equation. To demonstrate the scaling, this study simulates large-scale flow forced by a prescribed heat source, mimicking the intertropical convergence zone (ITCZ) using a linearized forced-dissipative model. The model solves two similar equations, between which the only difference is the inclusion of NCTs. The equations are derived using the following approximations: anelastic, equatorial beta-plane, linearized, zonally symmetric, steady, and a constant dissipation coefficient. The large-scale flows simulated with and without NCTs are compared in terms of the meridional-vertical circulation, the zonal wind, and the potential temperature. Both results appear like the Hadley circulation. With the model parameters controlled, the differences between the results without NCTs and those with NCTs yield the linear biases due to omitting NCTs. The most prominent bias is a westerly wind bias in the ITCZ heating region that emerges because omitting NCTs prevents the associated westward acceleration when heating-induced vertical motion is present. The zonal wind bias divided by the zonal wind with NCTs is 0.120 ± 0.007 in terms of the westerly maximum and 0.0452 ± 0.0005 in terms of the root mean square (RMS) when the prescribed ITCZ mimics the observed ITCZ in May over the East Pacific. These normalized measures of the zonal wind bias increase with a narrower ITCZ or an ITCZ closer to the Equator, because of a weaker subtropical jet stream given the same vertical heating profile. This difference can be traced by a nondimensional parameter scaling the ratio of the NCT to the traditional Coriolis term. The scaling encourages the restoration of NCTs into global models. K E Y W O R D Scosine Coriolis term, Hadley circulation, intertropical convergence zone, large scale, nondimensional parameter, nontraditional Coriolis term, zonal wind bias 1 INTRODUCTION Nontraditional Coriolis terms (NCTs) are terms involving the meridional component of the planetary vorticity, 2Ωcos (Ω and denote the rotation rate of the Earth and the latitude), in the zonal and vertical momentum equations. NCTs are omitted when the hydrostatic approximation is applied. The NCT in the vertical momentum equation is omitted when deriving the hydrostatic equation, and the NCT in the zonal momentum equation is omitted for dynamical consistency and Q J R Meteorol Soc. 2019;145:2445-2453. wileyonlinelibrary.com/journal/qj

In this study, a hybrid mass flux cumulus scheme (HYMACS) is developed for the Weather Research and Forecasting Model (WRF). Idealized experiments are performed to evaluate its effects on tropical cyclone simulations. Classical cumulus schemes assume artificial local compensation of convective mass flux. In contrast, HYMACS treats subgrid‐scale mass flux convergence or divergence as parameterized mass sources or sinks. When the mass sources or sinks are introduced to the mass continuity equation in a nonhydrostatic fully compressible model, the model dynamics would resolve the mass‐compensating motion, i.e., dynamic compensation of convective mass flux. A hierarchy of experiments is conducted to demonstrate the effects of the artificial local compensation. The results of the mass compensation experiment show that the amplitude of the column mass change with the artificial local compensation is more sensitive to the change of the horizontal resolution between 3 and 27 km than the dynamic compensation. The results of the piggybacking tropical cyclone simulations at 9 km resolution suggest that the artificial local compensation in the Kain‐Fritsch scheme (KF) concentrates vertical exchange of dry static energy and moisture and induces secondary circulation, which could lead to sea level pressure decrease and enhanced precipitation. These results indicate that the artificial local compensation at the gray‐zone resolution could cause significant effects on tropical cyclone dynamics, so it is important to avoid the artificial local compensation for cumulus parameterization at such resolution.

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.