The Quasigeostrophic Omega Equation: Reappraisal, Refinements, and Relevance

Abstract

A two-component study is undertaken of the classical quasigeostrophic (QG) omega equation. First, a reappraisal is undertaken of extant formulations of the equation’s so-called forcing function. It pinpoints shortcomings of various formulations and prompts consideration of alternative forms. Particular consideration is given to the contribution of flow deformation to the forcing function, and to the role of the advection of the geostrophic flow by the thermal wind (the R vector). The latter is closely related to the Q vector, the horizontal component of the ageostrophic vorticity, and the forcing function itself. The reexamination promotes further examination of the physical interpretation and diagnostic use of the omega equation particularly for assessing richly structured subsynoptic flow features. Second, consideration is given to the dynamics associated with the equation and its more general utility. It is shown that the R vector is intrinsic to a quasigeostrophic cascade to finer-scaled flow, and that a fundamental feature of the QG omega equation—the in-phase relationship between cloud-diabatic heating and the attendant vertical velocity—has important potential ramifications for the assimilation of data in numerical weather prediction (NWP) models. Finally, it is shown that, in the context of considering NWP model output, mild generalizations of the quasigeostrophic R vector retain interpretative value for flow settings beyond geostrophy and warrant consideration when addressing some contemporary NWP challenges.

Modeling the Interaction between Quasigeostrophic Vertical Motion and Convection in a Single Column

“…The QGv equation is six decades old [e.g., review of Davies (2015)], but has been used mainly as a diagnostic equation. The novelty of the current study is in using it in a predictive modeling framework to quantify the interaction between convection and large-scale dynamics in a single column.…”

The Future of Midlatitude Cyclones

“…LH due to the formation of clouds and precipitation can increase ETC intensity (if all other factors affecting cyclone dynamics are unchanged) through its effect on buoyancy, vertical motion, and thus also sea-level pressure and vorticity [24][25][26]. The relative contribution of diabatic processes to ETC intensification can be quantified via the pressure tendency equation [27], the omega equation [28,29], or the Zwack-Okossi equation [30]. Another perspective on the influence of LH on cyclones can be obtained from the potential vorticity (PV) framework [31]: diabatic PV generation associated with LH in clouds leads to the formation of a cyclonic PV anomaly in the lower troposphere that contributes to the cyclonic circulation [25,26,[32][33][34].…”

Increase in the number of extremely strong fronts over Europe? A study based on ERA‐Interim reanalysis (1979–2014)

“…Finally, we note that the fact that frontal precipitation increases with stronger θ e gradients is solely a consequence of an increase in humidity and also due to more intense frontal dynamics. The forcing of vertical motion can be quantified using the Q-vector convergence [Hoskins et al, 1978;Barnes, 1985;Keyser et al, 1988;Davies, 2015]. Q-vectors computed at 850 hPa and attributed to the 850 hPa frontal strength, suggest stronger Q-vector convergence with increasing frontal strength ( Figure S9).…”