On the interpretation of the pressure vertical velocity

Pressure vertical velocity (ω = Dp/Dt), where Dp/Dt stands for material derivative, is commonly approximated from the geometric vertical velocity (w=Dz/Dt) as ω ≈ -ρgw, which invokes the hydrostatic relation ∂p/∂z ≈ -ρg together with the additional assumption that local pressure tendency and horizontal pressure advection terms are negligible at planetary and synoptic scales. Using global simulations with the Icosahedral Nonhydrostatic model, we show that the horizontal pressure advection term can be relatively large in comparison with the  the vertical pressure advection at planetary-to-synoptic scales in regions of strong jets such as in the winter stratosphere, contradicting the conventional assumption ω ≈ -ρgw. We further show that the horizontal and vertical pressure advection terms are predominantly out of phase with each other, so that their comparable amplitudes lead to substantial cancellation. As a consequence, ω can be suppressed or amplified at large scales relative to the -ρgw diagnostic, despite the validity of the hydrostatic balance. Scale diagnostics indicate that the large-scale enhancement of the horizontal pressure advection arises from interactions between the mean flow and Rossby waves. They also suggest a substantial ageostrophic component within otherwise predominantly geostrophic large-scale motions. It is hypothesized that the generation of these ageostrophic winds is related to the ubiquitous jet streaks and curvature of the polar night jet, and thus, that enhanced horizontal pressure advection is likely a general feature of any jets. From an energetic perspective, these advection terms correspond to compensating contributions of pressure-gradient work in different directions. Consequently, ω behaves more like the net pressure gradient work, rather than a direct measure of vertical motion.