On the interpretation of the pressure vertical velocity

Pressure vertical velocity (ω = Dp/Dt) 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 term are negligible at planetary and synoptic scales. Using global nonhydrostatic simulations with the ICON model, we show that the horizontal pressure advection term can be relatively large compared with the vertical pressure advection term 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 exhibit a predominantly out-of-phase structure and 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 eddies. 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.