Restoring Causality to Hydrostatic Vertical Motion

Synoptic-scale vertical motion is an important weather-maker, but explanations are often muddled. Traditionally, the mass field (pressure height Z) is taken as given, perhaps because it was the first field to be meaningfully measurable. Geostrophic wind is then computed as the entree to theory culminating in the glorious quasi-geostrophic omega equation. But the horizontal momentum field (now available easily in reanalyses) seems more causally fundamental than Z, the more meaningful locus of feature identity through time. Its divergence obeys a prognostic equation with the Laplacian of geopotential as a driver. Geostrophic geopotential can be defined and computed as the 'velocity potential' for the Coriolis force field, with ageostrophic as the residual. Momentum advection explains a large chunk of that, defining the gradignt geopotential and its a-gradient residue. In this way, one can decompose the total divergence acceleration, and thereby the rate of change of omega through the rigidly diagnostic mass continuity equation. Using the convenient and intuitive Windspharm packge of Python codes for spherical harmonic computations, the power and limits of these ideas are illustrated in high quality modern reanalysis data. What light can this framework shed on longstanding ideas such as the role of upper-level “jet streaks” or “outflow channels” on the development of subtropical and tropical cyclones, for instance?