The Impact of Effective Buoyancy and Dynamic Pressure Forcing on Vertical Velocities within 2 Dimensional Updrafts

This research develops simple diagnostic expressions for dw/dt and w within updrafts that account for effective buoyancy and the dynamic pressure gradient force. Effective buoyancy (EFF BUOY) is the sum of buoyancy and the vertical gradient in the buoyancy pressure field. The diagnostic expressions derived herein show that the effective buoyancy of an updraft is dependent on the magnitude of the temperature perturbation within an updraft relative to the air along the updraft's immediate periphery (delta theta'_v; rather than relative to an arbitrary base state as in theta'_v), the updraft's height-to-width aspect ratio, and the updraft's slant relative to the vertical.

The diagnostic expressions are significantly improved over parcel theory (where pressure forces are ignored) in their portrayal of the vertical profile of w through updrafts from a cloud model simulation, and accurately diagnosed the maximum w (w_max) within updrafts. The largest improvements to the diagnostic expression over parcel theory resulted from their dependency on delta theta'_v rather than theta'_v. Whereas the actual w_max within simulated updrafts was located approximately 2/3 to 3/4 of the distance between the updraft base and the updraft top, the w_max within profiles diagnosed by expressions was portrayed at the updraft top when the dynamic pressure force was ignored. A rudimentary representation of the dynamic pressure force in the diagnostic expressions improved their portrayal of simulated w profile. These results augment our conceptual understanding of convective updrafts, and provide avenues for improving the representation of vertical mass flux in cumulus parameterizations.