P vectors as a Diagnostic Tool for Synoptic-Scale Circulations

Abstract

The quasigeostrophic geopotential tendency equation is derived using P vectors in both pressure and entropy coordinates. This vector form of the geostrophic forcing in the geopotential tendency equation is similar to the Q-vector form of the ? equation. It is shown that the horizontal components of P are the advection of geostrophic momentum and the vertical component of P is the horizontal temperature advection. The P vectors are shown to be related to Q and C vectors, as well as the ageostrophic circulation. The three-dimensional pseudocurl of the P vector gives the C vector that equals the ageostrophic pseudovorticity in the quasigeostrophic model. The horizontal components of the pseudocurl of P are perpendicular and proportional to the Q. The horizontal divergence of the P vector is the geostrophic absolute vorticity advection while the three-dimensional divergence of the P vector is the geostrophic quasigeostrophic potential vorticity advection. The ageostrophic wind can be partitioned into the P vector (geostrophic advective) and isallobaric wind contributions. A numerical simulation of an idealized cyclone is used to characterize the distribution of the P vectors and P-vector diagnostics in order to demonstrate their potential application to the diagnosis of synoptic-scale circulations. The distribution of the P vectors clearly indicates the advections of geostrophic momentum and temperature that characterize cyclogenesis. An examination of the P vectors and the isallobaric wind demonstrates that the P vectors provide insight into the ageostrophic circulation of the cyclone. Diagnoses of the three-dimensional P-vector divergence and curl are shown to produce useful depictions of cyclonic vortex spinup and the propagation of both the large- and smaller-scale features of the system. These diagnostics can be interpreted from a variety of perspectives, including the height tendency and the advection of quasigeostrophic potential vorticity. The use of P vectors to diagnose synoptic-scale circulations appears to provide potentially useful insights into the dynamics of synoptic-scale disturbances not readily obtained from other diagnoses.