Ageostrophic Pseudovorticity and Geostrophic C-Vector Forcing—A New Look at the Q Vector in Three Dimensions

Abstract

By combining the two Q-vector component equations with the third quasigeostrophic (QG) diagnostic equation (the vertical ageostrophic vorticity equation) a complete set of QG diagnostic equations is formed in a three-dimensional vector form with the ageostrophic pseudovorticity vector on the left-hand side and a newly defined geostrophic forcing vector (the C vector) on the right-hand side. The horizontal projection of the C vector is a rotated Q vector (by 90° to the right). The vertical C-vector component is proportional to the Gaussian curvature of the geopotential surface of constant pressure. Since C-vector streamlines can be viewed as ageostrophic pseudovortex lines, ageostrophic circulations can be easily inferred through three-dimensional ?vorticity thinking,? which considers both the boundary effect and moist processes. The C vector is interpreted physically in terms of generation of Coriolis force curl and buoyancy curl due to the geostrophic advection alone. The basic techniques and possible merits of C-vector analyses are explored with simple examples. The C-vector concept is shown to be useful not only for qualitative analyses but also for quantitative computations of three-dimensional ageostrophic circulations. In particular, the pseudorotational part of the ageostrophic wind can be obtained from a convolution integral of the Green's function and C vector.