FREE AND RIGID BOUNDARY QUASI-GEOSTROPHIC MODELS IN PRESSURE COORDINATES

Scarring from the hydrostatic primitive equations in pressure coordina tes, a quasigeostrophic (QG) model is different tendency equations for the GSP exist: one expressing mass conservation, and the other the co ndition of zero vertical velocity at the ground in common physical spa ce. Comparison of these equations lends to a diagnostic relationship t hat provides a boundary condition for the omega equation. Equivalence of the system of equations to the QG model that employs the potential vorticity equation is established, Introduction of the GSP as one of t he main prognostic fields highlights the problem of the lower boundary condition in pressure coordinates. Two models are introduced and stud ied, and their main features are compared-the free surface (FS) and th e rigid boundary (RB) models, the latter bring most common in pressure coordinate QG studies. The choice has an effect on the boundary condi tions for the omega equation and affects the physical qualities of the model. The model with the FS has additional energy, similar to the en ergy of an elastic membrane, which the RB model lacks. Both models giv e similar results for synoptic-scale processes but differ essentially for scales larger than the external Rossby deformation radius (similar to 3000 km). As the scale analysis shows, the FS model is accurate in this case, while the RB model, which filters mass fluctuations of ver tical unit columns of the atmosphere, seriously distorts the phase spe eds.