A new treatment of the lower boundary and surface pressure equation in GCMs

The atmospheric equations of motion are most naturally described using pressure as the vertical coordinate. The surface pressure is a function of space and time and in a pressure coordinate model represents a moving boundary problem.

Traditionally, this difficulty is avoided by using a normalized Philips coordinate (sigma) or some similar function in the vertical. However, sigma-coordinates have some draw-backs such as hydrostatic consistency criteria and the generation of spontaneous motion from a resting state. Here, we apply the finite volume method to the original pressure coordinate equations and model the moving boundary with a variable thickness layer at the surface. This method has previously proven accurate at representing dynamical interactions over topography. One immediate advantage of this method is that there are no pressure gradient errors in the interior of the fluid over topographic slopes.

A second advantage is that the pressure coordinate equations are isomorphic with the incompressible z-coordinate equations for the ocean, therefore allowing the same approach to be applied for both atmosphere and ocean dynamics. The isomorphism extends naturally to the surface boundary condition that is analogous to the free surface problem. By using the finite volume method to model the moving lower boundary in the atmosphere, we have been able to produce a hydro-dynamical code that can model either the atmosphere or ocean. We test the model using simplified physics and compare with AMIP runs.