A Reformulation and Implementation of the Bryan-Cox-Semtner Ocean Model on the Connection Machine

Abstract

Certain aspects of the Semtner-Chervin version of the Bryan-Cox-Semtner global ocean model are reformulated for improved efficiency on parallel computer architectures and on the Connection Machine CM-2 in particular. These changes involve (a) the switch from a streamfunction to a surface pressure formulation in the barotropic equations, (b) the splitting off of the Coriolis terms from the barotropic equations to produce a symmetric surface pressure equation, which then permits (c) the use of a preconditioned conjugate-gradient method for the solution of this equation. The switch to a surface pressure formulation (a) eliminates global equations associated with island boundary conditions and therefore improves performance as well as allows an unlimited number of islands, (b) reduces sensitivity to rapidly varying bottom topography and therefore obviates the need for smoothing the topography, and (c) makes the surface pressure a prognostic variable, thus potentially making it easier to assimilate surface altimetry data. Care is taken to retain the energetic consistency built into the original model. The nine-point operator for the pressure equation is found necessary to maintain energy consistency, in contrast to the streamfunction formulation where both nine-point and five-point operators are usable. Computational results closely resemble those of the original model, but with significantly improved performance. The barotropic part of the calculations in the surface pressure formulation is newly three times faster than in the streamfunction formulation, and the full calculation involving both barotropic and baroclinic parts is nearly two times faster. These changes are described and details of the performance of the new formulation on the CM-2 are given.