A Reduced Grid Method for a Parallel Global Ocean General Circulation Model

Abstract

A limitation of many explicit finite-difference global climate models is the timestep restriction caused by the decrease in cell size associated with the convergence of meridians near the poles. A computational grid in which the number of cells in the longitudinal direction is reduced toward high-latitudes, keeping the longitudinal width of the resulting cells as uniform as possible and increasing the allowable timestep, is applied to a three-dimensional primitive equation ocean-climate model. This "reduced" grid consists of subgrids which interact at interfaces along their northern and southern boundaries, where the resolution changes by a factor of three. Algorithms are developed to extend the finite difference techniques to this interface, focusing on the conservation required to perform long time integrations, while preserving the staggered spatial arrangement of variables and the numerics used on subgrids. The reduced grid eliminates the common alternative of filtering high-frequency modes from the solution at high-latitudes to allow a larger timestep and reduces execution time per model step by roughly 20 percent. The reduced grid model is implemented for parallel computer architectures with two-dimensional domain decomposition and message passing, with speedup results comparable to those of the original model. Both idealized and realistic model runs are presented to show the effect of the interface numerics on the model solution. First, a rectangular, mid-latitude, flat-bottomed basin with vertical walls at the boundaries is driven only by surface wind stress to compare three resolutions of the standard grid to reduced grid cases which use various interface conditions. Next, a similar basin with wind stress, heat, and fresh water forcing is used to compare the results of a reduced grid with those of a standard grid result while exercising the full set of model equations. Finally, global model runs, with topography, forcing, and physical parameters similar to those used for ocean-climate studies, are advanced to a near equilibrium state for both the reduced grid and the standard grid. Differences between the two are presented for typical fields of interest, and very little degradation of the solution due to the reduced grid is observed.