An ocean general circulation model on a quasi-homogeneous cubic grid

Abstract

An ocean general circulation model (OGCM) on a non-orthogonal cubic grid originally proposed by Purser and Rančić [Purser, R.J., Rančić, M.A., 1998. Smooth quasi-homogeneous gridding of the sphere, Q.J.R. Meteorol. Soc., 124, 637–647] is developed. The grid size is very homogeneous with the ratio of the minimum to the maximum grid intervals being about 0.7. Hence this OGCM is free from severe time step limitation which the traditional latitude–longitude grid based OGCMs are subjected. In other aspects, the OGCM is similar to OGCMs used for climate research: Boussinesq and hydrostatic approximations, Arakawa B-grid and level coordinates. Since the grid is non-orthogonal, we formulated and discretized the equations on a general curvilinear coordinate system by careful treatment of non-orthogonality including variation of the directions of the local basis vectors. The performance of the model was evaluated by two tests. First the results of the long-term global integration of the cubic grid OGCM are compared with those of a latitude–longitude grid model. Except for small differences that could be attributed to the different representation of the bottom topography and coastline, the two results agree quite well. Thus the fidelity of the cubic grid OGCM has been shown to be equally good as the latitude–longitude OGCM. Next, we investigated the resolution dependence of the maximum allowable time step in linear and realistic situations. In the linear situations, the maximum allowable time step agrees with the analytical values. In the realistic situations, though the baroclinic time step is shorter than that derived from analytical estimation, it is still long enough to retain the advantage compared with latitude–longitude models. By measurements of computational costs, we confirmed that the cubic grid model is roughly five times faster than a corresponding latitude–longitude model which has nearly the same resolution and covers a ±85° latitude range by the relocation of the North and South Poles on continents.