Grid geometry effects on convection in ocean climate models: a conceptual study

Ocean convection is a highly non-linear and local process. Typically, a small-scale phenomenon of this kind entails numerical problems in the modelling of ocean circulation. One of the tasks to solve is the improvement of convection parameterization schemes, but the question of grid geometry also plays a considerable role. Here, this question is studied in the context of global ocean models coupled to an atmosphere model. Such ocean climate models have mostly structured, coarsely resolved grids. a simple conceptual two-layer model, we compare the discretization effects of a rectangular grid with those of a grid with hexagonal grid cells, focussing on average properties of the ocean. It turns out that systematic errors tend to be clearly smaller with the hexagonal grid. In a hysteresis experiment with the atmospheric boundary condition as a hysteresis parameter, the spatially averaged behaviour shows non-negligible artificial steps for quadratic grid cells. This bias is reduced with the hexagonal grid. The same holds for the directional sensitivity (or horizontal anisotropy) which is found for different angles of the advection velocity. The grid with hexagonal grid cells shows much more isotropic results. From the limited viewpoint of these test experiments, it seems that the hexagonal grid (i.e. icosahedral–hexagonal grids on the sphere) is recommendable for ocean climate models.