Vertical resolution of baroclinic modes in global ocean models

Improvements in the horizontal resolution of global ocean models, motivated by the horizontal resolution requirements for specific flow features, has advanced modelling capabilities into the dynamical regime dominated by mesoscale variability. In contrast, the choice of the vertical grid remains a subjective choice, and it is not clear that efforts to improve vertical resolution adequately support their horizontal counterparts. Indeed, considering that the bulk of the vertical ocean dynamics (including convection) are parameterized, it is not immediately obvious what the vertical grid is supposed to resolve. Here, we propose that the primary purpose of the vertical grid in a hydrostatic ocean model is to resolve the vertical structure of horizontal flows, rather than to resolve vertical motion. With this principle we construct vertical grids based on their abilities to represent baroclinic modal structures commensurate with the theoretical capabilities of a given horizontal grid. This approach is designed to ensure that the vertical grids of global ocean models complement (and, importantly, to not undermine) the resolution capabilities of the horizontal grid. We find that for z-coordinate global ocean models, at least 50 well-positioned vertical levels are required to resolve the first baroclinic mode, with an additional 25 levels per subsequent mode. High-resolution ocean-sea ice simulations are used to illustrate some of the dynamical enhancements gained by improving the vertical resolution of a 1/10° global ocean model. These enhancements include substantial increases in the sea surface height variance (∼30% increase south of 40°S), the barotropic and baroclinic eddy kinetic energies (up to 200% increase on and surrounding the Antarctic continental shelf and slopes), and the overturning streamfunction in potential density space (near-tripling of the Antarctic Bottom Water cell at 65°S).