Foundations of Global Ocean Climate Modelling at all Scales

Abstract

We introduce a computational method that extends the range of current global ocean climate models to non-hydrostatic scales, and establishes a convection resolving ocean model. The main obstruction towards this goal at global scale -the calculation of the non-hydrostatic pressure- is resolved by computing the pressure locally in a manner that capitalizes on particular conditions of ocean dynamics, and the structure of ocean models. Our claims are substantiated 1) by a theoretical analysis, which shows that the proposed method is compatible with ocean physics, 2) by numerical experiments, which evidence by comparison that it represents faithfully and to high accuracy non-hydrostatic dynamics, and 3) by a performance analysis that establishes that our non-hydrostatic method exceeds the cost of a hydrostatic model by a fixed factor of about $1.2$ in operation count and $1.3$ in runtime at any resolution. We show how to use the additional information contained in non-hydrostatic scales can be used to calculate the diffusivity free from numerical contributions and the mixing efficiency, transforming both from prescribed values by the modeller to calculated values from the dynamics.