Super-parameterisation of ocean deep convection

Technical report on the use of emulators in the parameterisation of ocean convectionSub-grid scale processes play an important role in ocean and climate modelling. Typical examples include clouds in atmospheric models, flows over restricted topographies or the resolution of con- vective plumes in ocean models. Detailed numerical models of these sub-grid scale processes exist, but embedding them in a Global Circulation Model (GCM) for example, would be computationally prohibitive. In the present work we investigate the applicability of emulators for representing the sub-grid scale processes within a GCM simulation. Emulators can be thought as encapsulating our beliefs about the sub-grid dynamical model, derived from a designed computer experiment using a Bayesian framework. In particular, we propose to employ an emulator for parameterising the sub-grid scale process, and embed this within a GCM as a surrogate for the actual sub-grid scale model. The result of combining the GCM with the emulator will be a Super-parameterised model, which will also be computationally efficient, since the emulator incurs a very small computational overhead. The example we chose to illustrate the proposed methodology is deep ocean convection. The sub-grid scale dynamical model simulates deep convective plumes, while the large scale dy- namics simulate the geostrophic eddy scale. We present details on building the emulator of the convective plumes and its coupling with the large scale process model. We also discuss whether the emulator should be run as a deterministic or stochastic parameterisation