Statistical parameterization of surface lateral diffusivity from satellite data

Mesoscale eddies dominate the oceanic variability, mixing heat, salt, carbon, and other tracers laterally. At present, most coarse resolution ocean models represent this mixing through diffusive parameterizations, in which the tracer fluxes due to the subgridscale motions are taken to be proportional to the large scale tracer gradients through a diffusion tensor. Here we use a recently developed python package MicroInverse to estimate the diffusion tensor from satellite observed sea surface temperature and sea surface height anomalies. MicroInverse deduces diffusivity from the time dependent spatial covariance field of a given tracer. Our results suggest that diffusivity is strongest in regions of high eddy kinetic energy, but suppressed by strong mean currents as previously suggested. While such a diffusivity estimate alone is difficult to use directly in an ocean model, it can be used to build a statistical model for the diffusivity. To this end we train a neural network, using the diffusivity estimates from MicroInverse, and several other variables that can be easily evaluated online within an ocean model simulation, such as mean fields of surface velocity, sea surface height, and temperature, their lateral gradients, and Rossby wave speed. The trained neural network has considerable skill globally as long as the training set includes different dynamical regions. While some challenges remain, the trained neural network could be used as a parameterization in an ocean model with a very low computational cost.