  The parameterizations of submesoscale ($<10$km) ocean surface flows are
critical in capturing the subgrid effects of vertical fluxes in the ocean mixed
layer, yet they struggle to infer the full-complexity of these fluxes in
relation to the large scale variables that help set them. In this work, we
present a data-driven approach for the submesoscale parameterization, utilizing
information from the high-resolution submesoscale-permitting MITgcm-LLC4320
simulation (LLC4320). The new parameterization is given by a Convolutional
Neural Network (CNN) trained to infer the subgrid mixed layer vertical buoyancy
fluxes as a function of relevant large scale variables. In contrast to previous
physics-based approaches, such as the Mixed Layer Eddy (MLE) parameterization,
here the CNN infers vertical fluxes that are directly computed from the LLC4320
data, where the submesoscales are resolved down to a resolution of
approximately 2km. The CNN has significantly high skill compared with the MLE
parameterization, which we demonstrate over a wide range of dynamical regimes
and resolutions. We find that the improved skill can be attributed to learned
physical relationships between submesoscale fluxes and the large scale strain
field, currently missing from submesoscale parameterizations in General
Circulation Models.
