  Submesoscale processes, with spatio-temporal scales of O(0.01-10) km and
hours to 1 day which are hardly resolved by current ocean models, are important
sub-grid processes in ocean models. Due to the strong vertical currents,
submesoscale processes can lead to submesoscale vertical heat flux (SVHF) in
the upper ocean which plays a crucial role in the heat exchange between the
atmosphere and the ocean interior, and further modulates the global heat
redistribution. At present, simulating a submesoscale-resolving ocean model is
still expensive and time-consuming. Parameterizing SVHF becomes a feasible
alternative by introducing it into coarse-resolution models. Traditionally,
researchers tend to parameterize SVHF by a mathematically fitted relationship
based on one or two key background state variables, which fail to represent the
relationship between SVHF and the background state variables comprehensively.
In this study, we propose a data-driven SVHF parameterization scheme based on a
deep neural network and implement it into the Regional Ocean Modeling System
(ROMS). In offline tests, our scheme can accurately calculate SVHF using
mesoscale-averaged variables and characterize how it varies with depth. In
online tests, we simulate an idealized model of an anticyclonic mesoscale eddy
and a realistic model of the Gulf Stream, respectively. Compared to the
coarse-resolution cases without the SVHF effect, the coarse-resolution cases
with the SVHF scheme tend to reproduce results closer to the high-resolution
case and the observational state in terms of the temperature structure and
mixed layer depth, indicating a good performance of the neural network-based
SVHF scheme. Our results show the potential of applying the neural network in
parameterizing sub-grid processes in ocean models.
