Parameterizing Vertical Turbulent Mixing Coefficients for The Ocean Surface Boundary Layer Using Machine Learning

The ocean surface boundary layer plays a crucial role in the ocean by modulating exchange of mass and energy between the atmosphere and ocean interior via turbulent vertical mixing. The processes that drive this mixing are not resolved in ocean climate models and hence need to be parameterized. Vertical mixing parameterizations in ocean models are formulated based on the physical principles that govern turbulent mixing. However, numerous parameterizations include ad hoc components that are not well constrained by theory or data. Here, we improve a parameterization of vertical mixing in the ocean surface boundary layer by enhancing its eddy diffusivity model using data-driven methods, specifically neural networks. The neural networks take extrinsic and intrinsic forcing parameters as input to predict the eddy diffusivity profile. They are trained on output from a second moment closure turbulent mixing scheme. The modified vertical mixing scheme predicts the eddy diffusivity profile through online inference of neural networks and maintains the conservation principles of the standard ocean model equations, which is pertinent for its targeted use in climate simulations. We describe the development and stable implementation of neural networks in an ocean general circulation model and show that the enhanced scheme outperforms its predecessor by reducing biases in the mixed-layer depth and tropical upper ocean stratification. In addition, we use equation discovery technique to parameterize the mixing coefficients and compare it with the neural network approach in terms of interpretability and performance. We show that data-driven and physics-aware parameterizations can improve global climate models.