Parameterizing Vertical Mixing Coefficients in the Ocean Surface Boundary Layer Using Neural Networks.

Vertical mixing parameterizations in ocean models are formulated on the basis of the physical principles that govern turbulent mixing. However, many parameterizations include ad hoc components that are not well constrained by theory or data. One such component is the eddy diffusivity model, where vertical turbulent fluxes of a quantity are parameterized from a variable eddy diffusion coefficient and the mean vertical gradient of the quantity. In this work, 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 are designed to take extrinsic and intrinsic forcing parameters as input to predict the eddy diffusivity profile and are trained using output data 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 particularly important for its targeted use in climate simulations. We describe the development and stable implementation of neural networks in an ocean general circulation model and demonstrate that the enhanced scheme outperforms its predecessor by reducing biases in the mixed‐layer depth and upper ocean stratification. Our results demonstrate the potential for data‐driven physics‐aware parameterizations to improve global climate models. Plain Language Summary: The upper region of the ocean is highly energetic and is responsible for transferring mass, energy and biogeochemical tracers between the atmosphere and the deeper regions of the ocean. This transport takes place because of turbulent swirling motions, which are found to be of varying sizes. Climate models cannot represent all of these motions because smaller‐scale swirls are complex and require additional computational resources. As we cannot neglect those small swirls, we try to approximate their effects on larger‐scale motions using mathematical models. These models have a few ad hoc or empirical assumptions that lead to uncertainty when these climate models are used to project the future climate. To reduce this uncertainty, we augment an existing model of turbulent swirling process with machine learning, which replaces some ad hoc approximations with data‐driven neural networks. Neural networks can learn those missing processes more accurately than a traditional physics‐based model. The neural networks are shown to improve physics in climate simulations. Although we only touch on one component in an ocean climate model, this approach can be replicated to improve any other component that was using ad hoc assumptions and replace them with data‐driven models using techniques from machine learning. Key Points: We improve a parameterization of vertical mixing in the ocean surface boundary layer using neural networksNeural networks are trained to predict the diffusivity of second moment closure and maintain energetic constraints of the original parameterizationThe improved scheme reduces biases of mixed layer depth and thermocline in an atmospherically forced ocean model [ABSTRACT FROM AUTHOR]