Parameterizing ocean vertical mixing using deep learning trained from high-resolution simulations

Ocean vertical mixing plays a fundamental role in phenomena such as upwelling of nutrient-rich deep waters, and is crucial for determining net primary productivity in the ocean [1]. Simulating vertical mixing requires careful consideration and ingenuity for stable execution, as vertical mixing is often turbulent. Direct Numerical Simulations, in which the Navier-Stokes equations are solved without a turbulence model, are not realistic due to the enormous computational complexity. Ocean General Circulation Models (OGCMs) have low resolution and cannot directly resolve small-scale turbulence such as vertical mixing. Consequently, OGCMs based on the Reynolds Averaged Navier-Stokes equations use turbulence parameterizations to model the effect of unresolved motions on the mean flow [2]. Although K-Profile Parameterization (KPP) is widely recognized as a method for parameterizing vertical mixing [3], recent advancements in machine learning have triggered active exploration of data-driven approaches to parameterization [4, 5]. This study aims to develop a novel vertical mixing parameterization method using deep learning. High-resolution simulation results (O(10³) m) are used as training data for a neural network to estimate vertical diffusion and viscosity. These estimates are then used to parameterize fine-scale dynamics in a low-resolution simulation (O(10⁴) m).

The input parameters of the neural network are the state variables R_L = (v_L, θ_L, S_L)^T, where v_L is the flow velocity field, θ_L is the potential temperature, and S_L is the salinity. Here, the L and H subscripts will be used to indicate the low and high-resolution simulations. The output parameters are P = (κ_h, A_h)^T, where κ_h and A_h are the estimated vertical diffusion and viscosities respectively. The loss function is defined as the mean squared error between the state variables of the high and low-resolution simulations R_L−R_H. Verification experiments for the proposed parameterization method are conducted for an idealized double-gyre configuration, which models western boundary currents such as the Gulf Stream in the North Atlantic Ocean. We confirm the performance and efficiency of the proposed method compared to traditional KPP for conducting high-resolution simulations at low computational cost.

Acknowledgements
This work used computational resources of supercomputer Fugaku provided by the RIKEN Center for Computational Science through the HPCI System Research Project (Project ID: hp230382).

References
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