EGU24-2297, updated on 08 Mar 2024
EGU General Assembly 2024
© Author(s) 2024. This work is distributed under
the Creative Commons Attribution 4.0 License.

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

Rin Irie1, Helen Stewart1, Tsuneko Kura1, Masaki Hisada1, and Takaharu Yaguchi2
Rin Irie et al.
  • 1NTT Space Environment and Energy Laboratories, Tokyo, Japan (
  • 2Graduate School of Science, Kobe University, Kobe, Japan (

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 RL = (vL, θL, SL)T, where vL is the flow velocity field, θL is the potential temperature, and SL 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 = (κh, Ah)T, where κh and Ah 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 RLRH. 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.

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).

[1] D. Couespel et. al (2021), Oceanic primary production decline halved in eddy-resolving simulations of global warming, Biogeosciences, 18(14), 4321-4349.
[2] M. Solano, and Y. Fan (2022), A new K-profile parameterization for the ocean surface boundary layer under realistic forcing conditions, Ocean Modelling, 171, 101958.
[3] W. G. Large et. al (1994), Oceanic vertical mixing: A review and a model with a nonlocal boundary layer parameterization, Reviews of geophysics, 32(4), 363–403.
[4] Y. Han et. al (2020), A moist physics parameterization based on deep learning, Journal of Advances in Modeling Earth Systems, 12(9), e2020MS002076.
[5] Y. Zhu et. al (2022), Physics-informed deep-learning parameterization of ocean vertical mixing improves climate simulations, National Science Review, 9(8), nwac044. 

How to cite: Irie, R., Stewart, H., Kura, T., Hisada, M., and Yaguchi, T.: Parameterizing ocean vertical mixing using deep learning trained from high-resolution simulations, EGU General Assembly 2024, Vienna, Austria, 14–19 Apr 2024, EGU24-2297,, 2024.