Global Estimation of Subsurface Eddy Kinetic Energy of Mesoscale Eddies Using Machine Learning

• Published in: Journal of geophysical research. Machine learning and computation Vol. 2; no. 3
• Main Authors: Xie, Chenyue, Gao, An‐Kang, Lu, Xiyun
• Format: Journal Article
• Language: English
• Published: 01.09.2025
• DOI: 10.1029/2024JH000578
• ISSN: 2993-5210

Oceanic eddy kinetic energy (EKE) is a key quantity for measuring the intensity of mesoscale eddies and developing mesoscale eddy parameterizations in ocean circulation models. Three decades of satellite observations enable a global assessment of sea surface EKE. However, due to the sparseness of in situ observational data, subsurface EKE with a spatial filter has not been systematically studied. Subsurface EKE can be inferred theoretically and numerically from sea surface observations, but is limited by the problem of decreasing correlation with sea surface variables as depth increases. In this study, we propose a dual‐branch neural network approach to reconstruct the monthly mean subsurface EKE using sea surface variables and subsurface climatological variables (e.g., horizontal filtered velocity gradients), inspired by the Taylor‐series expansion of subsurface EKE. Four neural network models are trained on a high‐resolution global ocean reanalysis data set: surface input fully connected neural network model (FCNN), surface input residual neural network model (ResNet), dual‐branch fully connected neural network model (DB‐FCNN), and dual‐branch residual neural network model (DB‐ResNet). The proposed DB‐FCNN and DB‐ResNet models integrate the surface input variables and the vertical profiles of subsurface variables. The DB‐ResNet model outperforms the FCNN, ResNet, DB‐FCNN, and traditional physics‐based models in both regional and global reconstruction of subsurface EKE in the upper 2,000 m. In addition, the DB‐ResNet model performs well for both regional and global observational data based on transfer learning. These results reveal the potential of the DB‐ResNet model for efficient and accurate reconstruction of subsurface oceanic variables. Mesoscale eddies, which are loosely defined as swirling water masses of tens to hundreds of kilometers in horizontal width, are crucial in shaping ocean circulation and influencing global climate dynamics. Eddy kinetic energy (EKE) is a key indicator of mesoscale eddy intensity and is essential for global ocean modeling and applications in oceanography and climate studies. Although surface EKE can be derived from satellite altimetry data measuring the sea surface height, subsurface EKE is challenging to measure because there are not enough in situ observations. This study explores machine learning methods to predict subsurface EKE using sea surface variables and sparse vertical profiles of variables from reanalysis and observational data sets. We develop a dual‐branch residual neural network model that can effectively reconstruct the global subsurface EKE. This work not only enhances the prediction of subsurface processes but also supports broader applications in climate modeling. Dual‐branch neural network models are proposed to estimate the subsurface eddy kinetic energy (EKE) by integrating surface data and sparse subsurface variables The proposed DB‐ResNet model outperforms models that rely only on surface data in reconstructing the vertical structure of EKE The locally trained DB‐ResNet model can be applied to global ocean and further adapted to observational data through transfer learning