Global Estimation of Subsurface Eddy Kinetic Energy of Mesoscale Eddies Using a Multiple-input Residual Neural Network

TL;DR

The paper tackles the challenge of estimating subsurface eddy kinetic energy (EKE) globally by leveraging a multiple-input residual neural network (MI-ResNet) that fuses surface observations with sparse subsurface profiles, guided by a Taylor-series expansion of EKE. It compares surface-only and multi-input architectures, showing MI-ResNet most accurately reconstructs the vertical EKE profile up to 2000 m and generalizes well to observational data through transfer learning. Across regions with intense eddy activity and in weak-EKE areas, MI-ResNet consistently achieves high correlation with eddy-resolving reanalysis, outperforming traditional physics-based models and surface-only approaches. The work demonstrates a practical path to reconstruct subsurface oceanic variability from widely available surface data, with implications for improving climate models and ocean transport parameterizations.

Abstract

Oceanic eddy kinetic energy (EKE) is a key quantity for measuring the intensity of mesoscale eddies and for parameterizing eddy effects in ocean climate models. Three decades of satellite altimetry observations allow a global assessment of sea surface information. However, the subsurface EKE with spatial filter has not been systematically studied due to the sparseness of subsurface observational data. The subsurface EKE can be inferred both theoretically and numerically from sea surface observations but is limited by the issue of decreasing correlation with sea surface variables as depth increases. In this work, inspired by the Taylor-series expansion of subsurface EKE, a multiple-input neural network approach is proposed to reconstruct the subsurface monthly mean EKE from sea surface variables and subsurface climatological variables (e.g., horizontal filtered velocity gradients). Four neural networks are trained on a high-resolution global ocean reanalysis dataset, namely, surface-input fully connected neural network model (FCNN), surface-input Residual neural network model (ResNet), multiple-input fully connected neural network model (MI-FCNN), and multiple-input residual neural network model (MI-ResNet). The proposed MI-FCNN and MI-ResNet models integrate the surface input variables and the vertical profiles of subsurface variables. The MI-ResNet model outperforms the FCNN, ResNet, and MI-FCNN models, and traditional physics-based models in both regional and global reconstruction of subsurface EKE in the upper 2000 m. In addition, the MI-ResNet model performs well for both regional and global observational data based on transfer learning. These findings reveal the potential of the MI-ResNet model for efficient and accurate reconstruction of subsurface oceanic variables.

Figures (12)

• Figure 1: The multiple-year averaged surface EKE and meridional velocity ($u$) as functions of longitude and latitude using the eddy-resolving GLORYS reanalysis and altimetric data for the period 2001-2020: (a) $\mathrm{EKE}_\mathrm{Truth}^{s}$, (b) $\mathrm{EKE}_\mathrm{Obs.}^{s}$, (c) $\mathrm{u}_\mathrm{Truth}^{s}$, (d) $\mathrm{u}_\mathrm{Obs.}^{s}$. The latitude region between $10^\circ\mathrm{S}$ and $10^\circ\mathrm{N}$ is shaded in grey. Gray dashed lines in (a) and (b) denote the isopleths of EKE with $0.01~\mathrm{m}^2/\mathrm{s}^2$. The five representative regions are chosen for training the neural network models.
• Figure 2: Schematic diagram of the MI-ResNet structure used in this study for estimating subsurface EKE. The first branch of inputs (Input 1) denotes sea surface variables, the second branch of inputs (Input 2) denotes the vertical profiles of variables, and the output of the network is the profile of EKE.
• Figure 3: Performance of the MI-ResNet model in predicting EKE. (a) the loss function of the neural network uses the training data from 2001 to 2016, with the first 4/5 of the data for training and the last 1/5 as validation data, (b) the ensemble-averaged time series of $\mathrm{R}^2$ for the training regions, (c) the ensemble-averaged time series of $\mathrm{R}^2$ for the global ocean. The dashed black line in panel (b) divides data into training and test datasets
• Figure 4: The temporally averaged coefficients of efficiency $R^2$ of $\mathrm{EKE}$ produced by different models (BC1, SM1, FCNN, ResNet, MI-FCNN, and MI-ResNet) for the test dataset (2017-2020): (a) GSR, (b) KR, (c) AR, (d) BMCR.
• Figure 5: The temporally averaged relative error $E_{r}$ of $\mathrm{EKE}$ produced by different models (BC1, SM1, FCNN, ResNet, MI-FCNN, and MI-ResNet) for the test dataset (2017-2020): (a) GSR, (b) KR, (c) AR, (d) BMCR.