Tian Jing ¹ Ru Chen ^1* Chuanyu Liu ² Chunhua Qiu ^3,4 Cuicui Zhang ^1* Mei Hong ^5*

• ¹ Tianjin Key Laboratory for Marine Environmental Research and Service, School of Marine Science and Technology, Tianjin University, Tianjin, China
• ² Key Laboratory of Ocean Observation and Forecasting, and Key Laboratory of Ocean Circulation and Waves, Institute of Oceanology, Chinese Academy of Sciences, Qingdao, China
• ³ School of Marine Sciences, Sun Yat-Sen University, and Southern Marine Science and Engineering Guangdong Laboratory (Zhuhai), Zhuhai, China
• ⁴ Guangdong Provincial Key Laboratory of Marine Resources and Coastal Engineering School of Marine Sciences, Sun Yat-sen University, Guangzhou, China
• ⁵ College of Meteorology and Oceanography, National University of Defense Technology, Changsha, China

Mesoscale eddy mixing significantly influences ocean circulation and climate system. Coarse-resolution climate models are sensitive to the specification of eddy diffusivity tensor. Mixing ellipses, derived from eddy diffusivity tensor, illustrate mixing geometry, i.e., the magnitude, anisotropy, and dominant direction of eddy mixing. Using satellite altimetry data and the Lagrangian single-particle method, we estimate eddy mixing ellipses across the global surface ocean, revealing substantial spatio-temporal variability. Notably, large mixing ellipses predominantly occur in eddy-rich and energetic ocean regions. We also assessed the predictability of global mixing ellipses using machine learning algorithms, including Spatial Transformer Networks (STN), Convolutional Neural Network (CNN) and Random Forest (RF), with mean-flow and eddy- properties as features. All three models effectively represent and predict spatiotemporal variations, with the STN model, which incorporates an adaptive spatial attention mechanism, outperforming RF and CNN models in predicting mixing anisotropy. Feature importance rankings indicate that eddy velocity magnitude and eddy size are the most significant factors in predicting the major axis and anisotropy. Furthermore, training the models with a 2-year temporal duration, aligned with the El Niño Southern Oscillation (ENSO) timescale, improved predictions in the northern equatorial central Pacific region compared to models trained with a 12-year duration. This resulted in a spatially averaged correlation increase of over 0.5 for predicting the minor axis and anisotropy, along with a reduction of more than 0.15 in the Normalized Root Mean Square Error. These findings highlight the considerable potential of machine learning algorithms in predicting mixing ellipses and parameterizing eddy mixing processes within climate models.