[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-126085-en":3,"doc-seo-126085-105":31,"detail-sidebar-cat-0-en-105":93},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":20,"is_deleted":4,"is_public":21,"is_downloadable":21,"audit_status":21,"page_count":22,"language":23,"language_code":24,"site_id":25,"html_lang":24,"table_of_contents":26,"faqs":27,"seo_title":28,"seo_description":14,"update_tm":29,"read_time":30},126085,962084931830,"Theodore","https://ap-avatar.wpscdn.com/davatar_a8503ba1806abce46bf441b54a3ca4cd",8,"Research & Report","Global surface eddy mixing ellipses - spatio-temporal variability and machine learning prediction - Original Research","Mesoscale eddies strongly shape ocean circulation and the climate system through mixing and stirring of key tracers. This study uses satellite altimetry data and a Lagrangian single-particle approach to estimate global surface eddy mixing ellipses and reveal pronounced spatio-temporal variability in magnitude, anisotropy, and dominant direction. Predictability is evaluated with Spatial Transformer Networks, CNN, and Random Forest using mean-flow and eddy properties, showing STN’s superior performance for anisotropy. Feature importance highlights eddy velocity magnitude and size as critical predictors, and training with a 2-year temporal window improves correlations in the northern equatorial central Pacific.","TYPE Original Research PUBLISHED 07 January 2025  \nDOI 10.3389/fmars.2024.1506419  \nOPEN ACCESS  \nEDITED BY  \nXi Zhang,  \nMinistry of Natural Resources, China  \nREVIEWED BY  \nGui Gao,  \nSouthwest Jiaotong University, China Genwang Liu,  \nMinistry of Natural Resources, China  \n*CORRESPONDENCE  \nRu Chen  \n [ruchen@tju.edu.cn](ruchen@tju.edu.cn)[ ](ruchen@tju.edu.cn)Cuicui Zhang  \n [cuicui.zhang@tju.edu.cn](cuicui.zhang@tju.edu.cn)[ ](cuicui.zhang@tju.edu.cn)Mei Hong  \n fl[owerrainhongmei@126.com](owerrainhongmei@126.com)  \nRECEIVED 05 October 2024  \nACCEPTED 06 December 2024  \nPUBLISHED 07 January 2025  \nCITATION  \nJing T, Chen R, Liu C, Qiu C, Zhang C and Hong M (2025) Global surface eddy mixing ellipses: spatio-temporal variability and machine learning prediction.  \nFront. Mar. Sci. 11:1506419 .  \ndoi: 10.3389/fmars.2024.1506419  \nCOPYRIGHT  \n© 2025 Jing, Chen, Liu, Qiu, Zhang and Hong. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY) . The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.  \nGlobal surface eddy mixing ellipses: spatio-temporal variability and machine learning prediction  \nTian Jing 1, Ru Chen 1*, Chuanyu Liu 2, Chunhua Qiu 3,4, Cuicui Zhang 1* and Mei Hong 5*  \n1Tianjin 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, 3School of Marine Sciences, Sun Yat-sen University, and Southern Marine Science and Engineering Guangdong Laboratory (Zhuhai), Zhuhai, China, 4Guangdong Provincial Key Laboratory of Marine Resources and Coastal Engineering School of Marine Sciences, Sun Yat-sen University, Guangzhou, China, 5College of Meteorology and Oceanography, National University of Defense Technology, Changsha, China  \nMesoscale 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-flowand 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  \nFrontiers in Marine Science 01 [frontiersin.org](frontiersin.org)  \nand anisotropy, along with a reduction of more than 0.15 in the Normali","cbCaitfL2o3MBFCM","https://ap.wps.com/l/cbCaitfL2o3MBFCM","pdf",25086501,7,1,17,"English","en",105,"# Introduction\n## Motivation for eddy mixing parameterization\n## Limits of coarse-resolution climate models\n## Need for tensor-based, anisotropic representation\n# Materials and Methods\n## Satellite altimetry and Lagrangian single-particle estimation\n## Deriving mixing ellipses from eddy diffusivity tensor\n## Machine learning models and input features\n# Results\n## Global patterns and spatio-temporal variability\n## Model performance in predicting mixing anisotropy\n## Feature importance for ellipse major axis and anisotropy\n# Discussion\n## Implications for climate model parameterization\n## Temporal-window effects related to ENSO\n# Conclusion","[{\"question\":\"What are eddy mixing ellipses and how are they used in this study?\",\"answer\":\"Eddy mixing ellipses are derived from the eddy diffusivity tensor and summarize mixing geometry, including magnitude, anisotropy, and dominant direction. They are estimated across the global surface ocean using satellite altimetry and a Lagrangian single-particle method.\"},{\"question\":\"Which machine learning models are compared for predicting mixing ellipses?\",\"answer\":\"The study evaluates Spatial Transformer Networks (STN), Convolutional Neural Networks (CNN), and Random Forest (RF). All three capture spatio-temporal variation, but STN performs best for predicting mixing anisotropy.\"},{\"question\":\"What factors most influence prediction of the ellipse major axis and anisotropy?\",\"answer\":\"Feature importance rankings indicate that eddy velocity magnitude and eddy size are the most significant factors for predicting the major axis and anisotropy.\"}]","Global surface eddy mixing ellipses - spatio-temporal variability and machine learning prediction - Original Research | PDF",1785903011,43,{"code":4,"msg":32,"data":33},"ok",{"site_id":25,"language":24,"slug":34,"title":13,"keywords":35,"description":14,"schema_data":36,"social_meta":88,"head_meta":90,"extra_data":92,"updated_unix":29},"global-surface-eddy-mixing-ellipses-spatio-temporal-variability-and-machine-learning-prediction-original-research","",{"@graph":37,"@context":87},[38,55,70],{"@type":39,"itemListElement":40},"BreadcrumbList",[41,45,49,52],{"item":42,"name":43,"@type":44,"position":21},"https://docshare.wps.com","Home","ListItem",{"item":46,"name":47,"@type":44,"position":48},"https://docshare.wps.com/document/","Document",2,{"item":50,"name":12,"@type":44,"position":51},"https://docshare.wps.com/document/research-report/",3,{"item":53,"name":13,"@type":44,"position":54},"https://docshare.wps.com/document/global-surface-eddy-mixing-ellipses-spatio-temporal-variability-and-machine-learning-prediction-original-research/126085/",4,{"url":53,"name":13,"@type":56,"author":57,"headline":13,"publisher":59,"fileFormat":62,"inLanguage":24,"description":14,"dateModified":63,"datePublished":64,"encodingFormat":62,"isAccessibleForFree":65,"interactionStatistic":66},"DigitalDocument",{"name":9,"@type":58},"Person",{"url":42,"name":60,"@type":61},"DocShare","Organization","application/pdf","2026-08-24","2026-08-05",true,{"@type":67,"interactionType":68,"userInteractionCount":20},"InteractionCounter",{"@type":69},"ViewAction",{"@type":71,"mainEntity":72},"FAQPage",[73,79,83],{"name":74,"@type":75,"acceptedAnswer":76},"What are eddy mixing ellipses and how are they used in this study?","Question",{"text":77,"@type":78},"Eddy mixing ellipses are derived from the eddy diffusivity tensor and summarize mixing geometry, including magnitude, anisotropy, and dominant direction. They are estimated across the global surface ocean using satellite altimetry and a Lagrangian single-particle method.","Answer",{"name":80,"@type":75,"acceptedAnswer":81},"Which machine learning models are compared for predicting mixing ellipses?",{"text":82,"@type":78},"The study evaluates Spatial Transformer Networks (STN), Convolutional Neural Networks (CNN), and Random Forest (RF). All three capture spatio-temporal variation, but STN performs best for predicting mixing anisotropy.",{"name":84,"@type":75,"acceptedAnswer":85},"What factors most influence prediction of the ellipse major axis and anisotropy?",{"text":86,"@type":78},"Feature importance rankings indicate that eddy velocity magnitude and eddy size are the most significant factors for predicting the major axis and anisotropy.","https://schema.org",{"og:url":53,"og:type":89,"og:title":13,"og:site_name":60,"og:description":14},"article",{"robots":91,"canonical":53},"index,follow",{"doc_id":7,"site_id":25},{"code":4,"msg":5,"data":94},[95,99,103,107,112,117,121,124,129,132,136],{"id":21,"doc_module":4,"doc_module_name":47,"category_name":96,"show_sort_weight":97,"slug":98},"Story & Novel",90,"story-novel",{"id":48,"doc_module":4,"doc_module_name":47,"category_name":100,"show_sort_weight":101,"slug":102},"Literature",80,"literature",{"id":54,"doc_module":4,"doc_module_name":47,"category_name":104,"show_sort_weight":105,"slug":106},"Exam",70,"exam",{"id":108,"doc_module":4,"doc_module_name":47,"category_name":109,"show_sort_weight":110,"slug":111},5,"Comic",60,"comic",{"id":113,"doc_module":4,"doc_module_name":47,"category_name":114,"show_sort_weight":115,"slug":116},6,"Technology",50,"technology",{"id":20,"doc_module":4,"doc_module_name":47,"category_name":118,"show_sort_weight":119,"slug":120},"Healthcare",40,"healthcare",{"id":11,"doc_module":4,"doc_module_name":47,"category_name":12,"show_sort_weight":122,"slug":123},30,"research-report",{"id":125,"doc_module":4,"doc_module_name":47,"category_name":126,"show_sort_weight":127,"slug":128},9,"Religion & Spirituality",20,"religion-spirituality",{"id":127,"doc_module":4,"doc_module_name":47,"category_name":130,"show_sort_weight":127,"slug":131},"World Cup","world-cup",{"id":133,"doc_module":4,"doc_module_name":47,"category_name":134,"show_sort_weight":133,"slug":135},10,"Lifestyle","lifestyle",{"id":137,"doc_module":4,"doc_module_name":47,"category_name":138,"show_sort_weight":108,"slug":139},19,"General","general"]