Using Machine Learning to Investigate the Continuity of the Rhythm of Solar Activity as Reflected in Hemispheric Total Sunspot Area Data

Using Machine Learning to Investigate the Continuity of the Rhythm of Solar Activity as Reflected in Hemispheric Total Sunspot Area Data | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Using Machine Learning to Investigate the Continuity of the Rhythm of Solar Activity as Reflected in Hemispheric Total Sunspot Area Data Julio Valdes, Antonio Pou, Kenneth Tapping This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-9060761/v1 This work is licensed under a CC BY 4.0 License Status: Under Revision Version 1 posted 7 You are reading this latest preprint version Abstract The purpose of this paper is to characterize solar cycle hemisphericalbehaviour of cycles 12 to 24 using Sunspot Area indices, via a data-drivenapproach with a combination of unsupervised and supervised machine learningmethods, and statistical techniques. Time-dependent models, autoregressivemodels, nonlinear time series analysis methods, Gamma test, and different statisticaltests were used, aiming to extract information associated with behavioralpatterns and to expose interdependencies present within the data. Some findingswere that the behavior of Sunspot Area in the Northern and Southern hemispheressignificantly diverges, that in most cases, activity cycles are asymmetricin time, and that there are important changes in the rhythm of solar activity, particularlyin the last cycles. The results obtained may be useful for solar modelersand hopefully contribute to the understanding of the complex but synchronizednature of the solar hemispherical machinery. It would be very interesting to investigate theoretical models of Solar activity capable of generating simulateddata that exhibits patterns like the ones observed in the real data. Solar cycles Sunspot Area indices Northern and Southern hemispheres Rhythms of solar activity Unsupervised and supervised machine learning Time-dependent models Autoregressive models Gamma test Explainable AI Nonlinear methods Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Under Revision Version 1 posted Editorial decision: Revision requested 20 Apr, 2026 Reviews received at journal 16 Apr, 2026 Reviewers agreed at journal 26 Mar, 2026 Reviewers invited by journal 13 Mar, 2026 Editor assigned by journal 10 Mar, 2026 Submission checks completed at journal 10 Mar, 2026 First submitted to journal 07 Mar, 2026 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-9060761","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":605668539,"identity":"153a2a9c-5393-444a-a2e1-a7f76f9cb632","order_by":0,"name":"Julio Valdes","email":"","orcid":"","institution":"National Research Council","correspondingAuthor":false,"prefix":"","firstName":"Julio","middleName":"","lastName":"Valdes","suffix":""},{"id":605668540,"identity":"b5df873e-b9e2-41d8-be91-01b764df1dd6","order_by":1,"name":"Antonio Pou","email":"","orcid":"","institution":"University of Madrid","correspondingAuthor":false,"prefix":"","firstName":"Antonio","middleName":"","lastName":"Pou","suffix":""},{"id":605668541,"identity":"cd305793-5f1f-4410-b639-2f6697a155be","order_by":2,"name":"Kenneth Tapping","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA/0lEQVRIiWNgGAWjYBACCSjNw8DAfPjBByCLjZ2wFsYGiBa2NMMZIC3MRGoB6VKQ5gHRhLRItvcef/Bzxx0Zc/41DMY2v7bJ8zEzMH74mINbizTPucTG3jPPeCxnvD3wOLfvtmEbMwOz5MxtuLXISeQYNvC2HeYxuHEuwTi35zYjUAsbMy8+LfJvDBv/grWcMZC27LltT1CLtASPYTPYlvM9BtIMP24nEtQi2ZNjOFsW6BeDG8BA7m24ndzGzNiM1y8Sx88YfHy74469wfnDhx/8+HPbdn5788EPH/FoAQPGhgNAzQlARhuES0A9TAs/EDP8Iax4FIyCUTAKRh4AAMONVoh8kX3DAAAAAElFTkSuQmCC","orcid":"","institution":"National Research Council","correspondingAuthor":true,"prefix":"","firstName":"Kenneth","middleName":"","lastName":"Tapping","suffix":""}],"badges":[],"createdAt":"2026-03-07 20:53:13","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-9060761/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-9060761/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":104783413,"identity":"ce289ea4-b1af-4361-8e5a-db0ae4a0f663","added_by":"auto","created_at":"2026-03-17 07:58:53","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1846894,"visible":true,"origin":"","legend":"","description":"","filename":"SolarPhysicsValdesPouTappingV220251226Version2702.pdf","url":"https://assets-eu.researchsquare.com/files/rs-9060761/v1_covered_6ca43efc-affc-42c2-be22-58c178ed9a95.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"\u003cp\u003eUsing Machine Learning to Investigate the Continuity of the Rhythm of Solar Activity as Reflected in Hemispheric Total Sunspot Area Data\u003c/p\u003e","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"solar-physics","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"sola","sideBox":"Learn more about [Solar Physics](http://link.springer.com/journal/11207)","snPcode":"11207","submissionUrl":"https://submission.nature.com/new-submission/11207/3","title":"Solar Physics","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"Solar cycles, Sunspot Area indices, Northern and Southern hemispheres, Rhythms of solar activity, Unsupervised and supervised machine learning, Time-dependent models, Autoregressive models, Gamma test, Explainable AI, Nonlinear methods","lastPublishedDoi":"10.21203/rs.3.rs-9060761/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-9060761/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThe purpose of this paper is to characterize solar cycle hemisphericalbehaviour of cycles 12 to 24 using Sunspot Area indices, via a data-drivenapproach with a combination of unsupervised and supervised machine learningmethods, and statistical techniques. 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