Disentangling Density and Geometry in Weather Regime Dimensions using Stochastic Twins

Disentangling Density and Geometry in Weather Regime Dimensions using Stochastic Twins | 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 Article Disentangling Density and Geometry in Weather Regime Dimensions using Stochastic Twins Paul Platzer, Bertrand Chapron, Gabriele Messori This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-5880040/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 28 May, 2025 Read the published version in npj Climate and Atmospheric Science → Version 1 posted 9 You are reading this latest preprint version Abstract Large-scale atmospheric variability can be summarised using a small number of recurring patterns called \say{weather regimes}. The properties of weather regimes have been widely investigated in the literature, including through the \say{local dimension}: an instantaneous geometrical estimate of the number of degrees of freedom, emanating from the multifractal formalism of dynamical systems. In atmospheric and ocean science, the local dimension has been interpreted as a measure of predictability. The different weather regimes display differing values of local dimension. It was also shown that the local dimension decreases when the atmosphere projects most strongly on a single weather regime, and increases during regime transitions. This was interpreted as confirming the physical grounding and dynamical footprint of weather regimes. However, the drivers of local dimension variations remain to be elucidated. In particular, recent work has shown that variations in local dimension originate not only from changes in multifractal geometric properties but also from changes in sampling density. In this work, we propose a methodology to isolate the density-based variations of local dimension for the large-scale atmospheric circulation in the North-Atlantic. We build \say{stochastic twins} of the atmosphere in the space of truncated empirical orthogonal functions, based on the Gaussian mixture model used to define weather regimes from ERA5-reanalysis 500 hPa geopotential height fields. These stochastic twins bear a similar sampling density as the atmosphere, but they are not multifractal and therefore they have a constant local geometry and a fixed number of degrees of freedom. Estimates of density-based variations of local dimension using stochastic twins allow to explain more than 50% of the total variations of local dimension, proving that a large fraction of local dimension variations is not related to changes in local geometry. The dimension estimated from stochastic twins also allows to reproduce the previously observed decrease of dimension near peak weather regime index, indicating that this universal behavior is a density-based phenomenon, and cannot be attributed to the multifractal nature of atmospheric circulation. However, the sampling density-based variations of the local dimension can still provide useful information on the properties of weather regimes. Additionally, we show that the full range of local dimension variations cannot be explained by density-based estimates alone, so that the remaining variability is likely due to changes in local geometry, and therefore in number of degrees of freedom. The methodology presented in this paper can be applied to any observed system whose sampling distribution can be approximated, and provides a new means to interpret local dimension estimates of real-world atmospheric or ocean data. Earth and environmental sciences/Climate sciences/Atmospheric science/Atmospheric dynamics Physical sciences/Mathematics and computing/Statistics weather regimes atmospheric circulation fractal dimension density geometry dynamical systems random stochastic transition geopotential height Full Text Additional Declarations No competing interests reported. Supplementary Files WRmultifractalorrandomnpjClimateandatmosphericscienceCopySupplInformation.pdf Cite Share Download PDF Status: Published Journal Publication published 28 May, 2025 Read the published version in npj Climate and Atmospheric Science → Version 1 posted Editorial decision: Revision requested 21 Mar, 2025 Reviews received at journal 20 Mar, 2025 Reviews received at journal 21 Feb, 2025 Reviewers agreed at journal 20 Feb, 2025 Reviewers agreed at journal 29 Jan, 2025 Reviewers invited by journal 28 Jan, 2025 Editor assigned by journal 24 Jan, 2025 Submission checks completed at journal 24 Jan, 2025 First submitted to journal 22 Jan, 2025 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. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. 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-5880040","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":414426071,"identity":"f98d3e43-6f56-4c97-a8d9-a7d5ba9ae25e","order_by":0,"name":"Paul Platzer","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA+0lEQVRIie3PsWrDMBCA4ROCdDFoC4JC8wpXNCQGB7+KjcCTIIG+QKZ2EXR18FNky2gweDJ0DRhCIdCpg4OXDBkiJx5Ki0zGDvoHIQ4+pANwuf5nJAeY3a4NPvXDYNgYwsHrcIqinyV3EurBHWT6UGFOtnwSsqJsgyUu2LgoG4j2VuJrZUjFnzWUMlOI/jpLZArRi5Vg3pFXTjTRgio8I9ZKADlFdvLxfSWhpqylM0QM60ULEA2Q3e2VWI88SsEQfFR0kPjp1zKPKy51NRJEG8HrRBhhJ1MmN5/HbTB/ey8OcDKrsEweoBn6WHfEq99jO+gJ+UNcLpfL9aMLyAFMlU+zug8AAAAASUVORK5CYII=","orcid":"","institution":"Laboratory for Ocean Physics and Satellite Remote Sensing","correspondingAuthor":true,"prefix":"","firstName":"Paul","middleName":"","lastName":"Platzer","suffix":""},{"id":414426072,"identity":"04644331-c3f2-4985-afe9-9ac1a7ec73d0","order_by":1,"name":"Bertrand Chapron","email":"","orcid":"","institution":"Laboratory for Ocean Physics and Satellite Remote Sensing","correspondingAuthor":false,"prefix":"","firstName":"Bertrand","middleName":"","lastName":"Chapron","suffix":""},{"id":414426073,"identity":"ceef662d-3b22-4ccd-9c51-372625059245","order_by":2,"name":"Gabriele Messori","email":"","orcid":"","institution":"Uppsala University","correspondingAuthor":false,"prefix":"","firstName":"Gabriele","middleName":"","lastName":"Messori","suffix":""}],"badges":[],"createdAt":"2025-01-22 10:38:29","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-5880040/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-5880040/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1038/s41612-025-01086-w","type":"published","date":"2025-05-28T15:57:47+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":83782945,"identity":"0abcefbe-f0e1-42a3-bea2-5500b5d22bfe","added_by":"auto","created_at":"2025-06-02 16:09:04","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1739160,"visible":true,"origin":"","legend":"","description":"","filename":"WRmultifractalorrandomnpjClimateandatmosphericscienceCopy.pdf","url":"https://assets-eu.researchsquare.com/files/rs-5880040/v1_covered_e5a670e1-3fe2-4673-806b-1b674990e9ce.pdf"},{"id":76069310,"identity":"66ecfea2-673a-46e7-9776-c5c9fe66acef","added_by":"auto","created_at":"2025-02-12 03:59:07","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"supplement","size":1353613,"visible":true,"origin":"","legend":"","description":"","filename":"WRmultifractalorrandomnpjClimateandatmosphericscienceCopySupplInformation.pdf","url":"https://assets-eu.researchsquare.com/files/rs-5880040/v1/edd4bd40ab330946fa16b33a.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Disentangling Density and Geometry in Weather Regime Dimensions using Stochastic Twins","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"npj-climate-and-atmospheric-science","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"npjclimatsci","sideBox":"Learn more about [npj Climate and Atmospheric Science](http://www.nature.com/npjclimatsci/)","snPcode":"41612","submissionUrl":"https://submission.springernature.com/new-submission/41612/3","title":"npj Climate and Atmospheric Science","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"NPJ","inReviewEnabled":true,"inReviewRevisionsEnabled":true},"keywords":"weather regimes, atmospheric circulation, fractal, dimension, density, geometry, dynamical systems, random, stochastic, transition, geopotential height","lastPublishedDoi":"10.21203/rs.3.rs-5880040/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-5880040/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eLarge-scale atmospheric variability can be summarised using a small number of recurring patterns called \\say{weather regimes}. The properties of weather regimes have been widely investigated in the literature, including through the \\say{local dimension}: an instantaneous geometrical estimate of the number of degrees of freedom, emanating from the multifractal formalism of dynamical systems. In atmospheric and ocean science, the local dimension has been interpreted as a measure of predictability. The different weather regimes display differing values of local dimension. It was also shown that the local dimension decreases when the atmosphere projects most strongly on a single weather regime, and increases during regime transitions. This was interpreted as confirming the physical grounding and dynamical footprint of weather regimes. However, the drivers of local dimension variations remain to be elucidated. In particular, recent work has shown that variations in local dimension originate not only from changes in multifractal geometric properties but also from changes in sampling density. In this work, we propose a methodology to isolate the density-based variations of local dimension for the large-scale atmospheric circulation in the North-Atlantic. We build \\say{stochastic twins} of the atmosphere in the space of truncated empirical orthogonal functions, based on the Gaussian mixture model used to define weather regimes from ERA5-reanalysis 500 hPa geopotential height fields. These stochastic twins bear a similar sampling density as the atmosphere, but they are not multifractal and therefore they have a constant local geometry and a fixed number of degrees of freedom. Estimates of density-based variations of local dimension using stochastic twins allow to explain more than 50% of the total variations of local dimension, proving that a large fraction of local dimension variations is not related to changes in local geometry. The dimension estimated from stochastic twins also allows to reproduce the previously observed decrease of dimension near peak weather regime index, indicating that this universal behavior is a density-based phenomenon, and cannot be attributed to the multifractal nature of atmospheric circulation. However, the sampling density-based variations of the local dimension can still provide useful information on the properties of weather regimes. Additionally, we show that the full range of local dimension variations cannot be explained by density-based estimates alone, so that the remaining variability is likely due to changes in local geometry, and therefore in number of degrees of freedom. The methodology presented in this paper can be applied to any observed system whose sampling distribution can be approximated, and provides a new means to interpret local dimension estimates of real-world atmospheric or ocean data.\u003c/p\u003e","manuscriptTitle":"Disentangling Density and Geometry in Weather Regime Dimensions using Stochastic Twins","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-02-12 03:27:02","doi":"10.21203/rs.3.rs-5880040/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Revision requested","date":"2025-03-21T19:30:43+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-03-20T17:40:16+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-02-21T13:48:01+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"257360251937047985927530071539115386329","date":"2025-02-20T17:17:55+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"328670451942549495505354027525687106012","date":"2025-01-29T10:46:44+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2025-01-28T21:56:26+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2025-01-24T14:28:02+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2025-01-24T12:05:22+00:00","index":"","fulltext":""},{"type":"submitted","content":"npj Climate and Atmospheric Science","date":"2025-01-22T10:28:31+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"npj-climate-and-atmospheric-science","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"npjclimatsci","sideBox":"Learn more about [npj Climate and Atmospheric Science](http://www.nature.com/npjclimatsci/)","snPcode":"41612","submissionUrl":"https://submission.springernature.com/new-submission/41612/3","title":"npj Climate and Atmospheric Science","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"NPJ","inReviewEnabled":true,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"733e6fc4-316c-4a23-b640-e5346abe6953","owner":[],"postedDate":"February 12th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"published-in-journal","subjectAreas":[{"id":44194692,"name":"Earth and environmental sciences/Climate sciences/Atmospheric science/Atmospheric dynamics"},{"id":44194693,"name":"Physical sciences/Mathematics and computing/Statistics"}],"tags":[],"updatedAt":"2025-06-02T16:02:40+00:00","versionOfRecord":{"articleIdentity":"rs-5880040","link":"https://doi.org/10.1038/s41612-025-01086-w","journal":{"identity":"npj-climate-and-atmospheric-science","isVorOnly":false,"title":"npj Climate and Atmospheric Science"},"publishedOn":"2025-05-28 15:57:47","publishedOnDateReadable":"May 28th, 2025"},"versionCreatedAt":"2025-02-12 03:27:02","video":"","vorDoi":"10.1038/s41612-025-01086-w","vorDoiUrl":"https://doi.org/10.1038/s41612-025-01086-w","workflowStages":[]},"version":"v1","identity":"rs-5880040","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-5880040","identity":"rs-5880040","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}