Kalmag: a high spatio temporal model of the geomagnetic field

Kalmag: a high spatio temporal model of the geomagnetic field | 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 Kalmag: a high spatio temporal model of the geomagnetic field Julien Baerenzung, Matthias Holschneider, Jan Saynisch-Wagner, and 1 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-1512979/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 16 Sep, 2022 Read the published version in Earth, Planets and Space → Version 1 posted 7 You are reading this latest preprint version Abstract We present the extension of the Kalmag model, proposed as a candidate for IGRF-13, to the 20th century. The dataset serving its derivation has been complemented by new measurements coming from satellites, ground-based observatories and land, marine and airborne surveys. As its predecessor, this version is derived from a combination of a Kalman filter and a smoothing algorithm, providing mean models and associated uncertainties. These quantities permit a precise estimation of locations where mean solutions can be considered as reliable or not. The temporal resolution of the core field and the secular variation was set to 0.1 year over the 122 years the model is spanning. Nevertheless, it can be shown through ensembles a posteriori sampled, that this resolution can be effectively achieved only by a limited amount of spatial scales and during certain time periods. Unsurprisingly, highest accuracy in both space and time of the core field and the secular variation is achieved during the CHAMP and Swarm era. In this version of Kalmag, a particular effort was made for resolving the small scale lithospheric field. Under specific statistical assumptions, the latter was modeled up to spherical harmonic degree and order 1000, and signal coming from both satellite and survey measurements was contributing to its development. The model is available through various physical and statistical quantities on a dedicated website at https://ionocovar.agnld.uni-potsdam.de/Kalmag/ Geomagnetic field lithospheric field secular variation assimilation Kalman filter machine learning Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 Full Text Supplementary Files abstract.png Cite Share Download PDF Status: Published Journal Publication published 16 Sep, 2022 Read the published version in Earth, Planets and Space → Version 1 posted Reviews received at journal 09 Apr, 2022 Reviewer # 1 agreed at journal 08 Apr, 2022 Reviewers invited by journal 07 Apr, 2022 Editor assigned by journal 04 Apr, 2022 Submission checks completed at journal 03 Apr, 2022 Editor invited by journal 03 Apr, 2022 First submitted to journal 01 Apr, 2022 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. 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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-1512979","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":96779388,"identity":"18a2d185-b83b-430f-8ae9-1df03c87b75b","order_by":0,"name":"Julien Baerenzung","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA1ElEQVRIiWNgGAWjYBACAwST+QCIZGwgQQtbAslaeAyI02LOfvjYh4876hK386/5/OpmG4NsPyEtlj1pyTNnnmFL3Dnj7TbrnDMMxjMJWWNwIMeYmbeNJ3HDjbPbjHMqGBI3HCCk5fz7z8x/2ySAWs48M84xYEjcT1DLjRxmZsY2g8QN53uYH4NtIeiXGc+MGXvbEow33GAzY845I2E8g5At5vzJjxl+ttXJbjh/+PHn3DYb2f4GQtbAgUQCmwSQJFo9EPAfYP5AivpRMApGwSgYOQAAEzxHOiO5SMoAAAAASUVORK5CYII=","orcid":"https://orcid.org/0000-0002-0607-3695","institution":"GFZ: Deutsches Geoforschungszentrum Potsdam","correspondingAuthor":true,"submittingAuthor":false,"prefix":"","firstName":"Julien","middleName":"","lastName":"Baerenzung","suffix":""},{"id":96779389,"identity":"45843155-e4e6-4147-a1e6-f08715163a92","order_by":1,"name":"Matthias Holschneider","email":"","orcid":"","institution":"University of Potsdam: Universitat Potsdam","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Matthias","middleName":"","lastName":"Holschneider","suffix":""},{"id":96779390,"identity":"e50f4a92-d09a-4cb0-91a9-df5617f0736f","order_by":2,"name":"Jan Saynisch-Wagner","email":"","orcid":"","institution":"GFZ: Deutsches Geoforschungszentrum Potsdam","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Jan","middleName":"","lastName":"Saynisch-Wagner","suffix":""},{"id":96779391,"identity":"074929eb-60d2-444f-9ddd-4c69443f0b1a","order_by":3,"name":"Maik Thomas","email":"","orcid":"","institution":"GFZ: Deutsches Geoforschungszentrum Potsdam","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Maik","middleName":"","lastName":"Thomas","suffix":""}],"badges":[],"createdAt":"2022-04-01 10:26:07","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-1512979/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-1512979/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1186/s40623-022-01692-5","type":"published","date":"2022-09-16T08:06:12+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":20120343,"identity":"1e4d9d2d-2035-449a-a9ec-21e60dd1f938","added_by":"auto","created_at":"2022-04-08 14:31:26","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":362778,"visible":true,"origin":"","legend":"\u003cp\u003e\u0026nbsp;Locations (dots) and epoch (color) of each land, airborne and marine survey measurement. Black triangles correspond to every ground based observatories feeding the model with data.\u003c/p\u003e","description":"","filename":"1.png","url":"https://assets-eu.researchsquare.com/files/rs-1512979/v1/dc197899ff8dd2d658c037d6.png"},{"id":20121249,"identity":"70abfad3-437d-4913-9537-41aa60f188d2","added_by":"auto","created_at":"2022-04-08 14:41:26","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":385007,"visible":true,"origin":"","legend":"\u003cp\u003eRadial component at the Earth’s surface of the sum of the core field and the lithospheric field expanded up to spherical harmonics degree l= 20. Each panel corresponds to a different epoch which is displayed on their bottom left. Isocontours are showing mean solutions and color maps their associated standard deviation. White triangles represent the locations of ground-based observatories available at the presented epochs. On the bottom right of each maps is indicated the r.m.s standard deviation ¯σ in nT.\u003c/p\u003e","description":"","filename":"2.png","url":"https://assets-eu.researchsquare.com/files/rs-1512979/v1/bd34bb2b805f3fd934f2a89a.png"},{"id":20120348,"identity":"400ba9d0-1848-4121-b859-3223a2336703","added_by":"auto","created_at":"2022-04-08 14:31:26","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":444673,"visible":true,"origin":"","legend":"\u003cp\u003eSame as figure 2 for the secular variation. Each quantity is expressed in nT/yr.\u003c/p\u003e","description":"","filename":"3.png","url":"https://assets-eu.researchsquare.com/files/rs-1512979/v1/1722ab031f241139a7ca10ae.png"},{"id":20120761,"identity":"d12c637d-3b6b-4e9d-9ab1-3d9a395079af","added_by":"auto","created_at":"2022-04-08 14:36:26","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":137204,"visible":true,"origin":"","legend":"\u003cp\u003eTime series between 1900 and 2022 of selected spherical harmonics coefficients (indicated on the top of each panel) of the secular variation at the Earth’s surface. 68.2% confidence interval of the Kalmag solution (red areas) and the COV-OBS.x2 solution (blue areas) of Huder et al. (2020).\u003c/p\u003e","description":"","filename":"4.png","url":"https://assets-eu.researchsquare.com/files/rs-1512979/v1/735c7672c0fc8ee02b73d605.png"},{"id":20120344,"identity":"0de21bb2-948a-48e7-93cb-835727f6be03","added_by":"auto","created_at":"2022-04-08 14:31:26","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":80036,"visible":true,"origin":"","legend":"\u003cp\u003eLeft: energy spectra at the Earth’s surface for the mean secular variation (solid line) and its associated standard deviation (dashed lines) in 1960 (thin lines) and 1980 (thick lines). Right: Fourier transform degree spectra at the Earth’s surface for the 1980.0 − 2000.0 time period (see equation 20). Spectra for the spherical harmonics degrees l= 3 (thick lines) and l= 13 (thin lines) of the mean coefficients (solid line) and their standard deviation (dashed lines).\u003c/p\u003e","description":"","filename":"5.png","url":"https://assets-eu.researchsquare.com/files/rs-1512979/v1/12502d7808ede53a31167d4a.png"},{"id":20120759,"identity":"0e22b4e6-344f-4844-a9fa-10738f23f115","added_by":"auto","created_at":"2022-04-08 14:36:26","extension":"png","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":532615,"visible":true,"origin":"","legend":"\u003cp\u003eLithospheric field at the Earth’s surface expanded up to spherical harmonics degree l= 150. Left: mean downward component solution for the FR model estimated with full covariance information (top) and for the PR model estimated with variance only information from l= 30 (bottom). Top right: difference between FR and PR models mean downward components. Bottom right: energy spectra of the means (solid lines), the standard deviations (dashed lines) and the difference (crosses) between the FR model (black lines) and PR model (blue lines).\u003c/p\u003e","description":"","filename":"6.png","url":"https://assets-eu.researchsquare.com/files/rs-1512979/v1/26cca1174781a18f459fe351.png"},{"id":20120345,"identity":"92dff167-7370-401b-aa6e-eba5c1e6a08b","added_by":"auto","created_at":"2022-04-08 14:31:26","extension":"png","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":869381,"visible":true,"origin":"","legend":"\u003cp\u003eLithospheric field at the Earth’s surface. Left: mean downward component solution for the Kalmag model (top) expanded up to SH degree l = 1000 and for the WDMAM model of Lesur et al. (2016) (bottom) expanded up to SH degree l = 800. Top right: standard deviation associated with the mean downward component of the lithospheric field expanded up to l = 100. Bottom right: energy spectra of the means (solid lines) and standard deviations (dashed lines) associated with the lithospheric field, for the Kalmag model (black), the FR model (blue) and the WDMAM model (red).\u0026nbsp;\u003c/p\u003e","description":"","filename":"7.png","url":"https://assets-eu.researchsquare.com/files/rs-1512979/v1/2558bebe869d9ac27bb961a9.png"},{"id":20120351,"identity":"bf16f220-351d-4bd7-ae11-67cdc7a9b75a","added_by":"auto","created_at":"2022-04-08 14:31:26","extension":"png","order_by":8,"title":"Figure 8","display":"","copyAsset":false,"role":"figure","size":492988,"visible":true,"origin":"","legend":"\u003cp\u003eLithospheric field update at the level of Afghanistan. Top left: prior mean downward component in 2006.0 expanded up to l= 1000. Bottom left: locations of airborne intensity measurements taken in 2006 (blue dots) and 2008 (red dots). The second to the fourth map on the top show different models of the downward component of the lithospheric field. These are respectively from from left to right, the posterior mean expanded up to l= 2000, the EMM model by Maus (2010) taken up to l= 790 and posterior mean truncated at l= 790. Under each solution, the absolute value of the difference between measured intensities and predicted ones is shown. For predictions, the Kalmag mean core field was included. The values given on the bottom left of these maps correspond to the r.m.s. values of the differences between the model and the data.\u003c/p\u003e","description":"","filename":"8.png","url":"https://assets-eu.researchsquare.com/files/rs-1512979/v1/82709a4e8b240cbb2d33cafd.png"},{"id":20121319,"identity":"d7615833-ec3d-49c1-9dca-666314c7610a","added_by":"auto","created_at":"2022-04-08 14:41:34","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1289105,"visible":true,"origin":"","legend":"","description":"","filename":"EPSPD2200089reviewer.pdf","url":"https://assets-eu.researchsquare.com/files/rs-1512979/v1_covered.pdf"},{"id":20120350,"identity":"222c1b11-a80b-4810-b984-13265f86d881","added_by":"auto","created_at":"2022-04-08 14:31:26","extension":"png","order_by":1,"title":"","display":"","copyAsset":false,"role":"supplement","size":1102431,"visible":true,"origin":"","legend":"","description":"","filename":"abstract.png","url":"https://assets-eu.researchsquare.com/files/rs-1512979/v1/652dacdb125e49f07d6565b1.png"}],"financialInterests":"","formattedTitle":"Kalmag: a high spatio temporal model of the geomagnetic field","fulltext":[{"header":"Full Text","content":"This preprint is available for \u003ca href='/article/rs-1512979/latest.pdf' target='_blank'\u003edownload as a PDF\u003c/a\u003e."}],"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":true,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"earth-planets-and-space","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"epsp","sideBox":"Learn more about [Earth, Planets and Space](http://earth-planets-space.springeropen.com)","snPcode":"","submissionUrl":"https://www.editorialmanager.com/epsp/default.aspx","title":"Earth, Planets and Space","twitterHandle":"@SpringerOpen","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"BMC/SO AJ","inReviewEnabled":true,"inReviewRevisionsEnabled":true},"keywords":"Geomagnetic field, lithospheric field, secular variation, assimilation, Kalman filter, machine learning","lastPublishedDoi":"10.21203/rs.3.rs-1512979/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-1512979/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"We present the extension of the Kalmag model, proposed as a candidate for IGRF-13, to the 20th century. The dataset serving its derivation has been complemented by new measurements coming from satellites, ground-based observatories and land, marine and airborne surveys.\n\nAs its predecessor, this version is derived from a combination of a Kalman filter and a smoothing algorithm, providing mean models and associated uncertainties.\n\nThese quantities permit a precise estimation of locations where mean solutions can be considered as reliable or not.\n\nThe temporal resolution of the core field and the secular variation was set to 0.1 year over the 122 years the model is spanning. Nevertheless, it can be shown through ensembles a posteriori sampled, that this resolution can be effectively achieved only by a limited amount of spatial scales and during certain time periods. Unsurprisingly, highest accuracy in both space and time of the core field and the secular variation is achieved during the CHAMP and Swarm era.\n\nIn this version of Kalmag, a particular effort was made for resolving the small scale lithospheric field. 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