MSWD: A Hybrid Machine-Learning Framework for Slant Wet Delay Modeling

MSWD: A Hybrid Machine-Learning Framework for Slant Wet Delay Modeling | 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 MSWD: A Hybrid Machine-Learning Framework for Slant Wet Delay Modeling Zhenyi Zhang, Benedikt Soja This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8770150/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract Space geodetic techniques such as Global Navigation Satellite Systems (GNSS) and Very Long Baseline Interferometry (VLBI) are limited by direction-dependent tropospheric delays, with the slant wet delay (SWD) being the most variable component and a major source of error. Accurate SWD priors can accelerate convergence, stabilize parameter estimation, and improve positioning and atmospheric retrievals. Existing global empirical models, such as the state-of-the-art GPT3 model, reconstruct SWD through a fixed pipeline of zenith wet delay (ZWD), wet mapping function (MFw), and wet horizontal gradients. They rely on simplified parameterizations and fixed coefficient tables, and because re-estimating the full set of parameters is burdensome, products are rarely updated to reflect current conditions. In this paper, we present a hybrid machine-learning (ML) framework that embeds the established tilting mapping function formulation directly into the network, enabling end-to-end prediction of SWD. To our knowledge, this is the first ML model that outputs SWD directly. We also developed augmented variants that accept temperature and water vapor pressure as optional inputs for higher accuracy. Trained on five years of globally distributed ERA5-based SWD samples, the model delivers markedly lower errors than GPT3 over continental regions, where most space-geodetic stations operate. As ancillary products it can also output ZWD and MFw, with ZWD surpassing GPT3 and MFw exceeding the performance of the symmetric GPT3 variant while remaining slightly below that of the asymmetric variant. Besides the performance gains, this hybrid ML framework streamlines model maintenance and advances SWD modeling in space geodesy. Geophysics Atmospheric Sciences Slant wet delay Machine learning Hybrid framework Space geodesy Ray-tracing Tropospheric mapping function Zenith wet delay Full Text Additional Declarations The authors declare no competing interests. Cite Share Download PDF Status: Posted Version 1 posted 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-8770150","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":584704235,"identity":"5fc616bd-a32d-4fba-89bf-905c19102fc1","order_by":0,"name":"Zhenyi Zhang","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA5klEQVRIiWNgGAWjYDACCTB5AIiZDzAwNsBFiNLClsBwkEQtPAbEaZGf3XzsMc+fO/Lm/Gs+Pv64o46Bf3YDfi2Mc46lG/PwPDPcOePtZoODZ9gYJO4cwK+FWSLHTJpH4jDjhhtnt0kcbONhMJBIwK+FTSL/mzSPwWH7DTfOPP9xsE2CsBYeiRw2aZ6Ew4kbzvewMRxsMyCsRUIizUxyzoHDyRtusBlLnG1L4JG4QUCL/IzkZxJv/hy23XD+8MMPlW11cvwzCGgBASYesH0QlTyE1QMB4w8QyX+AKMWjYBSMglEwAgEA3YJIkB6HEJwAAAAASUVORK5CYII=","orcid":"https://orcid.org/0000-0002-8792-4497","institution":"Institute of Geodesy and Photogrammetry, ETH Zurich, 8093 Zurich, Switzerland","correspondingAuthor":true,"prefix":"","firstName":"Zhenyi","middleName":"","lastName":"Zhang","suffix":""},{"id":584704243,"identity":"7018c84d-eb6b-4adb-8314-543e12203eb2","order_by":1,"name":"Benedikt Soja","email":"","orcid":"https://orcid.org/0000-0002-7010-2147","institution":"Institute of Geodesy and Photogrammetry, ETH Zurich, 8093 Zurich, Switzerland","correspondingAuthor":false,"prefix":"","firstName":"Benedikt","middleName":"","lastName":"Soja","suffix":""}],"badges":[],"createdAt":"2026-02-03 02:42:42","currentVersionCode":1,"declarations":{"humanSubjects":false,"vertebrateSubjects":false,"conflictsOfInterestStatement":false,"humanSubjectEthicalGuidelines":false,"humanSubjectConsent":false,"humanSubjectClinicalTrial":false,"humanSubjectCaseReport":false,"vertebrateSubjectEthicalGuidelines":false},"doi":"10.21203/rs.3.rs-8770150/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-8770150/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":101826081,"identity":"ea90be65-b690-4a35-86c7-12b97de547d0","added_by":"auto","created_at":"2026-02-04 05:08:20","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1173001,"visible":true,"origin":"","legend":"","description":"","filename":"manuscriptSWD260114final.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8770150/v1_covered_ff2c3b70-b9f7-4e36-b67e-8066a7e72513.pdf"}],"financialInterests":"The authors declare no competing interests.","formattedTitle":"\u003cp\u003e\u003cstrong\u003eMSWD: A Hybrid Machine-Learning Framework for Slant Wet Delay Modeling\u003c/strong\u003e\u003c/p\u003e","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":true,"highlight":"","institution":"ETH Zurich","isAcceptedByJournal":false,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"Slant wet delay, Machine learning, Hybrid framework, Space geodesy, Ray-tracing, Tropospheric mapping function, Zenith wet delay","lastPublishedDoi":"10.21203/rs.3.rs-8770150/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8770150/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eSpace geodetic techniques such as Global Navigation Satellite Systems (GNSS) and Very Long Baseline Interferometry (VLBI) are limited by direction-dependent tropospheric delays, with the slant wet delay (SWD) being the most variable component and a major source of error. Accurate SWD priors can accelerate convergence, stabilize parameter estimation, and improve positioning and atmospheric retrievals. Existing global empirical models, such as the state-of-the-art GPT3 model, reconstruct SWD through a fixed pipeline of zenith wet delay (ZWD), wet mapping function (MFw), and wet horizontal gradients. They rely on simplified parameterizations and fixed coefficient tables, and because re-estimating the full set of parameters is burdensome, products are rarely updated to reflect current conditions. In this paper, we present a hybrid machine-learning (ML) framework that embeds the established tilting mapping function formulation directly into the network, enabling end-to-end prediction of SWD. To our knowledge, this is the first ML model that outputs SWD directly. We also developed augmented variants that accept temperature and water vapor pressure as optional inputs for higher accuracy. Trained on five years of globally distributed ERA5-based SWD samples, the model delivers markedly lower errors than GPT3 over continental regions, where most space-geodetic stations operate. As ancillary products it can also output ZWD and MFw, with ZWD surpassing GPT3 and MFw exceeding the performance of the symmetric GPT3 variant while remaining slightly below that of the asymmetric variant. Besides the performance gains, this hybrid ML framework streamlines model maintenance and advances SWD modeling in space geodesy.\u003c/p\u003e","manuscriptTitle":"MSWD: A Hybrid Machine-Learning Framework for Slant Wet Delay Modeling","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2026-02-04 05:07:58","doi":"10.21203/rs.3.rs-8770150/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"67b36c9d-f710-4cb5-aae5-00b60c087116","owner":[],"postedDate":"February 4th, 2026","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[{"id":62200465,"name":"Geophysics"},{"id":62200466,"name":"Atmospheric Sciences"}],"tags":[],"updatedAt":"2026-02-04T05:07:58+00:00","versionOfRecord":[],"versionCreatedAt":"2026-02-04 05:07:58","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-8770150","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-8770150","identity":"rs-8770150","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}