Improved empirical zenith tropospheric wet delay models based on a novel machine learning fusion algorithm

Improved empirical zenith tropospheric wet delay models based on a novel machine learning fusion algorithm | 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 Improved empirical zenith tropospheric wet delay models based on a novel machine learning fusion algorithm Jiahao Zhang, Qin Liang, Yunqing Huang This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-5301285/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 Zenith tropospheric wet delay (ZWD) plays a vital role in the analysis of space geodetic observations. In recent years, machine learning methods have been increasingly applied to improve the accuracy of ZWD calculations. The most widely used approaches are random forest (RF) and back propagation neural network (BPNN) models, both of which have shown promising results in terms of internal accuracy (where test stations are included in the training set). However, the external accuracy (where test stations are excluded from the training set) of these models still requires improvement. To address this issue, this study introduces two new methods: Extra Trees (ET) and a novel machine learning fusion (MLF) algorithm, aimed at enhancing ZWD accuracy. The MLF algorithm utilizes a two-layer structure that integrates ET, BPNN, and linear regression models. By comparing the root mean squared error (RMSE) of these models, we found that both ET-based and MLF-based models outperform RF-based and BPNN-based models in terms of internal and external accuracy, across both surface meteorological data-based and blind models. The improvement in external accuracy is particularly significant in the blind models. Our results show that the MLF (with an RMSE of 3.93 cm) and ET (3.99 cm) models outperform the traditional GPT3 model (4.07 cm), while the RF (4.21cm) and BPNN (4.14cm) have worse external accuracies than the GPT3 model. In summary, regardless of the availability of surface meteorological data, the MLF-based empirical models demonstrate superior internal and external accuracy compared to the other tested models in this study. Zenith tropospheric wet delay machine learning extra trees machine learning fusion algorithm empirical models. Full Text Additional Declarations No competing interests reported. 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-5301285","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":369103163,"identity":"92269879-536b-4fcd-8bbb-b894901546c7","order_by":0,"name":"Jiahao Zhang","email":"","orcid":"","institution":"Xiangtan University","correspondingAuthor":false,"prefix":"","firstName":"Jiahao","middleName":"","lastName":"Zhang","suffix":""},{"id":369103164,"identity":"658b4a70-d112-46c4-b8bc-73a6b671f4a4","order_by":1,"name":"Qin Liang","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA+ElEQVRIiWNgGAWjYBACPmYwJcHAxt58/McHiKABXi1sMC18PMcSJGdAVBPQAmPISeQYSPMQpYWd+dnDL2UWeWxALca2bX8SG9ibt0kw1NzB4zA2c2OZcxLFbDzPCpJzzhgkNvAcK5NgOPYMn1/MpCXbJBLb2JM3HM6pAGqRyDGTYGw4jEcL+zeIFoYEw2YLA6AW+TeEtPCYSX4EaeFIMWZmANvCQ1BLmTTDOaAWnmNpjD1njI3beNKKLRKO4dbCz398m+SPsrrE+e3Nxxh+tsnJ9rMf3njjQw1uLSDAzMOGxAOzE/BqYGBg/MFGQMUoGAWjYBSMbAAABlpIyxrQT8wAAAAASUVORK5CYII=","orcid":"","institution":"Xiangtan University","correspondingAuthor":true,"prefix":"","firstName":"Qin","middleName":"","lastName":"Liang","suffix":""},{"id":369103165,"identity":"3da21f6e-ae34-4c25-b0a2-c30decf56843","order_by":2,"name":"Yunqing Huang","email":"","orcid":"","institution":"Xiangtan University","correspondingAuthor":false,"prefix":"","firstName":"Yunqing","middleName":"","lastName":"Huang","suffix":""}],"badges":[],"createdAt":"2024-10-21 05:23:31","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-5301285/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-5301285/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":68088780,"identity":"4f71f7d3-b341-4783-b8f9-e703d89ba297","added_by":"auto","created_at":"2024-11-02 16:08:42","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1696915,"visible":true,"origin":"","legend":"","description":"","filename":"Improvedempiricalzenithtroposphericwetdelaymodelsbasedonanovelmachinelearningfusionalgorithm.pdf","url":"https://assets-eu.researchsquare.com/files/rs-5301285/v1_covered_be3255dd-6dd1-434a-91df-bb77038e2739.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Improved empirical zenith tropospheric wet delay models based on a novel machine learning fusion algorithm","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"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":"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":"Zenith tropospheric wet delay, machine learning, extra trees, machine learning fusion algorithm, empirical models.","lastPublishedDoi":"10.21203/rs.3.rs-5301285/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-5301285/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"Zenith tropospheric wet delay (ZWD) plays a vital role in the analysis of space geodetic observations. In recent years, machine learning methods have been increasingly applied to improve the accuracy of ZWD calculations. The most widely used approaches are random forest (RF) and back propagation neural network (BPNN) models, both of which have shown promising results in terms of internal accuracy (where test stations are included in the training set). However, the external accuracy (where test stations are excluded from the training set) of these models still requires improvement. To address this issue, this study introduces two new methods: Extra Trees (ET) and a novel machine learning fusion (MLF) algorithm, aimed at enhancing ZWD accuracy. The MLF algorithm utilizes a two-layer structure that integrates ET, BPNN, and linear regression models. By comparing the root mean squared error (RMSE) of these models, we found that both ET-based and MLF-based models outperform RF-based and BPNN-based models in terms of internal and external accuracy, across both surface meteorological data-based and blind models. The improvement in external accuracy is particularly significant in the blind models. Our results show that the MLF (with an RMSE of 3.93 cm) and ET (3.99 cm) models outperform the traditional GPT3 model (4.07 cm), while the RF (4.21cm) and BPNN (4.14cm) have worse external accuracies than the GPT3 model. 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