Semi-Analytical Prediction of Pyroclastic Flow Distance Using Adomian Decomposition and Real-Time Dome Growth Data: A Case Study of Mount Merapi

Semi-Analytical Prediction of Pyroclastic Flow Distance Using Adomian Decomposition and Real-Time Dome Growth Data: A Case Study of Mount Merapi | 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 Semi-Analytical Prediction of Pyroclastic Flow Distance Using Adomian Decomposition and Real-Time Dome Growth Data: A Case Study of Mount Merapi RACHID LIBOURKI, TJANG DANIEL CHANDRA This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7988521/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 Accurate prediction of pyroclastic flow runout distances is crucial for mitigating volcanic hazards, especially for Mount Merapi, Indonesia, where frequent eruptions threaten nearby communities. This study develops a semi-analytical model to forecast flow distances during the May 5–11, 2021 eruption, utilizing the Porous Medium Equation (PME) to capture nonlinear flow dynamics and the Adomian Decomposition Method (ADM) to provide effective, recursive solutions.A custom application built in Replit, leveraging Python with SymPy and NumPy, automates simulations, enabling rapid computation of flow profiles. Initial conditions were iteratively refined from a narrow Gaussian u(x, 0) = 1.5e-100x2 to a broader profile u(x, 0) = 3e-0.68x2, calibrated with BPPTKG’s dome growth data (1.1 × 106 m³). The model predicts runouts up to 3.0 km, validated against six-hourly observations (2km) and tested for sensitivity to the nonlinearity exponent (m = 3).Unlike resource-intensive numerical models or less accurate empirical approaches, this Replit-based solution offers fast and reliable predictions, enhancing semi-analytic methods and improving real-time volcanic hazard forecasting for Merapi Applied Mathematics Adomian Decomposition Method Mount Merapi Porous Medium Equation Pyroclastic Flow 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. 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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-7988521","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":537437551,"identity":"545f2a2c-3b99-4ed2-b133-b1bdca7a0ec6","order_by":0,"name":"RACHID LIBOURKI","email":"data:image/png;base64,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","orcid":"https://orcid.org/0009-0008-9741-8353","institution":"Universitas Negeri Malang","correspondingAuthor":true,"prefix":"","firstName":"RACHID","middleName":"","lastName":"LIBOURKI","suffix":""},{"id":537437628,"identity":"d1743a25-fac3-4ee1-b15b-85040e16ceee","order_by":1,"name":"TJANG DANIEL CHANDRA","email":"","orcid":"","institution":"Universitas Negeri Malang","correspondingAuthor":false,"prefix":"","firstName":"TJANG","middleName":"DANIEL","lastName":"CHANDRA","suffix":""}],"badges":[],"createdAt":"2025-10-30 10:56:31","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-7988521/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-7988521/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":94826141,"identity":"07893c60-b845-4a73-a364-853a67eecd22","added_by":"auto","created_at":"2025-10-31 06:51:11","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":2038842,"visible":true,"origin":"","legend":"","description":"","filename":"SEMIANALYTICALPREDICTIONOFPYROCLASTICFLOWDISTANCEUSINGADOMIANDECOMPOSITIONANDREALTIMEDOMEGROWTHDATAACASESTUDYOFMOUNTMERAPI.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7988521/v1_covered_bd27c945-ec92-42a2-a3da-c1489b159596.pdf"}],"financialInterests":"The authors declare no competing interests.","formattedTitle":"\u003cp\u003eSemi-Analytical Prediction of Pyroclastic Flow Distance Using Adomian Decomposition and Real-Time Dome Growth Data: A Case Study of Mount Merapi\u003c/p\u003e","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"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":"Adomian Decomposition Method, Mount Merapi, Porous Medium Equation, Pyroclastic Flow","lastPublishedDoi":"10.21203/rs.3.rs-7988521/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-7988521/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eAccurate prediction of pyroclastic flow runout distances is crucial for mitigating volcanic hazards, especially for Mount Merapi, Indonesia, where frequent eruptions threaten nearby communities. 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