Modelling Mountain Accidents and Assessing Risk Through Spatio-Temporal Point Processes

Modelling Mountain Accidents and Assessing Risk Through Spatio-Temporal Point Processes | 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 Modelling Mountain Accidents and Assessing Risk Through Spatio-Temporal Point Processes Albert Martínez, Carles Comas, Angel Blanch This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-9520795/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 7 You are reading this latest preprint version Abstract Historically, mountain activities have been associated to accidents, injuries and fatalities. The spatial and temporal context, however, has been largely neglected, with most studies focusing on proximal causes of accidents. The objective of the present study is to analyse the effects of spatial and temporal covariables on the distribution of mountain accidents in a specific area over a span of 11 years. The current dataset includes 572 rescues on Montserrat Natural Protected Area between 2011 and 2021 and comprises 249 climbing rescues and 310 hiking rescues. We assume that mountain accidents follow a Log-Gaussian Cox Process (LGCP) and we consider an empirical analysis of the first-order characteristic. Then we propose a model in which the conditional intensity of the point process depends on some specific spatial and temporal covariables affecting the distribution of this space-time point pattern. We use the inhomogeneous spatio-temporal K-function to estimate second-order properties. Finally, we model the residual spatio-temporal variation as a stochastic process using a space-time covariance function under a separable space-time structure, and we conduct a risk analysis based on the resulting full LGCP through the Value-at-Risk (VaR). The results indicate that rescues are clustered over short distances, typically below 100–300 m. Spatial and temporal predictors differ across activities, while risk remains consistently concentrated in specific areas throughout the study period. Overall, the full LGCP model shows a good fit and is able to generate simulations consistent with the observed data. Inhomogeneous space-time point patterns Mountain accidents Mountain rescues Poisson log-linear models Risk assessment Spatio-temporal point process Value at Risk Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Under Review Version 1 posted Reviewers agreed at journal 12 May, 2026 Reviews received at journal 07 May, 2026 Reviewers agreed at journal 29 Apr, 2026 Reviewers invited by journal 29 Apr, 2026 Editor assigned by journal 28 Apr, 2026 Submission checks completed at journal 27 Apr, 2026 First submitted to journal 24 Apr, 2026 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-9520795","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":631608407,"identity":"cf450c76-41c0-43c5-b690-6b56dd3e4045","order_by":0,"name":"Albert Martínez","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA9UlEQVRIie3PMQrCMBSA4VcKukRd61Kv0CLo4k1cKgWdAo4KIgHBSZ0VQa9Qb2AI2CXo6qh4AhGkgohJHMQh1dEhPwQSyEfyAEymfyyL3vu1WC5ASNKJLUmgdoqUARqSeL8Rmbj/hRQGOXrqJlAvzHeUtTv9VhQLkvTuWuKwfOjzAPB0GwKb8gyO+JFYo03KxxiqFIkghNvAckOEo32D2JDRkxJD1ZskS0UeTstT5KEnnnjFkiRShHiBItZQT3wxS5E0HbzituCbwJ+JWeh4UtYSNx7TM6nV8IJbpwvq9Uv5OKSH5Orqx3/lfB7X3+6bTCaTKb0n4SNVWcfzTyUAAAAASUVORK5CYII=","orcid":"","institution":"University of Lleida","correspondingAuthor":true,"prefix":"","firstName":"Albert","middleName":"","lastName":"Martínez","suffix":""},{"id":631608409,"identity":"9333f621-f360-4aa5-a299-40ccc0b8fdcf","order_by":1,"name":"Carles Comas","email":"","orcid":"","institution":"University of Lleida","correspondingAuthor":false,"prefix":"","firstName":"Carles","middleName":"","lastName":"Comas","suffix":""},{"id":631608411,"identity":"3622af46-6fbe-46fe-8bc9-9119c07cf55c","order_by":2,"name":"Angel Blanch","email":"","orcid":"","institution":"University of Lleida","correspondingAuthor":false,"prefix":"","firstName":"Angel","middleName":"","lastName":"Blanch","suffix":""}],"badges":[],"createdAt":"2026-04-24 21:27:46","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-9520795/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-9520795/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":108805662,"identity":"b1e5e716-ab0f-41a2-818d-aa0af54e3b00","added_by":"auto","created_at":"2026-05-08 15:26:33","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1960742,"visible":true,"origin":"","legend":"","description":"","filename":"SpacetimeMontserrat.pdf","url":"https://assets-eu.researchsquare.com/files/rs-9520795/v1_covered_961bec82-ab9c-44c4-8fb2-e039f7b688d6.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Modelling Mountain Accidents and Assessing Risk Through Spatio-Temporal Point Processes","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"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":"stochastic-environmental-research-and-risk-assessment","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"serr","sideBox":"Learn more about [Stochastic Environmental Research and Risk Assessment](https://www.springer.com/journal/477)","snPcode":"477","submissionUrl":"https://submission.nature.com/new-submission/477/3","title":"Stochastic Environmental Research and Risk Assessment","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"Inhomogeneous space-time point patterns, Mountain accidents, Mountain rescues, Poisson log-linear models, Risk assessment, Spatio-temporal point process, Value at Risk","lastPublishedDoi":"10.21203/rs.3.rs-9520795/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-9520795/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eHistorically, mountain activities have been associated to accidents, injuries and fatalities. 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