Modelling correlations between meteoric forcing and groundwater level in a karst aquifer well

Modelling correlations between meteoric forcing and groundwater level in a karst aquifer well | 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 correlations between meteoric forcing and groundwater level in a karst aquifer well Paolo Martano, Marco Delle Rose, Antonio Donateo This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8733640/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 8 You are reading this latest preprint version Abstract This study uses two complementary stochastic approaches to obtain information about the time response of the groundwater level (output) from a well in the Salento Miocene karst aquifer (southern Italy), subjected to the meteoric forcing of both precipitation and atmospheric pressure (inputs). First, a Langevin equation is used to study the shape of the output correlation functions when forced by two correlated random inputs (a delta-correlated process as precipitation and an exponentially correlated process as atmospheric pressure). The presence of a delayed maximum as consequence of the non-vanishing covariance of the inputs is found. Then, a least square deconvolution is applied as a discrete transfer function model to obtain the response function coefficients for the cross-correlograms of the measured groundwater levels with the precipitation or net infiltration and the atmospheric pressure. Atmospheric pressure has a relevant effect on the groundwater level and is cross correlated to the precipitation in the observed time series. The cross correlograms between output and inputs have been reconstructed with the aim to disentangle the effects of the observed meteoric inputs on the groundwater levels. Thus, the effect of correlations in the deconvolution coefficients is discussed and the inferred results for the groundwater level dynamics in the well are outlined in both the time and the frequency domain. Both approaches suggest the attribution of the short-term maximum in the precipitation-groundwater level cross-correlograms to the correlations between the input forcings, and not specifically to the precipitation recharge. Consequently, as result of the least square deconvolution for the response function, only a delayed medium-term response of about 80 days duration in the groundwater level is attributed to the net infiltration, groundwater level precipitation atmospheric pressure linear response function Langevin equation Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Under Review Version 1 posted Reviews received at journal 02 Apr, 2026 Reviewers agreed at journal 16 Mar, 2026 Reviewers agreed at journal 23 Feb, 2026 Reviewers agreed at journal 06 Feb, 2026 Reviewers invited by journal 05 Feb, 2026 Editor assigned by journal 05 Feb, 2026 Submission checks completed at journal 04 Feb, 2026 First submitted to journal 29 Jan, 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-8733640","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":587811702,"identity":"cbf625ee-11d6-4099-aba2-a9517799860c","order_by":0,"name":"Paolo Martano","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA2ElEQVRIiWNgGAWjYHACxgMIdgVYoIGgHogWNhBxBqylkaAehBbGNgbC1pizHz5w4APDNnnz+c3PHnycZ5dn3sDc/gCfFsuetISDMxhuG845xmZuOHNbcrHMAQIOMziQY3CYh+E24ww2BjNp3m0HEmcQ8ovB+TdgLfYz2Ni/SfPOIUbLDYgtiTPYeIC2NBChxXLGM6BfDG4nz2DLKZOccSw5cQYzY+MMfFrM+ZMPPvhQcdt2BvPxbRIfauwSZ7C3P/iA12FIJBQw41OPrngUjIJRMApGAVYAAN0OSzGCLATZAAAAAElFTkSuQmCC","orcid":"","institution":"National Research Council (CNR)","correspondingAuthor":true,"prefix":"","firstName":"Paolo","middleName":"","lastName":"Martano","suffix":""},{"id":587811704,"identity":"e0f8dbbe-d97a-4e9d-9882-afa05bdcdb7f","order_by":1,"name":"Marco Delle Rose","email":"","orcid":"","institution":"National Research Council (CNR)","correspondingAuthor":false,"prefix":"","firstName":"Marco","middleName":"Delle","lastName":"Rose","suffix":""},{"id":587811705,"identity":"f02c17dd-398c-4589-a1f3-cfe39b0f78e7","order_by":2,"name":"Antonio Donateo","email":"","orcid":"","institution":"National Research Council (CNR)","correspondingAuthor":false,"prefix":"","firstName":"Antonio","middleName":"","lastName":"Donateo","suffix":""}],"badges":[],"createdAt":"2026-01-29 16:23:14","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-8733640/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-8733640/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":102404211,"identity":"a9096d62-fbc0-4495-a8fa-6497616acde3","added_by":"auto","created_at":"2026-02-11 11:03:06","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1325888,"visible":true,"origin":"","legend":"","description":"","filename":"FinaleSERRA3.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8733640/v1_covered_b0f0c6a3-97bb-4f8e-9b09-45bc43f7242b.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Modelling correlations between meteoric forcing and groundwater level in a karst aquifer well","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":"groundwater level, precipitation, atmospheric pressure, linear response function, Langevin equation","lastPublishedDoi":"10.21203/rs.3.rs-8733640/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8733640/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThis study uses two complementary stochastic approaches to obtain information about the time response of the groundwater level (output) from a well in the Salento Miocene karst aquifer (southern Italy), subjected to the meteoric forcing of both precipitation and atmospheric pressure (inputs). First, a Langevin equation is used to study the shape of the output correlation functions when forced by two correlated random inputs (a delta-correlated process as precipitation and an exponentially correlated process as atmospheric pressure). The presence of a delayed maximum as consequence of the non-vanishing covariance of the inputs is found. Then, a least square deconvolution is applied as a discrete transfer function model to obtain the response function coefficients for the cross-correlograms of the measured groundwater levels with the precipitation or net infiltration and the atmospheric pressure. Atmospheric pressure has a relevant effect on the groundwater level and is cross correlated to the precipitation in the observed time series. The cross correlograms between output and inputs have been reconstructed with the aim to disentangle the effects of the observed meteoric inputs on the groundwater levels. Thus, the effect of correlations in the deconvolution coefficients is discussed and the inferred results for the groundwater level dynamics in the well are outlined in both the time and the frequency domain. Both approaches suggest the attribution of the short-term maximum in the precipitation-groundwater level cross-correlograms to the correlations between the input forcings, and not specifically to the precipitation recharge. Consequently, as result of the least square deconvolution for the response function, only a delayed medium-term response of about 80 days duration in the groundwater level is attributed to the net infiltration,\u003c/p\u003e","manuscriptTitle":"Modelling correlations between meteoric forcing and groundwater level in a karst aquifer well","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2026-02-10 15:13:36","doi":"10.21203/rs.3.rs-8733640/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"editorInvitedReview","content":"","date":"2026-04-02T10:09:28+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"278451517176665511911421433793637589240","date":"2026-03-16T10:12:10+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"66124109364237586390632403756564768386","date":"2026-02-23T10:14:02+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"156404804625107138551362879213579649757","date":"2026-02-06T08:21:04+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2026-02-05T15:26:10+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2026-02-05T14:50:27+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2026-02-04T14:12:46+00:00","index":"","fulltext":""},{"type":"submitted","content":"Stochastic Environmental Research and Risk Assessment","date":"2026-01-29T15:58:11+00:00","index":"","fulltext":""}],"status":"published","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}}],"origin":"","ownerIdentity":"2bee011c-858d-4c18-9998-d0574e927653","owner":[],"postedDate":"February 10th, 2026","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"under-review","subjectAreas":[],"tags":[],"updatedAt":"2026-02-10T15:13:36+00:00","versionOfRecord":[],"versionCreatedAt":"2026-02-10 15:13:36","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-8733640","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-8733640","identity":"rs-8733640","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}