Scaling Laws of Tidal Wave Dispersion: Multi-frequency, Multi-estuary Analysis

Scaling Laws of Tidal Wave Dispersion: Multi-frequency, Multi-estuary Analysis | 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 Article Scaling Laws of Tidal Wave Dispersion: Multi-frequency, Multi-estuary Analysis Ying-Fan Lin, Jun-Hong Lin, Tung-Chou Hsieh This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7767603/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted You are reading this latest preprint version Abstract Tidal transmission in estuaries reflects a balance between amplitude damping and phase progression. Yet observations consistently show frequency-dependent variability that exceeds the explanatory reach of a single wave--diffusion model. To address this gap, we analyze boundary--inland gauge pairs from five U.S. estuaries and externally validate the findings in nine non-U.S. systems---Tokyo Bay (Japan), Port Phillip Bay (Australia), the Waitemat={a} Harbour (Auckland, New Zealand), the Fraser River estuary (Canada), the Tamsui River estuary (Taiwan), and four European estuaries: Elbe and Weser (Germany) and Gironde and Loire (France). From these records, we quantify amplitude decay and phase lag for leading diurnal and semidiurnal constituents. The results reveal a striking asymmetry: phase accumulates roughly an order of magnitude faster than amplitude decays, placing most systems in a propagation-dominated, weak-memory regime. Instances of inland amplification occur but remain rare and do not dominate the population. To interpret this behavior, we propose a lagging framework with two characteristic timescales. From a minimal parameter set, the framework predicts frequency-dependent slopes, reproduces phase-lag behavior with near one-to-one accuracy, and captures damping with moderate scatter. When applied across systems, the results collapse onto two nondimensional controls: the ratio of forcing period to travel time and the ratio of storage to propagation timescales. We further synthesize constituent-wise slopes into estuary-level ''memory'' features and apply an unsupervised clustering, which objectively groups estuaries into low- to mid--low-memory archetypes---convergent or inlet-restricted, tidal--fluvial, and a non-passive reflection class---consistent with independent geomorphic descriptors. All nine non-U.S. estuaries fall within the same low-memory envelopes, underscoring the framework's generality. A companion distance--frequency chart translates these fits into estimates of tidal penetration, revealing shorter inland reaches for semidiurnal than for diurnal tides. Overall, the analysis offers a compact mechanistic view of estuarine memory and a demonstrably transferable tool for network design, forecasting, and change detection. Earth and environmental sciences/Ocean sciences/Physical oceanography Earth and environmental sciences/Hydrology Estuarine dynamics Tidal propagation Amplitude attenuation Phase lag Frequency-dependent memory Nondimensional scaling Full Text Additional Declarations There is NO Competing Interest. Cite Share Download PDF Status: Under Review 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. 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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-7767603","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":525268252,"identity":"da60bb87-8520-4960-9311-3dc1321ad800","order_by":0,"name":"Ying-Fan Lin","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA4klEQVRIiWNgGAWjYDAC5sMNBxgMJHjY2BugIgcIaWFLBGopsJDh54EpPcDA2IBHA1gLA8OHChvJGQlEajE4xth4uADoMIObj59J/GxjkOO7kcD+mAe/lobDM0BabqeZSfa2MRhL3khgbMar5X5jw2EesJYcNmnGNobEDSAtOYRsAWu5eQaspZ54LZIzeMBaEgwIaZGEaeHnSTO27DknYTjzzMPG2X/waOE7xnz4M8+fOns29sMPb/wos5HnO5584OMMPFoUDiDYLBIMDEBEKCblkaSZP+BVOgpGwSgYBSMWAADoSU9IXm9l0gAAAABJRU5ErkJggg==","orcid":"https://orcid.org/0000-0002-4853-3944","institution":"Chung Yuan Christian University","correspondingAuthor":true,"prefix":"","firstName":"Ying-Fan","middleName":"","lastName":"Lin","suffix":""},{"id":525268253,"identity":"3eab1adb-c713-4312-91dc-3298c858948a","order_by":1,"name":"Jun-Hong Lin","email":"","orcid":"","institution":"Chung Yuan Christian University","correspondingAuthor":false,"prefix":"","firstName":"Jun-Hong","middleName":"","lastName":"Lin","suffix":""},{"id":525268254,"identity":"16040108-35c4-47f4-b859-ee09ec6734b4","order_by":2,"name":"Tung-Chou Hsieh","email":"","orcid":"","institution":"National Yang Ming Chiao Tung University","correspondingAuthor":false,"prefix":"","firstName":"Tung-Chou","middleName":"","lastName":"Hsieh","suffix":""}],"badges":[],"createdAt":"2025-10-02 15:21:11","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-7767603/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-7767603/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":94989145,"identity":"a19d3562-13b3-4f2b-bdd0-a1aa89c6933d","added_by":"auto","created_at":"2025-11-03 07:12:17","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":3931172,"visible":true,"origin":"","legend":"Article File","description":"","filename":"Lin3Manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7767603/v1_covered_dc5fbfa0-9e15-4d8f-b2ca-fcc95735cdbd.pdf"}],"financialInterests":"There is \u003cb\u003eNO\u003c/b\u003e Competing Interest.","formattedTitle":"Scaling Laws of Tidal Wave Dispersion: Multi-frequency, Multi-estuary Analysis","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":"nature-portfolio","isNatureJournal":true,"hasQc":false,"allowDirectSubmit":false,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"","title":"Nature Portfolio","twitterHandle":"","acdcEnabled":false,"dfaEnabled":false,"editorialSystem":"ejp","reportingPortfolio":"","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"Estuarine dynamics, Tidal propagation, Amplitude attenuation, Phase lag, Frequency-dependent memory, Nondimensional scaling","lastPublishedDoi":"10.21203/rs.3.rs-7767603/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-7767603/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"Tidal transmission in estuaries reflects a balance between amplitude damping and phase progression. Yet observations consistently show frequency-dependent variability that exceeds the explanatory reach of a single wave--diffusion model. To address this gap, we analyze boundary--inland gauge pairs from five U.S. estuaries and externally validate the findings in nine non-U.S. systems---Tokyo Bay (Japan), Port Phillip Bay (Australia), the Waitemat\\={a} Harbour (Auckland, New Zealand), the Fraser River estuary (Canada), the Tamsui River estuary (Taiwan), and four European estuaries: Elbe and Weser (Germany) and Gironde and Loire (France). From these records, we quantify amplitude decay and phase lag for leading diurnal and semidiurnal constituents. The results reveal a striking asymmetry: phase accumulates roughly an order of magnitude faster than amplitude decays, placing most systems in a propagation-dominated, weak-memory regime. Instances of inland amplification occur but remain rare and do not dominate the population. To interpret this behavior, we propose a lagging framework with two characteristic timescales. From a minimal parameter set, the framework predicts frequency-dependent slopes, reproduces phase-lag behavior with near one-to-one accuracy, and captures damping with moderate scatter. When applied across systems, the results collapse onto two nondimensional controls: the ratio of forcing period to travel time and the ratio of storage to propagation timescales. We further synthesize constituent-wise slopes into estuary-level ''memory'' features and apply an unsupervised clustering, which objectively groups estuaries into low- to mid--low-memory archetypes---convergent or inlet-restricted, tidal--fluvial, and a non-passive reflection class---consistent with independent geomorphic descriptors. All nine non-U.S. estuaries fall within the same low-memory envelopes, underscoring the framework's generality. 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