Assessment of Phase Uncertainty in NonlinearNearshore Wave Records

Assessment of Phase Uncertainty in NonlinearNearshore Wave Records | 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 Assessment of Phase Uncertainty in NonlinearNearshore Wave Records A. Spicer Bak, Patrick J. Lynett This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8552631/v1 This work is licensed under a CC BY 4.0 License Status: Under Revision Version 1 posted 12 You are reading this latest preprint version Abstract Given a time-series record of ocean surface elevation, spectral analysis is often used to determine characteristic statistics of therecord, such as wave height and mean period. A simple linear analysis shows that the phases of the Fourier components in atime-series have some effect on the value of the resulting characteristic statistics; two records with identical wave components,but different phases, will yield two different sets of bulk statistics (Hm0, Tp, etc.). In the linear sense, this variance from differentphase realizations is due to “spectral leakage”, or the existence of Fourier components with non-integer number of periods inthe record. It is also expected that variance due to nonlinearity should exist in nearshore wave records, as different phaserealizations may lead to different low-frequency motions, which may be poorly resolved in a typical time-series record. Thisphase-driven variance is a type of aleatory uncertainty, and must be quantified statistically. Here, in the context of a high energywave event in Duck, North Carolina, USA, the behavior of phase uncertainty is examined through numerical simulation. Theanalysis indicates that nonlinearity does play a role in uncertainty. The primary outcome of this study are empirical relations forthe expected value of phase-driven variance, which can be used to understand the baseline precision of spectral statisticsderived from time-series records. Earth and environmental sciences/Ocean sciences Physical sciences/Physics Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Under Revision Version 1 posted Editorial decision: Revision requested 27 Apr, 2026 Reviews received at journal 20 Apr, 2026 Reviewers agreed at journal 20 Apr, 2026 Reviewers agreed at journal 30 Mar, 2026 Reviewers agreed at journal 02 Mar, 2026 Reviews received at journal 02 Mar, 2026 Reviewers agreed at journal 01 Feb, 2026 Reviewers invited by journal 12 Jan, 2026 Editor invited by journal 12 Jan, 2026 Editor assigned by journal 09 Jan, 2026 Submission checks completed at journal 09 Jan, 2026 First submitted to journal 08 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-8552631","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":573667179,"identity":"2bf5cc8a-cb4b-4bfe-a216-311721a30875","order_by":0,"name":"A. Spicer Bak","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAABAklEQVRIiWNgGAWjYFACxgYQmcDAw3wARZyHj7AWtgRULWwE7AJq4TFAFcKlRX52c+OHj3sY8vh7znyT/FFjJ8fAfvbpZh6GbTK4tBjcOdgsOeMZQ7HE2d5t0jzHko0ZeNLNbvMw3MbpMAOJxDZmngMMiQ3nebdJM7AdSGxgSGPDq0V+BlDLH6CW+ed5nkn++HegvoH/GX4tDDeAWhiAWjac7WGT4G07kMAgQcAWsF96DkgUG545ZmzN25ds2CbxjO3mHAM8Dpvd/vDDjwM2eXJnkh/e/PHNTp6fP43txpuK2/b8uBwmgUSCAchwJvQ4wqIFDTD+wKNjFIyCUTAKRhwAAMHhVPjKG+97AAAAAElFTkSuQmCC","orcid":"","institution":"Engineer Research and Development Center","correspondingAuthor":true,"prefix":"","firstName":"A.","middleName":"Spicer","lastName":"Bak","suffix":""},{"id":573667180,"identity":"e33a9b18-6678-4971-93bf-f11d2bb57608","order_by":1,"name":"Patrick J. Lynett","email":"","orcid":"","institution":"University of Southern California","correspondingAuthor":false,"prefix":"","firstName":"Patrick","middleName":"J.","lastName":"Lynett","suffix":""}],"badges":[],"createdAt":"2026-01-08 14:42:11","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-8552631/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-8552631/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":100203850,"identity":"e95d9d65-1fda-49b5-91f5-82c0ed379188","added_by":"auto","created_at":"2026-01-14 05:55:12","extension":"json","order_by":0,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":4594,"visible":true,"origin":"","legend":"","description":"","filename":"3e89c38aa4d04be9baf0611fac0ee7d9.json","url":"https://assets-eu.researchsquare.com/files/rs-8552631/v1/137e6ffee24a269e2989f30c.json"},{"id":100369740,"identity":"869f5f2a-cc2e-4dfd-9586-8ef55f4a7c64","added_by":"auto","created_at":"2026-01-16 07:59:22","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":7588201,"visible":true,"origin":"","legend":"","description":"","filename":"zdzdxwkrhvzybdtxmkfyjntxnyzgzpdz.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8552631/v1_covered_6695f452-2616-4745-93c4-4dd7e6d02324.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Assessment of Phase Uncertainty in NonlinearNearshore Wave Records","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":"scientific-reports","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"scirep","sideBox":"Learn more about [Scientific Reports](http://www.nature.com/srep/)","snPcode":"","submissionUrl":"","title":"Scientific Reports","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Scientific Reports","inReviewEnabled":true,"inReviewRevisionsEnabled":true},"keywords":"","lastPublishedDoi":"10.21203/rs.3.rs-8552631/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8552631/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"Given a time-series record of ocean surface elevation, spectral analysis is often used to determine characteristic statistics of therecord, such as wave height and mean period. A simple linear analysis shows that the phases of the Fourier components in atime-series have some effect on the value of the resulting characteristic statistics; two records with identical wave components,but different phases, will yield two different sets of bulk statistics (Hm0, Tp, etc.). In the linear sense, this variance from differentphase realizations is due to “spectral leakage”, or the existence of Fourier components with non-integer number of periods inthe record. It is also expected that variance due to nonlinearity should exist in nearshore wave records, as different phaserealizations may lead to different low-frequency motions, which may be poorly resolved in a typical time-series record. Thisphase-driven variance is a type of aleatory uncertainty, and must be quantified statistically. Here, in the context of a high energywave event in Duck, North Carolina, USA, the behavior of phase uncertainty is examined through numerical simulation. Theanalysis indicates that nonlinearity does play a role in uncertainty. The primary outcome of this study are empirical relations forthe expected value of phase-driven variance, which can be used to understand the baseline precision of spectral statisticsderived from time-series records.","manuscriptTitle":"Assessment of Phase Uncertainty in NonlinearNearshore Wave Records","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2026-01-14 05:55:07","doi":"10.21203/rs.3.rs-8552631/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Revision requested","date":"2026-04-27T20:58:57+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2026-04-20T19:47:21+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"17328343989432212607034539543942667781","date":"2026-04-20T18:07:30+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"142106960547902086411021949404984002627","date":"2026-03-30T12:10:53+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"21574992692127299343693354699308869841","date":"2026-03-02T15:58:59+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2026-03-02T11:02:07+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"324335098049193595617459901114527134788","date":"2026-02-01T22:45:33+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2026-01-12T21:41:54+00:00","index":"","fulltext":""},{"type":"editorInvited","content":"","date":"2026-01-12T20:43:01+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2026-01-09T05:44:37+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2026-01-09T05:41:41+00:00","index":"","fulltext":""},{"type":"submitted","content":"Scientific Reports","date":"2026-01-08T14:33:39+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"scientific-reports","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"scirep","sideBox":"Learn more about [Scientific Reports](http://www.nature.com/srep/)","snPcode":"","submissionUrl":"","title":"Scientific Reports","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Scientific Reports","inReviewEnabled":true,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"7f912afb-78bc-4e31-96e7-44a91c08fc6b","owner":[],"postedDate":"January 14th, 2026","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"in-revision","subjectAreas":[{"id":61037616,"name":"Earth and environmental sciences/Ocean sciences"},{"id":61037617,"name":"Physical sciences/Physics"}],"tags":[],"updatedAt":"2026-04-27T21:09:18+00:00","versionOfRecord":[],"versionCreatedAt":"2026-01-14 05:55:07","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-8552631","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-8552631","identity":"rs-8552631","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}