Nonparametric approach to copula estimation in compounding the joint impact of storm surge and rainfall events in coastal flood analysis

Nonparametric approach to copula estimation in compounding the joint impact of storm surge and rainfall events in coastal flood 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 Research Article Nonparametric approach to copula estimation in compounding the joint impact of storm surge and rainfall events in coastal flood analysis SHAHID LATIF, Slobodan P. Simonovic This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-1939067/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 5 You are reading this latest preprint version Abstract The joint probability modelling of storm surge and rainfall events is the main task in assessing compound flood risk in low-lying coastal areas. These extreme or non-extreme events may not be dangerous if considered individually but can intensify flooding impact if they occur simultaneously or successively. Recently, the copula approach has been widely accepted in compound flooding but is often limited to parametric, or in limited number of cases to semiparametric, distribution settings. However, both parametric and semiparametric approaches assume the prior distribution type for univariate marginals and copula joint density. In that case, there is a high risk of misspecification if the underlying assumption is violated. In addition, both approaches suffer from a lack of flexibility. This study uses bivariate copula density in the nonparametric distribution setting. The joint copula structure is approximated nonparametrically by employing Beta kernel and Bernstein copula estimators, and their performances are also compared. The proposed model is tested with 46 years of rainfall and storm surge observations collected on Canada's west coast. Based on the different model compatibility tests, the Bernstein copula with normal KDE margins defined the joint dependence structure well. The selected nonparametric copula model is further employed to estimate joint and conditional return periods. The derived model is further used to estimate failure probability statistics to assess the variation of bivariate hydrologic risk during the project lifetime due to compounded storm surge and rainfall events. Flood Nonparametric copula Beta kernel copula estimator Bernstein copula estimator Bivariate joint analysis Return periods Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Full Text Tables Tables 1 to 5 are available in the Supplementary Files section Supplementary Files SupplementaryDatasps.docx Tablessps.docx Cite Share Download PDF Status: Under Review Version 1 posted Editorial decision: Major revisions 24 Aug, 2022 Reviewers agreed at journal 10 Aug, 2022 Reviewers invited by journal 10 Aug, 2022 Editor assigned by journal 09 Aug, 2022 First submitted to journal 07 Aug, 2022 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-1939067","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":127913886,"identity":"79e2252b-f94c-4bc9-a650-e2113de07e9a","order_by":0,"name":"SHAHID LATIF","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA70lEQVRIiWNgGAWjYBCDBAYJxgaJD0AWGzsx6g9AtUjOAGlhJl4LA4M0D4hHSItu++GHjz8w1OXxz25uvG3za5s8HzMD44ePObi1mJ1JMzY4wHC4WOLOwWbr3L7bhm3MDMySM7fh0XIgh03iAMOBxIYbiW3SuT23GYFa2Jh58Wk5/4b9xwGGusT5IC2WPbftCWu5kcMG9D5z4gaQFoYftxOJ0PLMWOKMweHEjTcSmy17G24ntzEzNuP3y/nkhx8qKuoS591If3jjx5/btvPbmw9++IhHCwQYQGnGNjDZQEg9MvhDiuJRMApGwSgYKQAAGupWmcLJUPIAAAAASUVORK5CYII=","orcid":"","institution":"Western University Faculty of Engineering","correspondingAuthor":true,"submittingAuthor":false,"prefix":"","firstName":"SHAHID","middleName":"","lastName":"LATIF","suffix":""},{"id":127913887,"identity":"ce832f47-1fb6-4d76-96c1-4c84e3cd2673","order_by":1,"name":"Slobodan P. 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[Note: Red colour circles are observed samples and light blue circles are generated flood samples from nonparametric copula models.]\u0026nbsp;\u003c/p\u003e\u003cp\u003e\u003cbr\u003e\u003c/p\u003e","description":"","filename":"2.png","url":"https://assets-eu.researchsquare.com/files/rs-1939067/v1/f74c2506ab9eb472716233a1.png"},{"id":25270040,"identity":"c054a5c3-2217-4f7d-becd-9fa76b4b974b","added_by":"auto","created_at":"2022-08-16 15:40:21","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":31570,"visible":true,"origin":"","legend":"\u003cp\u003eBivariate nonparametric Bernstein copula with normal KDE in the joint analysis of annual maximum 24-hr rainfall and maximum storm surge (time interval = ±4 days) events\u003c/p\u003e\u003cp\u003e\u003cbr\u003e\u003c/p\u003e","description":"","filename":"3.png","url":"https://assets-eu.researchsquare.com/files/rs-1939067/v1/def2c0dbc28a75594b074afc.png"},{"id":25270041,"identity":"206cdd88-9fe4-420b-8045-e1873d272f7b","added_by":"auto","created_at":"2022-08-16 15:40:21","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":63381,"visible":true,"origin":"","legend":"\u003cp\u003eConditional joint return periods of annual maximum 24-hr rainfall given different percentile values (i.e., 25\u003csup\u003eth\u003c/sup\u003e, 50\u003csup\u003eth\u003c/sup\u003e, 75\u003csup\u003eth\u003c/sup\u003e, 90\u003csup\u003eth\u003c/sup\u003e, 95\u003csup\u003eth\u003c/sup\u003e \u0026amp; 99\u003csup\u003eth\u003c/sup\u003e) of maximum storm surge (time interval = ±4 days)\u003c/p\u003e\u003cp\u003e\u003cbr\u003e\u003c/p\u003e","description":"","filename":"4.png","url":"https://assets-eu.researchsquare.com/files/rs-1939067/v1/a0bf513e4d5829bf4904193c.png"},{"id":25268937,"identity":"40cb69e5-7b71-448d-91e9-655adae2db94","added_by":"auto","created_at":"2022-08-16 15:35:21","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":40224,"visible":true,"origin":"","legend":"\u003cp\u003eConditional joint return periods of annual maximum 24-hr rainfall given different percentile values (i.e., 25\u003csup\u003eth\u003c/sup\u003e, 50\u003csup\u003eth\u003c/sup\u003e) of maximum storm surge (time interval = ±4 days)\u003c/p\u003e\u003cp\u003e\u003cbr\u003e\u003c/p\u003e","description":"","filename":"5.png","url":"https://assets-eu.researchsquare.com/files/rs-1939067/v1/2b75379f51ea9741d8ee557a.png"},{"id":25268935,"identity":"62aeff2d-1780-455f-b9fb-8f5cbbf342f2","added_by":"auto","created_at":"2022-08-16 15:35:21","extension":"png","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":347020,"visible":true,"origin":"","legend":"\u003cp\u003eBivariate flood risk through compounding the joint impact of storm surge and rainfall for different return periods (a) 500 years, (b) 200 years, (c) 100 years, (d) 50 years, (e) 20 years, (f) 10 years, and (g) 5 years\u003c/p\u003e\u003cp\u003e\u003cbr\u003e\u003c/p\u003e","description":"","filename":"6.png","url":"https://assets-eu.researchsquare.com/files/rs-1939067/v1/ec7fac3834b06ca27af3c0af.png"},{"id":25270819,"identity":"54287783-56b3-4ea9-91ea-7fffb140d812","added_by":"auto","created_at":"2022-08-16 15:45:21","extension":"png","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":138862,"visible":true,"origin":"","legend":"\u003cp\u003eVariation of bivariate compound flood risk with change of annual maximum 24-hr rainfall for different designed maximum storm surge (time interval = ±4 days)when (a) Service time = 100 years (b) Service time = 50 years (c) Service time = 30 years.\u0026nbsp;\u003c/p\u003e","description":"","filename":"7.png","url":"https://assets-eu.researchsquare.com/files/rs-1939067/v1/77bc0c611d43cdf4d690e703.png"},{"id":25270820,"identity":"f5189baf-94b7-4f93-ba10-02abd501665c","added_by":"auto","created_at":"2022-08-16 15:45:30","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":947975,"visible":true,"origin":"","legend":"","description":"","filename":"BivariateNonparametricdraftspsslsps.pdf","url":"https://assets-eu.researchsquare.com/files/rs-1939067/v1_covered.pdf"},{"id":25268932,"identity":"e1d3dc61-33b8-46a4-896d-6ba8f62b233d","added_by":"auto","created_at":"2022-08-16 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