A Comparative Study of Maximum Entropy Based and Traditional Copula Models for Joint Simulation of Bivariate Flood

A Comparative Study of Maximum Entropy Based and Traditional Copula Models for Joint Simulation of Bivariate Flood | 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 A Comparative Study of Maximum Entropy Based and Traditional Copula Models for Joint Simulation of Bivariate Flood Kuang Wang, Fan Li This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7252572/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 This study investigates the applicability and accuracy of Copula models constructed using the Principle of Maximum Entropy (POME) for simulating flood peak discharge and flood volume, and compares their performance with that of traditional Copula models to assess the potential of POME in developing objective probability models under multiple statistical constraints. Using annual maximum daily mean discharge (Q) and the corresponding maximum three-day flood volume (W) data from two hydrological stations as case studies, four modeling schemes were designed: M1 (traditional marginals + traditional Copula), M2 (MaxEnt marginals + MaxEnt Copula), M3 (traditional marginals + MaxEnt Copula), and M4 (MaxEnt marginals + traditional Copula). Model performance was comprehensively assessed using the Akaike Information Criterion (AIC), Root Mean Square Error (RMSE), and relative errors of statistical parameters. Results indicate that for marginal distribution fitting, the MaxEnt distribution exhibits superior performance in terms of RMSE, particularly in the upper tail region of the cumulative distribution function. For Copula fitting, the Gaussian Copula demonstrates the best performance in joint probability distribution modeling, whereas the MaxEnt Copula shows relatively weaker performance. Among the four schemes, M4 achieves the optimal simulation results for statistical parameters and linear correlation coefficients. By incorporating multiple statistical constraints, the POME offers an objective modeling framework for both marginal and joint distributions without the need for preassumed distributional forms, making it particularly suitable for capturing the complexity and uncertainty of hydrological events and enabling flexible stochastic modeling of interdependent hydrological variables. Principle of Maximum Entropy distribution fitting Copula function Flood Statistical simulation Full Text Cite Share Download PDF Status: Under Review Version 1 posted Editor invited by journal 23 Jan, 2026 Reviewers agreed at journal 21 Aug, 2025 Reviewers invited by journal 14 Aug, 2025 Editor assigned by journal 30 Jul, 2025 First submitted to journal 30 Jul, 2025 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-7252572","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":500593675,"identity":"d894f952-a30a-42f6-89a1-0c75a5c89bb7","order_by":0,"name":"Kuang Wang","email":"","orcid":"","institution":"Anhui and Huaihe River Institute of Hydraulic Research","correspondingAuthor":false,"prefix":"","firstName":"Kuang","middleName":"","lastName":"Wang","suffix":""},{"id":500593676,"identity":"29120cac-af90-4b6b-9dba-92817f552daa","order_by":1,"name":"Fan Li","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAuklEQVRIiWNgGAWjYBACPmbGBwwMFRCOBFFa2JiZDRgYzpCkhQGohbGNJC3szIyfC+cdtjc4wHzwNg+DXR4xDmOWnrntMLPBAbZkax6G5GIitPAfkObddpjN4ACPmTQPw4HEBmJs+c075zCPwQH+b0RrYZPmbTgsAbSFjXgt1jzH0g0kD7MZW84xSCashZ//MPNtnhpre77jzQ9vvKmwI6wFCpoZGJhBtAGR6oGgjnilo2AUjIJRMPIAAODrLUBqKXksAAAAAElFTkSuQmCC","orcid":"https://orcid.org/0000-0002-3389-5707","institution":"Yangzhou University","correspondingAuthor":true,"prefix":"","firstName":"Fan","middleName":"","lastName":"Li","suffix":""}],"badges":[],"createdAt":"2025-07-30 11:54:26","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-7252572/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-7252572/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":89629506,"identity":"039063fa-6471-4fcc-bbd2-360864b9d2db","added_by":"auto","created_at":"2025-08-22 06:32:59","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":3562900,"visible":true,"origin":"","legend":"","description":"","filename":"Manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7252572/v1_covered_aeea46ca-5c4d-4ae0-86db-5e61af922bcf.pdf"}],"financialInterests":"","formattedTitle":"A Comparative Study of Maximum Entropy Based and Traditional Copula Models for Joint Simulation of Bivariate Flood","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"water-resources-management","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"warm","sideBox":"Learn more about [Water Resources Management](https://www.springer.com/journal/11269)","snPcode":"11269","submissionUrl":"https://submission.nature.com/new-submission/11269/3","title":"Water Resources Management","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"Principle of Maximum Entropy, distribution fitting, Copula function, Flood, Statistical simulation","lastPublishedDoi":"10.21203/rs.3.rs-7252572/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-7252572/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"This study investigates the applicability and accuracy of Copula models constructed using the Principle of Maximum Entropy (POME) for simulating flood peak discharge and flood volume, and compares their performance with that of traditional Copula models to assess the potential of POME in developing objective probability models under multiple statistical constraints. Using annual maximum daily mean discharge (Q) and the corresponding maximum three-day flood volume (W) data from two hydrological stations as case studies, four modeling schemes were designed: M1 (traditional marginals + traditional Copula), M2 (MaxEnt marginals + MaxEnt Copula), M3 (traditional marginals + MaxEnt Copula), and M4 (MaxEnt marginals + traditional Copula). Model performance was comprehensively assessed using the Akaike Information Criterion (AIC), Root Mean Square Error (RMSE), and relative errors of statistical parameters. Results indicate that for marginal distribution fitting, the MaxEnt distribution exhibits superior performance in terms of RMSE, particularly in the upper tail region of the cumulative distribution function. For Copula fitting, the Gaussian Copula demonstrates the best performance in joint probability distribution modeling, whereas the MaxEnt Copula shows relatively weaker performance. Among the four schemes, M4 achieves the optimal simulation results for statistical parameters and linear correlation coefficients. 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