Modified Mann-Kendall with Higher-Order Statistics for Trend Analysis

Modified Mann-Kendall with Higher-Order Statistics for Trend 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 Modified Mann-Kendall with Higher-Order Statistics for Trend Analysis Yick Jing Then, Syafrina Abdul Halim This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7422488/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 03 Dec, 2025 Read the published version in Scientific Reports → Version 1 posted 11 You are reading this latest preprint version Abstract Trend analysis of rainfall events is crucial, especially in understanding changes in precipitation patterns over time, which can have significant implications for climate adaptation planning. The Mann-Kendall (MK) trend test is preferred by researchers, given its robustness in handling non-normal data with extreme out-liers. However, the assumption of independence is often not fulfilled. Researchers have begun proposing modifications to MK to enhance its interpretability when dealing with positive autocorrelation. Nevertheless, the issue of nonlinearity, where future values of time series data cannot be explained by a linear function, is not widely discussed. In this paper, a modified MK named Mann-Kendall with Third-Order Cumulant (MKC3) is proposed. A simulation study was conducted using MKC3, with comparisons made against MK and Mann-Kendall Rank Detrended (MKRD), alongside a case study of rainfall in Peninsular Malaysia. The simulation results reveal that MK, MKRD, and MKC3 are comparable, with MK suitable for independent data, MKRD for strongly autocorrelated data, and MKC3 for bilinear, nonlinear and sinusoidal models. The case study shows increasing trends for rainfall in the Northeast Monsoon (NEM) and decreasing trends in the Southwest Monsoon (SWM). Overall, the MKC3 is justified by its robustness, but the selection remains a trade-off. Earth and environmental sciences/Climate sciences Earth and environmental sciences/Environmental sciences Physical sciences/Mathematics and computing Mann-Kendall Trend analysis Rainfall Nonlinearity Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Published Journal Publication published 03 Dec, 2025 Read the published version in Scientific Reports → Version 1 posted Editorial decision: Revision requested 13 Oct, 2025 Reviews received at journal 28 Sep, 2025 Reviewers agreed at journal 10 Sep, 2025 Reviewers agreed at journal 10 Sep, 2025 Reviews received at journal 08 Sep, 2025 Reviewers agreed at journal 04 Sep, 2025 Reviewers invited by journal 04 Sep, 2025 Editor assigned by journal 02 Sep, 2025 Editor invited by journal 02 Sep, 2025 Submission checks completed at journal 28 Aug, 2025 First submitted to journal 28 Aug, 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. 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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-7422488","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":513341366,"identity":"b9436562-e315-4a74-9bf5-e9d421cb1f6e","order_by":0,"name":"Yick Jing Then","email":"","orcid":"","institution":"Universiti Putra Malaysia","correspondingAuthor":false,"prefix":"","firstName":"Yick","middleName":"Jing","lastName":"Then","suffix":""},{"id":513341367,"identity":"24044182-75fb-4a5f-99e9-ef42e24d9729","order_by":1,"name":"Syafrina Abdul Halim","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA3ElEQVRIiWNgGAWjYJCCDwwGDAz8EDYzUToYZ4C0SDaQpgUIDA4Qq0V+RvLD5oqCO/LGN3KPbmCosE5sEDtjgFeLwY00w8YzBs8Mt93IS7vBcCY9sUE6h4AWiQTzhw0Ghxm33cgxu8HYdpiwFvkZ6R8bgVrsN88AaflHhBaGGzmGIC2JGyRAWhqI0GJw5k0hSEvyjDPv0m4kHEs3bpNOK8DvsPb0jY0Nfw7b9rfnHrvxocZatl86eQN+hwkkwFg8DAwgNhsDBwG/8B9A0gIB7A/waxkFo2AUjIKRBgDImE5nyBJEvwAAAABJRU5ErkJggg==","orcid":"","institution":"Universiti Putra Malaysia","correspondingAuthor":true,"prefix":"","firstName":"Syafrina","middleName":"Abdul","lastName":"Halim","suffix":""}],"badges":[],"createdAt":"2025-08-21 05:38:18","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-7422488/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-7422488/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1038/s41598-025-30034-0","type":"published","date":"2025-12-03T15:57:13+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":97724091,"identity":"51cd39a3-0b23-4435-9d15-851fa8695aac","added_by":"auto","created_at":"2025-12-08 16:11:47","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1386502,"visible":true,"origin":"","legend":"","description":"","filename":"JOURNAL2.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7422488/v1_covered_711f892b-38ad-46f5-9764-e1ef02c78852.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Modified Mann-Kendall with Higher-Order Statistics for Trend Analysis","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":"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":"Mann-Kendall, Trend analysis, Rainfall, Nonlinearity","lastPublishedDoi":"10.21203/rs.3.rs-7422488/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-7422488/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"Trend analysis of rainfall events is crucial, especially in understanding changes in precipitation patterns over time, which can have significant implications for climate adaptation planning. 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The case study shows increasing trends for rainfall in the Northeast Monsoon (NEM) and decreasing trends in the Southwest Monsoon (SWM). 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