Forecasting Hydrological Time-Series with Uncertainty: An N-BEATS Approach for Low-Cost Sensor Data

Forecasting Hydrological Time-Series with Uncertainty: An N-BEATS Approach for Low-Cost Sensor Data | 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 Forecasting Hydrological Time-Series with Uncertainty: An N-BEATS Approach for Low-Cost Sensor Data Mohammadreza Masoudimoghaddam This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7285365/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract Effective water resource management and flood prediction represent critical global challenges, frequently hampered by the prohibitive cost and sparse deployment of traditional hydrological monitoring systems. To address this persistent data gap, this study proposes and validates a comprehensive, complete system that synergizes a custom-developed low-cost ultrasonic sensor with an Advanced deep learning architecture for high-accuracy, multi-horizon river water level forecasting. This work leverages a deep N-BEATS (Neural Basis Expansion Analysis for Time Series Forecasting) model, trained on high-frequency (15-minute) sensor data, to predict water levels at 1-hour and 6-hour future horizons. The model's robustness is rigorously benchmarked against two other powerful architectures: a modern Temporal Convolutional Network (TCN) and a classic Long Short-Term Memory (LSTM) network. Crucially, its predictive uncertainty is quantified using the Monte Carlo (MC) Dropout technique, transforming single-point predictions into reliable probabilistic forecasts. The optimally tuned N-BEATS model exhibited outstanding performance, achieving a coefficient of determination (R2) of 0.82 on the test set for 15-minute ahead forecasts, significantly outperforming both the TCN (R2 = 0.72) and the LSTM (R2 = 0.66). Furthermore, the uncertainty analysis successfully captured the model's confidence, with prediction intervals dynamically widening during periods of high hydrological volatility, thereby adding a crucial layer of reliability to the forecasts. Ultimately, this study demonstrates that the integration of affordable sensing technology with advanced, uncertainty-aware, and interpretable deep learning provides a viable and scalable path toward more resilient and democratized water management. Hydrological Forecasting Deep Learning N-BEATS Low-Cost Sensor Uncertainty Quantification Full Text Cite Share Download PDF Status: Posted 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. 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-7285365","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":510663597,"identity":"e67db1e4-2ffe-47bd-8c1b-2ab311a3a78d","order_by":0,"name":"Mohammadreza Masoudimoghaddam","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAABDUlEQVRIiWNgGAWjYBADxjYgwQxEjA0MzAeYoYINxGphSyBOSwNCC48BMz6lug3ciR9/VByW7RM7fPh1QY21bP+0M58/F7YxyPM3MLd9wKLF7ADvZmmeM4eN26TT0qxnHEs3nnE7d5v0zDYGwxkHGJtnYNeyQZqx7XBim3SOmTEP2+HEBqAWZt42BsYNDIzN2BwGsuXnT7iWf4cT59/OefwZqMUej5ZtErwQLcaPQYwNt3MYpIFaEvFpseY5kw72CzNvX7rxxttpZtIzzkkkzziM22E3f1RYy86fnXz4M883a9l5t5Mffy4os7Htb29/jDWU5R/AmWwSSOIS4GgiBJixxcIoGAWjYBSMAgYAIX9mgd6VzjEAAAAASUVORK5CYII=","orcid":"","institution":"Shahid Beheshti University","correspondingAuthor":true,"prefix":"","firstName":"Mohammadreza","middleName":"","lastName":"Masoudimoghaddam","suffix":""}],"badges":[],"createdAt":"2025-08-03 20:40:19","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-7285365/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-7285365/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":104780311,"identity":"c0dc0597-38cc-4207-b9f1-1bd11da43bed","added_by":"auto","created_at":"2026-03-17 07:52:15","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":907218,"visible":true,"origin":"","legend":"","description":"","filename":"NewLowcost.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7285365/v1_covered_c195f478-2e40-406c-ab83-f35dc97052b5.pdf"}],"financialInterests":"","formattedTitle":"Forecasting Hydrological Time-Series with Uncertainty: An N-BEATS Approach for Low-Cost Sensor Data","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"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":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"Hydrological Forecasting, Deep Learning, N-BEATS, Low-Cost Sensor, Uncertainty Quantification","lastPublishedDoi":"10.21203/rs.3.rs-7285365/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-7285365/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eEffective water resource management and flood prediction represent critical global challenges, frequently hampered by the prohibitive cost and sparse deployment of traditional hydrological monitoring systems. To address this persistent data gap, this study proposes and validates a comprehensive, complete system that synergizes a custom-developed low-cost ultrasonic sensor with an Advanced deep learning architecture for high-accuracy, multi-horizon river water level forecasting. This work leverages a deep N-BEATS (Neural Basis Expansion Analysis for Time Series Forecasting) model, trained on high-frequency (15-minute) sensor data, to predict water levels at 1-hour and 6-hour future horizons. The model's robustness is rigorously benchmarked against two other powerful architectures: a modern Temporal Convolutional Network (TCN) and a classic Long Short-Term Memory (LSTM) network. Crucially, its predictive uncertainty is quantified using the Monte Carlo (MC) Dropout technique, transforming single-point predictions into reliable probabilistic forecasts. The optimally tuned N-BEATS model exhibited outstanding performance, achieving a coefficient of determination (R2) of 0.82 on the test set for 15-minute ahead forecasts, significantly outperforming both the TCN (R2\u0026thinsp;=\u0026thinsp;0.72) and the LSTM (R2\u0026thinsp;=\u0026thinsp;0.66). Furthermore, the uncertainty analysis successfully captured the model's confidence, with prediction intervals dynamically widening during periods of high hydrological volatility, thereby adding a crucial layer of reliability to the forecasts. Ultimately, this study demonstrates that the integration of affordable sensing technology with advanced, uncertainty-aware, and interpretable deep learning provides a viable and scalable path toward more resilient and democratized water management.\u003c/p\u003e","manuscriptTitle":"Forecasting Hydrological Time-Series with Uncertainty: An N-BEATS Approach for Low-Cost Sensor Data","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-09-11 17:57:34","doi":"10.21203/rs.3.rs-7285365/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"d7334b1b-5f77-4835-88b7-b35ffcfbf1ec","owner":[],"postedDate":"September 11th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2026-03-11T14:53:03+00:00","versionOfRecord":[],"versionCreatedAt":"2025-09-11 17:57:34","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-7285365","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-7285365","identity":"rs-7285365","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}