A simple method to reconstruct coastal surface currents from single SAR Doppler observations using the continuity equation

A simple method to reconstruct coastal surface currents from single SAR Doppler observations using the continuity equation | 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 simple method to reconstruct coastal surface currents from single SAR Doppler observations using the continuity equation Anis Elyouncha, Göran Broström, Kai H. Christensen This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8620014/v1 This work is licensed under a CC BY 4.0 License Status: Under Revision Version 1 posted 7 You are reading this latest preprint version Abstract Doppler-derived surface currents from Synthetic Aperture Radar (SAR) provide only a single velocity component, the radial (range-directed) velocity $u_r$, which limits their direct use in oceanographic applications. Here we present a simple and physically constrained method to reconstruct the orthogonal azimuthal velocity component $v_{\varphi}$, yielding a two-dimensional estimate of the surface current field. The approach exploits the horizontal continuity equation together with solid boundary constraints, making it well suited for coastal and semi-enclosed regions. The method is applied to Sentinel-1 Doppler observations over the Skagerrak Sea and evaluated against two high-resolution ocean circulation models, Norkyst-800 and the data-assimilative Norkyst-DA. Despite relying on a single, noisy Doppler-derived velocity component, the reconstruction recovers coherent and dynamically consistent circulation patterns. Comparisons with the model fields yield correlation coefficients of about 0.9 for the observed radial component and 0.7--0.75 for the reconstructed azimuthal component, with root-mean-square errors on the order of 0.2 m s$^{-1}$. The azimuthal velocity exhibits larger biases than the radial component, consistent with the predominantly ageostrophic nature of the transverse circulation in the Skagerrak and its sensitivity to wind forcing and model formulation. The reduced bias relative to the data-assimilative model, together with consistency with inter-model differences, indicates that SAR observations can be used to diagnose model biases not only in the directly observed radial component $u_r$ but also in the reconstructed azimuthal component $v_{\varphi}$. These results demonstrate that single-look SAR Doppler measurements contain sufficient dynamical information to recover two-dimensional surface current structure when combined with physically based constraints, providing a valuable observational resource for coastal circulation studies and model evaluation. SAR Doppler surface currents continuity equation coastal circulation Norwegian Coastal Current Skagerrak Sea Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Under Revision Version 1 posted Editorial decision: Revision requested 15 Apr, 2026 Reviews received at journal 02 Mar, 2026 Reviewers agreed at journal 02 Feb, 2026 Reviewers invited by journal 28 Jan, 2026 Editor assigned by journal 22 Jan, 2026 Submission checks completed at journal 22 Jan, 2026 First submitted to journal 16 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-8620014","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":582342504,"identity":"f8ee3f45-ef8e-44d0-9289-f092e2878ac8","order_by":0,"name":"Anis Elyouncha","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA6klEQVRIiWNgGAWjYFACxgYgYQFmMjMw2BCtRQKmJY1oq+BaDhNWyz+7ufkDQ4VEYr9E7sHPBTXn7TYcYH/4AK/xdw62STCckUicOSMvWXrGsdvJGw7wGBvgteZGYhsDY5tE4oYbOWbMPGy3kw0O8LBJ4NMhfyOx+QPjP5iWf+eAWtif/8CnxeBGYoMEYwNUC2/bATuDAwxmeN1lCHSYRMIxCeOZPW+MpXn7khMkD/MY43WY3I30xx8+1NjI9rPnGH7m+WZnz3e8/eEHvNaAQAIDg2MDlJ3YwExQPQTYYzBGwSgYBaNgFMAAAIEZSfy5eXLPAAAAAElFTkSuQmCC","orcid":"","institution":"University of Gothenburg","correspondingAuthor":true,"prefix":"","firstName":"Anis","middleName":"","lastName":"Elyouncha","suffix":""},{"id":582342505,"identity":"3e8dd11c-320d-4c4d-b016-54872815ba2d","order_by":1,"name":"Göran Broström","email":"","orcid":"","institution":"University of Gothenburg","correspondingAuthor":false,"prefix":"","firstName":"Göran","middleName":"","lastName":"Broström","suffix":""},{"id":582342506,"identity":"fc792e5f-d35f-475a-bbdb-b84d8cd2cde1","order_by":2,"name":"Kai H. 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Here we present a simple and physically constrained method to reconstruct the orthogonal azimuthal velocity component $v_{\\varphi}$, yielding a two-dimensional estimate of the surface current field. The approach exploits the horizontal continuity equation together with solid boundary constraints, making it well suited for coastal and semi-enclosed regions. The method is applied to Sentinel-1 Doppler observations over the Skagerrak Sea and evaluated against two high-resolution ocean circulation models, Norkyst-800 and the data-assimilative Norkyst-DA. Despite relying on a single, noisy Doppler-derived velocity component, the reconstruction recovers coherent and dynamically consistent circulation patterns. Comparisons with the model fields yield correlation coefficients of about 0.9 for the observed radial component and 0.7--0.75 for the reconstructed azimuthal component, with root-mean-square errors on the order of 0.2~m~s$^{-1}$. The azimuthal velocity exhibits larger biases than the radial component, consistent with the predominantly ageostrophic nature of the transverse circulation in the Skagerrak and its sensitivity to wind forcing and model formulation. The reduced bias relative to the data-assimilative model, together with consistency with inter-model differences, indicates that SAR observations can be used to diagnose model biases not only in the directly observed radial component $u_r$ but also in the reconstructed azimuthal component $v_{\\varphi}$. 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