{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,31]],"date-time":"2026-01-31T11:51:43Z","timestamp":1769860303212,"version":"3.49.0"},"reference-count":58,"publisher":"MDPI AG","issue":"19","license":[{"start":{"date-parts":[[2021,9,29]],"date-time":"2021-09-29T00:00:00Z","timestamp":1632873600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100000270","name":"Natural Environment Research Council","doi-asserted-by":"publisher","award":["NE\/J004219\/1"],"award-info":[{"award-number":["NE\/J004219\/1"]}],"id":[{"id":"10.13039\/501100000270","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100008530","name":"European Regional Development Fund","doi-asserted-by":"publisher","award":["Marine-i 2"],"award-info":[{"award-number":["Marine-i 2"]}],"id":[{"id":"10.13039\/501100008530","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Remote Sensing"],"abstract":"<jats:p>An extensive record of current velocities at all levels in the water column is an indispensable requirement for a tidal resource assessment and is fully necessary for accurate determination of available energy throughout the water column as well as estimating likely energy capture for any particular device. Traditional tidal prediction using the least squares method requires a large number of harmonic parameters calculated from lengthy acoustic Doppler current profiler (ADCP) measurements, while long-term in situ ADCPs have the advantage of measuring the real current but are logistically expensive. This study aims to show how these issues can be overcome with the use of a neural network to predict current velocities throughout the water column, using surface currents measured by a high-frequency radar. Various structured neural networks were trained with the aim of finding the network which could best simulate unseen subsurface current velocities, compared to ADCP data. This study shows that a recurrent neural network, trained by the Bayesian regularisation algorithm, produces current velocities highly correlated with measured values: r2 (0.98), mean absolute error (0.05 ms\u22121), and the Nash\u2013Sutcliffe efficiency (0.98). The method demonstrates its high prediction ability using only 2 weeks of training data to predict subsurface currents up to 6 months in the future, whilst a constant surface current input is available. The resulting current predictions can be used to calculate flow power, with only a 0.4% mean error. The method is shown to be as accurate as harmonic analysis whilst requiring comparatively few input data and outperforms harmonics by identifying non-celestial influences; however, the model remains site specific.<\/jats:p>","DOI":"10.3390\/rs13193896","type":"journal-article","created":{"date-parts":[[2021,10,8]],"date-time":"2021-10-08T21:26:20Z","timestamp":1633728380000},"page":"3896","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":10,"title":["Using Artificial Neural Networks for the Estimation of Subsurface Tidal Currents from High-Frequency Radar Surface Current Measurements"],"prefix":"10.3390","volume":"13","author":[{"given":"Max C.","family":"Bradbury","sequence":"first","affiliation":[{"name":"Coastal Processes Research Group, School of Biological and Marine Sciences, Faculty of Science and Engineering, University of Plymouth, Plymouth, PL4 8AA, UK"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6822-5386","authenticated-orcid":false,"given":"Daniel C.","family":"Conley","sequence":"additional","affiliation":[{"name":"Coastal Processes Research Group, School of Biological and Marine Sciences, Faculty of Science and Engineering, University of Plymouth, Plymouth, PL4 8AA, UK"}]}],"member":"1968","published-online":{"date-parts":[[2021,9,29]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"227","DOI":"10.1007\/s40722-016-0044-8","article-title":"Current tidal power technologies and their suitability for applications in coastal and marine areas","volume":"2","author":"Roberts","year":"2016","journal-title":"J. Ocean Eng. Mar. Energy"},{"key":"ref_2","unstructured":"EMEC (2009). Assessment of Tidal Energy Resource. Marine Renewable Energy Guides, BSI. Assessment of Tidal Energy Resource."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"363","DOI":"10.1109\/JOE.2012.2191656","article-title":"Measurements of Turbulence at Two Tidal Energy Sites in Puget Sound, WA","volume":"37","author":"Thomson","year":"2012","journal-title":"J. Ocean. Eng."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"14","DOI":"10.1016\/j.renene.2013.06.036","article-title":"Marine current energy resource assessment and design of a marine current turbine for Fiji","volume":"65","author":"Goundar","year":"2014","journal-title":"Renew. Energy"},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Gooch, S., Thomson, J., Polagye, B., and Meggitt, D. (2009, January 26\u201329). Site Characterization of Tidal Power. Proceedings of the Oceans 2009, Biloxi, MS, USA.","DOI":"10.23919\/OCEANS.2009.5422134"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"96","DOI":"10.1175\/JTECH-D-11-00223.1","article-title":"Current Patterns in the Inner Sound (Pentland Firth) from Underway ADCP Data","volume":"30","author":"Woolf","year":"2013","journal-title":"J. Atmos. Ocean. Technol."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"337","DOI":"10.1016\/j.renene.2014.01.052","article-title":"The role of tidal asymmetry in characterizing the tidal energy resource of Orkney","volume":"68","author":"Neill","year":"2014","journal-title":"Renew. Energy"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"3206","DOI":"10.1016\/j.rser.2010.07.039","article-title":"Tidal current energy resource assessment in Ireland: Current status and future update","volume":"14","author":"Boyle","year":"2010","journal-title":"Renew. Sustain. Energy Rev."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"137","DOI":"10.1016\/j.renene.2012.01.046","article-title":"Tidal current power for Indonesia? An initial resource estimation for the Alas Strait","volume":"49","author":"Blunden","year":"2013","journal-title":"Renew. Energy"},{"key":"ref_10","first-page":"20190498","article-title":"Numerical modelling of hydrodynamics and tidal energy extraction in the Alderney Race: A review","volume":"378","author":"Coles","year":"2020","journal-title":"Philos. Trans. R. Soc. A Math. Phys. Eng. Sci."},{"key":"ref_11","first-page":"305","article-title":"The harmonic development of the tide-generating potential","volume":"100","author":"Doodson","year":"1921","journal-title":"Proc. R. Soc. Lond. Ser. A Math. Phys. Sci."},{"key":"ref_12","unstructured":"Godin, G. (1972). The Analysis of the Tides, University of Toronto Press. (No. 551.4708 G6)."},{"key":"ref_13","unstructured":"NOAA (2021, July 13). About Harmonic Analysis, Available online: https:\/\/tidesandcurrents.noaa.gov\/about_harmonic_constituents.html."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"18737","DOI":"10.1029\/97JC00049","article-title":"On the accuracy of HF radar surface current measurements: Intercomparisons with ship-based sensors","volume":"102","author":"Chapman","year":"1997","journal-title":"J. Geophys. Res. Space Phys."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s12040-021-01553-x","article-title":"Assessment of NEMO simulated surface current with HF radar along Andhra Pradesh coast","volume":"130","author":"Momin","year":"2021","journal-title":"J. Earth Syst. Sci."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"245","DOI":"10.1175\/JTECH-D-15-0159.1","article-title":"Calibration, Validation, and Analysis of an Empirical Algorithm for the Retrieval of Wave Spectra from HF Radar Sea Echo","volume":"33","author":"Lopez","year":"2016","journal-title":"J. Atmos. Ocean. Technol."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"36","DOI":"10.5670\/oceanog.1997.18","article-title":"Introduction to High-Frequency Radar: Reality and Myth","volume":"10","author":"Paduan","year":"1997","journal-title":"Oceanography"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"17","DOI":"10.1016\/j.egypro.2015.07.835","article-title":"Estimation of Tidal Stream Potential in the Iroise Sea from Velocity Observations by High Frequency Radars","volume":"76","author":"Sentchev","year":"2015","journal-title":"Energy Procedia"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"262","DOI":"10.1016\/j.ijome.2016.08.004","article-title":"Tidal stream resource assessment in the Dover Strait (eastern English Channel)","volume":"16","author":"Sentchev","year":"2016","journal-title":"Int. J. Mar. Energy"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"266","DOI":"10.1061\/(ASCE)0887-3801(1995)9:4(266)","article-title":"Prediction of Estuarine Instabilities with Artificial Neural Networks","volume":"9","author":"Grubert","year":"1995","journal-title":"J. Comput. Civ. Eng."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"553","DOI":"10.1007\/s11600-020-00419-y","article-title":"Simulating Caspian Sea surface water level by artificial neural network and support vector machine models","volume":"68","author":"Khaledian","year":"2020","journal-title":"Acta Geophys."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"54","DOI":"10.1061\/(ASCE)0733-950X(2001)127:1(54)","article-title":"Back-Propagation Neural Network in Tidal-Level Forecasting","volume":"127","author":"Kumar","year":"2001","journal-title":"J. Waterw. Port Coastal Ocean Eng."},{"key":"ref_23","unstructured":"Mandal, S. (2001, January 11\u201314). Predictions of tides using back propagation neural networks. Proceedings of the International Conference in Ocean Engineering, Chennai, India."},{"key":"ref_24","first-page":"54","article-title":"Prediction of Daily Tidal Levels along the central coast of Eastern Red Sea using Artificial Neural Networks","volume":"19","author":"Elbisy","year":"2020","journal-title":"Int. J. GEOMATE"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"764","DOI":"10.2112\/05-0492.1","article-title":"A Combined Harmonic Analysis\u2013Artificial Neural Network Methodology for Tidal Predictions","volume":"233","author":"Lee","year":"2007","journal-title":"J. Coast. Res."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"607","DOI":"10.1016\/j.proeng.2015.08.332","article-title":"Tidal Level Forecasting Using ANN","volume":"116","author":"Meena","year":"2015","journal-title":"Procedia Eng."},{"key":"ref_27","unstructured":"Salehinejad, H., Sankar, S., Barfett, J., Colak, E., and Valaee, S. (2018). Recent Advances in Recurrent Neural Network. arXiv."},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Boussaada, Z., Curea, O., Remaci, A., Camblong, H., and Bellaaj, N.M. (2018). A Nonlinear Autoregressive Exogenous (NARX) Neural Network Model for the Prediction of the Daily Direct Solar Radiation. Energies, 11.","DOI":"10.3390\/en11030620"},{"key":"ref_29","unstructured":"YR (2018, August 26). YR Tidal Current Model. Available online: https:\/\/www.yr.no\/kart\/."},{"key":"ref_30","unstructured":"Gurgel, K.W., and Schlick, T. (2007, January 5\u20137). Compatibility of FMCW modulated HF surface wave radars with radio services. Proceedings of the International Radar Symposium (IRS 2007), IRS-DGON, Cologne, Germany."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"1556","DOI":"10.1175\/1520-0426(1999)016<1556:UABAIA>2.0.CO;2","article-title":"Using a broadband ADCP in a tidal channel. Part I: Meanflow and shear","volume":"16","author":"Lu","year":"1999","journal-title":"J. Atmos. Ocean. Tech."},{"key":"ref_32","unstructured":"NOAA (2001). Towing Basin Speed Verification of Acoustic Doppler Current Profiling Instruments, NOAA Technical Report NOS CO-OPS 033."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"427","DOI":"10.1109\/72.750573","article-title":"A method to determine the required number of neural-network training repetitions","volume":"10","author":"Iyer","year":"1999","journal-title":"IEEE Trans. Neural Netw."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"282","DOI":"10.1016\/0022-1694(70)90255-6","article-title":"River flow forecasting through conceptual models part I\u2014A discussion of principles","volume":"10","author":"Nash","year":"1970","journal-title":"J. Hydrol."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"885","DOI":"10.13031\/2013.23153","article-title":"Model Evaluation Guidelines for Systematic Quantification of Accuracy in Watershed Simulations","volume":"50","author":"Moriasi","year":"2007","journal-title":"Trans. ASABE"},{"key":"ref_36","doi-asserted-by":"crossref","unstructured":"Ampazis, N., and Perantonis, S.J. (2000, January 24\u201327). Levenberg-Marquardt algorithm with adaptive momentum for the efficient training of feedforward networks. Proceedings of the IEEE & INNS International Joint Conference on Neural Networks (IJCNN), Como, Italy. Paper no. NN0401.","DOI":"10.1109\/IJCNN.2000.857825"},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"101","DOI":"10.1016\/j.compag.2007.01.005","article-title":"Optimization of an artificial neural network for thermal\/pressure food processing: Evaluation of training algorithms","volume":"56","author":"Torrecilla","year":"2007","journal-title":"Comput. Electron. Agric."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"1158","DOI":"10.1016\/j.renene.2008.07.007","article-title":"Daily means ambient temperature prediction using artificial neural network method: A case study of Turkey","volume":"34","year":"2009","journal-title":"Renew. Energy"},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"211","DOI":"10.1016\/j.rcim.2007.11.004","article-title":"The experimental investigation of the effects of uncoated, PVD- and CVD-coated cemented carbide inserts and cutting parameters on surface roughness in CNC turning and its prediction using artificial neural networks","volume":"25","author":"Nalbant","year":"2009","journal-title":"Robot. Comput. Manuf."},{"key":"ref_40","unstructured":"NOC (National Oceanography Centre) An Introduction to Tidal Numerical Modelling, NOC. Nation Oceanography Centre Marine Data Products."},{"key":"ref_41","unstructured":"Bontempi, G. (2008, January 17\u201319). Long term time series prediction with multi-input multi-output local learning. Proceedings of the 2nd European Symposium of Time Series Prediction, Porvoo, Finland."},{"key":"ref_42","unstructured":"Howard, D., and Beale, M. (1998). Neural Networks Toolbox: For use with Matlab, Mathworks Inc.. User\u2019s Guide, Version 3."},{"key":"ref_43","unstructured":"Hagen, M.T., Demuth, H.B., Beale, M., and De Jesus, O. (2002). Neural Network Design, Thomson Learning."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"431","DOI":"10.1137\/0111030","article-title":"An Algorithm for Least-Squares Estimation of Nonlinear Parameters","volume":"11","author":"Marquardt","year":"1963","journal-title":"J. Soc. Ind. Appl. Math."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"23","DOI":"10.1007\/978-1-60327-101-1_3","article-title":"Bayesian Regularization of Neural Networks","volume":"458","author":"Burden","year":"2008","journal-title":"Methods Mol. Biol."},{"key":"ref_46","unstructured":"Met Office (2012). Daily Weather Summary 2012."},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"403","DOI":"10.1016\/j.energy.2015.02.038","article-title":"Resource assessment for future generations of tidal-stream energy arrays","volume":"83","author":"Lewis","year":"2015","journal-title":"Energy"},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"1363","DOI":"10.1016\/j.renene.2017.05.023","article-title":"Tidal stream resource assessment uncertainty due to flow asymmetry and turbine yaw misalignment","volume":"114","author":"Piano","year":"2017","journal-title":"Renew. Energy"},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"133","DOI":"10.1260\/1759-3131.4.2.133","article-title":"Using Artificial Neural Networks to Forecast Monthly and Seasonal Sea Surface Temperature Anomalies in the Western Indian Ocean","volume":"4","author":"Mahongo","year":"2013","journal-title":"Int. J. Ocean Clim. Syst."},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"303","DOI":"10.1177\/003754979105700508","article-title":"Time series forecasting using neural networks vs. Box-Jenkins methodology","volume":"57","author":"Tang","year":"1991","journal-title":"Simulation"},{"key":"ref_51","first-page":"163","article-title":"Sand wave morphology and development in the Outer Bristol Channel (OBel) Sands","volume":"41","author":"James","year":"2008","journal-title":"Mar. Freshw. Behav. Physiol."},{"key":"ref_52","doi-asserted-by":"crossref","first-page":"857","DOI":"10.1016\/j.coastaleng.2006.05.001","article-title":"Multi-point tidal prediction using artificial neural network with tide-generating forces","volume":"53","author":"Chang","year":"2006","journal-title":"Coast. Eng."},{"key":"ref_53","unstructured":"Solomatine, D.P., and Torres, L.A. (1996, January 9\u201313). Neural network approximation of a hydrodynamic modelling in optimizing reservoir operation. Proceedings of the 2nd International Conference on Hydroinformatics, Zurich, Switzerland."},{"key":"ref_54","doi-asserted-by":"crossref","first-page":"247","DOI":"10.1016\/j.asoc.2015.05.044","article-title":"Combining deterministic modelling with artificial neural networks for suspended sediment estimates","volume":"35","author":"Makarynskyy","year":"2015","journal-title":"Appl. Soft Comput."},{"key":"ref_55","doi-asserted-by":"crossref","first-page":"929","DOI":"10.1016\/S0098-3004(02)00013-4","article-title":"Classical tidal harmonic analysis including error estimates in MATLAB using T_TIDE","volume":"28","author":"Pawlowicz","year":"2002","journal-title":"Comput. Geosci."},{"key":"ref_56","doi-asserted-by":"crossref","first-page":"497","DOI":"10.1017\/S0025315400042806","article-title":"Sand transport paths around the British Isles resulting from M2 and M4tidal interactions","volume":"59","author":"Pingree","year":"1979","journal-title":"J. Mar. Biol. Assoc. U. K."},{"key":"ref_57","doi-asserted-by":"crossref","first-page":"2803","DOI":"10.1016\/j.renene.2009.06.015","article-title":"The impact of tidal stream turbines on large-scale sediment dynamics","volume":"34","author":"Neill","year":"2009","journal-title":"Renew. Energy"},{"key":"ref_58","doi-asserted-by":"crossref","first-page":"238","DOI":"10.1016\/j.renene.2020.05.133","article-title":"Asymmetric effects of a modelled tidal turbine on the flow and seabed","volume":"159","author":"Murdoch","year":"2020","journal-title":"Renew. Energy"}],"container-title":["Remote Sensing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2072-4292\/13\/19\/3896\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T07:07:08Z","timestamp":1760166428000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2072-4292\/13\/19\/3896"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,9,29]]},"references-count":58,"journal-issue":{"issue":"19","published-online":{"date-parts":[[2021,10]]}},"alternative-id":["rs13193896"],"URL":"https:\/\/doi.org\/10.3390\/rs13193896","relation":{},"ISSN":["2072-4292"],"issn-type":[{"value":"2072-4292","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,9,29]]}}}