{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,25]],"date-time":"2026-02-25T13:21:41Z","timestamp":1772025701776,"version":"3.50.1"},"reference-count":30,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2020,10,1]],"date-time":"2020-10-01T00:00:00Z","timestamp":1601510400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["JMSE"],"abstract":"<jats:p>When waves propagate in coastal areas at depths lower than one half the wavelength, they exhibit a different signature at the sea surface and the observed wavelength pattern enables inferring bathymetries. Commonly, a spectral analysis using the fast Fourier transform (FFT) is employed to derive wavelength and wave direction of swell waves, in nearshore regions. Nevertheless, it is recognized that this method presents limitations, particularly regarding depth inversion limits that do not allow obtaining bathymetric data close to the shoreline. This work explores a wavelet spectral analysis to obtain bathymetric data. This new imaging methodology is applied over different seafloors with 2D and 3D features such as longshore bars or headlands. The synthetic images of the water surface are generated from a numerical Boussinesq-type model that simulates the propagation of both regular and irregular waves. The spectral analysis is carried to estimate the water depths, which are validated with the model\u2019s bathymetry. Wavelet image processing methodology shows very positive results, revealing the capabilities of this new methodology to map shallow marine environments.<\/jats:p>","DOI":"10.3390\/jmse8100772","type":"journal-article","created":{"date-parts":[[2020,10,1]],"date-time":"2020-10-01T11:28:57Z","timestamp":1601551737000},"page":"772","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":15,"title":["Estimation of Coastal Bathymetry Using Wavelets"],"prefix":"10.3390","volume":"8","author":[{"given":"Diogo","family":"Santos","sequence":"first","affiliation":[{"name":"Departamento de Geoci\u00eancias, Universidade de Aveiro, Campus de Santiago, 3810-193 Aveiro, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3438-3479","authenticated-orcid":false,"given":"Tiago","family":"Abreu","sequence":"additional","affiliation":[{"name":"Centro de Estudos do Ambiente e do Mar CESAM, Universidade de Aveiro, Campus de Santiago, 3810-193 Aveiro, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7305-5403","authenticated-orcid":false,"given":"Paulo A.","family":"Silva","sequence":"additional","affiliation":[{"name":"Centro de Estudos do Ambiente e do Mar CESAM, Universidade de Aveiro, Campus de Santiago, 3810-193 Aveiro, Portugal"},{"name":"Departamento de F\u00edsica, Universidade de Aveiro, Campus de Santiago, 3810-193 Aveiro, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6718-9528","authenticated-orcid":false,"given":"Paulo","family":"Baptista","sequence":"additional","affiliation":[{"name":"Departamento de Geoci\u00eancias, Universidade de Aveiro, Campus de Santiago, 3810-193 Aveiro, Portugal"},{"name":"Centro de Estudos do Ambiente e do Mar CESAM, Universidade de Aveiro, Campus de Santiago, 3810-193 Aveiro, Portugal"}]}],"member":"1968","published-online":{"date-parts":[[2020,10,1]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"147","DOI":"10.4236\/ars.2015.42013","article-title":"A Synoptic Review on Deriving Bathymetry Information Using Remote Sensing Technologies: Models, Methods and Comparisons","volume":"4","author":"Jawak","year":"2015","journal-title":"Adv. Remote Sens."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Bergsma, E.W.J., Almar, R., and Maisongrande, P. (2019). Radon-Augmented Sentinel-2 Satellite Imagery to Derive Wave-Patterns and Regional Bathymetry. Remote Sens., 11.","DOI":"10.3390\/rs11161918"},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Botha, E., Brando, V., Dekker, A., Botha, E.J., Brando, V.E., and Dekker, A.G. (2016). Effects of Per-Pixel Variability on Uncertainties in Bathymetric Retrievals from High-Resolution Satellite Images. Remote Sens., 8.","DOI":"10.3390\/rs8060459"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"397","DOI":"10.5194\/adgeo-45-397-2019","article-title":"Bathymetric Maps from Multi-Temporal Analysis of Sentinel-2 Data: The Case Study of Limassol, Cyprus","volume":"45","author":"Evagorou","year":"2019","journal-title":"Adv. Geosci."},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Sagawa, T., Yamashita, Y., Okumura, T., Yamanokuchi, T., Sagawa, T., Yamashita, Y., Okumura, T., and Yamanokuchi, T. (2019). Satellite Derived Bathymetry Using Machine Learning and Multi-Temporal Satellite Images. Remote Sens., 11.","DOI":"10.3390\/rs11101155"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"111263","DOI":"10.1016\/j.rse.2019.111263","article-title":"Wave-Derived Coastal Bathymetry from Satellite Video Imagery: A Showcase with Pleiades Persistent Mode","volume":"231","author":"Almar","year":"2019","journal-title":"Remote Sens. Environ."},{"key":"ref_7","unstructured":"Young, I.R. (1999). Wind Generated Ocean Waves, Elsevier Ocean Engineering Book Series. [1st ed.]."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"199","DOI":"10.1016\/j.coastaleng.2018.04.025","article-title":"Video-based depth inversion techniques, a method comparison with synthetic cases","volume":"138","author":"Bergsma","year":"2018","journal-title":"Coast. Eng."},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Salameh, E., Frappart, F., Almar, R., Baptista, P., Heygster, G., Lubac, B., Raucoules, D., Almeida, L.P., Bergsma, E.W.J., and Capo, S. (2019). Monitoring Beach Topography and Nearshore Bathymetry Using Spaceborne Remote Sensing: A Review. Remote Sens., 11.","DOI":"10.3390\/rs11192212"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"4527","DOI":"10.1080\/01431161.2010.489063","article-title":"Underwater bottom topography in coastal areas from Terra SAR-X data","volume":"32","author":"Brusch","year":"2011","journal-title":"Int. J. Remote Sens."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"671","DOI":"10.1109\/LGRS.2013.2274475","article-title":"Estimation of coastal bathymetry using RISAT 1 C-band microwave SAR data","volume":"11","author":"Mishra","year":"2014","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"166","DOI":"10.1016\/j.rse.2019.01.003","article-title":"Estimation of the Nearshore Bathymetry from High Temporal Resolution Sentinel-1A C-Band SAR Data\u2014A Case Study","volume":"223","author":"Pereira","year":"2019","journal-title":"Remote Sens. Environ."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"1061","DOI":"10.1016\/S1474-6670(17)54869-7","article-title":"Wavelet Transformations in Signal Detection","volume":"21","author":"Tuteur","year":"1988","journal-title":"IFAC Proc."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"228","DOI":"10.1016\/j.apor.2015.09.008","article-title":"Development of wavelet network model for accurate water levels prediction with meteorological effects","volume":"53","year":"2015","journal-title":"Appl. Ocean Res."},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"El-Diasty, M. (2019). Satellite-Based Bathymetric Modeling Using a Wavelet Network Model. ISPRS Int. J. Geo. Inf., 8.","DOI":"10.3390\/ijgi8090405"},{"key":"ref_16","first-page":"144","article-title":"Surf hydrodynamics in front of collapsing coastal dunes","volume":"1","author":"Sancho","year":"2011","journal-title":"J. Coast. Res."},{"key":"ref_17","unstructured":"Fernandes, F., Malheiro, A., and Chamin\u00e9, H. (2020). Analysis of Nonlinear Wave Parameters on Ofir Sandy Beach (NW Portugal). Advances in Natural Hazards and Hydrological Risks: Meeting the Challenge, Springer."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"102","DOI":"10.1016\/j.rse.2014.12.004","article-title":"Retrieval of nearshore bathymetry from Landsat 8 images: A tool for coastal monitoring in shallow waters","volume":"159","author":"Pacheco","year":"2015","journal-title":"Remote Sens. Environ."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"71","DOI":"10.1177\/1759313116679672","article-title":"Estimation of bathymetry along the coast of Mangaluru using Landsat-8 imagery","volume":"8","author":"Pushparaj","year":"2017","journal-title":"Int. J. Ocean Clim. Syst."},{"key":"ref_20","unstructured":"Abreu, T., Matos, J., Pereira, P., Cunha, T.R., Baptista, P., and Silva, P.A. (2017, January 3\u20136). Acquisition of Bathymetric Data from Satellite Images. Proceedings of the 8th SCACR\u2014International Short Course\/Conference on Applied Coastal Research, Santander, Spain."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"2099","DOI":"10.1007\/s10236-011-0460-1","article-title":"Synergy and Fusion of Optical and Synthetic Aperture Radar Satellite Data for Underwater Topography Estimation in Coastal Areas","volume":"61","author":"Pleskachevsky","year":"2011","journal-title":"Ocean Dyn."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"7337","DOI":"10.1080\/01431161.2012.685975","article-title":"High-resolution satellite measurements of coastal wind field and sea state","volume":"33","author":"Lehner","year":"2012","journal-title":"Int. J. Remote Sens."},{"key":"ref_23","unstructured":"Wiehle, S., and Pleskachevsky, A. (2018, January 4\u20137). Bathymetry Derived from Sentinel-1 Synthetic Aperture Radar Data. Proceedings of the 12th European Conference on Synthetic Aperture Radar Electronic, Aachen, Germany."},{"key":"ref_24","first-page":"61","article-title":"Wavelet transform applications in instrumentation and measurement: Tutorial and literature survey","volume":"11","year":"2004","journal-title":"Metrol. Meas. Syst."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"101","DOI":"10.1023\/A:1013847512432","article-title":"Construction of a Morlet Wavelet Power Spectrum","volume":"13","author":"Shyu","year":"2002","journal-title":"Multidimens. Syst. Signal Process."},{"key":"ref_26","unstructured":"Kirby, J.T., Wei, G., Chen, Q., Kennedy, A.B., and Dalrymple, R.A. (1998). FUNWAVE 1.0, Fully Nonlinear Boussinesq Wave Model, Documentation and User\u2019s Manual, ReportCACR98-06, Center for Applied Coastal Research, Department of Civil and Environmental Engineering, University of Delaware."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"36","DOI":"10.1016\/j.ocemod.2011.12.004","article-title":"A high-order adaptive time-stepping TVD solver for Boussinesq modeling of breaking waves and coastal inundation","volume":"43\u201344","author":"Shi","year":"2012","journal-title":"Ocean Model."},{"key":"ref_28","first-page":"425","article-title":"Wavelet Methods for the Numerical Solution of Boundary Value Problems on the Interval","volume":"5","author":"Bertoluzza","year":"1994","journal-title":"Wavelet Anal. Appl."},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"Ge, H., Liu, H., and Zhang, L. (2020). Accurate Depth Inversion Method for Coastal Bathymetry: Introduction of Water Wave High-Order Dispersion Relation. J. Mar. Sci. Eng., 8.","DOI":"10.3390\/jmse8030153"},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Flampouris, S., Seeman, J., and Ziemer, F. (2009, January 11\u201314). Sharing our Experience Using Wave Theories Inversion for the Determination of the Local Depth. Proceedings of the OCEANS 2009-EUROPE Conference, Bremen, Germany.","DOI":"10.1109\/OCEANSE.2009.5278331"}],"container-title":["Journal of Marine Science and Engineering"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2077-1312\/8\/10\/772\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T10:15:52Z","timestamp":1760177752000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2077-1312\/8\/10\/772"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,10,1]]},"references-count":30,"journal-issue":{"issue":"10","published-online":{"date-parts":[[2020,10]]}},"alternative-id":["jmse8100772"],"URL":"https:\/\/doi.org\/10.3390\/jmse8100772","relation":{},"ISSN":["2077-1312"],"issn-type":[{"value":"2077-1312","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,10,1]]}}}