{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T03:24:13Z","timestamp":1760239453133,"version":"build-2065373602"},"reference-count":59,"publisher":"MDPI AG","issue":"22","license":[{"start":{"date-parts":[[2020,11,16]],"date-time":"2020-11-16T00:00:00Z","timestamp":1605484800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100002322","name":"Coordena\u00e7\u00e3o de Aperfei\u00e7oamento de Pessoal de N\u00edvel Superior","doi-asserted-by":"publisher","award":["Financial Code: 001"],"award-info":[{"award-number":["Financial Code: 001"]}],"id":[{"id":"10.13039\/501100002322","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100000844","name":"European Space Agency","doi-asserted-by":"publisher","award":["ESA-MOST Dragon-5 cooperation project ID 57979"],"award-info":[{"award-number":["ESA-MOST Dragon-5 cooperation project ID 57979"]}],"id":[{"id":"10.13039\/501100000844","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>The total energy dissipation rate on the ocean surface, \u03f5t (W m\u22122), provides a first-order estimation of the kinetic energy input rate at the ocean\u2013atmosphere interface. Studies on the spatial and temporal distribution of the energy dissipation rate are important for the improvement of climate and wave models. Traditional oceanographic research normally uses remote measurements (airborne and platforms sensors) and in situ data acquisition to estimate \u03f5t; however, those methods cover small areas over time and are difficult to reproduce especially in the open oceans. Satellite remote sensing has proven the potential to estimate some parameters related to breaking waves on a synoptic scale, including the energy dissipation rate. In this paper, we use polarimetric Synthetic Aperture Radar (SAR) data to estimate \u03f5t under different wind and sea conditions. The used methodology consisted of decomposing the backscatter SAR return in terms of two contributions: a polarized contribution, associated with the fast response of the local wind (Bragg backscattering), and a non-polarized (NP) contribution, associated with wave breaking (Non-Bragg backscattering). Wind and wave parameters were estimated from the NP contribution and used to calculate \u03f5t from a parametric model dependent of these parameters. The results were analyzed using wave model outputs (WAVEWATCH III) and previous measurements documented in the literature. For the prevailing wind seas conditions, the \u03f5t estimated from pol-SAR data showed good agreement with dissipation associated with breaking waves when compared to numerical simulations. Under prevailing swell conditions, the total energy dissipation rate was higher than expected. The methodology adopted proved to be satisfactory to estimate the total energy dissipation rate for light to moderate wind conditions (winds below 10 m s\u22121), an environmental condition for which the current SAR polarimetric methods do not estimate \u03f5t properly.<\/jats:p>","DOI":"10.3390\/s20226540","type":"journal-article","created":{"date-parts":[[2020,11,16]],"date-time":"2020-11-16T21:48:52Z","timestamp":1605563332000},"page":"6540","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":10,"title":["Estimating Energy Dissipation Rate from Breaking Waves Using Polarimetric SAR Images"],"prefix":"10.3390","volume":"20","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7591-7284","authenticated-orcid":false,"given":"Rafael D.","family":"Viana","sequence":"first","affiliation":[{"name":"Earth Observation and Geoinformatics Division, National Institute for Space Research (OTG\/INPE), S\u00e3o Jos\u00e9 dos Campos 12201-970, SP, Brazil"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jo\u00e3o A.","family":"Lorenzzetti","sequence":"additional","affiliation":[{"name":"Earth Observation and Geoinformatics Division, National Institute for Space Research (OTG\/INPE), S\u00e3o Jos\u00e9 dos Campos 12201-970, SP, Brazil"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1225-3457","authenticated-orcid":false,"given":"Jonas T.","family":"Carvalho","sequence":"additional","affiliation":[{"name":"Laboratory of Ocean and Atmosphere Studies (LOA), Earth Observation and Geoinformatics Division, National Institute for Space Research (OTG\/INPE), S\u00e3o Jos\u00e9 dos Campos 12201-970, SP, Brazil"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4567-0377","authenticated-orcid":false,"given":"Ferdinando","family":"Nunziata","sequence":"additional","affiliation":[{"name":"Dipartimento di Ingegneria, Universit\u00e1 degli Studi di Napoli Parthenope, 80143 Napoli, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2020,11,16]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"279","DOI":"10.1146\/annurev.fl.28.010196.001431","article-title":"The role of surface-wave breaking in air-sea interaction","volume":"28","author":"Melville","year":"1996","journal-title":"Annu. Rev. Fluid Mech."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Zappa, C.J., McGillis, W.R., Raymond, P.A., Edson, J.B., Hintsa, E.J., Zemmelink, H.J., Dacey, J.W.H., and Ho, D.T. (2007). Environmental turbulent mixing controls on air-water gas exchange in marine and aquatic systems. Geophys. Res. Lett., 34.","DOI":"10.1029\/2006GL028790"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"3041","DOI":"10.1002\/2016JC012088","article-title":"Parameterizing air-sea gas transfer velocity with dissipation","volume":"122","author":"Esters","year":"2017","journal-title":"J. Geophys. Res."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"2546","DOI":"10.1175\/1520-0485(1994)024<2546:MWETIT>2.0.CO;2","article-title":"Modeling wave-enhanced turbulence in the ocean surface layer","volume":"24","author":"Craig","year":"1994","journal-title":"J. Phys. Oceanogr."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"792","DOI":"10.1175\/1520-0485(1996)026<0792:EOKEDU>2.0.CO;2","article-title":"Estimates of kinetic energy dissipation under breaking waves","volume":"26","author":"Terray","year":"1996","journal-title":"J. Phys. Oceanogr."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"1707","DOI":"10.5194\/os-15-1707-2019","article-title":"The FluxEngine air\u2013sea gas flux toolbox: Simplified interface and extensions for in situ analyses and multiple sparingly soluble gases","volume":"15","author":"Holding","year":"2019","journal-title":"Ocean Sci."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"16815","DOI":"10.1029\/2000JC000496","article-title":"Bubble entrainment by breaking waves and their influence on optical scattering in the upper ocean","volume":"106","author":"Terrill","year":"2001","journal-title":"J. Geophys. Res."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"58","DOI":"10.1038\/417058a","article-title":"Distribution of breaking waves at the ocean surface","volume":"417","author":"Melville","year":"2002","journal-title":"Nature"},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Anguelova, M.D., and Webster, F. (2006). Whitecap coverage from satellite measurements: A first step toward modeling the variability of oceanic whitecaps. J. Geophys. Res., 111.","DOI":"10.1029\/2005JC003158"},{"key":"ref_10","first-page":"1","article-title":"Quantitative expression of the breaking of wind waves on the sea surface","volume":"12","author":"Toba","year":"1973","journal-title":"Rec. Oceanogr. Works Jpn."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"1448","DOI":"10.1175\/1520-0485(1988)018<1448:VOWCWW>2.0.CO;2","article-title":"Variations of whitecap coverage with wind stress and water temperature","volume":"18","author":"Wu","year":"1988","journal-title":"J. Phys. Oceanogr."},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Hwang, P.A., and Sletten, M.A. (2008). Energy dissipation of wind-generated waves and whitecap coverage. J. Geophys. Res., 113.","DOI":"10.1029\/2007JC004277"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"107","DOI":"10.1007\/BF00232479","article-title":"On the spectral dissipation of ocean waves due to white capping","volume":"6","author":"Hasselmann","year":"1974","journal-title":"Bound.-Layer Meteorol."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"505","DOI":"10.1017\/S0022112085002221","article-title":"Spectral and statistical properties of the equilibrium range in wind-generated gravity waves","volume":"156","author":"Phillips","year":"1985","journal-title":"J. Fluid Mech."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"2497","DOI":"10.1175\/1520-0485(1996)026<2497:STIATG>2.0.CO;2","article-title":"Source terms in a third-generation wind wave model","volume":"26","author":"Tolman","year":"1996","journal-title":"J. Phys. Oceanogr."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"1917","DOI":"10.1175\/2010JPO4324.1","article-title":"Semiempirical dissipation source functions for ocean waves. Part I: Definition, calibration, and validation","volume":"40","author":"Ardhuin","year":"2010","journal-title":"J. Phys. Oceanogr."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"513","DOI":"10.1175\/1520-0485(1995)025<0513:CBANAT>2.0.CO;2","article-title":"Correlations between ambient noise and the ocean surface wave field","volume":"25","author":"Felizardo","year":"1995","journal-title":"J. Phys. Oceanogr."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"1633","DOI":"10.1175\/1520-0485(1999)029<1633:WSGADI>2.0.CO;2","article-title":"Wind sea growth and dissipation in the open ocean","volume":"29","author":"Hanson","year":"1999","journal-title":"J. Phys. Oceanogr."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"63","DOI":"10.1016\/j.ocemod.2018.04.004","article-title":"On the upper ocean turbulent dissipation rate due to microscale breakers and small whitecaps","volume":"126","author":"Banner","year":"2018","journal-title":"Ocean Model."},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Guan, C., Hu, W., Sun, J., and Li, R. (2007). The whitecap coverage model from breaking dissipation parametrizations of wind waves. J. Geophys. Res., 112.","DOI":"10.1029\/2006JC003714"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"3145","DOI":"10.1175\/1520-0485(2000)030<3145:BPFDWO>2.0.CO;2","article-title":"Breaking probability for dominant waves on the sea surface","volume":"30","author":"Banner","year":"2000","journal-title":"J. Phys. Oceanogr."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"599","DOI":"10.1175\/JTECH1853.1","article-title":"Passive acoustic determination of wave-breaking events and their severity across the spectrum","volume":"23","author":"Manasseh","year":"2006","journal-title":"J. Atmos. Ocean. Technol."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"52","DOI":"10.1038\/385052a0","article-title":"Infrared remote sensing of breaking waves","volume":"385","author":"Jessup","year":"1997","journal-title":"Nature"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"943","DOI":"10.1175\/JPO-D-14-0133.1","article-title":"Field measurements of surface and near-surface turbulence in the presence of breaking waves","volume":"45","author":"Sutherland","year":"2015","journal-title":"J. Phys. Oceanogr."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"450","DOI":"10.1175\/1520-0485(2001)031<0450:HRRRMO>2.0.CO;2","article-title":"High range resolution radar measurements of the speed distribution of breaking events in wind-generated ocean waves: Surface impulse and wave energy dissipation rates","volume":"31","author":"Phillips","year":"2001","journal-title":"J. Phys. Oceanogr."},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Hwang, P.A., Sletten, M.A., and Toporkov, J.V. (2008). Breaking wave contribution to low grazing angle radar backscatter from the ocean surface. J. Geophys. Res., 113.","DOI":"10.1029\/2008JC004752"},{"key":"ref_27","first-page":"8054","article-title":"A semiempirical model of the normalized radar cross-section of the sea surface 1. Background model","volume":"108","author":"Kudryavtsev","year":"2003","journal-title":"J. Geophys. Res."},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Hwang, P.A., Zhang, B., and Perrie, W. (2010). Depolarized radar return for breaking wave measurement and hurricane wind retrieval. Geophys. Res. Lett., 37.","DOI":"10.1029\/2009GL041780"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"761","DOI":"10.1109\/LGRS.2012.2222341","article-title":"On dual co-polarized SAR measurements of the ocean surface","volume":"10","author":"Kudryavtsev","year":"2013","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"627","DOI":"10.1080\/01431168608954716","article-title":"Whitecaps and the passive remote sensing of the ocean surface","volume":"7","author":"Monahan","year":"1986","journal-title":"Int. J. Remote Sens."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"6046","DOI":"10.1002\/2014JC010173","article-title":"Quad-polarization SAR features of ocean currents","volume":"119","author":"Kudryavtsev","year":"2014","journal-title":"J. Geophys. Res."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"8362","DOI":"10.1109\/TGRS.2019.2920750","article-title":"On quad-polarized SAR measurements of the ocean surface","volume":"57","author":"Kudryavtsev","year":"2019","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_33","unstructured":"Macdonald, Dettwiler and Associates Ltd. (2018). RADARSAT-2 Product Format Definition, MacDonald, Dettwiler and Associates Ltd.. Technical Report RN-SP-52-1238."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"727","DOI":"10.1109\/TGRS.2003.810702","article-title":"Inversion of surface parameters from polarimetric SAR","volume":"41","author":"Hajnsek","year":"2003","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"1999","DOI":"10.1002\/qj.3803","article-title":"The ERA5 global reanalysis","volume":"146","author":"Hersbach","year":"2020","journal-title":"Q. J. R. Meteorol. Soc."},{"key":"ref_36","doi-asserted-by":"crossref","unstructured":"Komen, G.J., Cavaleri, L., Donelan, M., Hasselmann, K., Hasselmann, S., and Janssen, P.A.E.M. (1994). Dynamics and Modelling of Ocean Waves, Cambridge University Press.","DOI":"10.1017\/CBO9780511628955"},{"key":"ref_37","unstructured":"The WAVEWATCH III\u00ae Development Group (2016). User Manual and System Documentation of WAVEWATCH III\u00ae Version 5.16, NOAA\/NWS\/NCEP\/MMAB. Tech. Note 329."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"1065","DOI":"10.1175\/1520-0485(1988)018<1065:RRFTSS>2.0.CO;2","article-title":"Radar returns from the sea surface\u2014Bragg scattering and breaking waves","volume":"18","author":"Phillips","year":"1988","journal-title":"J. Phys. Oceanogr."},{"key":"ref_39","first-page":"1","article-title":"Radar scattering of the ocean surface and sea-roughness properties: A combined analysis from dual-polarizations airborne radar observations and models in C band","volume":"111","author":"Mouche","year":"2006","journal-title":"J. Geophys. Res."},{"key":"ref_40","doi-asserted-by":"crossref","unstructured":"Hwang, P.A., and Plant, W.J. (2010). An analysis of the effects of swell and surface roughness spectra on microwave backscatter from the ocean. J. Geophys. Res., 115.","DOI":"10.1029\/2009JC005558"},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"3640","DOI":"10.1002\/2015JC010782","article-title":"Surface roughness and breaking wave properties retrieved from polarimetric microwave radar backscattering","volume":"1","author":"Hwang","year":"2015","journal-title":"J. Geophys. Res."},{"key":"ref_42","first-page":"43","article-title":"A unified approach to bistatic scattering for active and passive remote sensing of rough ocean surfaces","volume":"1","author":"Guissard","year":"1992","journal-title":"Trends Geophys. Res."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"1949","DOI":"10.1109\/TGRS.2009.2013135","article-title":"The two-scale BPM scattering model for sea biogenic slicks contrast","volume":"47","author":"Nunziata","year":"2009","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"4970","DOI":"10.1109\/JSTARS.2016.2605151","article-title":"X-Band two-scale sea surface scattering model to predict the contrast due to an oil slick","volume":"9","author":"Montuori","year":"2016","journal-title":"IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"15781","DOI":"10.1029\/97JC00467","article-title":"A unified directional spectrum for long and short wind-driven waves","volume":"102","author":"Elfouhaily","year":"1997","journal-title":"J. Geophys. Res."},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"727","DOI":"10.1175\/1520-0485(1980)010<0727:WSCOSS>2.0.CO;2","article-title":"Wind-stress coefficients over sea surface near neutral conditions: A revisit","volume":"10","author":"Wu","year":"1980","journal-title":"J. Phys. Oceanogr."},{"key":"ref_47","first-page":"306723","article-title":"Swell and wind-sea distributions over the mid-latitude and tropical North Atlantic for the period 2002\u20132008","volume":"2012","author":"Lorenzzetti","year":"2012","journal-title":"Int. J. Oceanogr."},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"2609","DOI":"10.1175\/JPO-D-17-0124.1","article-title":"On the relationship between the energy dissipation rate of surface-breaking waves and oceanic whitecap coverage","volume":"48","author":"Callaghan","year":"2018","journal-title":"J. Phys. Oceanogr."},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"753","DOI":"10.1109\/TGRS.2005.843951","article-title":"Dual-polarization measurements at C-band over the ocean: Results from airborne radar observations and comparison with ENVISAT ASAR data","volume":"43","author":"Mouche","year":"2005","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"1100","DOI":"10.1109\/JSTARS.2013.2242848","article-title":"A systematic comparison of the effect of polarization ratio models on sea surface wind retrieval from C-band synthetic aperture radar","volume":"6","author":"Liu","year":"2013","journal-title":"IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens."},{"key":"ref_51","doi-asserted-by":"crossref","unstructured":"Mouche, A.A., Chapron, B., Reul, N., Hauser, D., and Quilfen, Y. (2007). Importance of the sea surface curvature to interpret the normalized radar cross section. J. Geophys. Res., 112.","DOI":"10.1029\/2006JC004010"},{"key":"ref_52","unstructured":"Freeman, A. (1993, January 18\u201321). The effects of noise on polarimetric SAR data. Proceedings of the IGARSS\u201993\u2014IEEE International Geoscience and Remote Sensing Symposium, Tokyo, Japan."},{"key":"ref_53","doi-asserted-by":"crossref","first-page":"3812","DOI":"10.1109\/TGRS.2012.2185804","article-title":"Polarimetric analysis of backscatter from the Deepwater Horizon oil spill using L-band synthetic aperture radar","volume":"50","author":"Minchew","year":"2012","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_54","doi-asserted-by":"crossref","first-page":"4194","DOI":"10.1109\/TGRS.2019.2961684","article-title":"The impact of system noise in polarimetric SAR imagery on oil spill observations","volume":"58","author":"Espeseth","year":"2020","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_55","doi-asserted-by":"crossref","first-page":"445","DOI":"10.1109\/JOE.1985.1145133","article-title":"A physical radar cross-section model for a wind-driven sea with swell","volume":"10","author":"Durden","year":"1985","journal-title":"IEEE J. Ocean. Eng."},{"key":"ref_56","doi-asserted-by":"crossref","unstructured":"Zhang, B., Perrie, W., and He, Y. (2011). Wind speed retrieval from RADARSAT-2 quad-polarization images using a new polarization ratio model. J. Geophys. Res., 116.","DOI":"10.1029\/2010JC006522"},{"key":"ref_57","doi-asserted-by":"crossref","first-page":"10735","DOI":"10.1029\/JC091iC09p10735","article-title":"A two-scale model of short wind-generated waves and scatterometry","volume":"91","author":"Plant","year":"1986","journal-title":"J. Geophys. Res."},{"key":"ref_58","unstructured":"Phillips, O.M. (1977). The Dynamics of the Upper Ocean, Cambridge University Press."},{"key":"ref_59","doi-asserted-by":"crossref","first-page":"5181","DOI":"10.1029\/JZ069i024p05181","article-title":"A proposed spectral form for fully developed wind seas based on the similarity theory of S. A. Kitaigorodskii","volume":"69","author":"Pierson","year":"1964","journal-title":"J. Geophys. Res."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/20\/22\/6540\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T10:33:56Z","timestamp":1760178836000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/20\/22\/6540"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,11,16]]},"references-count":59,"journal-issue":{"issue":"22","published-online":{"date-parts":[[2020,11]]}},"alternative-id":["s20226540"],"URL":"https:\/\/doi.org\/10.3390\/s20226540","relation":{},"ISSN":["1424-8220"],"issn-type":[{"type":"electronic","value":"1424-8220"}],"subject":[],"published":{"date-parts":[[2020,11,16]]}}}