{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,10]],"date-time":"2026-09-10T03:16:42Z","timestamp":1789010202986,"version":"build-2803163510"},"reference-count":46,"publisher":"National Academy of Sciences","issue":"38","license":[{"start":{"date-parts":[[2025,9,16]],"date-time":"2025-09-16T00:00:00Z","timestamp":1757980800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100002830","name":"Centre National d'Etudes Spatiales","doi-asserted-by":"publisher","award":["SWOT"],"award-info":[{"award-number":["SWOT"]}],"id":[{"id":"10.13039\/501100002830","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100000844","name":"European Space Agency","doi-asserted-by":"publisher","award":["SeaStateCCI"],"award-info":[{"award-number":["SeaStateCCI"]}],"id":[{"id":"10.13039\/501100000844","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["www.pnas.org"],"crossmark-restriction":true},"short-container-title":["Proc. Natl. Acad. Sci. U.S.A."],"published-print":{"date-parts":[[2025,9,23]]},"abstract":"<jats:p>\n                    Winds generate waves over the oceans with a wide range of properties. The largest wave heights and periods are important parameters in the design of marine structures. Extreme waves also play an outsize role in air\u2013sea fluxes and coastal dynamics, and leave imprints on seismic and sediment records. Rare events have so far escaped measurements, with few wave heights from satellite altimeters exceeding 16 m, and no associated measurement of wave periods. Here, we use swells radiated from storms to reveal long wave periods within the storms, and their generation mechanism. Swells are resolved in the Surface Water and Ocean Topography (SWOT) satellite sea level measurements. Patterns of increasing swell wavelength and decreasing swell height away from storms are consistent with a nonlinear transfer of energy from short to long period waves. We propose an updated parametric shape for wave spectra in storms that aligns with SWOT swell measurements. It reduces energy levels by a factor of 20 at 1.2 to 1.4 times the peak period compared to commonly used spectral shapes and allows estimation of storm wave periods from swell heights. Consistent with less extreme conditions, the peak period generally increases with wave height. This was particularly verified for the largest storm peak period of 20.2\n                    <jats:inline-formula>\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"inline\" overflow=\"scroll\">\n                        <mml:mo>\u00b1<\/mml:mo>\n                      <\/mml:math>\n                    <\/jats:inline-formula>\n                    0.6 s, obtained for the event with the largest significant wave height 19.7\n                    <jats:inline-formula>\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"inline\" overflow=\"scroll\">\n                        <mml:mo>\u00b1<\/mml:mo>\n                      <\/mml:math>\n                    <\/jats:inline-formula>\n                    0.3 m measured by altimeters. These observations of long period swells should have a wide range of applications from coastal dynamics to seismology.\n                  <\/jats:p>","DOI":"10.1073\/pnas.2513381122","type":"journal-article","created":{"date-parts":[[2025,9,16]],"date-time":"2025-09-16T17:55:08Z","timestamp":1758045308000},"update-policy":"https:\/\/doi.org\/10.1073\/pnas.cm10313","source":"Crossref","is-referenced-by-count":13,"title":["Sizing the largest ocean waves using the SWOT mission"],"prefix":"10.1073","volume":"122","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9309-9681","authenticated-orcid":false,"given":"Fabrice","family":"Ardhuin","sequence":"first","affiliation":[{"name":"Universit\u00e9 de Brest, CNRS, Ifremer, Institut de Recherche pour le D\u00e9veloppement, Laboratoire d\u2019Oc\u00e9anographie Physique et Spatiale (LOPS)","place":["Plouzan\u00e9, France"]},{"name":"Institut Universitaire Europ\u00e9en de la Mer","place":["Plouzan\u00e9, France"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Taina","family":"Postec","sequence":"additional","affiliation":[{"name":"Universit\u00e9 de Brest, CNRS, Ifremer, Institut de Recherche pour le D\u00e9veloppement, Laboratoire d\u2019Oc\u00e9anographie Physique et Spatiale (LOPS)","place":["Plouzan\u00e9, France"]},{"name":"Institut Universitaire Europ\u00e9en de la Mer","place":["Plouzan\u00e9, France"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1125-7568","authenticated-orcid":false,"given":"Mickael","family":"Accensi","sequence":"additional","affiliation":[{"name":"Universit\u00e9 de Brest, CNRS, Ifremer, Institut de Recherche pour le D\u00e9veloppement, Laboratoire d\u2019Oc\u00e9anographie Physique et Spatiale (LOPS)","place":["Plouzan\u00e9, France"]},{"name":"Institut Universitaire Europ\u00e9en de la Mer","place":["Plouzan\u00e9, France"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jean-Fran\u00e7ois","family":"Piolle","sequence":"additional","affiliation":[{"name":"Universit\u00e9 de Brest, CNRS, Ifremer, Institut de Recherche pour le D\u00e9veloppement, Laboratoire d\u2019Oc\u00e9anographie Physique et Spatiale (LOPS)","place":["Plouzan\u00e9, France"]},{"name":"Institut Universitaire Europ\u00e9en de la Mer","place":["Plouzan\u00e9, France"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0200-6858","authenticated-orcid":false,"given":"Guillaume","family":"Dodet","sequence":"additional","affiliation":[{"name":"Universit\u00e9 de Brest, CNRS, Ifremer, Institut de Recherche pour le D\u00e9veloppement, Laboratoire d\u2019Oc\u00e9anographie Physique et Spatiale (LOPS)","place":["Plouzan\u00e9, France"]},{"name":"Institut Universitaire Europ\u00e9en de la Mer","place":["Plouzan\u00e9, France"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3372-3948","authenticated-orcid":false,"given":"Marcello","family":"Passaro","sequence":"additional","affiliation":[{"name":"Deutsches Geod\u00e4tisches Forschungsinstitut der Technischen Universit\u00e4t M\u00fcnchen, Arcisstra\u00dfe 21","place":["Munich, Germany"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Marine","family":"De Carlo","sequence":"additional","affiliation":[{"name":"Collecte Localisation Satellites","place":["Plouzan\u00e9, France"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8275-433X","authenticated-orcid":false,"given":"Romain","family":"Husson","sequence":"additional","affiliation":[{"name":"Collecte Localisation Satellites","place":["Plouzan\u00e9, France"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Gilles","family":"Guitton","sequence":"additional","affiliation":[{"name":"OceanDataLab","place":["Locmaria-Plouzane, France"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Fabrice","family":"Collard","sequence":"additional","affiliation":[{"name":"OceanDataLab","place":["Locmaria-Plouzane, France"]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"341","published-online":{"date-parts":[[2025,9,16]]},"reference":[{"key":"e_1_3_4_1_2","doi-asserted-by":"publisher","DOI":"10.1007\/s10712-019-09557-5"},{"key":"e_1_3_4_2_2","first-page":"496","volume-title":"Wave Mechanics for Ocean Engineering","author":"Boccotti P.","year":"2000","unstructured":"P. Boccotti, Wave Mechanics for Ocean Engineering (Elsevier, Amsterdam, 2000), p. 496."},{"key":"e_1_3_4_3_2","doi-asserted-by":"publisher","DOI":"10.1002\/we.347"},{"key":"e_1_3_4_4_2","doi-asserted-by":"publisher","DOI":"10.1038\/nature03176"},{"key":"e_1_3_4_5_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.earscirev.2017.12.014"},{"key":"e_1_3_4_6_2","doi-asserted-by":"publisher","DOI":"10.1016\/0031-9201(90)90013-N"},{"key":"e_1_3_4_7_2","doi-asserted-by":"publisher","DOI":"10.1038\/s41467-023-42673-w"},{"key":"e_1_3_4_8_2","doi-asserted-by":"publisher","DOI":"10.1038\/s43247-023-00837-y"},{"key":"e_1_3_4_9_2","doi-asserted-by":"publisher","DOI":"10.1029\/2023JC020832"},{"key":"e_1_3_4_10_2","unstructured":"M. Accensi WAVEWATCH III model simulations GLOB-30M_LOPS_2025 (2025). https:\/\/sextant.ifremer.fr\/record\/87209a81-2c27-452b-86ae-b9c2cc4d43a9\/."},{"key":"e_1_3_4_11_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF02108528"},{"key":"e_1_3_4_12_2","doi-asserted-by":"publisher","DOI":"10.1029\/JZ069i024p05181"},{"key":"e_1_3_4_13_2","first-page":"1","article-title":"Measurements of wind-wave growth and swell decay during the Joint North Sea Wave Project","volume":"8","author":"Hasselmann K.","year":"1973","unstructured":"K. Hasselmann . Measurements of wind-wave growth and swell decay during the Joint North Sea Wave Project. Deut. Hydrogr. Z. 8, 1\u201395 (1973).","journal-title":"Deut. Hydrogr. Z"},{"key":"e_1_3_4_14_2","doi-asserted-by":"publisher","DOI":"10.1098\/rsta.1985.0054"},{"key":"e_1_3_4_15_2","doi-asserted-by":"publisher","DOI":"10.1175\/JPO-D-17-0017.1"},{"key":"e_1_3_4_16_2","doi-asserted-by":"publisher","DOI":"10.1017\/S0022112062000373"},{"key":"e_1_3_4_17_2","doi-asserted-by":"publisher","DOI":"10.1038\/srep05306"},{"key":"e_1_3_4_18_2","doi-asserted-by":"publisher","DOI":"10.1017\/S002211209100085X"},{"key":"e_1_3_4_19_2","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511628955"},{"key":"e_1_3_4_20_2","doi-asserted-by":"publisher","DOI":"10.1029\/2024GL109658"},{"key":"e_1_3_4_21_2","doi-asserted-by":"publisher","DOI":"10.1029\/2023GL107652"},{"key":"e_1_3_4_22_2","doi-asserted-by":"publisher","DOI":"10.1029\/2022JC019581"},{"key":"e_1_3_4_23_2","doi-asserted-by":"publisher","DOI":"10.1002\/qj.3803"},{"key":"e_1_3_4_24_2","doi-asserted-by":"publisher","DOI":"10.1175\/2009JPO4067.1"},{"key":"e_1_3_4_25_2","doi-asserted-by":"publisher","DOI":"10.1109\/TGRS.2025.3551605"},{"key":"e_1_3_4_26_2","unstructured":"SWOT project SWOT level-2 Karin low rate SSH unsmoothed reprocessed version C products (v2.0) (2023). https:\/\/podaac.jpl.nasa.gov\/dataset\/SWOT_L2_LR_SSH_Unsmoothed_2.0."},{"key":"e_1_3_4_27_2","unstructured":"SWOT project SWOT_L3_LR_WIND_WAVE product. Derived from the SWOT_L3_LR_SSH product is produced and made freely available by AVISO DUACS and LOPS teams as part of the DESMOS and VAGUES Science Team projects (2025). https:\/\/www.aviso.altimetry.fr\/en\/data\/products\/windwave-products\/swot-karin-level-3-wind-wave-product.html."},{"key":"e_1_3_4_28_2","doi-asserted-by":"publisher","DOI":"10.1175\/1520-0469(1947)004<0045:TSBFOS>2.0.CO;2"},{"key":"e_1_3_4_29_2","doi-asserted-by":"publisher","DOI":"10.1029\/JZ071i022p05271"},{"key":"e_1_3_4_30_2","doi-asserted-by":"publisher","DOI":"10.1029\/2008JC005215"},{"key":"e_1_3_4_31_2","first-page":"431","article-title":"Propagation of ocean swell across the Pacific","volume":"249","author":"Snodgrass F. E.","year":"1966","unstructured":"F. E. Snodgrass , Propagation of ocean swell across the Pacific. Philos. Trans. R. Soc. Lond. A249, 431\u2013497 (1966).","journal-title":"Philos. Trans. R. Soc. Lond."},{"key":"e_1_3_4_32_2","doi-asserted-by":"publisher","DOI":"10.1029\/2008GL037030"},{"key":"e_1_3_4_33_2","doi-asserted-by":"publisher","DOI":"10.1175\/1520-0485(2003)033<0499:ANSOAN>2.0.CO;2"},{"key":"e_1_3_4_34_2","doi-asserted-by":"publisher","DOI":"10.5194\/npg-24-237-2017"},{"key":"e_1_3_4_35_2","doi-asserted-by":"publisher","DOI":"10.1029\/2006JC003835"},{"key":"e_1_3_4_36_2","doi-asserted-by":"publisher","DOI":"10.1175\/JCLI3815.1"},{"key":"e_1_3_4_37_2","doi-asserted-by":"publisher","DOI":"10.1175\/2009BAMS2755.1"},{"key":"e_1_3_4_38_2","doi-asserted-by":"publisher","DOI":"10.1029\/2022JC018925"},{"key":"e_1_3_4_39_2","unstructured":"F. Ardhuin M. De Carlo Storm tracks based on wave heights from LOPS WAVEWATCH III hindcast and ERA5 reanalysis years 1991\u20132024 (2025). https:\/\/www.pigma.org\/geonetwork\/srv\/api\/records\/seanoe:105148."},{"key":"e_1_3_4_40_2","unstructured":"F. Ardhuin A database of \u201cvery high\u201d and \u201cphenomenal\u201d sea states from the ESA Seastate CCI V4 database with complements from CNES CFOSAT and SWOT nadir altimeters. version 1 (not inter-calibrated) (2025)."},{"key":"e_1_3_4_41_2","unstructured":"F. Ardhuin T. Postec Storm tracks wave heights and peak periods for \u201cphenomenal\u201d sea states combining model altimeter wave heights and swells measured by the SWOT satellite mission. version 1 (2025). https:\/\/www.seanoe.org\/data\/00943\/105447\/."},{"key":"e_1_3_4_42_2","doi-asserted-by":"publisher","DOI":"10.1029\/2020JC016564"},{"key":"e_1_3_4_43_2","doi-asserted-by":"publisher","DOI":"10.1038\/s43017-023-00502-0"},{"key":"e_1_3_4_44_2","doi-asserted-by":"publisher","DOI":"10.9753\/icce.v1.1"},{"key":"e_1_3_4_45_2","doi-asserted-by":"publisher","DOI":"10.1017\/S0022112058000550"},{"key":"e_1_3_4_46_2","doi-asserted-by":"publisher","DOI":"10.1029\/97JC00467"}],"container-title":["Proceedings of the National Academy of Sciences"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/pnas.org\/doi\/pdf\/10.1073\/pnas.2513381122","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,9,23]],"date-time":"2025-09-23T15:00:37Z","timestamp":1758639637000},"score":1,"resource":{"primary":{"URL":"https:\/\/pnas.org\/doi\/10.1073\/pnas.2513381122"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,9,16]]},"references-count":46,"journal-issue":{"issue":"38","published-print":{"date-parts":[[2025,9,23]]}},"alternative-id":["10.1073\/pnas.2513381122"],"URL":"https:\/\/doi.org\/10.1073\/pnas.2513381122","relation":{"has-preprint":[{"id-type":"doi","id":"10.22541\/essoar.174250978.85245614\/v1","asserted-by":"object"},{"id-type":"doi","id":"10.22541\/essoar.174250978.85245614\/v2","asserted-by":"object"},{"id-type":"doi","id":"10.22541\/essoar.174250978.85245614\/v3","asserted-by":"object"}]},"ISSN":["0027-8424","1091-6490"],"issn-type":[{"value":"0027-8424","type":"print"},{"value":"1091-6490","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,9,16]]},"assertion":[{"value":"2025-05-28","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2025-08-04","order":2,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2025-09-16","order":3,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}],"article-number":"e2513381122"}}