{"id":"https://openalex.org/W2912647535","doi":"https://doi.org/10.1073/pnas.1820467116","title":"Statistical dynamical model to predict extreme events and anomalous features in shallow water waves with abrupt depth change","display_name":"Statistical dynamical model to predict extreme events and anomalous features in shallow water waves with abrupt depth change","publication_year":2019,"publication_date":"2019-02-13","ids":{"openalex":"https://openalex.org/W2912647535","doi":"https://doi.org/10.1073/pnas.1820467116","mag":"2912647535","pmid":"https://pubmed.ncbi.nlm.nih.gov/30760588"},"language":"en","primary_location":{"id":"doi:10.1073/pnas.1820467116","doi":"https://doi.org/10.1073/pnas.1820467116","is_oa":true,"landing_page_url":"https://doi.org/10.1073/pnas.1820467116","pdf_url":null,"source":{"id":"https://openalex.org/S125754415","display_name":"Proceedings of the National Academy of Sciences","issn_l":"0027-8424","issn":["0027-8424","1091-6490"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-class-a","anvur-scientific","cwts-core","dongbi-a","doyens","erih-plus","jufo-3","ki-jl-3","medline","norway-2","poland-200","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310320052","host_organization_name":"National Academy of Sciences","host_organization_lineage":["https://openalex.org/P4310320052"],"host_organization_lineage_names":["National Academy of Sciences"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the National Academy of Sciences","raw_type":"journal-article"},"volume":null,"type":"article","indexed_in":["crossref","pubmed"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://doi.org/10.1073/pnas.1820467116","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5110096032","display_name":"Andrew J. Majda","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I36672615","display_name":"Courant Institute of Mathematical Sciences","ror":"https://ror.org/037tm7f56","country_code":"US","type":"education","lineage":["https://openalex.org/I36672615","https://openalex.org/I57206974"]},{"id":"https://openalex.org/I57206974","display_name":"New York University","ror":"https://ror.org/0190ak572","country_code":"US","type":"education","lineage":["https://openalex.org/I57206974"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Andrew J. Majda","raw_affiliation_strings":["Center for Atmosphere and Ocean Science, Courant Institute of Mathematical Sciences, New York University, New York, NY 10012;","Department of Mathematics, Courant Institute of Mathematical Sciences, New York University, New York, NY 10012;"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Center for Atmosphere and Ocean Science, Courant Institute of Mathematical Sciences, New York University, New York, NY 10012;","institution_ids":["https://openalex.org/I36672615","https://openalex.org/I57206974"]},{"raw_affiliation_string":"Department of Mathematics, Courant Institute of Mathematical Sciences, New York University, New York, NY 10012;","institution_ids":["https://openalex.org/I36672615","https://openalex.org/I57206974"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5051877960","display_name":"Nicholas J. Moore","orcid":"https://orcid.org/0000-0001-9578-7982","observed_orcids":["https://orcid.org/0000-0001-9578-7982"]},"institutions":[{"id":"https://openalex.org/I103163165","display_name":"Florida State University","ror":"https://ror.org/05g3dte14","country_code":"US","type":"education","lineage":["https://openalex.org/I103163165"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"M. N. J. Moore","raw_affiliation_strings":["Department of Mathematics, Florida State University, Tallahassee, FL 32304;","Geophysical Fluid Dynamics Institute, Florida State University, Tallahassee, FL 32306"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Florida State University, Tallahassee, FL 32304;","institution_ids":["https://openalex.org/I103163165"]},{"raw_affiliation_string":"Geophysical Fluid Dynamics Institute, Florida State University, Tallahassee, FL 32306","institution_ids":["https://openalex.org/I103163165"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5053428885","display_name":"Di Qi","orcid":"https://orcid.org/0000-0002-9865-2327","observed_orcids":["https://orcid.org/0000-0002-9865-2327"]},"institutions":[{"id":"https://openalex.org/I36672615","display_name":"Courant Institute of Mathematical Sciences","ror":"https://ror.org/037tm7f56","country_code":"US","type":"education","lineage":["https://openalex.org/I36672615","https://openalex.org/I57206974"]},{"id":"https://openalex.org/I57206974","display_name":"New York University","ror":"https://ror.org/0190ak572","country_code":"US","type":"education","lineage":["https://openalex.org/I57206974"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Di Qi","raw_affiliation_strings":["Center for Atmosphere and Ocean Science, Courant Institute of Mathematical Sciences, New York University, New York, NY 10012;","Department of Mathematics, Courant Institute of Mathematical Sciences, New York University, New York, NY 10012;"],"raw_orcid":"https://orcid.org/0000-0002-9865-2327","affiliations":[{"raw_affiliation_string":"Center for Atmosphere and Ocean Science, Courant Institute of Mathematical Sciences, New York University, New York, NY 10012;","institution_ids":["https://openalex.org/I36672615","https://openalex.org/I57206974"]},{"raw_affiliation_string":"Department of Mathematics, Courant Institute of Mathematical Sciences, New York University, New York, NY 10012;","institution_ids":["https://openalex.org/I36672615","https://openalex.org/I57206974"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":4.3404,"has_fulltext":false,"cited_by_count":88,"citation_normalized_percentile":{"value":0.95323294,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":100},"biblio":{"volume":"116","issue":"10","first_page":"3982","last_page":"3987"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10248","display_name":"Nonlinear Waves and Solitons","score":0.9872999787330627,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10248","display_name":"Nonlinear Waves and Solitons","score":0.9872999787330627,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11061","display_name":"Ocean Waves and Remote Sensing","score":0.0026000000070780516,"subfield":{"id":"https://openalex.org/subfields/1910","display_name":"Oceanography"},"field":{"id":"https://openalex.org/fields/19","display_name":"Earth and Planetary Sciences"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11654","display_name":"Advanced Mathematical Physics Problems","score":0.0019000000320374966,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/extreme-events","display_name":"extreme events","score":0.8510000109672546},{"id":"https://openalex.org/keywords/shallow-water-waves","display_name":"shallow water waves","score":0.871999979019165},{"id":"https://openalex.org/keywords/hamiltonian-systems","display_name":"Hamiltonian systems","score":0.7639999985694885},{"id":"https://openalex.org/keywords/positive-skewness","display_name":"positive skewness","score":0.7110000252723694},{"id":"https://openalex.org/keywords/statistical-dynamical-model","display_name":"statistical-dynamical model","score":0.796999990940094},{"id":"https://openalex.org/keywords/dispersive-media","display_name":"dispersive media","score":0.7360000014305115},{"id":"https://openalex.org/keywords/probability-density-function","display_name":"probability density function","score":0.5379999876022339}],"concepts":[{"id":"https://openalex.org/C122342681","wikidata":"https://www.wikidata.org/wiki/Q330828","display_name":"Skewness","level":2,"score":0.7156433463096619},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.6848665475845337},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.5340911746025085},{"id":"https://openalex.org/C114289077","wikidata":"https://www.wikidata.org/wiki/Q3284399","display_name":"Statistical model","level":2,"score":0.5093148946762085},{"id":"https://openalex.org/C2780872131","wikidata":"https://www.wikidata.org/wiki/Q5558987","display_name":"Gibbs state","level":3,"score":0.4763467609882355},{"id":"https://openalex.org/C147581598","wikidata":"https://www.wikidata.org/wiki/Q729429","display_name":"Extreme value theory","level":2,"score":0.47541648149490356},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.42412734031677246},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.42350178956985474},{"id":"https://openalex.org/C127313418","wikidata":"https://www.wikidata.org/wiki/Q1069","display_name":"Geology","level":0,"score":0.37596195936203003},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.3568422794342041},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.31061434745788574},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.10388284921646118},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1073/pnas.1820467116","doi":"https://doi.org/10.1073/pnas.1820467116","is_oa":true,"landing_page_url":"https://doi.org/10.1073/pnas.1820467116","pdf_url":null,"source":{"id":"https://openalex.org/S125754415","display_name":"Proceedings of the National Academy of Sciences","issn_l":"0027-8424","issn":["0027-8424","1091-6490"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-class-a","anvur-scientific","cwts-core","dongbi-a","doyens","erih-plus","jufo-3","ki-jl-3","medline","norway-2","poland-200","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310320052","host_organization_name":"National Academy of Sciences","host_organization_lineage":["https://openalex.org/P4310320052"],"host_organization_lineage_names":["National Academy of Sciences"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the National Academy of Sciences","raw_type":"journal-article"},{"id":"pmid:30760588","doi":null,"is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/30760588","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the National Academy of Sciences of the United States of America","raw_type":"Journal Article"},{"id":"pmh:oai:europepmc.org:5399337","doi":null,"is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/6410832","pdf_url":null,"source":{"id":"https://openalex.org/S4306400806","display_name":"Europe PMC (PubMed Central)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I1303153112","host_organization_name":"European Bioinformatics Institute","host_organization_lineage":["https://openalex.org/I1303153112"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Text"},{"id":"pmh:oai:pubmedcentral.nih.gov:6410832","doi":null,"is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/6410832","pdf_url":null,"source":{"id":"https://openalex.org/S2764455111","display_name":"PubMed Central","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Proc Natl Acad Sci U S A","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.1073/pnas.1820467116","doi":"https://doi.org/10.1073/pnas.1820467116","is_oa":true,"landing_page_url":"https://doi.org/10.1073/pnas.1820467116","pdf_url":null,"source":{"id":"https://openalex.org/S125754415","display_name":"Proceedings of the National Academy of Sciences","issn_l":"0027-8424","issn":["0027-8424","1091-6490"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-class-a","anvur-scientific","cwts-core","dongbi-a","doyens","erih-plus","jufo-3","ki-jl-3","medline","norway-2","poland-200","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310320052","host_organization_name":"National Academy of Sciences","host_organization_lineage":["https://openalex.org/P4310320052"],"host_organization_lineage_names":["National Academy of Sciences"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the National Academy of Sciences","raw_type":"journal-article"},"sustainable_development_goals":[],"sustainable_development_goals_aurora":[{"display_name":"Clean water and sanitation","score":0.699999988079071,"id":"https://metadata.un.org/sdg/6"}],"study_designs":[],"awards":[{"id":"https://openalex.org/G4033799066","display_name":null,"funder_award_id":"524259","funder_id":"https://openalex.org/F4320306164","funder_display_name":"Simons Foundation"},{"id":"https://openalex.org/G4995868798","display_name":null,"funder_award_id":"MURI N00014-16-1-2161","funder_id":"https://openalex.org/F4320332923","funder_display_name":"U.S. Navy"},{"id":"https://openalex.org/G8512828309","display_name":null,"funder_award_id":"MURI N00014-16-1-2161","funder_id":"https://openalex.org/F4320337345","funder_display_name":"Office of Naval Research"}],"funders":[{"id":"https://openalex.org/F4320306164","display_name":"Simons Foundation","ror":"https://ror.org/01cmst727"},{"id":"https://openalex.org/F4320332923","display_name":"U.S. Navy","ror":"https://ror.org/03ar0mv07"},{"id":"https://openalex.org/F4320337345","display_name":"Office of Naval Research","ror":"https://ror.org/00rk2pe57"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":30,"referenced_works":["https://openalex.org/W1561892995","https://openalex.org/W1587788720","https://openalex.org/W1647323343","https://openalex.org/W1976244852","https://openalex.org/W2016848683","https://openalex.org/W2021433050","https://openalex.org/W2021968241","https://openalex.org/W2028374436","https://openalex.org/W2048129990","https://openalex.org/W2072036814","https://openalex.org/W2093274602","https://openalex.org/W2132429173","https://openalex.org/W2134513138","https://openalex.org/W2165384097","https://openalex.org/W2280240361","https://openalex.org/W2507269661","https://openalex.org/W2515838203","https://openalex.org/W2546435180","https://openalex.org/W2605625916","https://openalex.org/W2755344066","https://openalex.org/W2769705890","https://openalex.org/W2794734605","https://openalex.org/W2796676086","https://openalex.org/W2803553844","https://openalex.org/W2810234128","https://openalex.org/W2888321728","https://openalex.org/W2889346967","https://openalex.org/W2963202249","https://openalex.org/W3104382057","https://openalex.org/W3106456843"],"related_works":["https://openalex.org/W2189529952","https://openalex.org/W3122032734","https://openalex.org/W28389960","https://openalex.org/W3144675622","https://openalex.org/W3124374489","https://openalex.org/W1575594952","https://openalex.org/W3080076373","https://openalex.org/W2549038846","https://openalex.org/W3121128063","https://openalex.org/W2463389856"],"abstract_inverted_index":{"Understanding":[0],"and":[1,5,20,85,106,129,171],"predicting":[2,197],"extreme":[3,74,198],"events":[4],"their":[6],"anomalous":[7,43,90,153,187,199],"statistics":[8],"in":[9,17,31,114,202],"complex":[10],"nonlinear":[11],"systems":[12],"are":[13,97],"a":[14,37,79,123,162],"grand":[15],"challenge":[16],"climate,":[18],"material,":[19],"neuroscience":[21],"as":[22,24,45,93],"well":[23],"for":[25,185,196],"engineering":[26],"design.":[27],"Recent":[28],"laboratory":[29],"experiments":[30],"weakly":[32],"turbulent":[33],"shallow":[34],"water":[35],"reveal":[36],"remarkable":[38],"transition":[39],"from":[40],"Gaussian":[41,142],"to":[42,83,103],"behavior":[44,92,201],"surface":[46,62],"waves":[47],"cross":[48],"an":[49,70,182],"abrupt":[50],"depth":[51],"change":[52],"(ADC).":[53],"Downstream":[54],"of":[55,61,73,138,176],"the":[56,88,117,139,147,151,177,186],"ADC,":[57],"probability":[58],"density":[59],"functions":[60],"displacement":[63],"exhibit":[64],"strong":[65],"positive":[66],"skewness":[67],"accompanied":[68],"by":[69,161,167],"elevated":[71],"level":[72],"events.":[75],"Here,":[76],"we":[77],"develop":[78],"statistical":[80,91,131,136,200],"dynamical":[81],"model":[82],"explain":[84],"quantitatively":[86],"predict":[87],"above":[89],"experimental":[94],"control":[95],"parameters":[96],"varied.":[98],"The":[99,119,135,190],"first":[100],"step":[101],"is":[102,122,180],"use":[104],"incoming":[105,128,143],"outgoing":[107,130,154,188],"truncated":[108],"Korteweg-de":[109],"Vries":[110],"(TKdV)":[111],"equations":[112],"matched":[113],"time":[115],"at":[116,146],"ADC.":[118],"TKdV":[120],"equation":[121],"Hamiltonian":[124],"system,":[125],"which":[126,157],"induces":[127],"Gibbs":[132,144,155],"invariant":[133],"measures.":[134],"matching":[137],"known":[140],"nearly":[141],"state":[145],"ADC":[148],"completely":[149],"determines":[150],"predicted":[152],"state,":[156],"can":[158],"be":[159,194],"calculated":[160],"simple":[163],"sampling":[164],"algorithm":[165],"verified":[166],"direct":[168],"numerical":[169],"simulations,":[170],"successfully":[172],"captures":[173],"key":[174],"features":[175],"experiment.":[178],"There":[179],"even":[181],"analytic":[183],"formula":[184],"skewness.":[189],"strategy":[191],"here":[192],"should":[193],"useful":[195],"other":[203],"dispersive":[204],"media.":[205]},"counts_by_year":[{"year":2026,"cited_by_count":7},{"year":2025,"cited_by_count":8},{"year":2024,"cited_by_count":14},{"year":2023,"cited_by_count":21},{"year":2022,"cited_by_count":16},{"year":2021,"cited_by_count":9},{"year":2020,"cited_by_count":7},{"year":2019,"cited_by_count":5},{"year":2018,"cited_by_count":1}],"updated_date":"2026-10-14T16:39:01.820549","created_date":"2025-10-10T00:00:00"}