{"id":"https://openalex.org/W3093361033","doi":"https://doi.org/10.1137/19m1294848","title":"Nonlinear Conditional Model Bias Estimation for Data Assimilation","display_name":"Nonlinear Conditional Model Bias Estimation for Data Assimilation","publication_year":2021,"publication_date":"2021-01-01","ids":{"openalex":"https://openalex.org/W3093361033","doi":"https://doi.org/10.1137/19m1294848","mag":"3093361033"},"language":"en","primary_location":{"id":"doi:10.1137/19m1294848","is_oa":false,"landing_page_url":"https://doi.org/10.1137/19m1294848","pdf_url":null,"source":{"id":"https://openalex.org/S161160597","display_name":"SIAM Journal on Applied Dynamical Systems","issn_l":"1536-0040","issn":["1536-0040"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Applied Dynamical Systems","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5033759683","display_name":"Jason A. Otkin","orcid":"https://orcid.org/0000-0003-4034-7845"},"institutions":[{"id":"https://openalex.org/I71052956","display_name":"University of Reading","ror":"https://ror.org/05v62cm79","country_code":"GB","type":"education","lineage":["https://openalex.org/I71052956"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Jason A. Otkin","raw_affiliation_strings":["Department of Mathematics and Statistics, University of Reading, United Kingdom"],"raw_orcid":"https://orcid.org/0000-0003-4034-7845","affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, University of Reading, United Kingdom","institution_ids":["https://openalex.org/I71052956"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5030682100","display_name":"Roland Potthast","orcid":"https://orcid.org/0000-0001-6794-2500"},"institutions":[{"id":"https://openalex.org/I135310074","display_name":"University of Wisconsin\u2013Madison","ror":"https://ror.org/01y2jtd41","country_code":"US","type":"education","lineage":["https://openalex.org/I135310074"]},{"id":"https://openalex.org/I4210166037","display_name":"Cooperative Institute for Climate and Satellites","ror":"https://ror.org/05nc0nk71","country_code":"US","type":"facility","lineage":["https://openalex.org/I4210166037"]},{"id":"https://openalex.org/I71052956","display_name":"University of Reading","ror":"https://ror.org/05v62cm79","country_code":"GB","type":"education","lineage":["https://openalex.org/I71052956"]}],"countries":["GB","US"],"is_corresponding":false,"raw_author_name":"Roland W. E. Potthast","raw_affiliation_strings":["Department of Mathematics and Statistics, University of Reading, United Kingdom","Cooperative Institute for Meteorological Satellite Studies, Space Science and Engineering Cen-ter, University of Wisconsin-Madison, Madison, WI, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, University of Reading, United Kingdom","institution_ids":["https://openalex.org/I71052956"]},{"raw_affiliation_string":"Cooperative Institute for Meteorological Satellite Studies, Space Science and Engineering Cen-ter, University of Wisconsin-Madison, Madison, WI, USA","institution_ids":["https://openalex.org/I4210166037","https://openalex.org/I135310074"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5028604619","display_name":"Amos S. Lawless","orcid":"https://orcid.org/0000-0002-3016-6568"},"institutions":[{"id":"https://openalex.org/I172825728","display_name":"Deutscher Wetterdienst","ror":"https://ror.org/02nrqs528","country_code":"DE","type":"facility","lineage":["https://openalex.org/I172825728"]},{"id":"https://openalex.org/I4210128104","display_name":"National Centre for Earth Observation","ror":"https://ror.org/0375jbm11","country_code":"GB","type":"facility","lineage":["https://openalex.org/I141816643","https://openalex.org/I4210087105","https://openalex.org/I4210128104"]},{"id":"https://openalex.org/I71052956","display_name":"University of Reading","ror":"https://ror.org/05v62cm79","country_code":"GB","type":"education","lineage":["https://openalex.org/I71052956"]}],"countries":["DE","GB"],"is_corresponding":false,"raw_author_name":"Amos S. Lawless","raw_affiliation_strings":["German Meteorological Service -Deutscher Wetterdienst, Offenbach, Germany","Department of Meteorology, University of Reading, United Kingdom","National Centre for Earth Observations, University of Reading, United Kingdom","Department of Mathematics and Statistics, University of Reading, United Kingdom"],"raw_orcid":"https://orcid.org/0000-0002-3016-6568","affiliations":[{"raw_affiliation_string":"German Meteorological Service -Deutscher Wetterdienst, Offenbach, Germany","institution_ids":["https://openalex.org/I172825728"]},{"raw_affiliation_string":"Department of Meteorology, University of Reading, United Kingdom","institution_ids":["https://openalex.org/I71052956"]},{"raw_affiliation_string":"National Centre for Earth Observations, University of Reading, United Kingdom","institution_ids":["https://openalex.org/I4210128104","https://openalex.org/I71052956"]},{"raw_affiliation_string":"Department of Mathematics and Statistics, University of Reading, United Kingdom","institution_ids":["https://openalex.org/I71052956"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":5,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.1166,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.43256267,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":95},"biblio":{"volume":"20","issue":"1","first_page":"299","last_page":"332"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10466","display_name":"Meteorological Phenomena and Simulations","score":1.0,"subfield":{"id":"https://openalex.org/subfields/1902","display_name":"Atmospheric Science"},"field":{"id":"https://openalex.org/fields/19","display_name":"Earth and Planetary Sciences"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10466","display_name":"Meteorological Phenomena and Simulations","score":1.0,"subfield":{"id":"https://openalex.org/subfields/1902","display_name":"Atmospheric Science"},"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/T10029","display_name":"Climate variability and models","score":0.9991000294685364,"subfield":{"id":"https://openalex.org/subfields/2306","display_name":"Global and Planetary Change"},"field":{"id":"https://openalex.org/fields/23","display_name":"Environmental Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11371","display_name":"Wind and Air Flow Studies","score":0.9988999962806702,"subfield":{"id":"https://openalex.org/subfields/2305","display_name":"Environmental Engineering"},"field":{"id":"https://openalex.org/fields/23","display_name":"Environmental Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/data-assimilation","display_name":"Data assimilation","score":0.8171273469924927},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5625691413879395},{"id":"https://openalex.org/keywords/estimation","display_name":"Estimation","score":0.5201061964035034},{"id":"https://openalex.org/keywords/econometrics","display_name":"Econometrics","score":0.48550036549568176},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4799378514289856},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4662517309188843},{"id":"https://openalex.org/keywords/estimation-theory","display_name":"Estimation theory","score":0.4290620684623718},{"id":"https://openalex.org/keywords/assimilation","display_name":"Assimilation (phonology)","score":0.42247089743614197},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3796793222427368},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.3595358729362488},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.287826269865036},{"id":"https://openalex.org/keywords/meteorology","display_name":"Meteorology","score":0.1781643033027649},{"id":"https://openalex.org/keywords/geography","display_name":"Geography","score":0.11707565188407898},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.10476580262184143},{"id":"https://openalex.org/keywords/economics","display_name":"Economics","score":0.0842897891998291},{"id":"https://openalex.org/keywords/philosophy","display_name":"Philosophy","score":0.07050830125808716}],"concepts":[{"id":"https://openalex.org/C24552861","wikidata":"https://www.wikidata.org/wiki/Q2670177","display_name":"Data assimilation","level":2,"score":0.8171273469924927},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5625691413879395},{"id":"https://openalex.org/C96250715","wikidata":"https://www.wikidata.org/wiki/Q965330","display_name":"Estimation","level":2,"score":0.5201061964035034},{"id":"https://openalex.org/C149782125","wikidata":"https://www.wikidata.org/wiki/Q160039","display_name":"Econometrics","level":1,"score":0.48550036549568176},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4799378514289856},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4662517309188843},{"id":"https://openalex.org/C167928553","wikidata":"https://www.wikidata.org/wiki/Q1376021","display_name":"Estimation theory","level":2,"score":0.4290620684623718},{"id":"https://openalex.org/C75649859","wikidata":"https://www.wikidata.org/wiki/Q148877","display_name":"Assimilation (phonology)","level":2,"score":0.42247089743614197},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3796793222427368},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.3595358729362488},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.287826269865036},{"id":"https://openalex.org/C153294291","wikidata":"https://www.wikidata.org/wiki/Q25261","display_name":"Meteorology","level":1,"score":0.1781643033027649},{"id":"https://openalex.org/C205649164","wikidata":"https://www.wikidata.org/wiki/Q1071","display_name":"Geography","level":0,"score":0.11707565188407898},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.10476580262184143},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0842897891998291},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.07050830125808716},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0},{"id":"https://openalex.org/C187736073","wikidata":"https://www.wikidata.org/wiki/Q2920921","display_name":"Management","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/19m1294848","is_oa":false,"landing_page_url":"https://doi.org/10.1137/19m1294848","pdf_url":null,"source":{"id":"https://openalex.org/S161160597","display_name":"SIAM Journal on Applied Dynamical Systems","issn_l":"1536-0040","issn":["1536-0040"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Applied Dynamical Systems","raw_type":"journal-article"},{"id":"pmh:oai:centaur.reading.ac.uk:93076","is_oa":false,"landing_page_url":"https://centaur.reading.ac.uk/view/creators/90000514.html>","pdf_url":null,"source":{"id":"https://openalex.org/S4306402273","display_name":"CentAUR (University of Reading)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I71052956","host_organization_name":"University of Reading","host_organization_lineage":["https://openalex.org/I71052956"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":null,"raw_type":"Article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G424554497","display_name":null,"funder_award_id":"nceo020004","funder_id":"https://openalex.org/F4320320022","funder_display_name":"Sight Research UK"},{"id":"https://openalex.org/G5072611438","display_name":null,"funder_award_id":"NE/R016518/1","funder_id":"https://openalex.org/F4320320022","funder_display_name":"Sight Research UK"},{"id":"https://openalex.org/G7685872390","display_name":null,"funder_award_id":"NE/R016518/1","funder_id":"https://openalex.org/F4320334631","funder_display_name":"Natural Environment Research Council"},{"id":"https://openalex.org/G8944774407","display_name":null,"funder_award_id":"nceo020004","funder_id":"https://openalex.org/F4320334631","funder_display_name":"Natural Environment Research Council"}],"funders":[{"id":"https://openalex.org/F4320320022","display_name":"Sight Research UK","ror":"https://ror.org/03z2py885"},{"id":"https://openalex.org/F4320320326","display_name":"University of Reading","ror":"https://ror.org/05v62cm79"},{"id":"https://openalex.org/F4320334631","display_name":"Natural Environment Research Council","ror":"https://ror.org/02b5d8509"},{"id":"https://openalex.org/F4320338155","display_name":"National Centre for Earth Observation","ror":"https://ror.org/0375jbm11"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":77,"referenced_works":["https://openalex.org/W1525114282","https://openalex.org/W1530737205","https://openalex.org/W1541028045","https://openalex.org/W1546628974","https://openalex.org/W1864589048","https://openalex.org/W1965276348","https://openalex.org/W1966764026","https://openalex.org/W1976508675","https://openalex.org/W1987308763","https://openalex.org/W1995262681","https://openalex.org/W1996382496","https://openalex.org/W2008484670","https://openalex.org/W2010299042","https://openalex.org/W2018776204","https://openalex.org/W2019717948","https://openalex.org/W2019960424","https://openalex.org/W2022005834","https://openalex.org/W2022281931","https://openalex.org/W2023600937","https://openalex.org/W2024341519","https://openalex.org/W2025179796","https://openalex.org/W2025292785","https://openalex.org/W2033254155","https://openalex.org/W2035331188","https://openalex.org/W2035933721","https://openalex.org/W2039617885","https://openalex.org/W2045381799","https://openalex.org/W2045549826","https://openalex.org/W2046534255","https://openalex.org/W2056444889","https://openalex.org/W2063177672","https://openalex.org/W2063618362","https://openalex.org/W2063846207","https://openalex.org/W2065066378","https://openalex.org/W2066455064","https://openalex.org/W2073142925","https://openalex.org/W2074441553","https://openalex.org/W2076116040","https://openalex.org/W2086305681","https://openalex.org/W2096083228","https://openalex.org/W2098115494","https://openalex.org/W2101981609","https://openalex.org/W2103854834","https://openalex.org/W2105195639","https://openalex.org/W2106141943","https://openalex.org/W2109005173","https://openalex.org/W2112556970","https://openalex.org/W2113629826","https://openalex.org/W2114948422","https://openalex.org/W2115033621","https://openalex.org/W2123940107","https://openalex.org/W2126202478","https://openalex.org/W2128931495","https://openalex.org/W2132600099","https://openalex.org/W2136894371","https://openalex.org/W2137467781","https://openalex.org/W2138513194","https://openalex.org/W2138601027","https://openalex.org/W2141394518","https://openalex.org/W2147119488","https://openalex.org/W2150278270","https://openalex.org/W2154423634","https://openalex.org/W2157098139","https://openalex.org/W2165648362","https://openalex.org/W2172819965","https://openalex.org/W2173190456","https://openalex.org/W2174521210","https://openalex.org/W2179584279","https://openalex.org/W2237826530","https://openalex.org/W2469805270","https://openalex.org/W2563710438","https://openalex.org/W2572237602","https://openalex.org/W2588830025","https://openalex.org/W2770886878","https://openalex.org/W2809929756","https://openalex.org/W2963999581","https://openalex.org/W4244731586"],"related_works":["https://openalex.org/W2654527859","https://openalex.org/W1666666856","https://openalex.org/W2276167504","https://openalex.org/W3188177659","https://openalex.org/W17182576","https://openalex.org/W2393565244","https://openalex.org/W2991924068","https://openalex.org/W2394447903","https://openalex.org/W2354237351","https://openalex.org/W4238891807"],"abstract_inverted_index":{"In":[0,81,142],"this":[1,217],"study,":[2],"we":[3,51,83],"develop":[4],"model":[5,15,26,48,61,92,121,156,179,186,236,245],"bias":[6,62,193,237],"estimators":[7,32,63,194],"based":[8],"on":[9],"an":[10,171],"asymptotic":[11],"expansion":[12,130],"of":[13,37,56,89,98,119,126,154,177,191,204,211,222,249],"the":[14,31,35,44,57,87,90,113,117,120,124,127,145,152,155,164,175,178,189,202,205,209,212,220,235,242,247,250,261],"dynamics":[16],"for":[17,93],"small":[18,22,94],"time":[19,199],"scales":[20],"and":[21,28,60,101,122,208,252,263],"perturbations":[23],"in":[24,64,96,260],"a":[25,38,65,74,137,223,230],"parameter,":[27],"then":[29,102,160,188],"use":[30,103],"to":[33,110,169,257],"improve":[34,201],"performance":[36,203],"data":[39,107,143],"assimilation":[40,108,206],"system.":[41],"We":[42,215],"employ":[43],"well-known":[45],"Lorenz":[46,91,243],"(1963)":[47,244],"so":[49],"that":[50,68,112,123,195,254],"can":[52,131],"study":[53],"all":[54],"aspects":[55],"dynamical":[58],"system":[59,207],"detailed":[66],"way":[67],"would":[69],"not":[70],"be":[71,132],"possible":[72],"with":[73,163,198,229],"full":[75],"physics":[76],"numerical":[77],"weather":[78],"prediction":[79],"model.":[80],"particular,":[82],"first":[84],"work":[85],"out":[86],"asymptotics":[88,114],"changes":[95],"one":[97],"its":[99],"parameters":[100],"statistics":[104],"from":[105],"cycled":[106],"experiments":[109],"demonstrate":[111,216],"accurately":[115],"represent":[116],"behavior":[118],"coefficients":[125],"nonlinear":[128,192],"asymptotical":[129],"reasonably":[133],"estimated":[134],"by":[135,184],"solving":[136],"least":[138],"squares":[139],"minimization":[140],"problem.":[141],"assimilation,":[144],"background":[146,180,225],"error":[147,166,226],"covariance":[148,167,227],"matrix":[149,168,228,232],"usually":[150],"estimates":[151],"uncertainty":[153,176],"background,":[157],"which":[158],"is":[159,181],"used":[161],"along":[162],"observation":[165],"produce":[170],"updated":[172,213],"analysis.":[173,214],"If":[174],"strongly":[182],"influenced":[183],"time-dependent":[185],"biases,":[187],"development":[190],"also":[196],"vary":[197],"could":[200],"accuracy":[210],"improvement":[218],"through":[219],"combination":[221],"constant":[224],"dynamically-varying":[231],"computed":[233],"using":[234,241],"estimators.":[238],"Numerical":[239],"tests":[240],"illustrate":[246],"feasibility":[248],"approach":[251],"show":[253],"it":[255],"leads":[256],"clear":[258],"improvements":[259],"analysis":[262],"forecast":[264],"accuracy.":[265]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2022,"cited_by_count":1}],"updated_date":"2026-07-02T09:51:11.867554","created_date":"2025-10-10T00:00:00"}