{"id":"https://openalex.org/W4416504272","doi":"https://doi.org/10.1002/qj.70351","title":"Fair Gaussian Box ordinate transform for assessing the reliability of multivariate ensemble forecasts","display_name":"Fair Gaussian Box ordinate transform for assessing the reliability of multivariate ensemble forecasts","publication_year":2026,"publication_date":"2026-11-06","ids":{"openalex":"https://openalex.org/W4416504272","doi":"https://doi.org/10.1002/qj.70351"},"language":"en","primary_location":{"id":"doi:10.1002/qj.70351","doi":"https://doi.org/10.1002/qj.70351","is_oa":true,"landing_page_url":"https://doi.org/10.1002/qj.70351","pdf_url":"https://onlinelibrary.wiley.com/doi/pdfdirect/10.1002/qj.70351","source":{"id":"https://openalex.org/S70522100","display_name":"Quarterly Journal of the Royal Meteorological Society","issn_l":"0035-9009","issn":["0035-9009","1477-870X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","dongbi-b","jufo-2","norway-2","poland-200","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":"cc-by-nc","license_id":"https://openalex.org/licenses/cc-by-nc","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Quarterly Journal of the Royal Meteorological Society","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://onlinelibrary.wiley.com/doi/pdfdirect/10.1002/qj.70351","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5034327996","display_name":"S\u00e1ndor Baran","orcid":"https://orcid.org/0000-0003-1035-004X","observed_orcids":["https://orcid.org/0000-0003-1035-004X"]},"institutions":[{"id":"https://openalex.org/I132735039","display_name":"University of Debrecen","ror":"https://ror.org/02xf66n48","country_code":"HU","type":"education","lineage":["https://openalex.org/I132735039"]}],"countries":["HU"],"is_corresponding":true,"raw_author_name":"S\u00e1ndor Baran","raw_affiliation_strings":["Faculty of Informatics University of Debrecen  Debrecen Hungary"],"raw_orcid":"https://orcid.org/0000-0003-1035-004X","affiliations":[{"raw_affiliation_string":"Faculty of Informatics University of Debrecen  Debrecen Hungary","institution_ids":["https://openalex.org/I132735039"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5024633092","display_name":"Martin Leutbecher","orcid":"https://orcid.org/0000-0003-4160-0750","observed_orcids":["https://orcid.org/0000-0003-4160-0750"]},"institutions":[{"id":"https://openalex.org/I154986956","display_name":"European Centre for Medium-Range Weather Forecasts","ror":"https://ror.org/014w0fd65","country_code":"GB","type":"other","lineage":["https://openalex.org/I154986956"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Martin Leutbecher","raw_affiliation_strings":["European Centre for Medium\u2010Range Weather Forecasts  Reading UK"],"raw_orcid":"https://orcid.org/0000-0003-4160-0750","affiliations":[{"raw_affiliation_string":"European Centre for Medium\u2010Range Weather Forecasts  Reading UK","institution_ids":["https://openalex.org/I154986956"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5034327996"],"corresponding_institution_ids":["https://openalex.org/I132735039"],"apc_list":{"value":4320,"currency":"USD","value_usd":4320},"apc_paid":{"value":4320,"currency":"USD","value_usd":4320},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.00976875,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10466","display_name":"Meteorological Phenomena and Simulations","score":0.8032000064849854,"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":0.8032000064849854,"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/T11918","display_name":"Forecasting Techniques and Applications","score":0.13760000467300415,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T10330","display_name":"Hydrology and Watershed Management Studies","score":0.005100000184029341,"subfield":{"id":"https://openalex.org/subfields/2312","display_name":"Water Science and Technology"},"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/forecast-calibration","display_name":"forecast calibration","score":0.828000009059906},{"id":"https://openalex.org/keywords/normal-distribution","display_name":"normal distribution","score":0.43700000643730164},{"id":"https://openalex.org/keywords/probabilistic-forecasting","display_name":"probabilistic forecasting","score":0.5180000066757202},{"id":"https://openalex.org/keywords/ecmwf-ensemble-forecasts","display_name":"ECMWF ensemble forecasts","score":0.7059999704360962},{"id":"https://openalex.org/keywords/temperature-prediction","display_name":"temperature prediction","score":0.6259999871253967}],"concepts":[{"id":"https://openalex.org/C19499675","wikidata":"https://www.wikidata.org/wiki/Q232207","display_name":"Monte Carlo method","level":2,"score":0.708899974822998},{"id":"https://openalex.org/C129848803","wikidata":"https://www.wikidata.org/wiki/Q2564360","display_name":"Sample size determination","level":2,"score":0.6827999949455261},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.6743000149726868},{"id":"https://openalex.org/C198531522","wikidata":"https://www.wikidata.org/wiki/Q485146","display_name":"Sample (material)","level":2,"score":0.6662999987602234},{"id":"https://openalex.org/C165838908","wikidata":"https://www.wikidata.org/wiki/Q736777","display_name":"Calibration","level":2,"score":0.647599995136261},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5295000076293945},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.5073999762535095},{"id":"https://openalex.org/C177384507","wikidata":"https://www.wikidata.org/wiki/Q1149000","display_name":"Multivariate normal distribution","level":3,"score":0.5037000179290771},{"id":"https://openalex.org/C140779682","wikidata":"https://www.wikidata.org/wiki/Q210868","display_name":"Sampling (signal processing)","level":3,"score":0.4268999993801117},{"id":"https://openalex.org/C61326573","wikidata":"https://www.wikidata.org/wiki/Q1496376","display_name":"Gaussian process","level":3,"score":0.4025999903678894},{"id":"https://openalex.org/C49937458","wikidata":"https://www.wikidata.org/wiki/Q2599292","display_name":"Probabilistic logic","level":2,"score":0.38830000162124634},{"id":"https://openalex.org/C204323151","wikidata":"https://www.wikidata.org/wiki/Q905424","display_name":"Range (aeronautics)","level":2,"score":0.382999986410141},{"id":"https://openalex.org/C161584116","wikidata":"https://www.wikidata.org/wiki/Q1952580","display_name":"Multivariate statistics","level":2,"score":0.3587999939918518},{"id":"https://openalex.org/C149782125","wikidata":"https://www.wikidata.org/wiki/Q160039","display_name":"Econometrics","level":1,"score":0.3587000072002411},{"id":"https://openalex.org/C148220186","wikidata":"https://www.wikidata.org/wiki/Q7111912","display_name":"Outcome (game theory)","level":2,"score":0.35569998621940613},{"id":"https://openalex.org/C52740198","wikidata":"https://www.wikidata.org/wiki/Q1539564","display_name":"Importance sampling","level":3,"score":0.3546999990940094},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.3249000012874603},{"id":"https://openalex.org/C2776502983","wikidata":"https://www.wikidata.org/wiki/Q690182","display_name":"Contrast (vision)","level":2,"score":0.322299987077713},{"id":"https://openalex.org/C187192777","wikidata":"https://www.wikidata.org/wiki/Q381699","display_name":"Rejection sampling","level":5,"score":0.32100000977516174},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.28790000081062317},{"id":"https://openalex.org/C61797465","wikidata":"https://www.wikidata.org/wiki/Q1188986","display_name":"Term (time)","level":2,"score":0.25450000166893005},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.25279998779296875},{"id":"https://openalex.org/C149441793","wikidata":"https://www.wikidata.org/wiki/Q200726","display_name":"Probability distribution","level":2,"score":0.25189998745918274}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1002/qj.70351","doi":"https://doi.org/10.1002/qj.70351","is_oa":true,"landing_page_url":"https://doi.org/10.1002/qj.70351","pdf_url":"https://onlinelibrary.wiley.com/doi/pdfdirect/10.1002/qj.70351","source":{"id":"https://openalex.org/S70522100","display_name":"Quarterly Journal of the Royal Meteorological Society","issn_l":"0035-9009","issn":["0035-9009","1477-870X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","dongbi-b","jufo-2","norway-2","poland-200","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":"cc-by-nc","license_id":"https://openalex.org/licenses/cc-by-nc","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Quarterly Journal of the Royal Meteorological Society","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2506.22601","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2506.22601","pdf_url":"https://arxiv.org/pdf/2506.22601","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2506.22601","doi":"https://doi.org/10.48550/arxiv.2506.22601","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2506.22601","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.1002/qj.70351","doi":"https://doi.org/10.1002/qj.70351","is_oa":true,"landing_page_url":"https://doi.org/10.1002/qj.70351","pdf_url":"https://onlinelibrary.wiley.com/doi/pdfdirect/10.1002/qj.70351","source":{"id":"https://openalex.org/S70522100","display_name":"Quarterly Journal of the Royal Meteorological Society","issn_l":"0035-9009","issn":["0035-9009","1477-870X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","dongbi-b","jufo-2","norway-2","poland-200","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":"cc-by-nc","license_id":"https://openalex.org/licenses/cc-by-nc","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Quarterly Journal of the Royal Meteorological Society","raw_type":"journal-article"},"sustainable_development_goals":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G6322178875","display_name":null,"funder_award_id":"K142849","funder_id":"https://openalex.org/F4320336675","funder_display_name":"National Research, Development and Innovation Office"}],"funders":[{"id":"https://openalex.org/F4320336675","display_name":"National Research, Development and Innovation Office","ror":null}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4416504272.pdf","grobid_xml":"https://content.openalex.org/works/W4416504272.grobid-xml"},"referenced_works_count":33,"referenced_works":["https://openalex.org/W1910986034","https://openalex.org/W1970957555","https://openalex.org/W1984925443","https://openalex.org/W1988618328","https://openalex.org/W1990779154","https://openalex.org/W1991828334","https://openalex.org/W2001234880","https://openalex.org/W2025720061","https://openalex.org/W2069821006","https://openalex.org/W2091206738","https://openalex.org/W2102755693","https://openalex.org/W2113423637","https://openalex.org/W2122384070","https://openalex.org/W2154952449","https://openalex.org/W2309490420","https://openalex.org/W2518561078","https://openalex.org/W2805066877","https://openalex.org/W2810202692","https://openalex.org/W2826678630","https://openalex.org/W2903205861","https://openalex.org/W2913728931","https://openalex.org/W2940388134","https://openalex.org/W3000264364","https://openalex.org/W3016791436","https://openalex.org/W4239966440","https://openalex.org/W4288919818","https://openalex.org/W4318618362","https://openalex.org/W4390113904","https://openalex.org/W4391418112","https://openalex.org/W4404704236","https://openalex.org/W4405031167","https://openalex.org/W4410968302","https://openalex.org/W7127046044"],"related_works":["https://openalex.org/W4408429876","https://openalex.org/W4300384033","https://openalex.org/W4390113904","https://openalex.org/W3122083620","https://openalex.org/W4302802921","https://openalex.org/W3034306193","https://openalex.org/W7135205565","https://openalex.org/W2338182691","https://openalex.org/W2406456475","https://openalex.org/W3198537797"],"abstract_inverted_index":{"Abstract":[0],"Ensemble":[1],"techniques":[2],"are":[3,26,39,264],"the":[4,30,43,48,59,73,81,89,94,105,116,127,136,152,160,177,185,205,217,225,230,252,267,276,280,283,286,293],"method":[5,71],"of":[6,12,35,45,47,54,75,118,176,212,242,251,292],"choice":[7],"for":[8,86,130,196,255],"making":[9],"probabilistic":[10],"predictions":[11,24,38,53,241],"an":[13,76],"outcome":[14,268],"in":[15,41,132,222,282],"several":[16],"disciplines.":[17],"The":[18],"aim":[19],"is":[20,96,111,122,138,155,190,210,220,235,269,288],"to":[21,64,98,100,108,146,224,237,239],"generate":[22],"calibrated":[23],"that":[25,204,274],"statistically":[27],"indistinguishable":[28],"from":[29,299],"outcome.":[31],"Developers":[32],"and":[33,57,172,199,244,296],"users":[34],"such":[36],"ensemble":[37,68,106,120,128,153,249],"interested":[40],"evaluating":[42],"degree":[44],"calibration":[46,102,148],"forecasts.":[49],"Here,":[50],"we":[51,166],"consider":[52],"\u2010dimensional":[55],"outcomes":[56],"apply":[58],"Box":[60],"ordinate":[61],"transform":[62],"(BOT)":[63],"assess":[65,147],"calibration.":[66],"For":[67,113],"forecasts,":[69],"this":[70,164],"requires":[72],"assumption":[74],"underlying":[77],"parametric":[78],"distribution,":[79],"with":[80,192],"most":[82],"natural":[83],"starting":[84],"point":[85],"investigation":[87],"being":[88],"multivariate":[90],"Gaussian":[91,178,187,207,232],"law.":[92],"However,":[93],"BOT":[95,189,194,209,227,234,287],"known":[97],"fail":[99],"indicate":[101],"reliably":[103,149],"when":[104,135,151,216],"size":[107,154,171,219],"dimension":[109,173],"ratio":[110],"small.":[112],"some":[114],"applications,":[115],"cost":[117],"obtaining":[119],"estimates":[121,291],"significant,":[123],"which":[124],"can":[125],"limit":[126],"size:":[129],"instance,":[131],"model":[133,137],"development":[134],"improved":[139],"iteratively.":[140],"Thus,":[141],"it":[142],"would":[143],"be":[144],"beneficial":[145],"even":[150],"only":[156],"moderately":[157],"larger":[158],"than":[159],"dimension.":[161],"To":[162],"address":[163],"need,":[165],"introduce":[167],"a":[168,182,272],"fair":[169,186,206,231],"sample":[170,179,188,200,208,218,233],"dependent":[174],"version":[175],"BOT.":[180],"In":[181],"simulation":[183],"study,":[184],"compared":[191],"alternative":[193,226],"versions":[195],"different":[197],"miscalibrations":[198],"sizes.":[201],"Results":[202],"confirm":[203],"capable":[211],"identifying":[213],"miscalibration":[214],"correctly":[215],"moderate,":[221],"contrast":[223],"versions.":[228],"Subsequently,":[229],"applied":[236],"two\u2010":[238],"12\u2010dimensional":[240],"temperature":[243,295],"vector":[245,297],"wind":[246,298],"using":[247,290],"operational":[248],"forecasts":[250],"European":[253],"Centre":[254],"Medium\u2010Range":[256],"Weather":[257],"Forecasts":[258],"(ECMWF).":[259],"Firstly,":[260],"perfectly":[261],"reliable":[262],"situations":[263],"considered":[265],"where":[266],"replaced":[270],"by":[271],"forecast":[273],"samples":[275],"same":[277],"distribution":[278],"as":[279],"members":[281],"ensemble.":[284],"Secondly,":[285],"computed":[289],"actual":[294],"ECMWF":[300],"analyses.":[301]},"counts_by_year":[],"updated_date":"2026-11-10T11:39:43.021295","created_date":"2025-10-10T00:00:00"}