{"id":"https://openalex.org/W7224103404","doi":"https://doi.org/10.31223/x5jb8v","title":"Structure Function Sampling Uncertainty: A Gaussian-Increment Reference Framework","display_name":"Structure Function Sampling Uncertainty: A Gaussian-Increment Reference Framework","publication_year":2026,"publication_date":"2026-10-28","ids":{"openalex":"https://openalex.org/W7224103404","doi":"https://doi.org/10.31223/x5jb8v"},"language":"en","primary_location":{"id":"doi:10.31223/x5jb8v","doi":"https://doi.org/10.31223/x5jb8v","is_oa":true,"landing_page_url":"https://doi.org/10.31223/x5jb8v","pdf_url":"https://eartharxiv.org/repository/object/15784/download/27365/","source":null,"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":null,"raw_type":"posted-content"},"volume":null,"type":"preprint","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://eartharxiv.org/repository/object/15784/download/27365/","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5090653877","display_name":"Andrey Shcherbina","orcid":"https://orcid.org/0000-0002-4246-487X","observed_orcids":["https://orcid.org/0000-0002-4246-487X"]},"institutions":[{"id":"https://openalex.org/I201448701","display_name":"University of Washington","ror":"https://ror.org/00cvxb145","country_code":"US","type":"education","lineage":["https://openalex.org/I201448701"]},{"id":"https://openalex.org/I4210138199","display_name":"University of Washington Applied Physics Laboratory","ror":"https://ror.org/03d17d270","country_code":"US","type":"facility","lineage":["https://openalex.org/I201448701","https://openalex.org/I4210138199"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Andrey Shcherbina","raw_affiliation_strings":["Applied Physics Laboratory , University of Washington"],"raw_orcid":"https://orcid.org/0000-0002-4246-487X","affiliations":[{"raw_affiliation_string":"Applied Physics Laboratory , University of Washington","institution_ids":["https://openalex.org/I201448701","https://openalex.org/I4210138199"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5090653877"],"corresponding_institution_ids":["https://openalex.org/I201448701","https://openalex.org/I4210138199"],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":null,"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":0.2667999863624573,"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":0.2667999863624573,"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/T10360","display_name":"Fluid Dynamics and Turbulent Flows","score":0.2062000036239624,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10255","display_name":"Oceanographic and Atmospheric Processes","score":0.13429999351501465,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/structure-functions","display_name":"structure functions","score":0.8240000009536743},{"id":"https://openalex.org/keywords/sampling-uncertainty","display_name":"sampling uncertainty","score":0.9850000143051147},{"id":"https://openalex.org/keywords/sampling-variance","display_name":"sampling variance","score":0.5889999866485596},{"id":"https://openalex.org/keywords/spatial-covariance","display_name":"spatial covariance","score":0.6259999871253967},{"id":"https://openalex.org/keywords/effective-degrees-of-freedom","display_name":"effective degrees of freedom","score":0.6769999861717224},{"id":"https://openalex.org/keywords/confidence-intervals","display_name":"confidence intervals","score":0.7509999871253967},{"id":"https://openalex.org/keywords/scaling-exponents","display_name":"scaling exponents","score":0.9319999814033508},{"id":"https://openalex.org/keywords/fourth-order-cumulants","display_name":"fourth-order cumulants","score":0.8399999737739563},{"id":"https://openalex.org/keywords/geophysical-fields","display_name":"geophysical fields","score":0.7210000157356262}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7656999826431274},{"id":"https://openalex.org/C178650346","wikidata":"https://www.wikidata.org/wiki/Q201984","display_name":"Covariance","level":2,"score":0.7069000005722046},{"id":"https://openalex.org/C140779682","wikidata":"https://www.wikidata.org/wiki/Q210868","display_name":"Sampling (signal processing)","level":3,"score":0.6654000282287598},{"id":"https://openalex.org/C137250428","wikidata":"https://www.wikidata.org/wiki/Q5178897","display_name":"Covariance function","level":3,"score":0.6158000230789185},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.5454000234603882},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.46160000562667847},{"id":"https://openalex.org/C2778755073","wikidata":"https://www.wikidata.org/wiki/Q10858537","display_name":"Scale (ratio)","level":2,"score":0.40689998865127563},{"id":"https://openalex.org/C185142706","wikidata":"https://www.wikidata.org/wiki/Q1134404","display_name":"Covariance matrix","level":2,"score":0.40209999680519104},{"id":"https://openalex.org/C99844830","wikidata":"https://www.wikidata.org/wiki/Q102441924","display_name":"Scaling","level":2,"score":0.39590001106262207},{"id":"https://openalex.org/C82152865","wikidata":"https://www.wikidata.org/wiki/Q7208505","display_name":"Poisson sampling","level":5,"score":0.3675000071525574},{"id":"https://openalex.org/C170593435","wikidata":"https://www.wikidata.org/wiki/Q4128565","display_name":"Slice sampling","level":4,"score":0.35530000925064087},{"id":"https://openalex.org/C196083921","wikidata":"https://www.wikidata.org/wiki/Q7915758","display_name":"Variance (accounting)","level":2,"score":0.3522999882698059},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3517000079154968},{"id":"https://openalex.org/C52740198","wikidata":"https://www.wikidata.org/wiki/Q1539564","display_name":"Importance sampling","level":3,"score":0.3441999852657318},{"id":"https://openalex.org/C208081375","wikidata":"https://www.wikidata.org/wiki/Q274502","display_name":"Degrees of freedom (physics and chemistry)","level":2,"score":0.32589998841285706},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.325300008058548},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.3181000053882599},{"id":"https://openalex.org/C61326573","wikidata":"https://www.wikidata.org/wiki/Q1496376","display_name":"Gaussian process","level":3,"score":0.30970001220703125},{"id":"https://openalex.org/C184898388","wikidata":"https://www.wikidata.org/wiki/Q1435712","display_name":"Pairwise comparison","level":2,"score":0.3093000054359436},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.3021000027656555},{"id":"https://openalex.org/C62644790","wikidata":"https://www.wikidata.org/wiki/Q3454689","display_name":"Variance reduction","level":3,"score":0.28110000491142273},{"id":"https://openalex.org/C11577676","wikidata":"https://www.wikidata.org/wiki/Q134237","display_name":"Square root","level":2,"score":0.273499995470047},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.26499998569488525},{"id":"https://openalex.org/C71907059","wikidata":"https://www.wikidata.org/wiki/Q223323","display_name":"Root mean square","level":2,"score":0.26249998807907104},{"id":"https://openalex.org/C150060386","wikidata":"https://www.wikidata.org/wiki/Q7574054","display_name":"Spatial correlation","level":2,"score":0.2606000006198883},{"id":"https://openalex.org/C139945424","wikidata":"https://www.wikidata.org/wiki/Q1940696","display_name":"Mean squared error","level":2,"score":0.2567000091075897},{"id":"https://openalex.org/C180877172","wikidata":"https://www.wikidata.org/wiki/Q5401390","display_name":"Estimation of covariance matrices","level":3,"score":0.2547999918460846}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.31223/x5jb8v","doi":"https://doi.org/10.31223/x5jb8v","is_oa":true,"landing_page_url":"https://doi.org/10.31223/x5jb8v","pdf_url":"https://eartharxiv.org/repository/object/15784/download/27365/","source":null,"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":null,"raw_type":"posted-content"},{"id":"pmh:oai:EA:id:15784","doi":null,"is_oa":true,"landing_page_url":"https://eartharxiv.org/repository/object/15784/download/27365/","pdf_url":null,"source":{"id":"https://openalex.org/S4306402614","display_name":"EarthArXiv (California Digital Library)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I2801248553","host_organization_name":"California Digital Library","host_organization_lineage":["https://openalex.org/I2801248553"],"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":"EarthArXiv","raw_type":"PREPRINTS"}],"best_oa_location":{"id":"doi:10.31223/x5jb8v","doi":"https://doi.org/10.31223/x5jb8v","is_oa":true,"landing_page_url":"https://doi.org/10.31223/x5jb8v","pdf_url":"https://eartharxiv.org/repository/object/15784/download/27365/","source":null,"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":null,"raw_type":"posted-content"},"sustainable_development_goals":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G6132188576","display_name":"Exploration of Anisotropy and Inhomogeneity of Ocean Boundary Layer Turbulence","funder_award_id":"2344156","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G7381655226","display_name":null,"funder_award_id":"80NSSC21K0832","funder_id":"https://openalex.org/F4320306101","funder_display_name":"National Aeronautics and Space Administration"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320306101","display_name":"National Aeronautics and Space Administration","ror":"https://ror.org/027ka1x80"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7224103404.pdf","grobid_xml":"https://content.openalex.org/works/W7224103404.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W7148721614","https://openalex.org/W1485281150","https://openalex.org/W2188839588","https://openalex.org/W2134633420","https://openalex.org/W2114895985","https://openalex.org/W4280573143","https://openalex.org/W1552064830","https://openalex.org/W7135231267","https://openalex.org/W3048265245","https://openalex.org/W3105480629"],"abstract_inverted_index":{"Structure":[0],"functions":[1],"(SFs)":[2],"are":[3,24],"widely":[4],"used":[5,162],"to":[6,19,82,163,173,176,199],"characterize":[7],"scale-dependent":[8],"variability":[9],"in":[10,72],"geophysical":[11],"fields,":[12],"but":[13],"their":[14],"sampling":[15,49,80,91,96,213],"uncertainty":[16,128,172],"is":[17,51,196],"difficult":[18,198],"quantify":[20],"because":[21],"pairwise":[22],"increments":[23],"generally":[25],"dependent.":[26],"Dependence":[27],"arises":[28],"from":[29,85,184],"both":[30],"shared":[31],"observations":[32],"and":[33,90,132,215],"spatial":[34,216],"covariance":[35,54,71,170],"of":[36,74,113,121,151,154],"the":[37,63,75,104,141,147,152,185],"underlying":[38],"field,":[39],"so":[40],"pair":[41],"counts":[42],"alone":[43],"do":[44],"not":[45],"determine":[46],"uncertainty.":[47],"The":[48,119,201],"variance":[50,81,159],"governed":[52],"by":[53],"among":[55],"increment":[56],"powers,":[57],"termed":[58],"structure-function":[59],"contributions":[60],"(SFCs).":[61],"For":[62,93],"second-order":[64,88],"SF,":[65],"a":[66,86,98,206],"Gaussian-increment":[67],"closure":[68],"expresses":[69],"SFC":[70,101],"terms":[73],"SF":[76],"itself,":[77],"allowing":[78],"fractional":[79,142],"be":[83,161,174],"calculated":[84],"specified":[87],"model":[89],"geometry.":[92],"regular":[94],"one-dimensional":[95],"with":[97],"finite":[99],"integral":[100],"correlation":[102,116],"scale,":[103],"well-resolved,":[105],"long-record":[106],"limit":[107],"gives":[108],"approximately":[109],"one":[110],"effective":[111],"degree":[112],"freedom":[114],"per":[115],"scale":[117,123],"sampled.":[118,157],"dependence":[120],"this":[122],"on":[124],"separation":[125],"yields":[126],"simple":[127],"scalings":[129],"for":[130,137,212],"finite-scale":[131],"scale-free":[133],"models.":[134],"In":[135],"particular,":[136],"spectra":[138],"near":[139],"$k^{-2}$,":[140],"standard":[143],"error":[144],"scales":[145],"as":[146,180],"inverse":[148],"square":[149],"root":[150],"number":[153],"separation-length":[155],"intervals":[156],"Sampling":[158],"can":[160],"construct":[164],"approximate":[165],"confidence":[166],"intervals,":[167],"while":[168],"cross-scale":[169],"allows":[171],"propagated":[175],"derived":[177],"quantities":[178],"such":[179],"scaling":[181],"exponents.":[182],"Departures":[183],"Gaussian":[186,202],"reference":[187],"enter":[188],"through":[189],"an":[190],"additional":[191],"fourth-order":[192],"cumulant":[193],"contribution":[194],"that":[195,209],"more":[197],"quantify.":[200],"result":[203],"thus":[204],"provides":[205],"tractable":[207],"baseline":[208],"explicitly":[210],"accounts":[211],"geometry":[214],"dependence.":[217]},"counts_by_year":[],"updated_date":"2026-10-31T12:09:11.096373","created_date":"2026-10-29T00:00:00"}
