What limits the number of observations that can be effectively assimilated by EnKF?
The ability of ensemble Kalman filter (EnKF) algorithms to extract information from observations is analyzed with the aid of the concept of the degrees of freedom for signal (DFS). A simple mathematical argument shows that DFS for EnKF is bounded from above by the ensemble size, which entails that a...
Saved in:
Published in | arXiv.org |
---|---|
Main Authors | , |
Format | Paper Journal Article |
Language | English |
Published |
Ithaca
Cornell University Library, arXiv.org
31.05.2020
|
Subjects | |
Online Access | Get full text |
Cover
Loading…
Abstract | The ability of ensemble Kalman filter (EnKF) algorithms to extract information from observations is analyzed with the aid of the concept of the degrees of freedom for signal (DFS). A simple mathematical argument shows that DFS for EnKF is bounded from above by the ensemble size, which entails that assimilating much more observations than the ensemble size automatically leads to DFS underestimation. Since DFS is a trace of the posterior error covariance mapped onto the normalized observation space, underestimated DFS implies overconfidence (underdispersion) in the analysis spread, which, in a cycled context, requires covariance inflation to be applied. The theory is then extended to cases where covariance localization schemes (either B-localization or R-localization) are applied to show how they alleviate the DFS underestimation issue. These findings from mathematical argument are demonstrated with a simple one-dimensional covariance model. Finally, the DFS concept is used to form speculative arguments about how to interpret several puzzling features of LETKF previously reported in the literature such as why using less observations can lead to better performance, when optimal localization scales tend to occur, and why covariance inflation methods based on relaxation to prior information approach are particularly successful when observations are inhomogeneously distributed. A presumably first application of DFS diagnostics to a quasi-operational global EnKF system is presented in Appendix. |
---|---|
AbstractList | The ability of ensemble Kalman filter (EnKF) algorithms to extract information from observations is analyzed with the aid of the concept of the degrees of freedom for signal (DFS). A simple mathematical argument shows that DFS for EnKF is bounded from above by the ensemble size, which entails that assimilating much more observations than the ensemble size automatically leads to DFS underestimation. Since DFS is a trace of the posterior error covariance mapped onto the normalized observation space, underestimated DFS implies overconfidence (underdispersion) in the analysis spread, which, in a cycled context, requires covariance inflation to be applied. The theory is then extended to cases where covariance localization schemes (either B-localization or R-localization) are applied to show how they alleviate the DFS underestimation issue. These findings from mathematical argument are demonstrated with a simple one-dimensional covariance model. Finally, the DFS concept is used to form speculative arguments about how to interpret several puzzling features of LETKF previously reported in the literature such as why using less observations can lead to better performance, when optimal localization scales tend to occur, and why covariance inflation methods based on relaxation to prior information approach are particularly successful when observations are inhomogeneously distributed. A presumably first application of DFS diagnostics to a quasi-operational global EnKF system is presented in Appendix. The ability of ensemble Kalman filter (EnKF) algorithms to extract information from observations is analyzed with the aid of the concept of the degrees of freedom for signal (DFS). A simple mathematical argument shows that DFS for EnKF is bounded from above by the ensemble size, which entails that assimilating much more observations than the ensemble size automatically leads to DFS underestimation. Since DFS is a trace of the posterior error covariance mapped onto the normalized observation space, underestimated DFS implies overconfidence (underdispersion) in the analysis spread, which, in a cycled context, requires covariance inflation to be applied. The theory is then extended to cases where covariance localization schemes (either B-localization or R-localization) are applied to show how they alleviate the DFS underestimation issue. These findings from mathematical argument are demonstrated with a simple one-dimensional covariance model. Finally, the DFS concept is used to form speculative arguments about how to interpret several puzzling features of LETKF previously reported in the literature such as why using less observations can lead to better performance, when optimal localization scales tend to occur, and why covariance inflation methods based on relaxation to prior information approach are particularly successful when observations are inhomogeneously distributed. A presumably first application of DFS diagnostics to a quasi-operational global EnKF system is presented in Appendix. |
Author | Hotta, Daisuke Ota, Yoichiro |
Author_xml | – sequence: 1 givenname: Daisuke surname: Hotta fullname: Hotta, Daisuke – sequence: 2 givenname: Yoichiro surname: Ota fullname: Ota, Yoichiro |
BackLink | https://doi.org/10.48550/arXiv.2006.00517$$DView paper in arXiv https://doi.org/10.1002/qj.3970$$DView published paper (Access to full text may be restricted) |
BookMark | eNotj1FLwzAUhYMoOOd-gE8GfO5Mb5o0fRIZm4oDHyb4WJL0lnV06UzS4f79us2n83C_ezjfHbl2nUNCHlI2zZQQ7Fn7v2Y_BcbklDGR5ldkBJynicoAbskkhA1jDGQOQvARWf2sdaRts21ioHGN1PVbg552Ne1MQL_Xsenc6TRgVjtqkGJdo43NHtsD1SEMv62OWFFzoHP3uXi5Jze1bgNO_nNMVov59-w9WX69fcxel4kWIBMDhZagam5TYzkYa4qqsgVDJVCZtOCCS8MypSQAE5WVuTKoK17YuoJc8jF5vLSehcudb7baH8qTeHkWH4inC7Hz3W-PIZabrvdumFRCxlQ-lKeSHwFKd1z6 |
ContentType | Paper Journal Article |
Copyright | 2020. This work is published under http://arxiv.org/licenses/nonexclusive-distrib/1.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License. http://arxiv.org/licenses/nonexclusive-distrib/1.0 |
Copyright_xml | – notice: 2020. This work is published under http://arxiv.org/licenses/nonexclusive-distrib/1.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License. – notice: http://arxiv.org/licenses/nonexclusive-distrib/1.0 |
DBID | 8FE 8FG ABJCF ABUWG AFKRA AZQEC BENPR BGLVJ CCPQU DWQXO HCIFZ L6V M7S PIMPY PQEST PQQKQ PQUKI PRINS PTHSS AKZ EPD GOX |
DOI | 10.48550/arxiv.2006.00517 |
DatabaseName | ProQuest SciTech Collection ProQuest Technology Collection Materials Science & Engineering Database (Proquest) ProQuest Central (Alumni) ProQuest Central UK/Ireland ProQuest Central Essentials AUTh Library subscriptions: ProQuest Central Technology Collection ProQuest One Community College ProQuest Central SciTech Premium Collection (Proquest) (PQ_SDU_P3) ProQuest Engineering Collection ProQuest Engineering Database Publicly Available Content Database ProQuest One Academic Eastern Edition (DO NOT USE) ProQuest One Academic ProQuest One Academic UKI Edition ProQuest Central China Engineering Collection arXiv Mathematics arXiv Statistics arXiv.org |
DatabaseTitle | Publicly Available Content Database Engineering Database Technology Collection ProQuest Central Essentials ProQuest One Academic Eastern Edition ProQuest Central (Alumni Edition) SciTech Premium Collection ProQuest One Community College ProQuest Technology Collection ProQuest SciTech Collection ProQuest Central China ProQuest Central ProQuest Engineering Collection ProQuest One Academic UKI Edition ProQuest Central Korea Materials Science & Engineering Collection ProQuest One Academic Engineering Collection |
DatabaseTitleList | Publicly Available Content Database |
Database_xml | – sequence: 1 dbid: GOX name: arXiv.org url: http://arxiv.org/find sourceTypes: Open Access Repository – sequence: 2 dbid: 8FG name: ProQuest Technology Collection url: https://search.proquest.com/technologycollection1 sourceTypes: Aggregation Database |
DeliveryMethod | fulltext_linktorsrc |
Discipline | Physics |
EISSN | 2331-8422 |
ExternalDocumentID | 2006_00517 |
Genre | Working Paper/Pre-Print |
GroupedDBID | 8FE 8FG ABJCF ABUWG AFKRA ALMA_UNASSIGNED_HOLDINGS AZQEC BENPR BGLVJ CCPQU DWQXO FRJ HCIFZ L6V M7S M~E PIMPY PQEST PQQKQ PQUKI PRINS PTHSS AKZ EPD GOX |
ID | FETCH-LOGICAL-a526-b29a628f3c1bc32bcb9ddc90e85e8b193536b048862205dc678bead39cfd2763 |
IEDL.DBID | BENPR |
IngestDate | Mon Jan 08 05:50:05 EST 2024 Fri Sep 13 08:59:16 EDT 2024 |
IsDoiOpenAccess | true |
IsOpenAccess | true |
IsPeerReviewed | false |
IsScholarly | false |
Language | English |
LinkModel | DirectLink |
MergedId | FETCHMERGED-LOGICAL-a526-b29a628f3c1bc32bcb9ddc90e85e8b193536b048862205dc678bead39cfd2763 |
OpenAccessLink | https://www.proquest.com/docview/2408704816/abstract/?pq-origsite=%requestingapplication% |
PQID | 2408704816 |
PQPubID | 2050157 |
ParticipantIDs | arxiv_primary_2006_00517 proquest_journals_2408704816 |
PublicationCentury | 2000 |
PublicationDate | 20200531 2020-05-31 |
PublicationDateYYYYMMDD | 2020-05-31 |
PublicationDate_xml | – month: 05 year: 2020 text: 20200531 day: 31 |
PublicationDecade | 2020 |
PublicationPlace | Ithaca |
PublicationPlace_xml | – name: Ithaca |
PublicationTitle | arXiv.org |
PublicationYear | 2020 |
Publisher | Cornell University Library, arXiv.org |
Publisher_xml | – name: Cornell University Library, arXiv.org |
SSID | ssj0002672553 |
Score | 1.7688223 |
SecondaryResourceType | preprint |
Snippet | The ability of ensemble Kalman filter (EnKF) algorithms to extract information from observations is analyzed with the aid of the concept of the degrees of... The ability of ensemble Kalman filter (EnKF) algorithms to extract information from observations is analyzed with the aid of the concept of the degrees of... |
SourceID | arxiv proquest |
SourceType | Open Access Repository Aggregation Database |
SubjectTerms | Algorithms Covariance Kalman filters Localization Mathematical analysis Mathematics - Statistics Theory Physics - Atmospheric and Oceanic Physics Physics - Data Analysis, Statistics and Probability Statistics - Theory |
SummonAdditionalLinks | – databaseName: arXiv.org dbid: GOX link: http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwdV3BTsMwDLW2nbggEKANBsqBa8WWNElzQghtTCDgMJB6q-omlZCmDm0Dsb_Hbjs4IK5tUql2aj_X9jPAJfoQxyNPhzfxFKBYjCP26xHFy6OxT6zKHfc7Pz6Z2Wt8n-q0A2LXC5Ovvt4-G35gXF-1uQI9tl3oSsklW3fPaZOcrKm42vW_6whj1pf-mNbaX0wPYL8FeuKm0cwhdEJ1BHNmyhYLbipaC4JeohnIIZalWOLP_1G-RcvopQUG0VRckFFabAUhXdq7IHzoBW7FpHqYXh_DfDp5uZ1F7ViDKNfSRChdbmRSqmKMhZJYoPO-cKOQ6JAg4SmtDPJ3ZbgH1hfkTZDUrVxReknW4AR61bIKfRAWdQhSK6tMTj5GopKOHmyxtMahzwfQr2WRvTfEFTxykovYSEwDGO7Ek7WHdp0x25ll_hhz-v_OM9iTHHLWCfQh9Darj3BOfnmDF7VyvgHohYym priority: 102 providerName: Cornell University |
Title | What limits the number of observations that can be effectively assimilated by EnKF? |
URI | https://www.proquest.com/docview/2408704816/abstract/ https://arxiv.org/abs/2006.00517 |
hasFullText | 1 |
inHoldings | 1 |
isFullTextHit | |
isPrint | |
link | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwfV1La8JAEF7UUOitT7S1sodeg7qbbJKT0JIoLVqpLXiTzO4KBUms2lIv_e2dicYeCr0Ekk1ymJ2d98zH2C0Y63kdg8wbGnRQAvBc0usu-sudrgkDmUbU7zwcqcGr9zD1pxU2KHthqKyylImFoDa5phh5m0ZxBTTcRLVToCiA3rR7y3eX8KMoz7oH06gyR3Q9Stg6d_Fo_HyItwgVoPUsd4nNYoxXO119vX2W-QifIMuc4tEfsVzomuSEOeN0aVenrGKzM3ZUlGjq9Tmb0JRtvqCGpDVHs43vwDx4Puc5HGKrtISvIcE4WL6r1kCBtthytJLx2wXalobDlsfZY9K7YJMkfrkfuHtIBDf1hXJBRKkS4VzqLmgpQENkjI46NvRtCGiL-VIBnUlF_bNGoyYCZBUZ6bkRKEkuWS3LM1tnPADfWuHLQKoU9ZMAKSL8cQDzQEVg0garF7SYLXdDLwiukgrgkEwN1izJM9sz_Hr2uz1X_y9fs2NBLmuRgG-y2mb1YW9Qr2-gxaph0m_tNw7v-k9TvA6_4x8RkKWZ |
link.rule.ids | 228,230,786,790,891,12792,21416,27958,33408,33779,43635,43840 |
linkProvider | ProQuest |
linkToHtml | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwfV1LT8JAEN4oxOjNZ0BR9-C1AXbbbXviYKgoj5iACbem090mJoQiRSP_3pltwYOJ127bw-zsfLPz-hh7AG1ct6NReQONFxQfXIdw3cH7cqerA18mIfU7jydq8Oa-zL15FXArqrLKnU20hlrnKcXI2zSKy6fhJqq3-nCINYqyqxWFxiGruxKhkzrFo6d9jEUoHz1mWSYz7eiudrL-fv_a5SA8oimr20d_TLHFl-iU1V-TlVmfsQOzPGdHtiwzLS7YlCZr8wU1IRUcXTVeEnjwPOM57OOptISvoZA4GF5WaKARW2w5esb47QL9Sc1hy_vLYdS7ZNOoP3scOBUNgpN4QjkgwkSJIJNpF1IpIIVQ6zTsmMAzAaD_5UkFdA4V9czqFNEHUD1kmGZaoPW4YrVlvjQNxn3wjBGe9KVKEJMESBHij33IfBWCTpqsYWURr8pBF0RRSUVvKKYma-3EE1dKXsS_W3L9__I9Ox7MxqN49DwZ3rATQVdWm4Bvsdpm_WluEdc3cGc37wdns6BA |
openUrl | ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=What+limits+the+number+of+observations+that+can+be+effectively+assimilated+by+EnKF%3F&rft.jtitle=arXiv.org&rft.au=Hotta%2C+Daisuke&rft.au=Ota%2C+Yoichiro&rft.date=2020-05-31&rft.pub=Cornell+University+Library%2C+arXiv.org&rft.eissn=2331-8422&rft_id=info:doi/10.48550%2Farxiv.2006.00517 |