Covariance Modeling by Means of Eigenfunctions of Laplace Operator

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985807%3A_____%2F15%3A00457014" target="_blank" >RIV/67985807:_____/15:00457014 - isvavai.cz</a>

Výsledek na webu

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DOI - Digital Object Identifier

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Jazyk výsledku

angličtina

Název v původním jazyce

Covariance Modeling by Means of Eigenfunctions of Laplace Operator

Popis výsledku v původním jazyce

Large dimension of both state vector and data is a well-known challenge in environmental modeling (e.g., numerical weather forecast) and, in particular, in data assimilation. The Ensemble Kalman Filter addresses this problem by estimating the current system state and its uncertainty via their sample counterparts. However, sample covariance matrix based on a small ensemble is not a sufficiently good estimate of the true covariance. In this paper, we deal with techniques relying on transformation of the state to the spectral space and assuming a particular covariance structure based on the Laplace operator. Parameters, which this special structure depends on, are estimated by a least squares method and a maximum likelihood method. The behavior of both estimators is illustrated by a simulation. Both methods have a smaller error in Frobenius norm than the sample covariance, moreover, the latter method performs better than the former one, which corresponds to its stronger assumptions.

Název v anglickém jazyce

Covariance Modeling by Means of Eigenfunctions of Laplace Operator

Popis výsledku anglicky

Large dimension of both state vector and data is a well-known challenge in environmental modeling (e.g., numerical weather forecast) and, in particular, in data assimilation. The Ensemble Kalman Filter addresses this problem by estimating the current system state and its uncertainty via their sample counterparts. However, sample covariance matrix based on a small ensemble is not a sufficiently good estimate of the true covariance. In this paper, we deal with techniques relying on transformation of the state to the spectral space and assuming a particular covariance structure based on the Laplace operator. Parameters, which this special structure depends on, are estimated by a least squares method and a maximum likelihood method. The behavior of both estimators is illustrated by a simulation. Both methods have a smaller error in Frobenius norm than the sample covariance, moreover, the latter method performs better than the former one, which corresponds to its stronger assumptions.

Druh

D - Stať ve sborníku

CEP obor

BB - Aplikovaná statistika, operační výzkum

OECD FORD obor

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Projekt

<a href="/cs/project/GA13-34856S" target="_blank" >GA13-34856S: Pokročilé metody náhodných polí v asimilaci dat pro krátkodobou předpověď počasí</a><br>

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2015

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název statě ve sborníku

JSM 2015 Proceedings

ISBN

978-0-9839375-5-5

ISSN

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e-ISSN

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Počet stran výsledku

8

Strana od-do

3454-3461

Název nakladatele

ASA

Místo vydání

Alexandria

Místo konání akce

Seattle

Datum konání akce

8. 8. 2015

Typ akce podle státní příslušnosti

WRD - Celosvětová akce

Kód UT WoS článku

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