Covariance Modeling by Means of Eigenfunctions of Laplace Operator

Result code in 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>
Result on the web
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DOI - Digital Object Identifier
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Result language
angličtina
Original language name
Covariance Modeling by Means of Eigenfunctions of Laplace Operator
Original language description
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.
Czech name
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Czech description
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Project
<a href="/en/project/GA13-34856S" target="_blank" >GA13-34856S: Advanced random field methods in data assimilation for short-term weather prediction</a><br>
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2015
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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