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Accession Number ADA564384
Title Renormalization of the Covariance Operators.
Publication Date Feb 2012
Media Count 14p
Personal Author M. Carrier M. Yaremchuk
Abstract Many background error correlation (BEC) models in data assimilation are formulated in terms of a smoothing operator B, which simulates the action of the correlation matrix on a state vector normalized by respective BE variances. Under such formulation, B has to have a unit diagonal and requires appropriate renormalization by rescaling. The exact computation of the rescaling factors (diagonal elements of B) is a computationally expensive procedure, which needs an efficient numerical approximation. In this study approximate renormalization techniques based on the Monte Carlo (MC) and Hadamard matrix (HM) methods and on the analytic approximations derived under the assumption of the local homogeneity (LHA) of B are compared using realistic BEC models designed for oceanographic applications. It is shown that although the accuracy of the MC and HM methods can be improved by additional smoothing, their computational cost remains significantly higher than the LHA method, which is shown to be effective even in the zeroth-order approximation. The next approximation improves the accuracy 1.5-2 times at a moderate increase of CPU time. A heuristic relationship for the smoothing scale in two and three dimensions is proposed for the first-order LHA approximation.
Keywords Accuracy
Approximation(Mathematics)
Assimilation
Background
Computations
Correlation
Costs
Covariance
Efficiency
Error analysis
Errors
Formulations
Heuristic methods
Homogeneity
Models
Monte carlo method
Oceanography
Optimization
Reprints
Scale
Time
Vector analysis

 
Source Agency Non Paid ADAS
NTIS Subject Category 72B - Algebra, Analysis, Geometry, & Mathematical Logic
Corporate Author Naval Research Lab., Stennis Space Center, MS. Oceanography Div.
Document Type Journal article
Title Note Journal article.
NTIS Issue Number 1303
Contract Number N/A

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