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Accession Number ADA586882
Title Background Error Correlation Modeling with Diffusion Operators.
Publication Date 2013
Media Count 28p
Personal Author G. Jacobs M. Carrier M. Yaremchuk S. Smith
Abstract Many background error correlation (BEC) models in data assimilation are formulated in terms of a positive-definite smoothing operator B that is employed to simulate the action of correlation matrix on a vector in state space. In this chapter, a general procedure for constructing a BEC model as a rational function of the diffusion operator D is presented and analytic expressions for the respective correlation functions in the homogeneous case are obtained. It is shown that this class of BEC models can describe multi- scale stochastic fields whose characteristic scales can be expressed in terms of the polynomial coefficients of the model. In particular, the connection between the inverse binomial model and the well-known Gaussian model Bg = expD is established and the relationships between the respective decorrelation scales are derived. By its definition, the BEC operator 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, therefore an efficient numerical approximation is needed. Under the assumption of local homogeneity of D, a heuristic method for computing the diagonal elements of B is proposed. It is shown that the method is sufficiently accurate for realistic applications, and requires 102 times less computational resources than other methods of diagonal estimation that do not take into account prior information on the structure of B.
Keywords Assimilation
Background
Background error covariances
Coefficients
Computations
Correlation models
Data assimilations
Diffusion
Errors
Homogeneity
Normalization
Operators(Personnel)
Polynomials
Vector spaces


 
Source Agency Non Paid ADAS
NTIS Subject Category 72B - Algebra, Analysis, Geometry, & Mathematical Logic
72F - Statistical Analysis
63 - Detection & Countermeasures
Corporate Author Naval Research Lab., Stennis Space Center, MS. Oceanography Div.
Document Type Technical report
Title Note Book chapter.
NTIS Issue Number 1405
Contract Number N/A

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