Accession Number : ADA586882


Title :   Background Error Correlation Modeling with Diffusion Operators


Descriptive Note : Book chapter


Corporate Author : NAVAL RESEARCH LAB STENNIS DETACHMENT STENNIS SPACE CENTER MS OCEANOGRAPHY DIV


Personal Author(s) : Yaremchuk, Max ; Carrier, Matthew ; Smith, Scott ; Jacobs, Gregg


Full Text : https://apps.dtic.mil/dtic/tr/fulltext/u2/a586882.pdf


Report Date : Jan 2013


Pagination or Media Count : 28


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.


Descriptors :   *BACKGROUND , *DIFFUSION , *ERRORS , *OPERATORS(PERSONNEL) , ASSIMILATION , COEFFICIENTS , COMPUTATIONS , HOMOGENEITY , POLYNOMIALS , VECTOR SPACES


Subject Categories : Numerical Mathematics
      Statistics and Probability
      Target Direction, Range and Position Finding


Distribution Statement : APPROVED FOR PUBLIC RELEASE