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Math and StatisticsNumerical Mathematics

On the Correlation Functions Associated with Polynomials of the Diffusion Operator

Authors: Max Yaremchuk; Scott Smith; NAVAL RESEARCH LAB STENNIS DETACHMENT STENNIS SPACE CENTER MS OCEANOGRAPHY DIV
Abstract:
Correlation functions (CFs) associated with the inverse background-error correlations (iBECs) represented by polynomials of the diffusion operator D are obtained analytically for the binomial approximations of the Gaussian BEC and in the general case of a quadratic polynomial of D. The respective analytical expressions for one-, two- and three-dimensional cases have two tuning parameters, which provide enough freedom in adjusting the CFs' shape to, experimental data. The polynomial coefficients of the corresponding iBEC operator are obtained in terms of these tuning parameters and may be useful in the design of the BEC models for variational data assimilation.

Limitations: APPROVED FOR PUBLIC RELEASE
Description: Journal article
Pages: 7
Report Date: Oct 2011
Report Number: A456555
Keywords relating to this report:
APPROXIMATION(MATHEMATICS)
ASSIMILATION
BINOMIALS
CORRELATION
DIFFUSION
EXPERIMENTAL DATA
FUNCTIONS(MATHEMATICS)
INVERSION
MATHEMATICAL ANALYSIS
OPERATORS(PERSONNEL)
POLYNOMIALS
QUADRATIC EQUATIONS
SHAPE
THREE DIMENSIONAL
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