This article is a US Government work and is in the public domain in the USA.
Notes and Correspondence
On the correlation functions associated with polynomials of the diffusion operator
Article first published online: 16 AUG 2011
Published in 2011 by John Wiley & Sons Ltd.
Quarterly Journal of the Royal Meteorological Society
Special Issue: IPY-THORPEX
Volume 137, Issue 660, pages 1927–1932, October 2011 Part A
How to Cite
Yaremchuk, M. and Smith, S. (2011), On the correlation functions associated with polynomials of the diffusion operator. Q.J.R. Meteorol. Soc., 137: 1927–1932. doi: 10.1002/qj.893
- Issue published online: 27 OCT 2011
- Article first published online: 16 AUG 2011
- Manuscript Accepted: 5 JUL 2011
- Manuscript Revised: 2 JUL 2011
- Manuscript Received: 1 FEB 2011
- variational data assimilation;
- correlation modelling
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. Published in 2011 by John Wiley & Sons Ltd.