The contributions of these authors to this article were prepared as part of their official duties as United States Federal Government employees.
Multi-scale correlation functions associated with polynomials of the diffusion operator
Version of Record online: 6 FEB 2012
Copyright © 2012 Royal Meteorological Society
Quarterly Journal of the Royal Meteorological Society
Volume 138, Issue 668, pages 1948–1953, October 2012 Part A
How to Cite
Yaremchuk, M. and Sentchev, A. (2012), Multi-scale correlation functions associated with polynomials of the diffusion operator. Q.J.R. Meteorol. Soc., 138: 1948–1953. doi: 10.1002/qj.1896
- Issue online: 25 OCT 2012
- Version of Record online: 6 FEB 2012
- Manuscript Accepted: 6 JAN 2012
- Manuscript Revised: 4 JAN 2012
- Manuscript Received: 14 JUL 2011
- 1972. Handbook of Mathematical Functions with Formulas, Graphs and Mathematical Tables. Dover Publications: New York, NY. ,
- 2000. Digital Filters: Analysis, Design, and Applications. McGraw-Hill: New York, NY.
- 2004. Issues in high resolution limited area data assimilation for quantitative precipitation forecasting. Physica D 196 1–27.
- 2007. Weak and strong constraint data assimilation in the Inverse Ocean Modelling System (ROMS): development and application for a baroclinic coastal upwelling system. Ocean Model. 16: 160–187. , , , , , , ,
- 2006. Construction and application of covariance functions with variable length-fields. Q. J. R. Meteorol. Soc. 132: 1815–1838. , , ,
- 2003. Spartan Gibbs random field models for geostatistical applications. SIAM J. Sci. Comput. 24 2125–2162.
- 2007. Analytic properties and covariance functions of a new class of generalized Gibbs random fields. IEEE Trans. Inform. Theory 53: 4467–4679. ,
- 2009. Computationally efficient spatial interpolators based on Spartan spatial random fields. IEEE Trans. Signal Process. 57: 3475–3487. ,
- 2012. The effect of variable wind forcing on nearshore turbulence in the Eastern English Channel. Ocean Dynam. (in press). , ,
- 1997. Fractals and Scaling in Finance. Springer: Berlin.
- 1990. Oceanographic data interpolation: Objective analysis and splines. J. Geophys. Res. 95: 13529–13541.
- 1986. Bayesian optimal analysis for meteorological data. In Variational Methods in Geosciences, (ed.). Elsevier: Amsterdam; 167–172.
- 2003. Numerical aspects of the application of recursive filters to variational statistical analysis. Part II: Spatially inhomogeneous and anisotropic general covariances. Mon. Weather Rev. 131: 1536–1548. , , ,
- 1970. Numerical variational analysis formulated under constraints as determined by long wave equations, and low-pass filter. Mon. Weather Rev. 98: 884–898.
- 1980. Some new mathematical methods for variational objective analysis using splines and cross-validation. Mon. Weather Rev. 108: 36–57. ,
- 2003. Three and four-dimensional variational assimilation with a general circulation model of the Tropical Pacific Ocean. Part I: Formulation, internal diagnostics and consistency checks. Mon. Weather Rev. 131: 1360–1378. , ,
- 2002. Three-dimensional variational analysis with spatially inhomogeneous covariances. Mon. Weather Rev. 130: 2905–2916. , ,
- 2005. Representations of inverse covariances by differential operators. Adv. Atmos. Sci. 22: 181–198.
- 2012. On the renormalization of the covariance operators. Mon. Weather Rev. 140: 637–649. ,
- 2011. On the correlation functions associated with polynomials of the diffusion operator. Q. J. R. Meteorol. Soc. 137: 1927–1932. ,