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
- 1972. Handbook of mathematical functions with formulas, graphs and mathematical tables. Dover Publications: New York, NY. http://people.math.sfu.ca/∼cbm/aands/frameindex.htm. ,
- 1989. A global oceanic data assimilation system. J. Phys. Oceanogr. 19: 1333–1347. ,
- 2007. Weak and strong constraint data assimilation in the Inverse Ocean Modelling System (ROMS): development and application for a baroclinic coastal upwelling system. Ocean Modelling 16: 160–187. , , , , , , ,
- 1994. Topex/Poseidon tides estimated using a global inverse model. J. Geophys. Res. 99: 24821–24852. , ,
- 2006. Construction and application of covariance functions with variable length-fields. Q. J. R. Meteorol. Soc. 132: 1815–1838. , , ,
- 1980. Tables of integrals, series and products. Academic Press:. ,
- 2008. On potentially negative space–time covariances obtained as sum of products of marginal ones. Ann. Inst. Stat. Math. 60: 865–882. , , ,
- 2003. Spartan 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 Processing 57: 3475–3487. ,
- 2010. Representation of correlation functions in variational data assimilation using an implicit diffusion operator. Q. J. R. Meteorol. Soc. 136: 1421–1443. ,
- 2000. Generalized inversion of a reduced gravity primitive-equation ocean model and tropical atmosphere ocean data. Mon. Weather Rev. 128: 1757–1777. , ,
- 2008. Estimation of the local diffusion tensor and normalization for heterogeneous correlation modelling using a diffusion equation. Q. J. R. Meteorol. Soc. 134: 1425–1438. ,
- 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. , , ,
- 1975. Methods of Modern Mathematical Physics, vol. II. Academic Press: New York, NY; 361 pp. ,
- 1999. Interpolation of spatial data. Some theory for krigging. Springer: New York, NY; 257 pp.
- 2005. Representations of inverse covariances by differential operators. Adv. Atmos. Sci. 22: 181–198.
- 2001. Correlation modelling on a sphere using a generalized diffusion equation. Q. J. R. Meteorol. Soc. 127: 1815–1846. ,
- 2003. Three and fourdimensional 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. , ,
- 2011. ‘Predictive skill and computational cost of the correlation models in 3D-Var data assimilation’. In Proceedings of 8th AOGS Meeting, Taiwan. , , , ,