On the correlation functions associated with polynomials of the diffusion operator

Quarterly Journal of the Royal Meteorological Society

Volumn 137, Issue 660, 2011, Pages 1927-1932

  Yaremchuk, M ^a   Smith, S ^a  

^a NAVAL RESEARCH LABORATORY   (United States)

Author keywords

Correlation modelling; Variational data assimilation

Indexed keywords

ANALYTICAL EXPRESSIONS; BINOMIAL APPROXIMATION; CORRELATION FUNCTION; DIFFUSION OPERATORS; EXPERIMENTAL DATA; GAUSSIANS; POLYNOMIAL COEFFICIENTS; QUADRATIC POLYNOMIAL; TUNING PARAMETER; VARIATIONAL DATA ASSIMILATION;

DATA PROCESSING; THREE DIMENSIONAL;

POLYNOMIALS;

CORRELATION; DATA ASSIMILATION; ERROR ANALYSIS; INVERSE ANALYSIS; MODELING;

EID: 80055099999     PISSN: 00359009     EISSN: 1477870X     Source Type: Journal    
DOI: 10.1002/qj.893     Document Type: Article

References (20)

1. Abramowitz M, Stegun IA. 1972. Handbook of mathematical functions with formulas, graphs and mathematical tables. Dover Publications: New York, NY.
2. Derber J, Rosati A. 1989. A global oceanic data assimilation system. J. Phys. Oceanogr. 19: 1333-1347.
3. Di Lorenzo E, Moore AM, Arango HG, Cornuelle BD, Miller AJ, Powell BS, Chua BS, Bennett AF. 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.
4. Egbert GD, Bennett AF, Foreman MGG. 1994. Topex/Poseidon tides estimated using a global inverse model. J. Geophys. Res. 99: 24821-24852.
5. Gaspari G, Cohn SE, Guo J, Pawson S. 2006. Construction and application of covariance functions with variable length-fields. Q. J. R. Meteorol. Soc. 132: 1815-1838.
6. Gradshteyn IS, Ryzhik IM. 1980. Tables of integrals, series and products. Academic Press:.
7. Gregori P, Porcu E, Mateu J, Sasvari Z. 2008. On potentially negative space-time covariances obtained as sum of products of marginal ones. Ann. Inst. Stat. Math. 60: 865-882.
8. Hristopulos DT. 2003. Spartan random field models for geostatistical applications. SIAM J. Sci. Comput. 24: 2125-2162.
9. Hristopulos DT, Elogne SN. 2007. Analytic properties and covariance functions of a new class of generalized Gibbs random fields. IEEE Trans. Inform. Theory 53: 4467-4679.
10. Hristopulos DT, Elogne SN. 2009. Computationally efficient spatial interpolators based on Spartan spatial random fields. IEEE Trans. Signal Processing 57: 3475-3487.
11. Mirouze I, Weaver AT. 2010. Representation of correlation functions in variational data assimilation using an implicit diffusion operator. Q. J. R. Meteorol. Soc. 136: 1421-1443.
12. Ngodock HE, Chua BS, Bennett AF. 2000. Generalized inversion of a reduced gravity primitive-equation ocean model and tropical atmosphere ocean data. Mon. Weather Rev. 128: 1757-1777.
13. Pannekoucke O, Massart S. 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.
14. Purser RJ, Wu W, Parrish DF, Roberts NM. 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.
15. Reed M, Simon B. 1975. Methods of Modern Mathematical Physics, vol. II. Academic Press: New York, NY; 361 pp.
16. Stein ML. 1999. Interpolation of spatial data. Some theory for krigging. Springer: New York, NY; 257 pp.
17. Xu Q. 2005. Representations of inverse covariances by differential operators. Adv. Atmos. Sci. 22: 181-198.
18. Weaver AT, Courtier P. 2001. Correlation modelling on a sphere using a generalized diffusion equation. Q. J. R. Meteorol. Soc. 127: 1815-1846.
19. Weaver AT, Vialard J, Anderson DLT. 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.
20. Yaremchuk M, Carrier M, Ngodock H, Smith S, Shulman I. 2011. 'Predictive skill and computational cost of the correlation models in 3D-Var data assimilation'. In Proceedings of 8th AOGS Meeting, Taiwan.