The effective number of spatial degrees of freedom of a time-varying field

Journal of Climate

Volumn 12, Issue 7, 1999, Pages 1990-2009

  Bretherton, Christopher S ^a   Widmann, Martin ^a   Dymnikov, Valentin P ^a,b   Wallace, John M ^a   Bladé, Ileana ^a  

^a UNIVERSITY OF WASHINGTON   (United States)

^b INSTITUTE OF NUMERICAL MATHEMATICS   (Russian Federation)

Author keywords

[No Author keywords available]

Indexed keywords

CORRELATION METHODS; TIME SERIES ANALYSIS;

CHI-SQUARED DISTRIBUTION;

CLIMATOLOGY;

CLIMATE MODELING; SPATIAL ANALYSIS; STATISTICAL ANALYSIS;

EID: 0032738634     PISSN: 08948755     EISSN: None     Source Type: Journal    
DOI: 10.1175/1520-0442(1999)012<1990:TENOSD>2.0.CO;2     Document Type: Article

References (34)

1. Bagrov, N. A, 1969: On the equivalent number of independent data (in Russian). Tr. Gidrometeor. Cent., 44, 3-11.
2. Bartlett, M. S., 1935: Some aspects of the time-correlation problem in regard to tests of significance. J. Roy. Stat. Soc., 98, 536-543.
3. Bayley, G. V., and J. M. Hammersley, 1946: The "effective" number of independent observations in autocorrelated time series. J. Roy. Stat. Soc. Suppl., 8, 184-197.
4. Blackman, R. B., and J. W. Tukey, 1959: The Measurement of Power Spectra From the Point of View of Communications Engineering. Dover, 190 pp.
5. Da Costa, E., and R. Vautard, 1997: A qualitatively realistic low-order model of the extratropical low-frequency variability built from long records of potential vorticity. J. Atmos. Sci., 54, 1064-1084.
6. Davis, R. E., 1976: Predictability of sea surface temperature and sea level pressure anomalies over the North Pacific Ocean. J. Phys. Oceanogr., 6, 249-266.
7. Dymnikov, V. P., and A. S. Gritsun, 1996: Lyapunov exponents and the attractor dimension in a two-layer baroclinic model of atmospheric circulation (in Russian). Dokl. Ross. Akad. Nauk., 347 (4), 535-538.
8. _, and _, 1997: On the structure of the attractors of the finite-dimensional approximations of the barotropic vorticity equation on a rotating sphere. Russ. J. Numer. Anal. Math. Model., 12, 13-32.
9. Fraedrich, K., C. Ziehmann, and F. Sielmann, 1995: Estimates of spatial degrees of freedom. J. Climate, 8, 361-369.
10. Hogg, R. V., and A. T. Craig, 1978: Introduction to Mathematical Statistics. 4th ed. MacMillan Press, 438 pp.
11. Huang, J., H. M. van den Dool, and K. G. Georgakakos, 1996: Analysis of model-calculated soil moisture over the U.S. (1931-1993) and applications to long range temperature forecasts. J. Climate, 9, 1350-1362.
12. Jones, R. H., 1975: Estimating the variance of time averages. J. Appl. Meteor., 14, 159-163.
13. Keller, L. B., 1935: Expanding of limit theorems of probability theory on functions with continuous arguments (in Russian). Works Main Geophys. Observ., 4, 5-19.
14. Kikkawa, S., and M. Ishida, 1988: Number of degrees of freedom, correlation times, and equivalent bandwidths of a random process. IEEE Trans. Inf. Theory, 34, 151-155.
15. Laha, R. G., and V. K. Rohatgi, 1979: Probability Theory. Wiley, 557 pp.
16. Leith, C. E., 1973: The standard error of time-average estimates of climatic means. J. Appl. Meteor., 12, 1066-1069.
17. Livezey, R. E., and W. Y. Chen, 1983: Statistical field significance and its determination by Monte Carlo testing. Mon. Wea. Rev., 111, 46-59.
18. Lorenz, E. N., 1969: Atmospheric predictability by naturally occurring analogs. J. Atmos. Sci., 26, 636-646.
19. _, 1991: Dimension of weather and climate attractors. Nature. 353, 241-244.
20. North, G., T. R. Bell, R. Cahalan, and F. Moeng, 1982: Sampling errors in estimation of empirical orthogonal functions. Mon. Wea. Rev., 110, 699-706.
21. Orcutt, G. H., and S. F. James, 1948: Testing the significance of correlation between time series. Biometrika, 35, 397-413.
22. Percival, D. B., and A. T. Walden, 1993: Spectral Analysis for Physical Applications. Cambridge University Press, 583 pp.
23. Strang, G., 1988: Linear Algebra and Its Applications. 3d ed. Harcourt Brace Jovanovich, 505 pp.
24. Taylor, G. I., 1921: Diffusion by continuous movement. Proc. London Math. Soc., 20 (2), 196-212.
25. TerMegreditchian, M. G., 1969: On the determination of the number of independent stations which are equivalent to prescribed systems of correlated stations (in Russian). Meteor. Hydrol., 2, 24-36.
26. _, 1990: Meteorological networks optimization from a statistical poini of view. Comput. Stat. Data Anal., 9, 57-75.
27. Thiébaux, H. J., and F. W. Zwiers, 1984: The interpretation and estimation of effective sample size. J. Climate Appl. Meteor., 23, 800-811.
28. Toth, Z., 1995: Degrees of freedom in Northern Hemisphere circulation data. Tellus, 47A, 457-472.
29. van den Dool, H. M., 1987: An empirical study on the parameterization of precipitation in a model of the time mean atmosphere. J. Atmos. Sci., 44, 224-235.
30. _, and R. W. Chervin, 1986: A comparison of month-to-month persistence of anomalies in a general circulation model and in the Earth's atmosphere. J. Atmos. Sci., 43, 1454-1466.
31. Vautard, R., and M. Ghil, 1989: Singular spectum analysis in nonlinear dynamics, with applications to paleoclimatic time series. Physica D, 35, 395-424.
32. Wallace, J. M., X. Cheng, and D. Sun, 1991: Does low-frequency atmospheric variability exhibit regime-like behaviour? Tellus, 43AB, 16-26.
33. Widmann, M., and C. Schär, 1997: A principal component and long-term trend analysis of daily precipitation in Switzerland. Int. J. Climatol., 17, 1333-1356.
34. Yulaeva, E., and J. M. Wallace, 1994: The signature of ENSO in global temperature and precipitation fields derived from the microwave sounding unit. J. Climate. 7, 1719-1736.