A conceptual framework for predictability studies

Journal of Climate

Volumn 12, Issue 10, 1999, Pages 3133-3155

  Schneider, Tapio ^a   Griffies, Stephen M ^b  

^a PRINCETON UNIVERSITY   (United States)

^b NOAA EARTH SYSTEM RESEARCH LABORATORY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ATMOSPHERIC TEMPERATURE; EIGENVALUES AND EIGENFUNCTIONS; MATHEMATICAL MODELS; PROBABILITY DISTRIBUTIONS; REGRESSION ANALYSIS; WEATHER FORECASTING;

GAUSSIAN DISTRIBUTION; PREDICTIVE POWER;

CLIMATOLOGY;

CONCEPTUAL FRAMEWORK; PREDICTION; WEATHER FORECASTING;

EID: 0033208415     PISSN: 08948755     EISSN: None     Source Type: Journal    
DOI: 10.1175/1520-0442(1999)012<3133:ACFFPS>2.0.CO;2     Document Type: Article

References (64)

1. Ahmad, T. A., and P.-E. Lin, 1976: A nonparametric estimation of the entropy for absolutely continuous distributions. IEEE Trans. Inf. Theory, 22, 372-375.
2. Anderson, J. L., and W. F. Stern, 1996: Evaluating the potential predictive utility of ensemble forecasts. J. Climate, 9, 260-269.
3. Anderson, T. W., 1984: An Introduction to Multivariate Statistical Analysis. 2d ed. Series in Probability and Mathematical Statistics, Wiley, 675 pp.
4. Ansley, C. F., and R. Kohn, 1983: Exact likelihood of a vector autoregressive moving average process with missing or aggregated data. Biometrika, 70, 275-278.
5. _, and _, 1986: A note on reparameterising a vector autoregressive moving average model to enforce stationarity. J. Stat. Comput. Sim., 24, 99-106.
6. Bell, T. L., 1982: Optimal weighting of data to detect climatic change: Application to the carbon dioxide problem. J. Geophys. Res., 87, 11 161-11 170.
7. _, 1986: Theory of optimal weighting of data to detect climatic change. J. Atmos. Sci., 43, 1694-1710.
8. Box, G. E. P., and G. C. Tiao, 1977: A canonical analysis of multiple time series. Biometrika, 64, 355-365.
9. Brillouin, L., 1956: Science and Information Theory. Academic Press, 320 pp.
10. Brockwell, P. J., and A. Davis, 1991: Time Series: Theory and Methods. 2d ed. Springer, 577 pp.
11. Cheng, Y.-Q., Y.-M. Zhuang, and J.-Y. Yang, 1992: Optimal Fisher discriminant analysis using the rank decomposition. Pattern Recognit., 25, 101-111.
12. Delworth, T., S. Manabe, and R. J. Stouffer, 1993: Interdecadal variations of the thermohaline circulation in a coupled ocean-atmosphere model. J. Climate, 6, 1993-2011.
13. _, _, and _, 1997: Multidecadal climate variability in the Greenland Seas and surrounding regions: A coupled model simulation. Geophys. Res. Lett., 24, 257-260.
14. Dmitriev, Y. G., and F. P. Tarasenko, 1973: On the estimation of functionals of the probability density and its derivatives. Theory Probab. Appl., 18, 628-633.
15. Draper, D., 1995: Assessment and propagation of model uncertainty. J. Roy. Stat. Soc. B, 57, 45-97.
16. Engl, H. W., M. Hanke, and A. Neubauer, 1996: Regularization of Inverse Problems. Kluwer, 321 pp.
17. Friedman, J. H., 1989: Regularized discriminant analysis. J. Amer. Stat. Assoc., 84, 165-175.
18. Fukunaga, K., 1990: Introduction to Statistical Pattern Recognition. 2d ed. Academic Press, 591 pp.
19. Golub, G. H., and C. F. van Loan, 1993: Matrix Computations. 2d ed. Johns Hopkins University Press, 642 pp.
20. Griffies, S. M., and K. Bryan, 1997a: Predictability of North Atlantic multidecadal climate variability. Science, 275, 181-184.
21. _, and _, 1997b: A predictability study of simulated North Atlantic multidecadal variability. Climate Dyn., 8, 459-488.
22. Hall, P., and S. C. Morton, 1993: On the estimation of entropy. Ann. Inst. Stat. Math., 45, 69-88.
23. Halliwell, G. R., 1997: Decadal and multidecadal North Atlantic SST anomalies driven by standing and propagating basin-scale atmospheric anomalies. J. Climate, 10, 2405-2411.
24. _, 1998: Simulation of North Atlantic decadal/multidecadal winter SST anomalies driven by basin-scale atmospheric circulation anomalies. J. Phys. Oceanogr., 28, 5-21.
25. Hansen, P. C., 1997: Rank-Deficient and Discrete Ill-Posed Problems: Numerical Aspects of Linear Inversion. SIAM Monogr. on Mathematical Modeling and Computation, Society for Industrial and Applied Mathematics, 247 pp.
26. Harzallah, A., and R. Sadourny, 1995: Internal versus SST-forced atmospheric variability as simulated by an atmospheric circulation model. J. Climate, 8, 474-495.
27. Hasselmann, K., 1993: Optimal fingerprints for the detection of time-dependent climate change. J. Climate, 6, 1957-1971.
28. Hayashi, Y., 1986: Statistical interpretation of ensemble-time mean predictability. J. Meteor. Soc. Japan, 64, 167-181.
29. Hegerl, G. C., and G. R. North, 1997: Comparison of statistically optimal approaches to detecting anthropogenic climate change. J. Climate, 10, 1125-1133.
30. Joe, H., 1989: Estimation of entropy and other functionals of a multivariate density. Ann. Inst. Stat. Math., 41, 683-697.
31. Johnson, R. A., and D. W. Wichern, 1982: Applied Multivariate Statistical Analysis. Prentice-Hall, 594 pp.
32. Jolliffe, I. T., 1986: Principal Component Analysis. Springer Series in Statistics, Springer, 271 pp.
33. Krzanowski, W. J., P. Jonathan, W. V. McCarthy, and M. R. Thomas, 1995: Discriminant analysis with singular covariance matrices: Methods and applications to spectroscopic data. Appl. Stat. 44, 101-115.
34. Lawley, D. N., 1956: Tests of significance for the latent roots of covariance and correlation matrices. Biometrika, 43, 128-136.
35. Li, W. K., and A. I. McLeod, 1981: Distribution of the residual autocorrelations in multivariate ARMA time series models. J. Roy. Stat. Soc. B, 43, 231-239.
36. Lorenz, E. N., 1963: Deterministic nonperiodic flow. J. Atmos. Sci., 20, 130-141.
37. _, 1975: Climatic predictability. The Physical Basis of Climate and Climate Modelling, B. Bolin et al., Eds., GARP Publication Series, Vol. 16, World Meteorological Organization, 132-136.
38. Lütkepohl, H., 1985: Comparison of criteria for estimating the order of a vector autoregressive process. J. Time Ser. Anal., 6, 35-52; Correction, 8, 373.
39. _, 1993: Introduction to Multiple Time Series Analysis. 2d ed. Springer-Verlag, 545 pp.
40. McLachlan, G. J., 1992: Discriminant Analysis and Statistical Pattern Recognition. Series in Probability and Mathematical Statistics, Wiley, 544 pp.
41. Miller, A. J., 1984: Selection of subsets of regression variables. J. Roy. Stat. Soc. A. 147, 389-425.
42. Murphy, J. M., 1988: The impact of ensemble forecasts on predictability. Quart. J. Roy. Meteor. Soc., 114, 463-493.
43. Neumaier, A., 1998: Solving ill-conditioned and singular linear systems: A tutorial on regularization. SIAM Rev., 40, 636-666.
44. _, and T. Schneider, cited 1997: Multivariate autoregressive and Ornstein-Uhlenbeck processes: Estimates for order, parameters, spectral information, and confidence regions. [Available online at http:// www.aos.Princeton.EDU/WWWPUBLIC/tapio/arfit/.]
45. Palmer, T. N., 1996: Predictability of the atmosphere and oceans: From days to decades. Decadal Climate Variability: Dynamics and Predictability, D. L. T. Anderson and J. Willebrand, Eds., NATO ASI Series, Vol. I 44, Springer, 83-155.
46. _, R. Gelaro, J. Barkmeijer, and R. Buizza, 1998: Singular vectors, metrics, and adaptive observations. J. Atmos. Sci., 55, 633-653.
47. Papoulis, A., 1991: Probability, Random Variables, and Stochastic Processes. 3d ed. McGraw-Hill, 666 pp.
48. Prakasa Rao, B. L. S., 1983: Nonparametric Functional Estimation. Series in Probability and Mathematical Statistics, Academic Press, 522 pp.
49. Press, W. H., S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, 1992: Numerical Recipes. 2d ed. Cambridge University Press, 963 pp.
50. Ripley, B. D., 1996: Pattern Recognition and Neural Networks. Cambridge University Press, 403 pp.
51. Schneider, T., and A. Neumaier, cited 1997: Algorithm: ARfit - A Matlab package for estimation and spectral decomposition of multivariate autoregressive processes. [Available online at http: //www.aos.Princeton.EDU/WWWPUBLIC/tapio/arfit/.]
52. Schwarz, G., 1978: Estimating the dimension of a model. Ann. Stat., 6, 461-464.
53. Scott, D. W., 1992: Multivariate Density Estimation: Theory, Practice, and Visualization. Series in Probability and Mathematical Statistics, Wiley, 317 pp.
54. Shannon, C. E., 1948: A mathematical theory of communication. Bell Syst. Tech. J., 27, 370-423, 623-656.
55. _, and W. Weaver, 1949: The Mathematical Theory of Communication. University of Illinois Press, 117 pp.
56. Shukla, J., 1981: Dynamical predictability of monthly means. J. Atmos. Sci., 38, 2547-2572.
57. _, 1985: Predictability. Advances in Geophysics, Vo . 28b, Academic Press, 87-122.
58. Silverman, B. W., 1986: Density Estimation for Statistics and Data Analysis. Chapman and Hall, 175 pp.
59. Stern, W. F., and K. Miyakoda, 1995: The feasibility of seasonal forecasts inferred from multiple GCM simulations. J. Climate, 8, 1071-1085.
60. Thacker, W. C., 1996: Metric-based principal components: Data uncertainties. Tellus, 48A, 584-592.
61. Tiao, G. C., and G. E. P. Box, 1981: Modeling multiple time series with applications. J. Amer. Stat. Assoc., 76, 802-816.
62. Tikhonov, A. N., and V. Y. Arsenin, 1977: Solution of Ill-Posed Problems. Scripta Series in Mathematics, V. H. Winston and Sons, 258 pp.
63. Toth, Z., 1991: Circulation patterns in phase space: A multinormal distribution? Mon. Wea. Rev., 119, 1501-1511.
64. Zwiers, F. W., 1996: Interannual variability and predictability in an ensemble of AMIP climate simulations conducted with the CCC GCM2. Climate Dyn., 12, 825-848.