Quantifying the predictive skill in long-range forecasting. Part II: Model error in coarse-grained Markov models with application to ocean-circulation regimes

Journal of Climate

Volumn 25, Issue 6, 2012, Pages 1814-1826

  Giannakis, Dimitrios ^a   Majda, Andrew J ^a  

^a NEW YORK UNIVERSITY   (United States)

Author keywords

Classification; Ensembles; Model errors; Ocean models; Probability forecasts models distribution; Statistical forecasting

Indexed keywords

ENSEMBLES; MODEL ERRORS; OCEAN MODEL; PROBABILITY FORECASTS/MODELS/DISTRIBUTION; STATISTICAL FORECASTING;

CLASSIFICATION (OF INFORMATION); CLIMATOLOGY; FORECASTING; MARKOV PROCESSES;

CLIMATE MODELS;

CLIMATE CLASSIFICATION; CLIMATE MODELING; CLIMATE PREDICTION; ENSEMBLE FORECASTING; ERROR ANALYSIS; LONG RANGE FORECAST; MARKOV CHAIN; NUMERICAL MODEL; OCEANIC CIRCULATION; PROBABILITY;

EID: 84858599251     PISSN: 08948755     EISSN: None     Source Type: Journal    
DOI: 10.1175/JCLI-D-11-00110.1     Document Type: Article

References (50)

1. Abramov, R. V., A. J. Majda, and R. Kleeman, 2005: Information theory and predictability for low-frequency variability. J. Atmos. Sci., 62, 65-87.
2. Bengtsson, L., S. Hagemann, and K. I. Hodges, 2004: Can climate trends be calculated from reanalysis data? J. Geophys. Res., 109, D11111, doi:10.1029/2004jd004536.
3. Berloff, P. S., and J. C. McWilliams, 1999: Large-scale, low-frequency variability in wind-driven ocean gyres. J. Phys. Oceanogr., 29, 1925-1949.
4. Branstator, G., and H. Teng, 2010: Two limits of initial-value decadal predictability in a CGCM. J. Climate, 23, 6292-6311.
5. Collins, M., 2002: Climate predictability on interannual to decadal time scales: The initial value problem. Climate Dyn., 19, 671-692, doi:10.1007/s00382-002-0254-8.
6. Cover, T. A., and J. A. Thomas, 2006: Elements of Information Theory. 2nd ed. Wiley-Interscience, 776 pp.
7. Crommelin, D. T., and E. Vanden-Eijnden, 2006: Fitting timeseries by continuous-time Markov chains: A quadratic programming approach. J. Comput. Phys., 217, 782-805, doi:10.1016/j.jcp.2006.01.045.
8. DelSole, T., 2004: Predictability and information theory. Part I: Measures of predictability. J. Atmos. Sci., 61, 2425-2440.
9. DelSole, T., 2005: Predictability and information theory. Part II: Imperfect models. J. Atmos. Sci., 62, 3368-3381.
10. DelSole, T., and J. Shukla, 2010: Model fidelity versus skill in seasonal forecasting. J. Climate, 23, 4794-4806.
11. Duda, R. O., P. E. Hart, and D. G. Stork, 2000: Pattern Classification. 2nd ed. Wiley-Interscience, 654 pp.
12. Franzke, C., D. Crommelin, A. Fischer, and A. J. Majda, 2008: A hidden Markov model perspective on regimes and metastability in atmospheric flows. J. Climate, 21, 1740-1757.
13. Franzke, C., I. Horenko, A. J. Majda, and R. Klein, 2009: Systematic metastable regime identification in an AGCM. J. Atmos. Sci., 66, 1997-2012.
14. Gardiner, C., 2009: Stochastic Methods: A Handbook for the Natural and Social Sciences. Springer Series in Synergetics, Vol. 13, Springer, 447 pp.
15. Gershgorin, B., and A. J. Majda, 2010: Atest model for fluctuation-dissipation theorems with time-periodic statistics. Physica D, 239, 1741-1757, doi:10.1016/j.physd.2010.05.009.
16. Ghil, M., and A. W. Robertson, 2002: "Waves" vs. "particles" in the atmosphere's phase space: A pathway to long-range forecasting? Proc. Natl. Acad. Sci. USA, 99 (Suppl.), 2493-2500, doi:10.1073/pnas.012580899.
17. Giannakis, D., and A. J. Majda, 2012: Quantifying the predictive skill in long-range forecasting. Part I: Coarse-grained predictions in a simple ocean model. J. Climate, 25, 1793-1813.
18. Horenko, I., 2008: On simultaneous data-based dimension reduction and hidden phase identification. J. Atmos. Sci., 65, 1941-1954.
19. Horenko, I., 2009: On robust estimation of low-frequency variability trends in discrete Markovian sequences of atmospheric circulation patterns. J. Atmos. Sci., 66, 2059-2072.
20. Horenko, I. 2010: On the identification of nonstationary factor models and their application to atmospheric data analysis. J. Atmos. Sci., 67, 1559-1574.
21. Hurrell, J. W., and Coauthors, 2010: Decadal climate prediction: Opportunities and challenges. Proceedings of OceanObs'09: Sustained Ocean Observations and Information for Society, J. Hall, D. E. Harrison, and D. Stammer, Eds., Vol. 2, ESA Publ. WPP-306, 21-25.
22. Jaynes, E. T., 1957: Information theory and statistical mechanics. Phys. Rev., 106, 620-630.
23. Joe, H., 1989: Relative entropy measures of multivariate dependence. J. Amer. Stat. Assoc., 84, 157-164.
24. Keenlyside, N. S., M. Latif, J. Jungclaus, L. Kornblueh, and E. Roeckner, 2008: Advancing decadal-scale climate prediction in the North Atlantic sector. Nature, 453, 84-88, doi:10.1038/nature06921.
25. Kleeman, R., 2002: Measuring dynamical prediction utility using relative entropy. J. Atmos. Sci., 59, 2057-2072.
26. Kleeman, R., 2010: Information theory and dynamical system predictability. Preprints, Mathematical and Statistical Approaches to Climate Modelling and Prediction, Cambridge, United Kingdom, Isaac Newton Institute for Mathematical Sciences, NI10063, 33 pp. [Available online at http://www.newton.ac.uk/preprints/NI10063.pdf.]
27. Lawler, G. F., 2006: Introduction to Stochastic Processes. Chapman&Hall/CRC, 248 pp.
28. Leung, L.-Y., and G. R. North, 1990: Information theory and climate prediction. J. Climate, 3, 5-14.
29. MacQueen, J., 1967: Some methods for classification and analysis of multivariate observations. Statistics, L. M. Le Cam and J. Neyman, Eds., Vol. 1, Proceedings of the Fifth Berkeley Symposium on Mathematical Statistics and Probability, University of California Press, 281-287.
30. Majda, A. J., and B. Gershgorin, 2010: Quantifying uncertainty in climate change science through empirical information theory. Proc. Natl. Acad. Sci. USA, 107, 14 958-14 963, doi:10.1073/pnas.1007009107.
31. Majda, A. J., and X. Wang, 2010: Linear response theory for statistical ensembles in complex systems with time-periodic forcing. Commun. Math. Sci., 8, 145-172.
32. Majda, A. J., and B. Gershgorin, 2011: Link between statistical equilibrium fidelity and forecasting skill for complex systems with model error. Proc. Natl. Acad. Sci. USA, 108, 12 599-12 604, doi:10.1073/pnas.1108132108.
33. Majda, A. J., R. Kleeman, and D. Cai, 2002: A mathematical framework for predictability through relative entropy. Methods Appl. Anal., 9, 425-444.
34. Majda, A. J., R. V. Abramov, and M. J. Grote, 2005: Information Theory and Stochastics for Multiscale Nonlinear Systems. CRM Monogr., Vol. 25, American Mathematical Society, 133 pp.
35. Majda, A. J., C. L. Franzke, A. Fischer, and D. T. Crommelin, 2006: Distinct metastable atmospheric regimes despite nearly Gaussian statistics: A paradigm model. Proc. Natl. Acad. Sci. USA, 103, 8309-8314, doi:10.1073/pnas.0602641103.
36. Majda, A. J., C. L. Franzke, and D. Crommelin, 2009: Normal forms for reduced stochastic climate models. Proc. Natl. Acad. Sci. USA, 106, 3649-3653, doi:10.1073/pnas.0900173106.
37. McCalpin, J. D., and D. B. Haidvogel, 1996: Phenomenology of the low-frequency variability in a reduced-gravity quasigeostrophic double-gyre model. J. Phys. Oceanogr., 26, 739-752.
38. Meehl, G. A., and Coauthors, 2009: Decadal prediction: Can it be skillful? Bull. Amer. Meteor. Soc., 90, 1467-1485.
39. Metzner, P., E. Dittmer, T. Jahnke, and C. Schütte, 2007: Generator estimation of Markov jump processes. J. Comput. Phys., 227, 353-375, doi:10.1016/j.jcp.2007.07.032.
40. Penland, C., 1989: Random forcing and forecasting using principal oscillation pattern analysis. Mon. Wea. Rev., 117, 2165-2185.
41. Pohlmann, H., J. H. Jungclaus, A. Köhl, D. Stammer, and J. Marotzke, 2009: Initializing decadal climate predictions with the GECCO oceanic synthesis: Effects on the North Atlantic. J. Climate, 22, 3926-3938.
42. Reichler, T., and J. Kim, 2008a: How well do coupled models simulate today's climate? Bull. Amer. Meteor. Soc., 89, 303-311.
43. Reichler, T., and J. Kim, 2008b: Uncertainties in the climate mean state of global observations, reanalyses, and the GFDL climate model. J. Geophys. Res., 113, D05106, doi:10.1029/2007jd009278.
44. Roulston, M., and L. Smith, 2002: Evaluating probabilistic forecasts using information theory. Mon. Wea. Rev., 130, 1653-1660.
45. Schneider, T., and S. M. Griffies, 1999: Aconceptual framework for predictability studies. J. Climate, 12, 3133-3155.
46. Smith, D. M., S. Cusack, A. W. Colman, C. K. Folland, G. R. Harris, and J. M. Murphy, 2007: Improved surface temperature prediction for the coming decade from a global circulation model. Science, 317, 796-799, doi:10.1126/science. 1139540.
47. Solomon, A., and Coauthors, 2011: Distinguishing the roles of natural and anthropogenically forced decadal climate variability: Implications for prediction. Bull. Amer. Meteor. Soc., 92, 141-156.
48. Teng, H., and G. Branstator, 2010: Initial-value predictability of prominent modes of North Pacific subsurface temperature in a CGCM. Climate Dyn., 36, 1813-1834, doi:10.1007/s00382-010-0749-7.
49. Wikle, C. K., and L. M. Berliner, 2007: A Bayesian tutorial for data assimilation. Physica D, 230, 1-16, doi:10.1016/j.physd.2006.09.017.
50. Wikle, C. K., L. M. Berliner, and N. Cressie, 1998: Hierarchical Bayesian spacetime models. Environ. Ecol. Stat., 5, 117-154, doi:10.1023/a:1009662704779.