Predictability of extreme values in geophysical models

Nonlinear Processes in Geophysics

Volumn 19, Issue 5, 2012, Pages 529-539

  Sterk, A E ^a   Holland, M P ^a   Rabassa, P ^b   Broer, H W ^b   Vitolo, R ^a  

^a UNIVERSITY OF EXETER   (United Kingdom)

^b UNIVERSITY OF GRONINGEN   (Netherlands)

Author keywords

[No Author keywords available]

Indexed keywords

FINITE ELEMENT METHOD; GEOPHYSICAL METHOD; MODELING; THEORETICAL STUDY;

EID: 84866564898     PISSN: 10235809     EISSN: 16077946     Source Type: Journal    
DOI: 10.5194/npg-19-529-2012     Document Type: Article

References (41)

1. Abarbanel, H., Brown, R., and Kennel, M.: Variation of Lyapunov Exponents on a Strange Attractor, J. Nonlin. Sci., 1, 175-199, 1991.
2. Bailey, B., Ellner, S., and Nychka, D.: Chaos with confidence: asymptotics and applications of local Lyapunov exponents, Fields Institute Communications, 11, 115-133, 1997.
3. Beirlant, J., Goegebeur, Y., Teugels, J., and Segers, J.: Statistics of Extremes: Theory and Applications, John Wiley and Sons, Berlin, 2004.
4. Bowler, N., Arribas, A., Mylne, K., Robertson, K., and Beare, S.: The MOGREPS short-range ensemble prediction system, Q. J. Roy. Meteorol. Soc., 134, 703-722, 2008.
5. Broer, H. and Takens, F.: Dynamical Systems and Chaos, 172, Appl. Math. Sci., Springer, 2011.
6. Broer, H. and Vegter, G.: Subordinate Šilńikov bifurcations near some singularities of vector fields having low codimension, Er-godic Theor. Dynam. Syst., 4, 509-525, 1984.
7. Broer, H. and Vitolo, R.: Dynamical systems modelling of low-frequency variability in low-order atmospheric models, Discrete and Continuous Dynamical Systems B, 10, 401-419, 2008.
8. Buizza, R. and Palmer, T.: The singular-vector structure of the atmospheric global circulation, J. Atmos. Sci., 52, 1434-1456, 1995. (Pubitemid 26436665)
9. Charney, J. and DeVore, J.: Multiple Flow Equilibria in the Atmosphere and Blocking, J. Atmos. Sci., 36, 1205-1216, 1979.
10. Coles, S.: An Introduction to Statistical Modeling of Extreme Values, Springer Series in Statistics, Springer, New York, 2001.
11. Crommelin, D. and Vanden-Eijnden, E.: Subgrid scale parameterization with conditional Markov chains, J. Atmos. Sci., 65, 2661-2675, 2008.
12. Crommelin, D., Opsteegh, J., and Verhulst, F.: A Mechanism for Atmospheric Regime Behavior, J. Atmos. Sci., 61, 1406-1419, 2004. (Pubitemid 38945801)
13. Datta, S. and Ramaswamy, R.: Non-Gaussian fluctuations of local Lyapunov exponents at intermittency, J. Stat. Phys., 113, 283-295, 2003. (Pubitemid 38104200)
14. De Swart, H.: Low-Order Spectral Models of the Atmospheric Circulation: A Survey, Acta Applicandae Mathematicae, 11, 49-96, 1988.
15. De Swart, H.: Analysis of a six-component atmospheric spectral model: chaos, predictability and vacillation, Physica D, 36, 222-234, 1989.
16. Felici, M., Lucarini, V., Speranza, A., and Vitolo, R.: Extreme Value Statistics of the Total Energy in an Intermediate-Complexity Model of the Midlatitude Atmospheric Jet. Part I: Stationary Case, J. Atmos. Sci., 64, 2137-2158, 2007a. (Pubitemid 47233132)
17. Felici, M., Lucarini, V., Speranza, A., and Vitolo, R.: Extreme Value Statistics of the Total Energy in an Intermediate-Complexity Model of the Midlatitude Atmospheric Jet. Part II: Trend Detection and Assessment, J. Atmos. Sci., 64, 2159-2175, 2007b. (Pubitemid 47240722)
18. Freitas, A. and Freitas, J.: On the link between dependence and independence in extreme value theory for dynamical systems, Stat. Probab. Lett., 78, 1088-1093, 2008.
19. Freitas, A., Freitas, J., and Todd, M.: Extreme Value Laws in Dynamical Systems for Non-smooth Observations, J. Stat. Phys., 142, 108-126, 2010.
20. Gupta, C.: Extreme-value distributions for some classes of non-uniformly partially hyperbolic dynamical systems, Ergodic Theor. Dynam. Syst., 30, 757-771, 2010.
21. Haiman, G.: Extreme values of the tent map process, Stat. Probab. Lett., 65, 451-456, 2003. (Pubitemid 37501321)
22. Harle, M., Kwasniok, F., and Feudel, U.: Growth of finite errors in ensemble prediction, Nonlin. Processes Geophys., 13, 167-176, doi:10.5194/npg-13-167-2006, 2006. (Pubitemid 44123918)
23. Holland, M., Nicol, M., and Török, A.: Extreme value theory for non-uniformly expanding dynamical systems, T. Am. Math. Soc., 364, 661-688, 2012a.
24. Holland, M., Vitolo, R., Rabassa, P., Sterk, A., and Broer, H.: Extreme value laws in dynamical systems under physical observ-ables, Physica D, 241, 497-513, 2012b.
25. Lai, Y.-C.: Extreme fluctuations of finite-time Lyapunov exponents in chaotic systems, Int. J. Modern Phys. B, 21, 3941-3946, 2007.
26. Leadbetter, M., Lindgren, G., and Rootzén, H.: Extremes and related properties of random sequences and processes, Springer Series in Statistics, Springer-Verlag, New York, 1983.
27. Leutbecher, M. and Palmer, T.: Ensemble forecasting, J. Comput. Phys., 227, 3515-3539, 2008.
28. Lorenz, E.: Deterministic nonperiodic flow, J. Atmos. Sci., 20, 130-141, 1963.
29. Lorenz, E.: Predictability-A problem partly solved, in: Predictability of Weather and Climate, edited by: Palmer, T. and Hagedorn, R., Cambridge University Press, 40-58, 1996.
30. Mailier, P., Stephenson, D., Ferro, C., and Hodges, K.: Serial clustering of extratropical cyclones, Mon. Wea. Rev., 134, 2224-2240, 2006. (Pubitemid 44275534)
31. Nese, J.: Quantifying local predictability in phase space, Physica D, 35, 237-250, 1989.
32. Oseledec, V.: A multiplicative ergodic theorem: Lyapunov characteristic numbers for dynamical systems, Trudy Mosk. Mat. Obsc. 19, 197, 1968.
33. Palmer, T., Gelaro, R., Barkmeijer, J., and Buizza, R.: Singular vectors, metrics and adaptive observations, J. Atmos. Sci., 55, 633-653, 1998.
34. Pomeau, Y. and Manneville, P.: Intermittent Transition to Turbulence in Dissipative Dynamical Systems, Commun. Math. Phys., 74, 189-197, 1980.
35. Prasad, A. and Ramaswamy, R.: Characteristic distributions of finite-time Lyapunov exponents, Phys. Rev. E, 60, 2761-2766, 1999. (Pubitemid 129691458)
36. Sterk, A., Vitolo, R., Broer, H., Simó, C., and Dijkstra, H.: New nonlinear mechanisms of midlatitude atmospheric low-frequency variability, Physica D, 239, 702-718, 2010.
37. Trevisan, A. and Palatella, L.: On the Kalman Filter error covariance collapse into the unstable subspace, Nonlin. Processes Geophys., 18, 243-250, doi:10.5194/npg-18-243-2011, 2011.
38. Vitolo, R., Stephenson, D., Cook, I., and Mitchell-Wallace, K.: Serial clustering of intense European storms, Meteorol. Z., 18, 411-424, 2009.
39. Zaldívar, J.-M., Bosch, J., Strozzi, F., and Zbilut, J.: Early warning detection of runaway initiation using non-linear approaches, Commun. Nonlin. Sci. Numer. Simul., 10, 299-311, 2005.
40. Ziehmann, C., Smith, L., and Kurths, J.: The bootstrap and Lya-punov exponents in deterministic chaos, Physica D, 126, 49-59, 1999. (Pubitemid 129496515)
41. Ziehmann, C., Smith, L., and Kurths, J.: Localized Lyapunov exponents and the prediction of predictability, Phys. Lett. A, 271, 237-251, 2000.