A comparison of Lyapunov and optimal vectors in a low-resolution GCM

Tellus, Series A: Dynamic Meteorology and Oceanography

Volumn 49, Issue 2, 1997, Pages 200-227

  Szunyogh, Istvan ^a   Kalnay, Eugenia ^b   Toth, Zoltan ^b  

^a EÖTVÖS LORÁND UNIVERSITY   (Hungary)

^b CLIMATE PREDICTION CENTER   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ATMOSPHERIC CIRCULATION; GCM; LYAPUNOV VECTOR; OPTIMAL VECTOR; VECTOR;

EID: 0030723220     PISSN: 02806495     EISSN: None     Source Type: Journal    
DOI: 10.3402/tellusa.v49i2.14467     Document Type: Review

References (59)

1. Anderson, J. L. 1995. Selection of initial conditions for ensemble forecasts in a simple perfect model framework. J. Atmos. Sci. 53, 22-36.
2. Barkmeijer, J. 1992. Local error growth in a barotropic model. Tellus 44A, 314-323.
3. Barkmeijer, J. 1995. Approximating dominant eigenvalues and eigenvectors of the local forecast error covariance matrix. Tellus 47A. 495-501.
4. Benettin, G., Galgani, L. and Strelcyn, J. M. 1976. Kolmogorov entropy and numerical experiments. Physical Review A14. 2338-2345.
5. Benettin, G., Galgani, L., Giorgilli, A. and Strelcyn, J. M. 1980. Lyapunov characteristic exponents for smooth dynamical systems and for Hamiltonian systems; a method for computing all of them. Meccanica 15, 9.
6. Borges, M. D. and Hartman, D. L. 1992. Barotropic instability and optimal perturbations of observed nonzonal flow. J. Atmos. Sci. 49, 335-354.
7. Branstator, G. 1985. Analysis of general circulation model sea-surface temperature anomaly simulations using a linear model. Part II: Eigenanalysis. J. Atmos. Sci. 42, 2242-2254.
8. Brown, J. A. 1969. A numerical investigation of hydrodynamic instability and energy conversions in the quasigeostrophic atmosphere. Parts I. II. J. Atmos. Sci. 26, 352-365, 366-375.
9. Buizza, R., Tribbia, J., Molteni, F. and Palmer, T. 1993. Computation of optimal unstable structures for a numerical weather prediction model. Tellus 45A, 388-407.
10. Buizza, R. 1994a. Localization of optimal perturbations using a projection operator. Q. J. R. Meteorol. Soc. 120, 1647-1681.
11. Buizza, R. 1994b. Sensitivity of optimal unstable structures. Q. J. R. Meteorol. Soc. 120, 429-451.
12. Buizza, R. 1995. Optimal perturbation time evolution and sensitivity of ensemble prediction to perturbation amplitude. Q. J. R. Meteorol. Soc. 121, 1705-1738.
13. Buizza, R. and Palmer, T. 1995. The singular vector structure of the atmospheric general circulation., J. Atmos. Sci. 52, 1434-1456.
14. Charney, J. G. 1947. The dynamics of long waves in a baroclinic westerly current. J. Meteor. 4, 135-163.
15. Eady, E. T. 1949. Long waves and cyclone waves. Tellus 11, 33-52.
16. Ehrendorfer, M. and Errico, R. 1995. Mesoscale predictability and the spectrum of optimal perturbations. J. Atmos. Sci. 52, 3475-3500.
17. Farrell, B. 1988. Optimal excitation of neutral Rossby waves. J. Atmos. Sci. 45, 163-172.
18. Farrell, B. 1990. Small error dynamics and the predictability of atmospheric flows. J. Atmos. Sci. 47, 2409-2416.
19. Hartmann, D. L., Buizza, R. and Palmer, T. N. 1995. Singular vectors: The effect of spatial scale on linear growth of disturbances. J. Atmos. Sci. 52, 3885-3894.
20. Golub, G. H. and Van Loan, C. F. 1983. Matrix computations. The Johns Hopkins University Press, Baltimore, 642 pp.
21. Houtekamer, P. L. 1991. Variation of the predictability in a low order spectral model of the atmospheric circulation. Tellus, 43A, 177-190.
22. Houtekamer, P. L. 1995. The construction of optimal perturbations. Mon. Wea. Rev. 123, 2888-2898.
23. Houtekamer, P. L. and Derome, J. 1994. Prediction experiments with two-member ensembles. Mon. Wea. Rev. 122, 2179-2191.
24. Houtekamer, P. L. and Derome, J. 1995. Methods for ensemble prediction. Mon. Wea. Rev. 123, 2181-2196.
25. Kalnay, E. and Toth, Z. 1994. Removing growing errors in the analysis. Proceedings of the 10th Conference on Numerical weather prediction, 18-22 July, 1994, Portland, OR. AMS. p. 212-215.
26. James. I. N. 1994. Introduction to circulating atmospheres. Cambridge University Press, Cambridge, 422 pp.
27. Kanamitsu, M., Alpert, J. C., Campana, K. A., Caplan, P. M., Deaven, D. G., Iredell, M., Katz, B., Pan, H.-L., Sela, J. and White, G. H. 1991. Recent changes in the Global Forecast system at NMC. Wea. Forecasting 6, 425-435.
28. Kaplan, J. and Yorke, J. 1979. Chaotic behavior of multidimensional difference equations. In: Functional differential equations and approxiamtion afixed points, edited by: H. O. Peitgen and H. O. Walther, pp. 228-237. Pringler-Verlag, New York.
29. Kuo, H. L. 1949. Dynamic instability of two-dimensional nondivergent flow in a barotropic atmosphere. J. Meteor. 6, 105-122.
30. Lacarra, J. F. and Talagrand, O. 1988. Short range evolution of small perturbations in a barotropic model. Tellus 40A, 81-95.
31. Legras, B. and Vautard, R. 1996. A guide to Lyapunov vectors. Proceedings of the ECMWF Seminar on Predictability, 4-8 September, 1995, Reading, England, vol. I, 143-156.
32. Lorenz, E. N. 1963. Deterministic non-periodic flow. J. Atmos. Sci. 20, 130-141.
33. Lorenz, E. N. 1965. A study of the predictability of a 28-variable atmospheric model. Tellus 17, 321-333.
34. Lorenz, E. N. 1972. Barotropic instability of Rossby wave motion. J. Atmos. Sci. 29, 258-264.
35. Molteni, F. and Palmer, T. N. 1993. Predictability and finite-time instability of the nothern winter circulation. Q. J. R. Meteorol. Soc. 119, 269-298.
36. Molteni, F., Buizza, R., Palmer, T.N. and Petroliagis, T. 1996. The ECMWF ensemble system: Methodology and validation. Q. J. R. Meteorol. Soc. 122, 73-119.
37. Navon, I. M., Zou, X., Derber, J. and Sela, J. 1992. Variational data assimilation with an adiabatic version of the NMC Spectral Model. Mon. Wea. Rev. 120, 1433-1446.
38. Nese, J. M. 1989. Quantifying local predictability in phase space. Physica D 35, 237-250.
39. Nicolis, C, Vannitsem, S. and Royer, J.-F. 1995. Shortrange predictability of the atmosphere: mechanisms for superexponential error growth. Q. J. R. Meteorol. Soc. 121, 705-722.
40. Pedlosky, J. 1964. The stability of currents in the atmosphere and the ocean: Part II. J. Atmos. Sci. 21, 342-353.
41. Pedlosky, J. 1987. Geophysical fluid dynamics. SpringerVerlag, New-York, 710 pp.
42. Pires, C., Vautard, R. and Talagrand, O. 1996. On extending the limits of variational assimilation in chaotic systems. Tellus 48A, 96-121.
43. Rabier, F., Courtier, P., Pailleux, J., Talagrand, O. and Vasiljevic, D. 1993. A comparison between four-dimensional variational assimilation and simplified sequential assimilation relying on three-dimensional variational analysis. Q. J. R. Meteorol. Soc. 119, 845-880.
44. Rabier, F., Klinker, E., Courtier, P. and Hollingsworth, A. 1994. Sensitivity of two-day forecast errors over the Northern Hemisphere to initial conditions. ECMWF Research Department Technical Memorandum no. 203. Available from: ECMWF, Shienfield Park, Reading, Berkshire RG2 9AX, England.
45. Sela, J. G. 1980. Spectral modelling at the National Meteorological Center. Mon. Wea. Rev. 108, 1279-1292.
46. Shimada, I. and Nagashima, T. 1979. A numerical approach to ergodic problem of dissipative dynamical systems. Progress of Theoretical Physics 61, 1605-1615.
47. Tabor, M. 1989. Chaos and integrability in nonlinear dynamics. John Wiley & Sons, New York, 376 pp.
48. Talagrand, O. 1981. A study of the dynamics of four-dimensional data assimilation. Tellus 33, 43-60.
49. Toth, Z. and Kalnay, E. 1993. Ensemble Forecasting at NMC: The generation of perturbations. Bull. Amer. Meteorol. Soc. 74, 2317-2330.
50. Toth, Z. and Kalnay, E. 1996. Ensemble forecasting at NCEP and the breeding method. Mon. Wea. Rev., under review.
51. Tracton, S. and E. Kalnay, 1993. Ensemble forecasting at NMC: Operational implementation. Wea. Forecasting 8, 379-398.
52. Trevisan, A. 1993. Impact of transient error growth on global average predictability measures. J. Atmos. Sci. 50, 1016-1028.
53. Trevisan, A. and Legnani, R. 1995. Transient error growth and local predictability: a study in the Lorenz system. Tellus A47, 103-117.
54. Tsonis, A. A. 1992. Chaos: from theory to applications. Plenum Press, New York, pp. 83-96.
55. Vannitsem, S. and Nicolis, C. 1994. Predictability experiments on a simplified thermal convection model: The role of spatial scales. J. Geophys. Res. 99 (D5) 10.377-10.385.
56. Vukicevic, T. 1993. Possibility of skill forcasts based on the finite-time dominant linear solutions for a primitive equation regional model. J. Atmos. Sci. 50, 1777-1791.
57. Wolf, A., Swift, J. B., Swinney, H. L. and Vastano, J. A. 1985. Determining Lyapunov exponents from a time series. Physica 16D, 285-317.
58. Xue, Y., Cane, M. A. and Zebiak, S. E. 1996. Predictability of ENSO using singular vector analysis. Part I: Optimal growth in seasonal background and ENSO cycles. Mon. Wea. Rev., under review.
59. Zebiak, S. E. and Cane, M. A. 1987. A model EL Nino-Southern Oscillation. Mon. Wea. Rev. 115, 2262-2278.