The impact of nonlinear dynamics in the atmospheric sciences

International Journal of Bifurcation and Chaos in Applied Sciences and Engineering

Volumn 11, Issue 4, 2001, Pages 881-902

  Tsonis, A A ^a  

^a UNIVERSITY OF WISCONSIN MILWAUKEE   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0035297791     PISSN: 02181274     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218127401002663     Document Type: Review

References (66)

1. Abarbanel, H. D. I. & Kennel, M. B [1991] "Lyapunov exponents in chaotic systems: Their importance and their evaluation using observed data," Mod. Phys. Lett. B5, 1347-1375.
2. Bauer, S. T. & Brown, M. B. [1992] "Empirical low-order ENSO dynamics," Geophys. Res. Lett. 19, 2055-2058.
3. Broecker, W. S. & Denton, G. H. [1990] "What drives glacial cycles?" Sci. Amer. 262, 49-56.
4. Buizza, R. & Palmer, T. N. [1995] "The singular vector structure of the atmospheric general circulation," J. Atmos. Sci. 52, 1434-1456.
5. Davis, R. [1976] "Predictability of sea surface temperature and sea level pressure anomalies over the north Pacific Ocean," J. Phys. Oceanogr. 6, 249-266.
6. Elsner, J. B. & Tsonis, A. A. [1992] "Nonlinear prediction, chaos and noise," Bull. Amer. Meteor. Soc. 73, 49-60.
7. Elsner, J. B. & Tsonis, A. A. [1993] "Nonlinear dynamics established in the ENSO," Geophys. Res. Lett. 20, 213-216.
8. Elsner, J. B. & Tsonis, A. A. [1996] Singular Spectrum Analysis: A New Tool in Time Series Analysis (Plenum, NY).
9. Farmer, J. D. & Sidorowich, J. J. [1987] "Predicting chaotic time series," Phys. Rev. Lett. 59, 845-848.
10. Feder, J. [1988] Fractals (Plenum, NY).
11. Folland, C. K., Karl, T. R. & Vinnikov, K. Ya. [1990] "Observed climate variations and change," in Climate Change: The IPCC Scientific Assessment, eds. Houghton, J. T., Jenkins, G. I. & Ephramus, J. J. (Cambridge University Press, Cambridge), pp. 195-238.
12. Grassberger, P. & Procaccia, I. [1983a] "Characterization of strange attractors," Phys. Rev. Lett. 50, 346-349.
13. Grassberger, P. & Procaccia, I. [1983b] "Measuring the strangeness of strange attractors," Physica D9, 189-208.
14. Hense, A. [1987] "On the possible existence of a strange attractor for the southern oscillation," Beitr. Phys. Atmos. 60, 34-47.
15. Horel, J. D. & Wallace, J. M. [1981] "Planetary-scale atmospheric phenomena associated with the southern oscillation," Mon. Wea. Rev. 109, 813-829.
16. Hoskins, B. J. & Karoly, J. [1981] "The steady linear response of a spherical atmosphere to thermal and orographic forcing," J. Atmos. Sci. 38, 1179-1196.
17. Kendall, M. G. & Stuart, A. [1977] The Advanced Theory of Statistics, 4th edition (Griffin, London).
18. Kuo, S., Lindberg, C. & Thomson, D. J. [1990] "Coherence established between atmospheric carbon dioxide and global temperature," Nature 343, 709-714.
19. Lanzante, J. R. [1984] "A rotated eigenanalysis of the correlation between 700-mb heights and sea surface temperatures in the Pacific and Atlantic," Mon. Wea. Rev. 112, 2270-2280.
20. Latif, M. & Barnett, T. P. [1994] "Causes of decadal climate variability over the North Pacific and North America," Science 266, 634-637.
21. Latif, M. & Barnett, T. P. [1996] "Decadal climate variability over the North Pacific and North America: Dynamics and predictability," J. Climate 9, 2407-2423.
22. Latif, M., Grotzner, A., Munnich, M., Maier-Reimer, E., Venke, S. & Barnett, T. P. [1996] "A mechanism for decadal climate variability," in Decadal Climate Variability: Dynamics and Predictability, eds. Davis, L. T. et al., NATO ASI Series I, Vol. 44 (Springer, Berlin), pp. 263-292.
23. Lau, K.-M. & Chan, P. H. [1985] "Aspects of the 40-50 day oscillation during northern winter as inferred from outgoing longwave radiation," Mon. Wea. Rev. 113, 1889-1909.
24. Lau, N. C. & Nath, M. J. [1990] "A general circulation model study of the atmosphere response to extratropical SST anomalies observed in 1950-79," J. Climate 3, 965-989.
25. Lorenz, E. N. [1963] "Deterministic nonperiodic flow," J. Atmos. Sci. 20, 130-141.
26. Lorenz, E. N. [1991] "Dimension of weather and climate attractors," Nature 353, 241-244.
27. Madden, R. A. & Julian, P. R. [1971] "Detection of a 40-50 day oscillation in the zonal wind in the tropical Pacific," J. Atmos. Sci. 28, 702-708.
28. Mandelbrot, B. B. [1983] The Fractal Geometry of Nature (Freeman, NY).
29. Molteni, F., Buizza, R., Palmer, T. N. & Petroliagis, T. [1996] "The ECMWF ensemble system: Methodology and validation," Quart. J. R. Meteor. Soc. 122, 73-119.
30. Namias, J. [1969] "Seasonal interactions between the north Pacific Ocean and the atmosphere during the 1960s," Mon. Wea. Rev. 97, 173-192.
31. Neelin, D. J., Battisti, D. S., Hirst, A. C. & Jin, F.-F. [1998] "ENSO theories," J. Geophys. Res. 103(7), 14261-14290.
32. Neelin, D. J. & Latif, M. [1998] "El Niño dynamics," Physics Today 51, 32-36.
33. Nerenberg, M. A. H. & Essex, C. [1990] "Correlation dimension and systematic geometric effects," Phys. Rev. A42, 7065-7074.
34. Newell, N. E., Newell, R. E., Hsiung, J. & Zhong-Xiang, W. [1989] "Global marine temperature variation and the solar magnetic cycle," Geophys. Res. Lett. 16, 311-314.
35. Packard, N. H., Crutchfield, J. D. & Shaw, R. S. [1980] "Geometry from a time series," Phys. Rev. Lett. 45, 712-716.
36. Priestley, M. B. [1981] Spectral Analysis and Time Series (Academic Press, NY).
37. Ruelle, D. [1981] "Chemical kinetics and differentiable dynamical systems," in Nonlinear Phenomena in Chemical Dynamics, eds. Pacault, A. & Vidal, C. (Springer-Verlag, Berlin), pp. 57-72.
38. Schneider, E. K., Huang, B. & Shukla, J. [1995] "Ocean wave dynamics and El Niño," J. Climate 8, 2414-2439.
39. Smith, L. A. [1988] "Intrinsic limits on dimension calculations," Phys. Lett. A133, 283-288.
40. Sugihara, G. & May, R. M. [1990] "Nonlinear forecasting as a way of distinguishing chaos from measurement error in time series," Nature 344, 734-741.
41. Sun, D.-Z. & Trenberth, K. [1998] "Coordinated heat removal from the equatorial Pacific during the 1986-87 El Niño," Geophys. Res. Lett. 25, 2659-2662.
42. Takens, F. [1981] "Detecting strange attractors in turbulence," in Dynamical Systems and Turbulence, Lecture Notes in Mathematics, Vol. 898, eds. Rand, D. & Young, L. S. (Springer-Verlag, Berlin), pp. 366-381.
43. Thomson, D. J. [1982] "Spectrum estimation and harmonic analysis," Proc. IEEE 70, 1055-1096.
44. Toth, Z. & Kanlay, E. [1993] "Ensemble forecasting at NMC: The generation of pertubations," Bull. Amer. Meteor. Soc. 74, 2317-2330.
45. Toth, Z. & Kanlay, E. [1995] "Ensemble forecasting at NCEP and the breeding method," NMC Office Note 407, 58 pp. [Available from NCEP, 5200 Auth. Rd., Camp Springs, MD 20746].
46. Trenberth, K. E. & Hurrell, J. W. [1994] "Decadal atmosphere-ocean variations in the Pacific," Climate Dyn. 9, 303-319.
47. Trenberth, K. E. [1997] "The definition of El Niño," Bull. Amer. Meteor. Soc. 78, 2771-2777.
48. Tsonis, A. A. & Elsner, J. B. [1988] "The weather attractor over very short time scales," Nature 33, 545-547.
49. Tsonis, A. A. & Elsner, J. B. [1989] "Chaos, strange attractors and weather," Bull. Amer. Meteor. Soc. 70, 16-23.
50. Tsonis, A. A. [1992] Chaos: From Theory to Applications (Plenum, NY).
51. Tsonis, A. A. & Elsner, J. B. [1992] "Nonlinear prediction as a way of distinguishing chaos from random fractal sequences," Nature 358, 217-220.
52. Tsonis, A. A., Triantafyllou, G. N. & Elsner, J. B. [1994] "Searching for determinism in observed data: A review of the issues involved," Nonlin. Process. Geophys. 1, 12-25.
53. Tsonis, A. A. [1996] "Dynamical systems as models for physical processes," Complexity 1(5), 23-33.
54. Tsonis, A. A. & Elsner, J. B. [1996] "Mapping the channels of communication between the tropics and higher latitudes in the atmosphere," Physica D92, 237-244.
55. Tsonis, A. A. & Elsner, J. B. [1997] "Global temperature as a regulator of climate predictability," Physica D108, 191-196.
56. Tsonis, A. A. [1998] "Fractality in nature," Science 279, 1614-1615.
57. Tsonis, A. A., Roebber, P. J. & Elsner, J. B. [1998] "A characteristic time scale in the global temperature record," Geophys. Res. Lett. 25, 2821-2823.
58. Tsonis, A. A., Roebber, P. J. & Elsner, J. B. [1999] "Long-range correlations in the extratropical atmospheric circulation: Origins and implications," J. Climate 12, 1534-1541.
59. Tziperman, E., Stone, L., Cane, M. A. & Jarosh, H. [1994] "El Niño chaos: Overlapping of reasonances between the seasonal cycle and the Pacific Ocean-atmosphere oscillator," Science 264, 72-74.
60. UCAR Quarterly [1997] "El Niño and Global Warming: What's the Connection?" UCAR office of programs, Vol. 24, winter 1997.
61. Vallis, G. K. [1986] "El-Nino: A chaotic dynamical system?" Science 232, 243-245.
62. Wales, D. J. [1991] "Calculating the rate of loss of information from chaotic time series by forecasting," Nature 350, 485-488.
63. Wallace, J. M. & Gutzler, D. S. [1981] "Teleconnections in the geopotential height field during the Northern Hemisphere winter," Mon. Wea. Rev. 109, 784-817.
64. Wallace, J. M. & Jiang, Q. R. [1987] "On the observed structure of the interannual variability of the atmosphere/ocean climate system," in Atmospheric and Oceanic Variability, ed. Cattle, H. (Royal Meteorological Society, London), pp. 17-43.
65. Wallace, J. M., Smith, C. & Jiang, Q. R. [1990] "Spatial patterns of atmosphere ocean interactions in the northern winter," J. Climate 3, 990-988.
66. Wiin-Nielsen, A. & Chen, T.-C. [1993] Fundamentals Atmospheric Energetics (Oxford, NY).