Spectral analysis of climate data

Surveys in Geophysics

Volumn 17, Issue 6, 1996, Pages 619-663

  Yiou, P ^a   Baert, E ^b   Loutre, M F ^b  

^a CEA SACLAY   (France)

^b UNIVERSITÉ CATHOLIQUE DE LOUVAIN   (Belgium)

Author keywords

Geophysical time series analysis; Spectral analysis

Indexed keywords

CLIMATE DYNAMICS; FOURIER METHOD; GEOPHYSICAL TIME SERIES; MAXIMUM ENTROPY METHOD; SPECTRAL ANALYSIS; TIME SERIES ANALYSIS;

EID: 0030372499     PISSN: 01693298     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF01931784     Document Type: Article

References (120)

1. Akaike, H.: 1969, 'Fitting autoregressive models for prediction', Ann. Inst. Statist. Math. 21, 243-247.
2. Akaike, H.: 1974, 'A new look at the statistical model identification', IEEE Trans. Autom. Control 19, 716-723.
3. Allen, M.: 1992, 'Interactions between the atmosphere and oceans on time scales of weeks to years', PhD thesis St John's College, Oxford.
4. Allen, M.R. and Robertson, A.W.: 1996, 'Distinguishing modulated oscillations from coloured noise in multivariate datasets', Clim. Dyn. (in press).
5. Allen, M.R. and Smith, L. A.: 1996, 'Monte Carlo SSA: detecting irregular oscillations in the presence of coloured noise', J. Clim. (in press).
6. Allen, M.R. and Smith, L.A.: 1994, 'Investigating the origins and significance of low-frequency modes of climate variability', Geophys. Res. Lett. 21, 883-886.
7. Baert, E.: 1995a, 'Blackman-Tukey spectral analysis. Theory and user's guide', Scientific Report 1995/5, Institut d'Astronomie et de Géophysique G. Lemaître, Université catholique de Louvain, Louvain-la-Neuve, Belgium (available on the World Wide Web at http://www.agro.ucl.ac.be/biom-pub/www/EB-ELB/spectra.html).
8. Baert, E.: 1995b, 'Maximum entropy spectral analysis. Theory and user's guide', Scientific Report 1995/6, Institut d'Astronomie et de Géophysique G. Lemaître, Université catholique de Louvain, Louvain-la-Neuve, Belgium (available on the World Wide Web at http://www.agro.ucl.ac.be/biom-pub/www/EB-ELB/spectra.html).
9. Baert, E.: 1995c, 'Thomson (multi-taper) spectral analysis. Theory and user's guide', Scientific Report 1995/7, Institut d'Astronomie et de Géophysique G. Lemaître, Université catholique de Louvain, Louvain-la-Neuve, Belgium (available on the World Wide Web at http://www.agro.ucl.ac.be/biom-pub/www/EB-ELB/spectra.html).
10. Baert, E.: 1995d, 'Classical harmonic analysis. Theory and user's guide', Scientific Report 1995/8, Institut d'Astronomie et de Géophysique G. Lemaître, Université catholique de Louvain, Louvain-la-Neuve, Belgium (available on the World Wide Web at http://www.agro.ucl.ac.be/biom-pub/www/EB-ELB/spectra.html).
11. Baert, E.: 1995e, 'Cross-spectral analysis. Theory and user's guide', Scientific Report 1995/9, Institut d'Astronomie et de Géophysique G. Lemaître, Université catholique de Louvain, Louvain-la-Neuve, Belgium (available on the World Wide Web at http://www.agro.ucl.ac.be/biom-pub/www/EB-ELB/spectra.html).
12. Baert, E. and Yiou, P.: 1995, 'Wavelet analysis. Theory and user's guide', Scientific Report 1995/10, Institut d'Astronomie et de Géophysique G. Lemaître, Université catholique de Louvain, Louvain-la-Neuve, Belgium (available on the World Wide Web at http: //www.agro.ucl.ac.be/biom-pub/www/EB-ELB/spectra.html).
13. 2', Nature 329, 408-414.
14. Bender, M., Sowers, T., Dickson, M.L., Orchardo, J., Grootes, P., Mayewski, P.A. and Meeses, D.: 1994, 'Climate correlations between Greenland and Antarctica during the past 100,000 years', Nature 372, 663-666.
15. Benoist, J.P.: 1986, 'Analyse Spectrale de Signaux Glaciologiques: Etude des Glaces Sédimentaires Déposées à Dome C, Morphologie du Lit d'un Glacier', Thèse d'Etat, USMT Grenoble, France.
16. Bergé, P., Pomeau, Y. and Vidai, C.: 1984, L'Ordre dans le Chaos: Vers une Approche Déterministe de la Turbulence. Hermann, Paris.
17. Berger, A.L.: 1978, 'Long-term variations of daily insolation and Quaternary climatic changes', J. Geophys. Res. 35, 2362-2367.
18. Berger, A.L., Mélice, J.L. and Van der Mersch, I.: 1990, 'Evolutive spectral analysis of sunspot data over the past 300 years', Phil Trans. R. Soc. London A 330, 529-541.
19. Berger, A.L., Mélice, J.L. and Hinnov, L.: 1991, 'A strategy for frequency spectra of Quaternary climate records', Clim. Dyn. 5, 227-240.
20. Berger, A.L., Loutre, M.F. and Tricot, C.: 1993, 'Insolation and Earth's orbital periods', J. Geophys. Res. 98(D6), 10341-10362.
21. Beutler, J.F.: 1974, 'Recovery of randomly sampled signals by simple interpolators', Information and Control 26, 312-340.
22. 18 records and in simulations: internal variability versus orbital forcing', J. Geophys. Res. 98(DO), 10385-10399.
23. Blackman, R.B. and Tukey, J. W.: 1958, The Measurement of Power Spectra From The Point of View of Communication Engineering, Dover, New York.
24. Bolton, E.W., Maasch, K.A. and Lilly, J.M.: 1995, 'A wavelet analysis of Plio-Pleistocene climate indicators: A new view of periodicity', Geophys. Res. Lett. 22(20), 2753-2756.
25. Box, G.E.P. and Jenkins, G.M.: 1970, Time Series Analysis, Forecasting and Control, Holden-Day, San Francisco.
26. Broecker, W.S., Bond, G., Klas, M., Clark E. and McManus, J.: 1992, 'Origin of the northern Atlantic's Heinrich events', Clim. Dyn. 6, 265-273.
27. Broomhead, D.S. and King, G.P.: 1986, 'Extracting qualitative dynamics from experimental data', Physica D20, 217-236.
28. Burg, J.P.: 1967, 'Maximum entropy spectral analysis', in 37th Ann. Intern. Meeting. Soc. Explor. Geophys., Oklahoma City, OK.
29. Chappellaz, J., Barnola, J.M., Raynaud, D., Korotkevitch, Y.S. and Lorius, C.: 1990, 'Ice-core record of atmospheric methane over the past 160,000 years', Nature 345, 127-131.
30. Chatfield, C.: 1984, The Analysis of Time Series: An Introduction, 3rd ed., Chapman and Hall, New York.
31. Childers, D.G. (ed.): 1978, Modern Spectrum Analysis, IEEE Press, New York.
32. Combes, J. M., Grossmann, A. and Tchamitchian, P. (eds.): 1989, Wavelets, Time-Frequency Methods and Phase Space. 1st Int. Wavelet Conf., Marseille, Springer-Verlag, Berlin, Heidelberg, New York.
33. Crowley, T.J. and North, G.B.: 1991, Paleoclimatology, Oxford University Press, New York.
34. De Boor, C.: 1978, A Practical Guide to Splines, Springer-Verlag, New York.
35. Dettinger, M.D., Ghil, M., Strong, C.M., Weibel, W. and Yiou, P.: 1995, 'Software expedites singular-spectrum analysis of noisy time series', Eos Trans. AGU 76(2), 12, 20, 21 (available on the World Wide Web at http://www.atmos.ucla.edu/).
36. Ding, M., Grebogi, C., Ott, E., Sauer, T. and Yorke, J.A.: 1993, 'Plateau onset for correlation dimension: When does it occur?', Phys. Rev. Lett. 25, 3872-3875.
37. Farge, M.: 1992, 'Wavelet transforms and their applications to turbulence', Ann. Rev. Fluid Mech. 24, 395-457.
38. Farge, M. and Rabreau, G.: 1988, 'Transformée en ondelettes pour détecter et analyser les structures cohérentes dans les écoulements turbulents bidimensionnels', C. R. Acad. Sci. Paris 307, 1479-1486.
39. Fraser, A.M. and Swinney, H.L.: 1986, 'Independent coordinates for strange attractors from mutual information', Phys. Rev. A 33(2), 1134-1140.
40. Gao, W. and Li, B.L.: 1993, 'Wavelet analysis of coherent structures at the atmosphere-forest interface', J. Appl. Meteorol. 32, 1717-1725.
41. 2 and orbital forcing changes over the last climatic cycle', Nature 329, 414-418.
42. Gershenfeld, N. A.: 1988, 'An experimentalist's introduction to the observation of dynamical systems', in H. Bai-lin (ed.), Directions in Chaos, Vol. 2, World Scientific, Singapore.
43. Ghil, M. and Childress, S.: 1987, Topics in Geophysical Fluid Dynamics: Atmospheric Dynamics, Dynamo Theory and Climate Dynamics, Springer-Verlag, New York.
44. Ghil, M. and Mo, K.C.: 1991a, 'Intraseasonal oscillations in the global atmosphere. Part I: Northern hemisphere and tropics', J. Atmos. Sci. 48(5), 752-779.
45. Ghil, M. and Mo, K.C.: 1991b, 'Intraseasonal oscillations in the global atmosphere. Part II: Southern hemisphere', J. Atmos. Sci. 48(5), 780-790.
46. Ghil, M. and Vautard, R.: 1991, 'Interdecadal oscillations and the warming trend in global temperature time series', Nature 350(6316), 324-327.
47. Ghil, M., Kimoto, M. and Neelin, J.D.: 1991, 'Nonlinear dynamics and predictability in the atmospheric sciences', Rev. Geophys. 36(Supplement), 46-55 (U.S. National Report IUGG, 1987-91).
48. Grassberger, P.: 1986, 'Do climatic attractors exist?', Nature 323, 609-612.
49. Grassberger, P. and Procaccia, I.: 1983, 'Measuring the strangeness of strange attractors', Physica D9, 189-208.
50. GRIP Project Members: 1993, 'Climatic instability during the last Interglacial period recorded in the GRIP ice core', Nature 364, 203-207.
51. Grossmann, A., Kronland-Martinet, R. and Morlet, J.: 1989, 'Reading and understanding continuous wavelet transforms', in J.M. Combes, A. Grossmann and P. Tchamitchian (eds.), Wavelets: Time-Frequency Methods and Phase Space, pp. 2-20, Springer-Verlag, Berlin.
52. Guckenheimer, J. and Holmes, P.: 1983, Nonlinear Oscillations, Dynamical Systems and Bifurcations of Vector Fields, Springer-Verlag, New York.
53. Haykin, S. (ed.): 1983, Nonlinear Methods of Spectral Analysis. Topics in Applied Physics, 2nd ed., Springer-Verlag, Berlin.
54. Haykin, S. and Kesler, S.: 1983, 'Prediction-error filtering and maximum-entropy spectral estimation', in S. Haykin (ed.) Nonlinear Methods of Spectral Analysis, Vol. 34 of Topics in Applied Physics, pp. 9-72. Springer-Verlag, Berlin.
55. Hays, J.D., Imbrie, J. and Shackleton, N.J.: 1976, 'Variations in the Earth's orbit: Pacemaker of the ice ages', Science 194, 1121-1132.
56. Heinrich, H.: 1988, Origin and consequences of cyclic ice-rafting in the northeast Atlantic Ocean, during the past 130,000 yrs', Quat. Res. 29, 143-152.
57. Houghton, J.T., Jenkins, G.J. and Ephraums, J.T. (eds.): 1990, Climate Change: the IPCC Scientific Assessment. Cambridge University Press, Cambridge.
58. Imbrie, J., Boyle, E.A., Clemens, S.C., Duffy, A., Howard ,W.R., Kukla, G., Kutzbach, J., Martinson, D.G., McIntyre, A., Mix, A.C., Molfino, B., Morley, J.J., Peterson, L.C., Pisias, N., Prell, W.L., Raymo, M.E., Shackleton, N.J. and Toggweiler, J.R.: 1992, On the structure and origin of major glaciations cycles. 1: Linear responses to Milankovitch forcing', Paleoceanography 7(6), 701-738.
59. Imbrie, J. and Imbrie, K.P.: 1986, Ice Ages: Solving the Mystery. Harvard University Press, Cambridge.
60. Jenkins, G.M. and Watts, D.G.: 1968, Spectral Analysis and its Applications. Holden-Day, San Francisco.
61. Jouzel, J. and Merlivat, L.: 1984, 'Deuterium and oxygen 18 in precipitation: Modeling of the isotopic effects during snow formation', J. Geophys. Res. 89, 11749-11757.
62. Jouzel, J., Lorius, C., Petit, J.R., Genthon, C., Barkov, N.I., Kotlyakov, V.M. and Petrov, V.M.: 1987, 'Vostok ice core: a continuous temperature record over the last climatic cycle (160,000 years)', Nature 329, 403-408.
63. Jouzel, J., Barkov, N.I., Barnola, J.M., Bender, M., Chappellaz, J., Genthon, C., Kotlyakov, V.M., Lipenkov, V., Lorius, C., Petit, J.R., Raynaud, D., Raisbeck, G., Ritz, C., Sowers, T., Stievenard, M., Yiou, F. and Yiou, P.: 1993, 'Extending the Vostok ice-core records of palaeoclimate to the penultimate glacial period', Nature 364, 407-412.
64. Jouzel, J., Lorius, C., Johnsen, S. and Grootes, P.: 1994, 'Climate instabilities: Greenland and Antarctic records', C.R. Acad. Sci. Paris 319, 65-77.
65. Kay, S.M.: 1988, Modern Spectral Analysis: Theory and Applications, Prentice-Hall, New Jersey.
66. Kay, S.M. and Marple, S.L.: 1981, 'Spectrum analysis: A modern perspective', IEEE Proc. 69, 1380-1419.
67. Keppenne, C.L. and Ghil, M.: 1992a, 'Adaptive filtering and prediction of the Southern Oscillation Index', J. Geophys. Res. 97, 20449-20454.
68. Keppenne, C.L. and Ghil, M.: 1992b, 'Extreme weather events', Nature 358, 547.
69. Kuo, C., Lindberg, C. and Thomson, D.J.: 1990, 'Coherence established between atmospheric carbon dioxide and global temperature', Nature 343, 709-713.
70. Lacoume, J.L., Gharbi, M., Lacombe, C. and Nicolas, J.L.: 1983, 'Close frequency resolution by maximum entropy spectral estimators', IEEE Trans. Acoustics, Speech and Signal Proc. 32(5), 977-983.
71. Lanzerotti, L.J., Thomson, D.J., Meloni, A., Medford, L.V. and Maclennan, C.G.: 1986, 'Electromagnetic study of the Atlantic continental margin using a section of a transatlantic cable', J. Geophys. Res. 91, 7417-7427.
72. Legrand, M., Lorius, C., Barkov, N.I. and Petrov, V.N.: 1988, 'Vostok (Antarctica) ice core: atmospheric chemistry changes over the last climatic cycle (160,000 years)', Atmospheric Environment 22, 317-331.
73. Lindberg, C.R.: 1986, 'Multiple Taper Spectral Analysis of Terrestrial Free Oscillations', PhD Thesis, Scripps Institution of Oceanography, University of California, San Diego.
74. Lorenz, E.N.: 1963, 'Deterministic nonperiodic flow', J. Atmos. Sci. 20, 130-141.
75. 18O records by the Grassberger-Procaccia algorithm', Clim. Dyn. 4, 45-55.
76. Mallat, S.G.: 1989, 'A theory for multiresolution signal decomposition: the wavelet representation', IEEE Trans. Pattern Anal. Mach. Intell. 11(7), 674-693.
77. Mann, M.E., Lees, J.M.: 1996, 'Robust estimation of background noise and signal detection in climatic time series', Clim. Change 33, 409-445.
78. Mann, M.E., Park, J. and Bradley, R.S.: 1995, 'Global interdecadal and century-scale climate oscillations during the past five centuries', Nature 378, 266-270.
79. Manneville, P.: 1991, Structures Dissipatives, Chaos et Turbulence, Aléa, Commissariat à l'Energie Atomique, Saclay, France.
80. Martin, N.: 1984, 'Développements de Méthodes d'Analyse Spectrale Autorégressive: Application à des Signaux Réels Non-Stationnaires à n Dimensions, Thèse de docteur ingénieur, Institut Polytechnique de Grenoble, France.
81. Meyer, Y.: 1989, Ondelettes et Opérateurs I: Ondelettes, Hermann, Paris.
82. Meyers, S.D., Kelly, B.C. and O'Brien, J.J.: 1993, 'An introduction to wavelet analysis in oceanography and meteorology: with application to the dispersion of Yanai waves', Mon. Wea. Rev. 121, 2858-2866.
83. Milankovitch, M.: 1941, 'Kanon der erdbestrahlung und seine anwendung auf das eiszeitenproblem', R. Acad. Spec. Publ. 132, section of mathematical and natural sciences, Vol 33, Belgrade, 633 pp, (Translated by the Israeli Program for Scientific Translation, Jerusalem, 1969).
84. Miller, R.N., Ghil, M. and Gauthiez, F.: 1994, 'Advanced data assimilation in strongly nonlinear dynamical systems', J. Atmos. Sci. 51(8), 1037-1056.
85. Nicolis, C. and Nicolis, G.: 1984, 'Is there a climatic attractor?', Nature 311, 529-532.
86. Ott, E.: 1993, Chaos in Dynamical Systems. Cambridge University Press, Cambridge.
87. Packard, N.H., Crutchfield, J.P., Farmer, J.D. and Shaw, R.S.: 1980, 'Geometry from a time series', Phys. Rev. Lett. 45,712-716.
88. Paillard, D. and Labeyrie, L.D.: 1994, 'Role of the thermohaline circulation in the abrupt warming after Heinrich events', Nature 372, 162-164.
89. Park, J. and Maasch, K.A.: 1993, 'Plio-Pleistocene time evolution of the 100-kyr cycle in marine paleoclimate records', J. Geophys. Res. 98, 447-461.
90. Park, J., Lindberg, C.R. and Vernon, F.L.I.: 1987, 'Multiktaper spectral analysis of high frequency seismograms', J. Geophys. Res. 92, 12675-12684.
91. Parzen, E.: 1976, 'An approach to time series modeling and forecasting illustrated by hourly electricity', Technical Report 37, Statistical Sci. Div., State University of New York in Buffalo.
92. Peixoto, J.P. and Oort, A.H.: 1992, Physics of Climate, American Institute of Physics, New York.
93. Penland, C., Ghil, M. and Weickmann, K.: 1991, 'Adaptive filtering and maximum entropy spectra, with application to changes in atmospheric angular momentum', J. Geophys. Res. 90(D12), 22659-22671.
94. Pestiaux, P.: 1984, 'Approche Spectrale en Modélisation Paléoclimatique', PhD Thesis, Université Catholique de Louvain, Belgium.
95. Pestiaux, P. and Berger, A.L.: 1984, 'An optimal approach to the spectral characteristics of deepsea climatic records', in A. L. Berger, J. Imbrie, J. Hays, G. Kukla, and B. Saltzman (eds.) Milankovitch and Climate: Understanding the Response to Astronomical Forcing, pp. 417-445, D. Reidel, Hingham, MA.
96. Petit, J.R., Mounier, L., Jouzel, J., Korotkevitch, Y.S., Kotlyakov, V.I. and Lorius, C.: 1990, 'Paleoclimatological and chronological implications of the Vostok dust record', Nature 343, 56-58.
97. Plaut, G. and Vautard, R.: 1994, 'Spells of low-frequency oscillations and weather regimes in the northern hemisphere', J. Atmos. Sci. 51(2), 210-236.
98. Press, W.H., Flannery, B.P., Teukolski, S.A. and Vettering, W.T.: 1988, Numerical Recipes: The Art of Scientific Computing, Cambridge University Press, Cambridge.
99. Procaccia, I.: 1988, 'Weather systems: Complex or just complicated?', Nature 333, 498-499.
100. Rasmusson, E.M., Wang, X. and Ropelewski, C.F.: 1990, 'The biennial component of ENSO variability', J. Mar. Syst. 1, 71-96.
101. Rögnvaldsson, Ö.E.: 1993, 'Spectral estimation using the multi-taper method', Technical Report RH-13-13 Science Institute, University of Iceland, Reykjavik, Iceland.
102. Roux, J.C., Rossi, A., Bachelart, S. and Vidai, C.: 1980, 'Representation of a strange attractor from an experimental study of chemical turbulence', Phys. Lett. A 77, 391-393.
103. Schlesinger, M.E. and Ramankutty, N.: 1994, 'An oscillation in the global climate system of period 65-70 years', Nature 367, 723-726.
104. Slepian, S.: 1978, 'Prolate spheroidal wave functions, Fourier analysis and uncertainty - V: The discrete case', Bell. Sys. Tech. J. 57, 1371-1430.
105. Smith, L.A.: 1988, 'Intrinsic limits on dimension calculations', Phys. Lett. A 133, 283-288.
106. 2 and ice volume changes during the penultimate déglaciation', Paleoceanography 6, 679-696.
107. Takens, F.: 1981, 'Detecting strange attractors in turbulence', in D.A. Rand and L.-S. Young (eds.), Dynamical Systems and Turbulence, Vol. 898 of Lecture Notes in Mathematics, pp. 366-381, Springer-Verlag, Berlin.
108. Thomson, D.J.: 1982, 'Spectrum estimation and harmonic analysis', IEEE Proc. 70(9), 1055-1096.
109. Thomson, D.J.: 1990a, 'Quadratic-inverse spectrum estimates: applications to palaeoclimatology', Phil. Trans. R. Soc. London A 332, 539-597.
110. Thomson, D.J.: 1990b, 'Time series analysis of Holocene climate data', Phil. Trans. R. Soc. London A 330, 601-616.
111. Thomson, D.J. and Chave, A.D.: 1990, 'Jackknifed error estimates for spectra, coherences, and transfer functions', in S. Haykin (ed.), Advances in Spectrum Analysis and Array Processing, pp. 58-113, Prentice-Hall, Englewood Cliffs, NJ.
112. Vautard, R. and Ghil, M.: 1989, 'Singular spectrum analysis in nonlinear dynamics, with applications to paleoclimatic time series', Physica D35, 395-424.
113. Vautard, R., Yiou, P. and Ghil, M.: 1992, 'Singular spectrum analysis: a toolkit for short noisy chaotic signals', Physica D58, 95-126.
114. Wahba, G.: 1990, Spline Models for Observational Data, SIAM, Philadelphia.
115. Weigend, A.S. and Gershenfeld, N.A. (eds.): 1993, Time Series Prediction: Forecasting the Future and Understanding the Past, Addison-Wesley, Reading, MA.
116. Yiou, P.: 1994, 'Dynamique du Paléolimat: Des Données et des Modèles. PhD Thesis, Université Pierre et Marie Curie, Paris, France.
117. 2 levels from Vostok ice-core records', J. Geophys. Res. 96(B12), 20365-20378.
118. Yiou, P., Ghil, M., Jouzel, J., Paillard, D. and Vautard, R.: 1994, 'Nonlinear variability of the climatic system, from singular and power spectra of Late Quaternary records', Clim. Dun. 9, 371-389.
119. Yiou, P., Jouzel, J., Johnsen, S. and Rögnvaldsson, Ö.E.: 1995, 'Rapid oscillations in Vostok and GRIP ice cores', Geophys. Res. Lett. 22(16), 2179-2182.
120. Yiou, P., Fuhrer, K., Meeker, L.D., Jouzel, J., Johnsen, S. and Mayewski, P.A.: 1996, 'Paleoclimatic variability inferred from the spectral analysis of Greenland and Antarctic ice core data', J. Geophys. Res. (in press).