The succession of ice ages and interglacials during the Pleistocene is understood to have been caused primarily by shifts in the earth's orbit. At the same time, there is evidence of high variability in climate at suborbital frequencies. This paper conducts a statistical analysis of Pleistocene climate using the Greenland Ice Core Research Project (GRIP) data. Factoring temperature into the component explained by orbital forcing and a residual demonstrates that variations at suborbital frequencies are nonlinear and aperiodic. There is evidence of a regular cycle at 7.9 kyr, evidently a subharmonic of the orbital frequencies. Apart from this, however, the proximate memory of both the actual data and the residual decays slowly over a period of 15 kyr. Residual variations in temperature show two prominent features, alternating periods of high and low volatility, and states of distance from and proximity to the path implied by orbital forcing. A parametric model incorporating both of these properties is fit to the data, and is found to significantly improve the forecastability of climate. Transitions between states of proximity and distance from the orbital path can be partially predicted using the statistical model.
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Berger, A.: 1992, ‘Astronomical Theory of Paleoclimates and the Last Glacial-Interglacial Cycle’, Quatern. Sci. Rev. 11, 571–581.
Berger, A. and Loutre, M. F.: 1991,’Insolation Values for the Climate of the Last Ten Million Years’, Quatern. Sci. Rev. 10, 297–317.
Berger, A., Tricot, C., Gallee, H., and Loutre, M. F.: 1993, ‘Water Vapour CO2 and Insolation overthe Last Glacial-Interglacial Cycles’, Phil. Trans. Royal Soc. Lond. 341, 253–261.
Birchfield, G. E.and Gill, M.: 1993, ‘Climate Evolution in the Pliocene and Pleistocene From Marine Sediment Records and Simulations: Internal Variability Versus Orbital Forcing’, J. Geophys. Res. 96, 10,385–10,399.
Bollerslev, T.: 1986, ‘Generalized Autoregressive Conditional Heteroskedasticity’, J. Econometrics 31, 307–327.
Dansgaard, W., Johnsen, S. J., Clausen, H. B., Dahl-Jensen, D., Gundestrup, N. S., Hammer, C. U., Hvldberg, C. S., Steffensen, J. P., Svelnbjornsdottir, A. E., Jouzel, J., and Bond, G.: 1993, ‘Evidence for General Instability of Past Climate from a 250-kyr Ice Core Record’, Nature 364, 218–220.
Engle, R. F.: 1982, ‘Autoregressive Conditional Heteroskedasticity’, Econometrica 50,997–1008.
Engle, R. F. and Granger, C. W. J.: 1987, ‘Cointegration and ErrorCorrection:Representation, Estimation and Testing’, Econometrica 55, 251–276.
Gallee, H., Van Ypersele, J.P., Fichefet, T., Tricot, C., and Berger, A.: 1992, ‘Simulation of the Last Glacial Cycle by a Coupled Sectorially Averaged Climate-Ice Sheet Model’, J. Geophys. Res. 96, 13,139–13,161.
Granger, C.W. J. and Terasvirta, T.: 1993, Modeling Nonlinear Economic Relationships, Oxford University Press, Oxford, p. 187.
Granger, C. W. J. and Joyeux, R.: 1980, ‘An Introduction to Long MemoryTime Series Models and Fractional Differencing’, J. Time Series Analysis 1, 15–29.
Hall, N. M. J., Valez, P. J., and Dong, B.: 1996, ‘The Maintenance of the Last Great Ice Sheets: A UGAMP GCM Study’, J. Clim. 9, 1004–1019.
Hays, J. D., Imbrie, J., and Shackleton, N. J.: 1976, ‘Variations inthe Earth's Orbit: Pacemaker of the Ice Ages’, Science 194, 1121–1132.
Hosking, Jonathan R. M.:1981, ‘Fractional Differencing’, Biometrika 68, 165–176.
Hosking, Jonathan R. M.:1984, ‘Modeling Persistence in Hydrological Time Series Using Fractional Differencing’, Water Res. J. 20, 1898–1908.
Imbrie, John: 1992, ‘On the Structure and Origin of Major Glaciation Cycles:Linear Responses to Milankovitch Forcing’, Paleoceanography, December 1992.
Lo, A. W.: 1991,’Long-Term Memory in Stock Market Prices’, Econometrica 50, 1279–1313.
McIntyre, A. and Molfino, B.: 1996, ‘Forcing of Atlantic Equatorial and Subpolar Millennial Cycles by Precession’, Science 274, 1867–1870.
Richards, G. R.: 1994, ‘Orbital Forcing and EndogenousInteractions: Nonlinearity, Persistence and Convergence in Late Pleistocene Climate’, Quatern. Sci. Rev. 13, 709–725.
Sirocko, F., GarbeSchonberg, D., McIntyre, A., and Molfino, B.: 1996, ‘Teleconnectionsbetween the Subtropical Monsoons and High-Latitude Climates during the Last Deglaciation’, Science 272, 526–529.
Taylor, K. C., Lamorey, G. W., Doyle, G. A., Alley, R. B., Grootes, P. M., Mayewski, P. A., White, J. W., and Barlow, L. K.: 1993, ‘The Flickering Switch of Late Pleistocene Climate Change’, Nature 361, 432–436.
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Richards, G.R. Orbital Forcing and Endogenous Nonlinearity in the Pleistocene: The Greenland Ice Core. Climatic Change 38, 235–246 (1998). https://doi.org/10.1023/A:1005327613287
- High Variability
- Actual Data
- Residual Variation