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Nonlinear variability of the climatic system from singular and power spectra of Late Quaternary records

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Abstract

Stable-isotope records from seven marine cores and one ice core provide invaluable information on the intricate behavior of the climatic system over time scales of 104 to 105 years. These records, in conjunction with a simple coupled climate model, help us understand major mechanisms of paleoclimatic variability. The time intervals covered by the records include the last glacial-interglacial cycle. In spite of the difference in the nature of the records, common features are revealed by advanced spectral-analysis tools. The dominant features are the presence of orbital frequencies, on the one hand, and a low number of internal degrees of freedom, on the other. The climatic system appears therefore to act on the Quaternary time scales considered as a forced nonlinear oscillator. The internal mechanisms giving rise to the aperiodic oscillations include ice-albedo feedback, precipitation-temperature feedback, and interactions between the ice sheets and the bedrock.

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References

  • Bard E, Arnold M, Duprat J, Moyes J, Duplessy JC (1987) Reconstruction of the last deglaciation: deconvolved records of 5180 profiles, micropaleontological variations and accelerator mass spectrometric 14C dating. Clim Dyn 1:101–112

    Google Scholar 

  • Barnola JM, Raynaud D, Korotkevitch YN, Lorius C (1987) Vostok ice core provides 160,000-year record of atmospheric CO2. Nature 329:408–414

    Google Scholar 

  • Berger AL (1978) Long-term variations of daily insolation and Quaternary climatic, changes. J Geophys Res 35:2362–2367

    Google Scholar 

  • Berger AL, Melice JL, Hinnov L (1991) A strategy for frequency spectra of Quaternary climate records. Clint Dyn 5:227–240

    Google Scholar 

  • Béthoux JP (1979) Budgets of the Mediterranean sea. Their dependence on the local climate and on the characteristics of the Atlantic waters. Oceanol Acta 7:289–296

    Google Scholar 

  • Birchfield GE (1977) A study of a model continental ice sheet subject to periodic variations in heat input. J Geophys Res 82:4909–4913

    Google Scholar 

  • Birchfield GE, Ghil M (1993) Climate evolution in the Pliocene-Pleistocene as seen in deep sea 8180 records and in simulations: internal variability versus orbital forcing. J Geophys Res 98:10385–10399

    Google Scholar 

  • Birchfield GE, Grumbine RW (1985) “Slow” physics of large continental ice sheets and underlying bedrock, and its relation to the Pleistocene ice ages. J Geophys Res 90:11294–11302

    Google Scholar 

  • Blanc PL, Duplessy JC (1982) The deep water circulation during the Neogene and the impact of the Messinian salinity crisis. Deep-Sea Res 29:1391–1414

    Google Scholar 

  • Bonnefille R, Chalier F, Guiot J, Vincens A (1992) Quantitative estimates of full glacial temperatures in equatorial Africa from palynological data. Clim Dyn 6:251–257

    Google Scholar 

  • Broecker WS, Van Donk J (1970) Insolation changes, ice volumes, and the 180 record in deep-sea cores. Rev Geophys Space Phys 8:169–197

    Google Scholar 

  • Broecker WS, Peteet DM, Rind D (1985) Does the ocean-atmosphere system have more than one stable mode of operation? Nature 315:21–25

    Google Scholar 

  • Broecker WS, Bond G, Klas M, Clark E, McManus J (1992) Origin of the northern Atlantic's Heinrich events. Clim Dyn 6:265–273

    Google Scholar 

  • Broomhead DS, King GP (1986) Extracting qualitative dynamics from experimental data. Physica D20:217–236

    Google Scholar 

  • Chappellaz J, Barnola JM, Raynaud D, Korotkevitch YS, Lorius C (1990) Icecore record of atmospheric methane over the past 160,000 years. Nature 345:127–131

    Google Scholar 

  • Chaté H (1985) Comment déduire la dynamique chaotique de la mesure d'observables? Projet de DEA, Université Pierre et Maria Curie

  • CLIMAP Project Members (1984) The last interglacial ocean. Quat Res (NY) 21:123–224

    Google Scholar 

  • Duplessy JC, Moyes J, Pujol C (1980) Deep water formation in the North Atlantic Ocean during the last ice age. Nature 286:479–482

    Google Scholar 

  • Duplessy JC, Arnold M, Maurice P, Bard E, Duprat J, Moyes J (1986) Direct dating of the oxygen-isotope record of the last deglaciation by 14C accelerator mass spectrometry. Nature 320:350–352

    Google Scholar 

  • Fraedrich K (1986) Estimating the dimension of weather and climate attractors. J Atmos Sci 43:419–432

    Google Scholar 

  • Ghil M (1989) Deceptively-simple models of climatic change. In: Berger AL, Schneider S, Duplessy JC (eds) Climate and geosciences. D Reidel, Dordrecht, pp 211–240

    Google Scholar 

  • Ghil M (1991) Quaternary glaciations: theory and observations. In: Sonnett CP, Giampapa MS, Matthews MS (eds) The sun in time. University of Arizona Press, pp 511–542

  • Ghil M, Childress S (1987) Topics in geophysical fluid dynamics: Atmospheric dynamics, dynamo theory and climate dynamics. Springer, New York

    Google Scholar 

  • Ghil M, Le Trent H (1981) A climate model with cryodynamics and geodynamics. J Geophys Res 86(C6):5262–5270

    Google Scholar 

  • Ghil M, Mo KC (1991) Intraseasonal oscillations in the global atmosphere. Part I: Northern hemisphere and tropics. J Atmos Sci 48:752–779

    Google Scholar 

  • Ghil M, Tavantzis J (1983) Global Hopf bifurcation in a simple climate model. SIAM J Appl Math 43:1019–1041

    Google Scholar 

  • Ghil M, Vautard R (1991) Interdecadal oscillations and the warming trend in global temperature time series. Nature 350:324–327

    Google Scholar 

  • Ghil M, Mullhaupt A, Pestiaux P (1987) Deep water formation and Quaternary glaciations. Clim Dyn 2:1–10

    Google Scholar 

  • Ghil M, Kimoto M, Neelin JD (1991) Nonlinear dynamics and predictability in the atmospheric sciences. Rev Geophys Supplement: 46–55

  • Grassberger P (1986) Do climatic attractors exist? Nature 323:609–612

    Google Scholar 

  • Grassberger P, Procaccia I (1983) Measuring the strangeness of strange attractors. Physica D9:189–208

    Google Scholar 

  • Guckenheimer J, Holmes P (1983) Nonlinear oscillations, dynamical systems and bifurcations of vector fields. Springer, New York

    Google Scholar 

  • Guinasso NL, Schink DR (1975) Quantitative estimates of biological mixing rates in abyssal sediments. J Geophys Res 80:3032–3043

    Google Scholar 

  • Harvey LDD, Schneider SH (1984) Sensitivity of internally-generated climate oscillations to ocean model formulation. In: Berger AL, Imbrie J, Hays J, Kukla G, Saltzman B (eds) Milankovitch and climate: Understanding the response to astronomical forcing. D Reidel, Hingham, Mass., pp 269–305

    Google Scholar 

  • Hays JD, Imbrie J, Shackleton NJ (1976) Variations in the Earth's orbit: pacemaker of the ice ages. Science 194:1121–1132

    Google Scholar 

  • Hutson WH (1980) Bioturbation of deep-sea sediments: oxygen isotopes and stratigraphic uncertainty. Geology 8:127–130

    Google Scholar 

  • Imbrie J, Hays JD, Martinson DJ, McIntyre A, Mix AC, Morley JJ, Pisias NG, Prell WL, Shackleton NJ (1984) The orbital theory of Pleistocene climate: Support from a revised chronology of the marine σ18O record. In: Berger AL, Imbrie J, Hays J, Kukla G, Saltzman B (eds) Milankovitch and climate: Understanding the response to astronomical forcing. D Reidel, Hingham, Mass., pp 269–305

    Google Scholar 

  • Imbrie J, Boyle EA, Clemens SC, Duffy A, Howard WR, Kukla G, Kutzbach J, Martinson DG, McIntyre A, Mix AC, Molfino B, Morley JJ, Peterson LC, Pisias N, Prell WL, Raymo ME, Shackleton NJ, Toggweiler JR (1992) On the structure and origin of major glaciations cycles. 1: Linear responses to Milankovitch forcing. Paleoceanogr 7:701–738

    Google Scholar 

  • Jouzel J, Merlivat L (1984) Deuterium and oxygen 18 in precipitation: Modeling of the isotopic effects during snow formation. J Geophys Res 89: 11749–11757

    Google Scholar 

  • Jouzel J, Lorius C, Petit JR, Genthon C, Barkov NI, Kotlyakov VM, Petrov VM (1987) Vostok ice core: a continuous temperature record over the last climatic cycle (160,000 years). Nature 329:403–408

    Google Scholar 

  • Kallel N, Labeyrie LD, Juillet-Leclerc A, Duplessy JC (1988) A deep hydrological front between intermediate and deep-water masses in the glacial Indian Ocean. Nature 333:651–655

    Google Scholar 

  • Kennett JP (1990) The Younger Dryas cooling event: an introduction. Paleoceanogr. 5:891–896

    Google Scholar 

  • Keppenne CL, Ghil M (1992a) Extreme weather events. Nature 358:547

    Google Scholar 

  • Keppenne CL, Ghil M (1992b) Adaptive filtering and prediction of the Southern Oscillation Index. J Geophys Res 97:20449–20454

    Google Scholar 

  • Kutzbach JE (1981) Monsoon climate of the early Holocene: climate experiment with the earth's orbital parameters for 9000 years ago. Science 214:59–61

    Google Scholar 

  • Labeyrie LD, Duplessy JC, Blanc PL (1987) Variations in mode of formation and temperature of oceanic deep waters over the past 125,000 years. Nature 327:477–482

    Google Scholar 

  • Lambeck K, Nakada M (1992) Constraints on the age and duration of the last interglacial period and on sea-level variations. Nature 357:125–128

    Google Scholar 

  • Le Trent H, Ghil M (1983) Orbital forcing, climate interactions, and glaciation cycles. J Geophys Res 88:5167–5190

    Google Scholar 

  • Le Trent H, Portès J, Jouzel J, Ghil M (1988) Isotopic modeling of climatic oscillations: implications for a comparative study of marine and ice core records. J Geophys Res 93(D):9365–5190

    Google Scholar 

  • Linsley BK, Thunell RC (1990) The record of deglaciation in the Sulu Sea: evidence for the Younger Dryas event in the Tropical Western Pacific. Paleoceanogr 5:1025–1040

    Google Scholar 

  • Lorius C, Merlivat L (1977) Distribution of mean surface stable isotope values in East Antarctica; Observed changes with depth in a coastal area. In: Isotopes and impurities in snow and ice. Proc. Grenoble Symp. IAHS, vol 118, pp 127–137

  • Lorius C, Jouzel J, Ritz C, Merlivat L, Barkov NI, Kotlyakov VM, Petrov VM (1985) A 150,000 year climatic record from Antarctic ice. Nature 316:591–596

    Google Scholar 

  • Lorius C, Jouzel J, Raynaud D, Hansen J, Le Trent H (1990) The ice-core record: climate sensitivity and future greenhouse warming. Nature 347:139–145

    Google Scholar 

  • Maasch KA (1989) Calculating climate attractor dimension from 5180 records by the Grassberger-Procaccia algorithm. Clim Dyn 4:45–55

    Google Scholar 

  • Malanotte-Rizzoli P, Robinson AR (1988) POEM: Physical oceanography of the eastern Mediterranean. EOS, The Oceanography Report 69:194–203

    Google Scholar 

  • Matteucci G (1990) Analysis of the probability distribution of the late Pleistocene climatic record: Implications for model validation. Clint Dyn 5:35–52

    Google Scholar 

  • Milankovitch M (1941) Kanon der Erdbestrahlung und seine Anwendung auf das Eiszeitenproblem. R Acad Spec Publ 133 (Translated by the Israeli Program for Scientific Translation, Jerusalem, 1969)

  • Millot C (1987) Circulation in the western Mediterranean Sea. Oceanol Acta 10:143–150

    Google Scholar 

  • Oerlemans J, van der Veen J (1984) Ice sheets and climate. D Reidel, Dordrecht, Boston, Lancaster

    Google Scholar 

  • Park J, Lindberg CR, Vernon FL III (1987) Multitaper spectral analysis of high frequency seismograms. J Geophys Res 92:12675–12684

    Google Scholar 

  • Paterne M, Guichard F, Labeyrie J, Gillot PY, Duplessy JC (1986) Tyrrhenian tephrochronology of the oxygen isotope recorded for the past 60,000 years. Mar Geol 72:259–285

    Google Scholar 

  • Peltier R, Hyde W (1984) A model of the ice age cycle. In: Berger AL, Imbrie J, Hays J, Kukla G, Saltzman B (eds) Milankovitch and climate: understanding the response to astronomical forcing. D Reidel, Hingham, Mass., pp 565–580

    Google Scholar 

  • Penland C, Ghil M, Weickmann K (1991) Adaptive filtering and maximum entropy spectra, with application to changes in atmospheric angular momentum. J Geophys Res 96(D12):22659–22671

    Google Scholar 

  • Pestiaux P, Berger AL (1984) Impacts of deep-sea processes on paleoclimatic spectra: In: Berger AL, Imbrie J, Hays J, Kukla G, Saltzman B (eds) Milankovitch and climate: understanding the response to astronomical forcing. D Reidel, Hingham, Mass., pp 493–510

    Google Scholar 

  • Pestiaux P, Van Der Mersch I, Berger AL, Duplessy JC (1988) Paleoclimatic variability at frequencies ranging from 1 cycle per 10,000 years to 1 cycle per 1000 year: evidence for nonlinear behaviour of the climate system. Clim Change 12:9–37

    Google Scholar 

  • Petit JR, Mounier L, Jouzel J, Korotkevitch YS, Kotlyakov VI, Lorius C (1990) Paleoclimatological and chronological implications of the Vostok dust record. Nature 343:56–58

    Google Scholar 

  • Pike ER, McWhirter JG, Bertero M, de Mol C (1984) Generalized information theory for inverse problems in signal processing. IEEE Proc 131:660–667

    Google Scholar 

  • Pollard D (1984) Some ice-age aspects of a calving ice-sheet model. In: Berger AL, Imbrie J, Hays J, Kukla G, Saltzman B (eds) Milankovitch and climate: understanding the response to astronomical forcing. D Reidel, Hingham, Mass., pp 541–564

    Google Scholar 

  • Procaccia I (1988) Weather systems: complex or just complicated? Nature 333:498–499

    Google Scholar 

  • Quon C, Ghil M (1992) Multiple equilibria in thermosolutal convection due to salt-flux boundary conditions. J Fluid Mech 245:449–483

    Google Scholar 

  • Ritz C (1993) Chronology of the Vostok ice core based on precipitation and ice flow modelling. J Glaciol (in press)

  • Rooth C (1982) Hydrology and ocean circulation. Prog. Oceanogr 11:131–149

    Google Scholar 

  • Saltzman B (1985) Paleoclimatic modeling. In: Hecht AD (ed) Paleoclimate analysis and modeling. John Wiley, New York, pp 341–396

    Google Scholar 

  • Saltzman B (1987) Carbon dioxide and the 6180 record of late-Quaternary climatic change: a global model. Clim Dyn 1:77–85

    Google Scholar 

  • Saltzman B (1990) Three basic problems of paleoclimatic modeling: A personal perspective and review. Clim Dyn 5:67–78

    Google Scholar 

  • Sarnthein M, Winn K, Duplessy JC, Fontugne MR (1988) Global variations of surface ocean productivity in low and mid latitudes: Influence on CO2 reservoirs of the deep ocean and atmosphere during the last 21,000 years. Paleoceanogr 3:361–399

    Google Scholar 

  • Shackleton NJ (1967) Oxygen isotope analyses and Pleistocene temperatures re-assessed. Nature 215:14–17

    Google Scholar 

  • Shackleton NJ, Pisias NG (1985) Atmospheric carbon dioxide, orbital forcing, and climate. In: The carbon cycle and atmospheric CO2 natural variations Archean to present, Geophysical Monographs, vol 32. Am Geophys Union, Washington DC, pp 303–317

    Google Scholar 

  • Shackleton NJ, Imbrie J, Hall MA (1983) Oxygen and carbon isotope record of East Pacific cose V19–30: implications for the formation of deep water in the late Pleistocene North Atlantic. Earth Planet Sci Lett 65:233–244

    Google Scholar 

  • Slepian S (1978) Prolate spheroidal wave functions, Fourier analysis and uncertainty—V: The discrete case. Bell Syst Tech J 57:1371–1430

    Google Scholar 

  • Sowers T, Bender M, Raynaud D, Korotkevitch YS, Orchardo J (1991) The σ18O of atmospheric O2 from air inclusions in the Vostok ice core: timing of CO2 and ice volume changes during the penultimate deglaciation. Paleoceanogr 6:679–696

    Google Scholar 

  • Stommel HM (1961) Thermohaline convection with two stable regime of flows. Tellus XIII 2:224–230

    Google Scholar 

  • Teller JT (1990) Meltwater and precipitation runoff to the North Atlantic, Arctic, and Gulf of Mexico from the Laurentide ice sheet and adjacent regions during the Younger Dryas, Paleoceanogr 5:897–906

    Google Scholar 

  • Thomson DJ (1982) Spectrum estimation and harmonic analysis. IEEE Proc 70(9):1055–1096

    Google Scholar 

  • Thual O, McWilliams JC (1992) The catastrophe structure of thermohaline convection in a two-dimensional fluid model and a comparison with low-order box model. J Geophys Astrophys Fluid Dyn 64:67–95

    Google Scholar 

  • Van Campo E, Duplessy JC, Prell WL, Barratt N, Sabatier R (1990) Comparison of terrestrial and marine temperature estimates for the past 135 kyr off southeast Africa: a test for GCM simulations of palaeoclimate. Nature 348:209–212

    Google Scholar 

  • Vautard R, Ghil M (1989) Singular spectrum analysis in nonlinear dynamics, with applications to paleoclimatic time series. Physica D35:295–424

    Google Scholar 

  • Vautard R, Yiou P, Ghil M (1992) Singular spectrum analysis a tool kit for short noisy chaotic signals. Physica D58:95–126

    Google Scholar 

  • Welander P (1986) Thermohaline effects in the ocean circulation and related simple models. In: Willebrand J, Anderson DTL (eds) Large-scale transport processes in oceans and atmospheres. D Reidel, Dordrecht, pp 163–200

    Google Scholar 

  • Wigley TML (1976) Spectral analyses and the astronomical theory of climate change. Nature 264:629–631

    Google Scholar 

  • Winograd IJ, Coplen TB, Landwehr JM, Riggs AC, Ludwig KR, Szabo BJ, Kolesar PT, Revesz KM (1992) Continuous 500,000 year climate record from vein calcite in Devils Hole, Nevada. Science 258:255–260

    Google Scholar 

  • Yiou P, Genthon C, Jouzel J, Ghil M, Le Trent H, Barnola JM, Lorius C, Korotkevitch YN (1991) High-frequency paleovariability in climate and in CO2 levels from Vostok ice-core records. J Geophys Res 96(B12):20365–20378

    Google Scholar 

  • Zahn R, Sarnthem M, Erlenkeuser H (1987) Benthic isotope evidence for changes of the Mediterranean outflow during the late Quaternary. Paleoceanogr 6:543–560

    Google Scholar 

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Yiou, P., Ghil, M., Jouzel, J. et al. Nonlinear variability of the climatic system from singular and power spectra of Late Quaternary records. Climate Dynamics 9, 371–389 (1994). https://doi.org/10.1007/BF00207933

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