• Alley, R. B., , P. U. Clark, , L. D. Keigwin, , and R. S. Webb, 1999: Making sense of millennial-scale climate change. Mechanisms of Global Climate Change at Millennial Time Scales, Geophys. Monogr., Vol. 112, Amer. Geophys. Union, 385–394.

  • Alley, R. B., , S. Anandakrishnan, , and P. Jung, 2001: Stochastic resonance in the North Atlantic. Paleoceanography, 16 , 190198.

  • Arzel, O., 2004: Mécanismes de variabilité climatique interdécennale dans des modèles idealisés. Ph.D. thesis, l’Université de Bretagne Occidentale, 242 pp.

  • Braun, H., , M. Christl, , S. Rahmstorf, , A. Ganopolski, , A. Mangini, , C. Kubatzki, , K. Roth, , and B. Kromer, 2005: Possible solar origin of the 1470-year glacial climate cycle demonstrated in a coupled model. Nature, 438 , 208211.

    • Search Google Scholar
    • Export Citation
  • Bretherton, F. P., 1982: Ocean climate modeling. Progress in Oceanography, Vol. 11, Pergamon Press, 93–129.

  • Broecker, W., , S. G. Bond, , and M. Klas, 1990: A salt oscillator in the glacial Atlantic? I. The concept. Paleoceanography, 5 , 469477.

  • Bryan, F., 1986: High latitude salinity effects and interhemispheric thermohaline circulation. Nature, 323 , 301304.

  • Cessi, P., 1996: Convective adjustment and thermohaline excitability. J. Phys. Oceanogr., 26 , 481491.

  • Colin de Verdière, A., , M. Ben Jelloul, , and F. Sévellec, 2006: Bifurcation structure of thermohaline millennial oscillations. J. Climate, 19 , 57775795.

    • Search Google Scholar
    • Export Citation
  • Dijkstra, H. A., , and M. Ghil, 2005: Low-frequency variability of the large-scale ocean circulation: A dynamical system approach. Rev. Geophys., 43 .RG3002, doi:10.1029/2002RG000122.

    • Search Google Scholar
    • Export Citation
  • Frankignoul, C., , A. Czaja, , and B. L’Heveder, 1998: Air–sea feedback in the North Atlantic and surface boundary conditions for ocean models. J. Climate, 11 , 23102324.

    • Search Google Scholar
    • Export Citation
  • Ganopolski, A., , and S. Rahmstorf, 2002: Abrupt glacial climate changes due to stochastic resonance. Phys. Rev. Lett., 88 .038501, doi:10.1103/PhysRevLett.88.038501.

    • Search Google Scholar
    • Export Citation
  • Held, I. M., 2005: The gap between simulation and understanding in climate modeling. Bull. Amer. Meteor. Soc., 86 , 16091614.

  • Huang, R. X., , J. R. Luyten, , and H. M. Stommel, 1992: Multiple equilibrium states in combined thermal and saline circulation. J. Phys. Oceanogr., 22 , 231246.

    • Search Google Scholar
    • Export Citation
  • Lenderink, G., , and R. J. Haarsma, 1994: Variability and multiple equilibria of the thermohaline circulation associated with deep-water formation. J. Phys. Oceanogr., 24 , 14801493.

    • Search Google Scholar
    • Export Citation
  • Longworth, H., , J. Marotzke, , and T. F. Stocker, 2005: Ocean gyres and abrupt change in the thermohaline circulation: A conceptual analysis. J. Climate, 18 , 24032416.

    • Search Google Scholar
    • Export Citation
  • Loving, J. L., , and G. K. Vallis, 2005: Mechanisms for climate variability during glacial and interglacial periods. Paleoceanogaphy., 20 .PA4024, doi:10.1029/2004PA001113.

    • Search Google Scholar
    • Export Citation
  • Ruddick, B., , and L. Zhang, 1996: Qualitative behavior and nonoscillation of Stommel’s thermohaline box model. J. Climate, 9 , 27682777.

    • Search Google Scholar
    • Export Citation
  • Sakai, K., , and W. R. Peltier, 1999: A dynamical system model of the Dansgaard–Oeschger oscillations and the origin of the Bond cycle. J. Climate, 12 , 22382255.

    • Search Google Scholar
    • Export Citation
  • Schmittner, A., , and A. J. Weaver, 2000: Dependence of multiple climate states on ocean mixing parameters. Geophys. Res. Lett., 28 , 10271030.

    • Search Google Scholar
    • Export Citation
  • Stommel, M. H., 1961: Thermohaline convection with two stable regimes of flow. Tellus, 13 , 224230.

  • Strogatz, S. H., 1994: Nonlinear Dynamics and Chaos with Applications to Physics, Biology, Chemistry and Engineering. Advanced Book Program, Perseus Books, 498 pp.

    • Search Google Scholar
    • Export Citation
  • Thual, O., , and J. C. McWilliams, 1992: The catastrophe structure of thermohaline convection in a two-dimensional fluid model and a comparison with low-order box models. Geophys. Astrophys. Fluid Dyn., 64 , 6795.

    • Search Google Scholar
    • Export Citation
  • Turner, J. S., 1973: Buoyancy Effects in Fluids. Cambridge University Press, 368 pp.

  • Velez-Belchi, P., , A. Alvarez, , P. Colet, , and J. Tintore, 2001: Stochastic resonance in the thermohaline circulation. Geophys. Res. Lett., 28 , 20532056.

    • Search Google Scholar
    • Export Citation
  • Weaver, A. J., , and T. M. C. Hughes, 1992: Stability and variability of the thermohaline circulation and its link to climate. Trends Phys. Oceanogr., 1 , 1570.

    • Search Google Scholar
    • Export Citation
  • Weaver, A. J., , J. Marotzke, , P. F. Cummins, , and E. S. Sarachik, 1993: Stability and variability of the thermohaline circulation. J. Phys. Oceanogr., 23 , 3960.

    • Search Google Scholar
    • Export Citation
  • Welander, P., 1982: A simple heat salt oscillator. Dyn. Atmos. Oceans, 6 , 233242.

  • Winton, M., 1993: Deep decoupling oscillations of the oceanic thermohaline circulation. Ice in the Climate System, W. R. Peltier, Ed., NATO ASI Series, Vol. 112, Springer-Verlag, 417–432.

    • Search Google Scholar
    • Export Citation
  • Winton, M., , and E. S. Sarachik, 1993: Thermohaline oscillations induced by strong steady salinity forcing of ocean general circulation models. J. Phys. Oceanogr., 23 , 13891410.

    • Search Google Scholar
    • Export Citation
  • Yin, F. L., 1995: A mechanistic model of ocean interdecadal thermohaline oscillations. J. Phys. Oceanogr., 25 , 32393246.

  • Zhang, R., , M. Follows, , and J. Marshall, 2002: Mechanisms of thermohaline mode switching with application to warm equable climates. J. Climate, 15 , 20562072.

    • Search Google Scholar
    • Export Citation
  • Zhang, S., , R. G. Greatbach, , and C. A. Lin, 1993: A reexamination of the polar halocline catastrophe and implications for coupled ocean–atmosphere modeling. J. Phys. Oceanogr., 23 , 287299.

    • Search Google Scholar
    • Export Citation
All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 55 55 5
PDF Downloads 47 47 4

A Simple Model of Millennial Oscillations of the Thermohaline Circulation

View More View Less
  • 1 Laboratoire de Physique des Océans, Brest, France
© Get Permissions
Restricted access

Abstract

Stommel’s two-box model of thermohaline circulation is modified to include the possibility of convection. When reduced to a two-degrees-of-freedom dynamical system, the model exhibits the well-known multiple (thermal and haline) steady states as well as new convective thermal steady states. However, for some values of the control parameters (such as the freshwater flux) oscillations occur. Millennial period oscillatory regimes correspond to switches between the Stommel’s haline fixed point and the convective thermal state, both of which are unstable in a window of precipitation values. The transitions between steady and oscillatory regimes at the boundaries of the window are global bifurcations, which in some cases have an infinite period character. This character is due either to the proximity of the Stommel saddle node bifurcation or to the infinite time it takes for the convection to resume when the system is in the haline regime. The oscillations bear a close relationship to those of Welander’s flip–flop model. The physics of this class of millennial oscillations may be relevant to those observed in more complex OGCMs and may help to rationalize certain features of the millennial band oscillations that punctuate the last glacial period.

Corresponding author address: Alain Colin de Verdière, Université de Bretagne Occidentale, Laboratoire de Physique des Océans, 6 Ave. Le Gorgeu, C.S. 93837, 29238 Brest CEDEX 3, France. Email: acolindv@univ-brest.fr

Abstract

Stommel’s two-box model of thermohaline circulation is modified to include the possibility of convection. When reduced to a two-degrees-of-freedom dynamical system, the model exhibits the well-known multiple (thermal and haline) steady states as well as new convective thermal steady states. However, for some values of the control parameters (such as the freshwater flux) oscillations occur. Millennial period oscillatory regimes correspond to switches between the Stommel’s haline fixed point and the convective thermal state, both of which are unstable in a window of precipitation values. The transitions between steady and oscillatory regimes at the boundaries of the window are global bifurcations, which in some cases have an infinite period character. This character is due either to the proximity of the Stommel saddle node bifurcation or to the infinite time it takes for the convection to resume when the system is in the haline regime. The oscillations bear a close relationship to those of Welander’s flip–flop model. The physics of this class of millennial oscillations may be relevant to those observed in more complex OGCMs and may help to rationalize certain features of the millennial band oscillations that punctuate the last glacial period.

Corresponding author address: Alain Colin de Verdière, Université de Bretagne Occidentale, Laboratoire de Physique des Océans, 6 Ave. Le Gorgeu, C.S. 93837, 29238 Brest CEDEX 3, France. Email: acolindv@univ-brest.fr

Save