Stochastic Stability of Open-Ocean Deep Convection

Till Kuhlbrodt Institute of Physics, University of Potsdam, and Potsdam Institute for Climate Impact Research, Potsdam, Germany

Search for other papers by Till Kuhlbrodt in
Current site
Google Scholar
PubMed
Close
and
Adam Hugh Monahan School of Earth and Ocean Sciences, University of Victoria, Victoria, British Columbia, and Earth System Evolution Program, Canadian Institute for Advanced Research, Toronto, Ontario, Canada

Search for other papers by Adam Hugh Monahan in
Current site
Google Scholar
PubMed
Close
Restricted access

Abstract

Open-ocean deep convection is a highly variable and strongly nonlinear process that plays an essential role in the global ocean circulation. A new view of its stability is presented here, in which variability, as parameterized by stochastic forcing, is central. The use of an idealized deep convection box model allows analytical solutions and straightforward conceptual understanding while retaining the main features of deep convection dynamics. In contrast to the generally abrupt stability changes in deterministic systems, measures of stochastic stability change smoothly in response to varying forcing parameters. These stochastic stability measures depend chiefly on the residence times of the system in different regions of phase space, which need not contain a stable steady state in the deterministic sense. Deep convection can occur frequently even for parameter ranges in which it is deterministically unstable; this effect is denoted wandering unimodality. The stochastic stability concepts are readily applied to other components of the climate system. The results highlight the need to take climate variability into account when analyzing the stability of a climate state.

Corresponding author address: Dr. Till Kuhlbrodt, Potsdam Institute for Climate Impact Research, P.O. Box 60 12 03, 14412 Potsdam, Germany. Email: kuhlbrodt@pik-potsdam.de

Abstract

Open-ocean deep convection is a highly variable and strongly nonlinear process that plays an essential role in the global ocean circulation. A new view of its stability is presented here, in which variability, as parameterized by stochastic forcing, is central. The use of an idealized deep convection box model allows analytical solutions and straightforward conceptual understanding while retaining the main features of deep convection dynamics. In contrast to the generally abrupt stability changes in deterministic systems, measures of stochastic stability change smoothly in response to varying forcing parameters. These stochastic stability measures depend chiefly on the residence times of the system in different regions of phase space, which need not contain a stable steady state in the deterministic sense. Deep convection can occur frequently even for parameter ranges in which it is deterministically unstable; this effect is denoted wandering unimodality. The stochastic stability concepts are readily applied to other components of the climate system. The results highlight the need to take climate variability into account when analyzing the stability of a climate state.

Corresponding author address: Dr. Till Kuhlbrodt, Potsdam Institute for Climate Impact Research, P.O. Box 60 12 03, 14412 Potsdam, Germany. Email: kuhlbrodt@pik-potsdam.de

Save
  • Belkin, I. M., S. Levitus, J. Antonov, and S-A. Malmberg, 1998: Great salinity anomalies in the North Atlantic. Progress in Oceanography, Vol. 41, Pergamon, 1–68.

    • Search Google Scholar
    • Export Citation
  • Cessi, P., 1994: A simple box model of stochastically forced thermohaline flow. J. Phys. Oceanogr., 24 , 19111920.

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

  • Corti, S., F. Molteni, and T. N. Palmer, 1999: Signature of recent climate change in frequencies of natural atmospheric circulation regimes. Nature, 398 , 799802.

    • Search Google Scholar
    • Export Citation
  • Dickson, R. R., J. Meincke, S-A. Malmberg, and A. J. Lee, 1988: The “great salinity anomaly” in the northern North Atlantic 1968–1972. Progress in Oceanography, Vol. 38, Pergamon. 103151.

    • Search Google Scholar
    • Export Citation
  • Dickson, R. R., J. Lazier, J. Meincke, P. Rhines, and J. Swift, 1996: Long-term coordinated changes in the convective activity of the North Atlantic. Progress in Oceanography, Vol. 38, Pergamon. 241295.

    • Search Google Scholar
    • Export Citation
  • Freidlin, M. I., and A. D. Wentzell, 1998: Random Perturbations of Dynamical Systems. 2d ed. Springer, 430 pp.

  • Ganachaud, A., and C. Wunsch, 2000: Improved estimates of global ocean circulation, heat transport and mixing from hydrographic data. Nature, 408 , 453456.

    • Search Google Scholar
    • Export Citation
  • Gardiner, C. W., 2002: Handbook of Stochastic Methods for Physics, Chemistry and the Natural Sciences. Springer Series in Synergetics, Vol. 13, 2d ed. Springer, 442 pp.

    • Search Google Scholar
    • Export Citation
  • Goosse, H., H. Renssen, F. M. Selten, R. J. Haarsma, and J. D. Opsteegh, 2002: Potential causes of abrupt climate events: A numerical study with a three-dimensional climate model. Geophys. Res. Lett., 29 .1860, doi:10.1029/2002GL014993.

    • Search Google Scholar
    • Export Citation
  • Hall, A., and R. J. Stouffer, 2001: An abrupt climate event in a coupled ocean–atmosphere simulation without external forcing. Nature, 409 , 171174.

    • Search Google Scholar
    • Export Citation
  • Hasselmann, K., 1976: Stochastic climate models, Part I: Theory. Tellus, 28 , 473485.

  • Hirschi, J., J. Sander, and T. F. Stocker, 1999: Intermittent convection, mixed boundary conditions and the stability of the thermohaline circulation. Climate Dyn., 15 , 277291.

    • Search Google Scholar
    • Export Citation
  • Houghton, J. T., Y. Ding, D. Griggs, M. Noguer, P. J. van der Linden, and D. Xiaosu, Eds.,. . 2001: Climate Change 2001: The Scientific Basis. Cambridge University Press, 944 pp.

    • Search Google Scholar
    • Export Citation
  • Houghton, R. W., and M. H. Visbeck, 2002: Quasi-decadal salinity fluctuations in the Labrador Sea. J. Phys. Oceanogr., 32 , 687701.

  • Hsu, C., and F. Zwiers, 2001: Climate change in recurrent regimes and modes of atmospheric variability. J. Geophys. Res., 106 , 2014520159.

    • Search Google Scholar
    • Export Citation
  • Imkeller, P., and A. H. Monahan, 2002: Conceptual stochastic climate models. Stochastics Dyn., 2 , 311326.

  • Khatiwala, S., B. E. Shaw, and M. A. Cane, 2001: Enhanced sensitivity of persistent events to weak forcing in dynamical and stochastic systems: Implications for climate change. Geophys. Res. Lett., 28 , 26332636.

    • Search Google Scholar
    • Export Citation
  • Khatiwala, S., P. Schlosser, and M. Visbeck, 2002: Rates and mechanisms of water mass transformations in the Labrador Sea as inferred from tracer observations. J. Phys. Oceanogr., 32 , 666686.

    • Search Google Scholar
    • Export Citation
  • Kramers, H., 1940: Brownian motion in a field of force and the diffusion model of chemical reactions. Physica, 7 , 284304.

  • Kuhlbrodt, T., 2002: Stability and variability of open-ocean deep convection in deterministic and stochastic simple models. Ph.D. thesis, University of Potsdam, 103 pp.

    • Search Google Scholar
    • Export Citation
  • Kuhlbrodt, T., S. Titz, U. Feudel, and S. Rahmstorf, 2001: A simple model of seasonal open ocean convection. Part II: Labrador Sea stability and stochastic forcing. Ocean Dyn., 52 , 3649.

    • Search Google Scholar
    • Export Citation
  • Lazier, J. R. N., 1980: Oceanographic conditions at Ocean Weather Ship Bravo, 1964–1974. Atmos.–Ocean, 18 , 227238.

  • Leadbetter, M., G. Lindgren, and H. Rootzen, 1983: Extremes and Related Properties of Random Sequences and Processes. Springer Series in Statistics, Springer-Verlag, 336 pp.

    • 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
  • Lenderink, G., and R. J. Haarsma, 1996: Modeling convective transitions in the presence of sea ice. J. Phys. Oceanogr., 36 , 14481467.

    • Search Google Scholar
    • Export Citation
  • Lilly, J. M., P. B. Rhines, M. Visbeck, R. Davis, J. R. N. Lazier, F. Schott, and D. Farmer, 1999: Observing deep convection in the Labrador Sea during winter 1994–1995. J. Phys. Oceanogr., 29 , 20652098.

    • Search Google Scholar
    • Export Citation
  • Lin, J. W-B., and J. D. Neelin, 2000: Influence of a stochastic moist convective parameterization on tropical climate variability. Geophys. Res. Lett., 27 , 36913694.

    • Search Google Scholar
    • Export Citation
  • Manabe, S., and R. J. Stouffer, 1988: Two stable equilibria of a coupled ocean–atmosphere model. J. Climate, 1 , 841866.

  • Manabe, S., and R. J. Stouffer, 1999: Are two modes of thermohaline circulation stable? Tellus, 51A , 400411.

  • Marshall, J., and F. Schott, 1999: Open-ocean convection: Observations, theory, and models. Rev. Geophys., 37 , 164.

  • Monahan, A. H., 2002a: Correlation effects in a simple model of the thermohaline circulation. Stochastics Dyn., 2 , 437462.

  • Monahan, A. H., 2002b: Stabilisation by noise of climate regimes in a simple model: Implications for stability of the thermohaline circulation. J. Phys. Oceanogr., 32 , 20722085.

    • Search Google Scholar
    • Export Citation
  • Monahan, A. H., L. Pandolfo, and J. C. Fyfe, 2001: The preferred structure of variability of the Northern Hemisphere atmospheric circulation. Geophys. Res. Lett., 28 , 10191022.

    • Search Google Scholar
    • Export Citation
  • Monahan, A. H., A. Timmermann, and G. Lohmann, 2002: Comments on “Noise-induced transitions in a simplified model of the thermohaline circulation.”. J. Phys. Oceanogr., 32 , 11121116.

    • Search Google Scholar
    • Export Citation
  • Palmer, T. N., 1999: A nonlinear dynamical perspective on climate prediction. J. Climate, 12 , 575591.

  • Palmer, T. N., 2001: A nonlinear dynamical perspective on model error: A proposal for nonlocal stochastic–dynamic parameterisation in weather and climate prediction models. Quart. J. Roy. Meteor. Soc., 127 , 279304.

    • Search Google Scholar
    • Export Citation
  • Rahmstorf, S., 2000: The thermohaline ocean circulation: A system with dangerous thresholds? Climatic Change, 46 , 247256.

  • Rahmstorf, S., 2001: A simple model of seasonal open ocean convection. Part I: Theory. Ocean Dyn., 52 , 2635.

  • Schaeffer, M., F. M. Selten, J. D. Opsteegh, and H. Goosse, 2002: Intrinsic limits to predictability of abrupt regional climate change in IPCC SRES scenarios. Geophys. Res. Lett., 29 .1767, doi:10.1029/2002GL015254.

    • Search Google Scholar
    • Export Citation
  • Sura, P., 2002: Noise-induced transitions in a barotropic beta-plane model. J. Atmos. Sci., 59 , 97110.

  • Timmermann, A., and G. Lohmann, 2000: Noise-induced transitions in a simplified model of the thermohaline circulation. J. Phys. Oceanogr., 30 , 18911900.

    • Search Google Scholar
    • Export Citation
  • von Storch, H., and F. Zwiers, 1999: Statistical Analysis in Climate Research. Cambridge University Press, 484 pp.

  • Welander, P., 1982: A simple heat-salt oscillator. Dyn. Atmos. Oceans, 6 , 233242.

  • Wood, R. A., A. B. Keen, J. F. B. Mitchell, and J. M. Gregory, 1999: Changing spatial structure of the thermohaline circulation in response to atmospheric CO2 forcing in a climate model. Nature, 399 , 572575.

    • Search Google Scholar
    • Export Citation
  • Yano, J. I., K. Fraedrich, and R. Blender, 2001: Tropical convective variability as 1/f noise. J. Climate, 14 , 36083616.

All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 245 50 6
PDF Downloads 65 20 1