Editorial Type:
Article
Article Type:
Research Article

A 2 Degree of Freedom Dynamical System for Interdecadal Oscillations of the Ocean–Atmosphere

Alain Colin de Verdière Laboratoire de Physique des Océans, Université de Bretagne Occidentale, Brest, France

Search for other papers by Alain Colin de Verdière in
Current site
Google Scholar
PubMed Close
and
Thierry Huck Princeton University, and Geophysical Fluid Dynamics Laboratory, Princeton, New Jersey

Search for other papers by Thierry Huck in
Current site
Google Scholar
PubMed Close
Print Publication:
01 Aug 2000
DOI:
https://doi.org/10.1175/1520-0442(2000)013<2801:ADOFDS>2.0.CO;2
Page(s):
2801–2817
Restricted access

Abstract

A four-box model of the ocean–atmosphere is constructed that exhibits self-sustained oscillations in the regime of decadal to interdecadal periods found in oceanic general circulation models under certain boundary conditions. The oscillations are assumed to be caused by a type of baroclinic instability that relies on the store of available potential energy in the ocean. To represent this process in a low-order model, the authors propose Landau’s equation to govern the evolution of the overturning branch of the oceanic circulation. The domains of the unstable oscillations are found from linear stability analysis, and the nonlinear regimes are explored numerically. On these long timescales the atmospheric temperatures follow the oceanic temperatures. If the atmospheric temperatures are forced to be constant, the oscillations become strongly damped and disappear. The implications of the simple physics of this model for the decadal oscillations observed in more complex two- or three-dimensional GCMs are discussed.

Corresponding author address: A. Colin de Verdière, Laboratoire de Physique des Océans, Université de Bretagne Occidentale, 6 avenue Le Gorgeu, B.P. 809, 29285 Brest Cedex, France.

Abstract

A four-box model of the ocean–atmosphere is constructed that exhibits self-sustained oscillations in the regime of decadal to interdecadal periods found in oceanic general circulation models under certain boundary conditions. The oscillations are assumed to be caused by a type of baroclinic instability that relies on the store of available potential energy in the ocean. To represent this process in a low-order model, the authors propose Landau’s equation to govern the evolution of the overturning branch of the oceanic circulation. The domains of the unstable oscillations are found from linear stability analysis, and the nonlinear regimes are explored numerically. On these long timescales the atmospheric temperatures follow the oceanic temperatures. If the atmospheric temperatures are forced to be constant, the oscillations become strongly damped and disappear. The implications of the simple physics of this model for the decadal oscillations observed in more complex two- or three-dimensional GCMs are discussed.

Corresponding author address: A. Colin de Verdière, Laboratoire de Physique des Océans, Université de Bretagne Occidentale, 6 avenue Le Gorgeu, B.P. 809, 29285 Brest Cedex, France.

Save
Cover Journal of Climate
Journal of Climate

  • Birchfield, G. E., 1989: A coupled ocean–atmosphere climate model:Temperature versus salinity effects on the thermohaline circulation. Climate Dyn.,4, 57–71.

  • Bryan, F., 1986: High-latitude salinity effects and interhemispheric thermohaline circulations. Nature,323, 301–304.

  • Budyko, M. I., 1969: The effect of solar radiation variations on the climate of the Earth. Tellus,21, 611–619.

  • Cai, W., R. J. Greatbatch, and S. Zhang, 1995: Interdecadal variability in an ocean model driven by a small, zonal redistribution of the surface buoyancy flux. J. Phys. Oceanogr.,25, 1998–2010.

  • Capotondi, A., and W. R. Holland, 1997: Decadal variability in an idealized ocean model and its sensitivity to surface boundary conditions. J. Phys. Oceanogr.,27, 1071–1093.

  • Chen, F., and M. Ghil, 1996: Interdecadal variability in a hybrid coupled ocean–atmosphere model. J. Phys. Oceanogr.,26, 1561–1578.

  • Colin de Verdière, A., and T. Huck, 1999: Baroclinic instability: An oceanic wavemaker for interdecadal variability. J. Phys. Oceanogr.,29, 893–910.

  • Delworth, T. L., and R. J. Greatbatch, 2000: Multidecadal thermohaline circulation variability excited by stochastic surface flux forcing. J. Climate,13, 1481–1495.

  • ——, and M. E. Mann, 2000: Observed and simulated multidecadal variability in the North Atlantic. Climate Dyn., in press.

  • ——, S. Manabe, and R. J. Stouffer, 1993: Interdecadal variations of the thermohaline circulation in a coupled ocean–atmosphere model. J. Climate,6, 1993–2011.

  • Deser, C., and M. L. Blackmon, 1993: Surface climate variations over the North Atlantic Ocean during winter: 1900–1989. J. Climate,6, 1743–1753.

  • Drazin, P. G., and W. H. Reid, 1981: Hydrodynamic Stability. Cambridge University Press, 519 pp.

  • Drbohlav, J., and F. F. Jin, 1998: Interdecadal variability in a zonally averaged ocean model: An adjustment oscillator. J. Phys. Oceanogr.,28, 1252–1270.

  • Greatbatch, R. J., and S. Zhang, 1995: An interdecadal oscillation in an idealized ocean basin forced by constant heat flux. J. Climate,8, 81–91.

  • ——, and K. A. Peterson, 1996: Interdecadal variability and oceanic thermohaline adjustment. J. Geophys. Res. (Oceans),101, 20 467–20 482.

  • Griffies, S. M., and E. Tziperman, 1995: A linear thermohaline oscillator driven by stochastic atmospheric forcing. J. Climate,8, 2440–2453.

  • Huang, R. X., and R. L. Chou, 1994: Parameter sensitivity of the saline circulation. Climate Dyn.,9, 391–409.

  • Huck, T., A. Colin de Verdière, and A. J. Weaver, 1999a: Interdecadal variability of the thermohaline circulation in box-ocean models forced by fixed surface fluxes. J. Phys. Oceanogr.,29, 865–892.

  • ——, A. J. Weaver, and A. Colin de Verdière, 1999b: On the influence of the parameterization of lateral boundary layers on the thermohaline circulation in coarse-resolution ocean models. J. Mar. Res.,57, 387–426.

  • Hurrell, J. W., and H. van Loon, 1997: Decadal variations in climate associated with the North Atlantic oscillation. Climatic Change,36, 301–326.

  • Kushnir, Y., 1994: Interdecadal variations in North Atlantic sea surface temperature and associated atmospheric conditions. J. Climate,7, 141–157.

  • Maas, L. R. M., 1994: A simple model for the three-dimensional thermally and wind-driven ocean circulation. Tellus,46A, 671–680.

  • Mann, M. E., R. S. Bradley, and M. K. Hughes, 1998: Global-scale temperature patterns and climate forcing over the past six centuries. Nature,392, 779–787.

  • Marotzke, J., 1990: Instabilities and multiple equilibria of the thermohaline circulation. Ph.D. thesis, Institut für Meereskunde, Christian-Albrechts Universität, Kiel, Germany, 126 pp.

  • ——, and J. Willebrand, 1991: Multiple equilibria of the global thermohaline circulation. J. Phys. Oceanogr.,21, 1372–1385.

  • ——, and P. H. Stone, 1995: Atmospheric transports, the thermohaline circulation, and flux adjustments in a simple coupled model. J. Phys. Oceanogr.,25, 1350–1364.

  • ——, and D. W. Pierce, 1997: On spatial scales and lifetime of SST anomalies beneath a diffusive atmosphere. J. Phys. Oceanogr.,27, 133–139.

  • ——, P. Welander, and J. Willebrand, 1988: Instability and multiple steady states in a meridional plane model of the thermohaline circulation. Tellus,40A, 162–172.

  • Rahmstorf, S., 1993: A fast and complete convection scheme for ocean models. Ocean Modelling, 101, 9–11.

  • Ruddick, B., and L. Zhang, 1996: Qualitative behavior and nonoscillation of Stommel’s thermohaline box model. J. Climate,9, 2768–2777.

  • Seager, R., Y. Kushnir, and M. A. Cane, 1995: On heat flux boundary conditions for ocean models. J. Phys. Oceanogr.,25, 3219–3230.

  • Stommel, H., 1961: Thermohaline convection with two stable regimes of flow. Tellus,13, 224–230.

  • Sutton, R. T., and M. R. Allen, 1997: Decadal predictability of North Atlantic sea surface temperature and climate. Nature,388, 563–567.

  • Weaver, A. J., and E. S. Sarachik, 1991: Evidence for decadal variability in an ocean general circulation model: An advective mechanism. Atmos.–Ocean,29, 197–231.

  • ——, J. Marotzke, P. F. Cummins, and E. S. Sarachik, 1993: Stability and variability of the thermohaline circulation. J. Phys. Oceanogr.,23, 39–60.

  • Welander, P., 1982: A simple heat–salt oscillator. Dyn. Atmos. Oceans,6, 233–242.

  • Winton, M., 1996: The role of horizontal boundaries in parameter sensitivity and decadal-scale variability of coarse-resolution ocean general circulation models. J. Phys. Oceanogr.,26, 289–304.

  • Wright, D. G., and T. F. Stocker, 1991: A zonally averaged model for the thermohaline circulation. Part I: Model development and flow dynamics. J. Phys. Oceanogr.,21, 1713–1724.

  • ——, C. B. Vreugdenhil, and T. M. C. Hughes, 1995: Vorticity dynamics and zonally averaged ocean circulation models. J. Phys. Oceanogr.,25, 2141–2154.

All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 587 391 18
PDF Downloads 57 26 2