Skip to main content

Reconciling theories of a mechanically driven meridional overturning circulation with thermohaline forcing and multiple equilibria

Abstract

It has recently been suggested that the structure and strength of the meridional overturning circulation in the global ocean is governed by the input of mechanical energy to the system by winds and tides. However, it is not clear how this suggestion relates to the existence of multiple equilibria of the meridional overturning circulation, which depends on thermohaline feedbacks and is more consistent with a buoyancy-driven view of the circulation. Both theories have been illustrated by box models in the past (Stommel in Tellus 13:224–230, 1961; Gnanadesikan in Science 283:2077–2079, 1999). Here we incorporate these two theories into a single box model in an attempt to reconcile the roles of mechanical and buoyancy forcing in driving the meridional overturning circulation. The box model has two equilibrium solutions, one with sinking at high northern latitudes as in the present-day Atlantic, and one without. The circulation is mechanically driven, but the northern sinking can be thought of as a release valve which acts as a sink of potential energy when the surface water at high northern latitudes is dense enough to convect. While the source of energy comes from mechanical forcing, the presence or otherwise of multiple equilibria is therefore determined by thermohaline feedbacks. In some areas of parameter space an oscillation between the model’s two circulation regimes occurs, reminiscent of a bipolar seesaw.

This is a preview of subscription content, access via your institution.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10

Notes

  1. In fact, Stommel used two different transfer coefficients for temperature and salinity. However, in the limit as the transfer coefficient goes to zero (infinitely slow relaxation timescale) and the effective salinity goes to infinity, the boundary condition on salinity tends to a fixed flux condition (Marotzke 1994).

  2. In practise, for numerical reasons q N is set to 0 when ρ d > ρ n + δ, in the limit where δ→ 0. The solutions are not sensitive to the value of δ provided it is small.

References

  • Broecker WS (1997) Thermohaline circulation, the Achilles heel of our climate system: will man-made CO2 upset the current balance? Science 278:1582–1588

    Article  Google Scholar 

  • Danabasoglu G, McWilliams JC, Gent PR (1994) The role of mesoscale tracer transports in the global ocean circulation. Science 264:1123–1126

    Article  Google Scholar 

  • Dansgaard W, Johnsen SJ, Clausen HB, Dahl-Jensen D, Gundestrup NS, Hammer CU, Hvidberg CS, Steffensen JP, Sveinbjrnsdottir AE, Jouzel J, Bond G (1993) Evidence for general instability of past climate from a 250-kyr ice-core record. Nature 364:218–220

    Article  Google Scholar 

  • Dijkstra HA, Ghil M (2005) Low frequency variability of the large-scale ocean circulation: a dynamical system approach. Rev Geophys 43:RG3002, doi:10.1029/2002RG000122

    Article  Google Scholar 

  • Fanning AF, Weaver AJ (1997) Temporal-geographical meltwater influences on the North Atlantic conveyor: implications for the Younger Dryas. Paleoceanography 12:307–320

    Article  Google Scholar 

  • Gent PR, McWilliams JC (1990) Isopycnal mixing in ocean circulation models. J Phys Oceanogr 20:150–155

    Article  Google Scholar 

  • Gnanadesikan A (1999) A simple predictive model for the structure of the oceanic pycnocline. Science 283:2077–2079

    Article  Google Scholar 

  • Gnanadesikan A, Slater RD, Samuels BL (2003) Sensitivity of water mass transformation and heat transport to subgridscale mixing in coarse-resolution ocean models. Geophys Res Lett 30:1967 doi:10.1029/2003GL018036

    Article  Google Scholar 

  • Gnanadesikan A, Slater RD, Swathi PS, Vallis GK (2005) The energetics of ocean heat transport. J Clim 18:2604–2616

    Article  Google Scholar 

  • Johnson HL, Marshall DP (2002) A theory for the surface Atlantic response to thermohaline variability. J Phys Oceanogr 32:1121–1132

    Article  Google Scholar 

  • Klinger BA, Drijfhout S, Marotzke J, Scott JR (2003) Sensitivity of basinwide meridional overturning to diapycnal diffusion and remote wind forcing in an idealized Atlantic-Southern Ocean geometry. J Phys Oceanogr 33:249–266

    Article  Google Scholar 

  • Kuhlbrodt T, Griesel A, Montoya M, Levermann A, Hofmann M, Rahmstorf S (2006). On the driving processes of the Atlantic meridional overturning circulation. Rev Geophys (in press)

  • Manabe S, Stouffer RJ (1988) Two stable equilibria of a coupled ocean-atmosphere model. J Clim 1:841–866

    Article  Google Scholar 

  • Manabe S, Stouffer RJ (1999) Are two modes of thermohaline circulation stable? Tellus 51:400–411

    Article  Google Scholar 

  • Marotzke J (1994) Ocean models in climate problems. In: Malanotte-Rizzoli P, Robinson AR (eds) Ocean processes in climate dynamics: global and mediterranean examples. Kluwer, Dordrecht, pp 79–109

    Google Scholar 

  • Marotzke J (1997) Boundary mixing and the dynamics of three-dimensional thermohaline circulations. J Phys Oceanogr 27:1713–1728

    Article  Google Scholar 

  • Marotzke J, Scott JR (1999) Convective mixing and the thermohaline circulation. J Phys Oceanogr 29:2962–2970

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Marshall DP (2007) Hydrographic variations along the sloping western and eastern boundaries of the oceans (in preparation)

  • Marshall DP, Naveira-Garabato AC (2007) A conjecture on the role of bottom-enhanced diapycnal mixing in the parameterization of geostrophic eddies. J Phys Oceanogr (submitted)

  • Marzeion B, Drange H (2006) Diapycnal mixing in a conceptual model of the Atlantic meridional overturning circulation. Deep Sea Res II 53:226–238

    Article  Google Scholar 

  • Marzeion B, Levermann A, Mignot J (2007) The role of stratification-dependent mixing for the stability of the Atlantic overturning in a global climate model J Phys Oceanogr (in press)

  • Mignone BK, Gnanadesikan A, Sarmiento JL, Slater RD (2006) Central role of Southern Hemisphere winds and eddies in modulating the oceanic uptake of anthropogenic carbon. Geophys Res Lett 33:L01604 doi:10.1029/2005GL024464

    Article  Google Scholar 

  • Molemaker MJ, McWilliams J (2005) Baroclinic instability and loss of balance. J Phys Oceanogr 35:1505–1517

    Article  Google Scholar 

  • Munk W, Wunsch C (1998) Abyssal recipes II: energetics of tidal and wind mixing. Deep Sea Res I 45:1977–2010

    Article  Google Scholar 

  • Nilsson J, Walin G (2001) Freshwater forcing as a booster of the thermohaline circulation. Tellus A 53:629–641

    Article  Google Scholar 

  • Nilsson J, Brostrom G, Walin G (2003) The thermohaline circulation and vertical mixing: does weaker density stratification give stronger overturning? J Phys Oceanogr 33:2781–2795

    Article  Google Scholar 

  • Park YG (1999) The stability of thermohaline circulation in a two-box model. J Phys Oceanogr 29:3101–3110

    Article  Google Scholar 

  • Pasquero C, Tziperman E (2004) Effects of a wind-driven gyre on thermohaline circulation variability. J Phys Oceanogr 34:805–816

    Article  Google Scholar 

  • Philander SG, Fedorov AV (2003) Role of tropics in changing the response to Milankovich forcing some three million years ago. Paleoceanography 18:1045, doi:10.1029/2002PA000837

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Ruddick B, Zhang L (1996) Qualitative behaviour and non-oscillation of Stommel’s thermohaline box model. J Clim 9:2768–2777

    Article  Google Scholar 

  • Samelson RM (2004) Simple mechanistic models of middepth meridional overturning. J Phys Oceanogr 34:2096–2103

    Article  Google Scholar 

  • Sandström JW (1916) Meteorologische Studien im schwedischen Hochebirge. Goteborgs K. Vetensk. Vitterhets-Samh Handl., Series 4 22(2):48

  • Schmittner A, Weaver AJ (2001) Dependence of multiple climate states on ocean mixing parameters. Geophys Res Lett 28:1027–1030

    Article  Google Scholar 

  • Stocker TF (2000) Past and future reorganizations in the climate system. Quat Sci Rev 19:301–319

    Article  Google Scholar 

  • Stocker TF, Wright DG, Mysak LA (1992) A zonally averaged, coupled ocean-atmosphere model for paleoclimate studies. J Clim 5:773–797

    Article  Google Scholar 

  • Stommel HM (1961) Thermohaline convection with two stable regimes of flow. Tellus 13:224–230

    Article  Google Scholar 

  • Stommel H, Rooth C (1968) On the interaction of gravitational and dynamic forcing in simple circulation models. Deep Sea Res 15:165–170

    Google Scholar 

  • Toggweiler JR, Samuels B (1995) Effect of Drake passage on the global thermohaline circulation. Deep Sea Res 42:477–500

    Article  Google Scholar 

  • Whitehead JA (1995) Thermohaline ocean processes and models. Annu Rev Fluid Mech 27:89–113

    Article  Google Scholar 

  • Wunsch C (1998) The work done by the wind on the oceanic general circulation. J Phys Oceanogr 28:2332–2340

    Article  Google Scholar 

  • Wunsch C (2005) Thermohaline loops, Stommel box models, and the Sandström theorem. Tellus 57A:84–99

    Google Scholar 

  • Wunsch C, Ferrari R (2004) Vertical mixing, energy, and the general circulation of the oceans. Annu Rev Fluid Mech 36:281–314

    Article  Google Scholar 

  • Yuan S, Wunsch C (2005) Stress-driven thermohaline loops. Phys Fluids 17:066601

    Article  Google Scholar 

Download references

Acknowledgments

HLJ is funded under a Royal Society University Research Fellowship. DPM acknowledges support from the RAPID programme of the UK Natural Environment Research Council.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Helen L. Johnson.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Johnson, H.L., Marshall, D.P. & Sproson, D.A.J. Reconciling theories of a mechanically driven meridional overturning circulation with thermohaline forcing and multiple equilibria. Clim Dyn 29, 821–836 (2007). https://doi.org/10.1007/s00382-007-0262-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00382-007-0262-9

Keywords

  • Southern Ocean
  • Equilibrium Solution
  • Deep Ocean
  • Volume Flux
  • Thermocline Depth