Climate Dynamics

, Volume 39, Issue 9–10, pp 2127–2142 | Cite as

Characterising meridional overturning bistability using a minimal set of state variables

  • Willem P. SijpEmail author


A close approximation of key state variables and salt fluxes for both the North Atlantic Deep Water (NADW) “on” and “off” states in a General Circulation Model (GCM) is constructed, yielding a natural stability condition. Here, stability is linked to the effect of feedbacks on infinitesimal salinity anomalies on the average Atlantic salinity. The stability condition simply states that the total advective salt feedback must be negative in each steady state, ensuring stability by damping the growth of infinitesimal salinity perturbations. However, a decomposition of the salt feedback into three components shows that only the interaction between the mean salinity and infinitesimal perturbations of the meridional flow have the potential to render a state unstable, holding the key to state transitions. In contrast, the interaction between the mean meridional flow and infinitesimal salinity perturbations yields a negative (stabilising) component feedback. Similarly, the gyre salt flux also stabilises the overturning states. Furthermore, the nodes limiting the “on” and “off” state regimes in the GCM can be accurately computed based on linear fits of basic state variables and the gyre salt flux. It is shown that the NADW “on” state closest to collapse must be contained within a neighbourhood of fresh water exporting states. Finally, the role of temperature in the bistability structure is elucidated.


AMOC Atlantic Atlantic meridional overturning circulation Bistability Non-linear system Climate change NADW formation NADW shutdown Gulf stream shutdown North Atlantic deep water Deep sinking Convection shutdown Poleward heat transport Halocline catastrophe Box model Two stable states Critical points Non-linear theory Saddle nodes Limit point 



We thank the University of Victoria staff for support in usage of the their coupled climate model. This research was supported by the Australian Research Council and the Australian Antarctic Science Program. This research was undertaken on the NCI National Facility in Canberra, Australia, which is supported by the Australian Commonwealth Government. We thank Jonathan M. Gregory for hosting several visits to the University of Reading, UK, and many stimulating discussions.


  1. Arzel O, England MH, Sijp WP (2008) Reduced stability of the Atlantic meridional overturning circulation due to wind stress feedback during glacial times. J Clim 21:6260–6282CrossRefGoogle Scholar
  2. Boris JP, Book DL (1973) Flux-corrected transport. part I: SHASTA: a fluid transport algorithm that works. J Comput Phys 11:38–69CrossRefGoogle Scholar
  3. Boyle EA, Keigwin L (1987) North Atlantic thermohaline circulation during the past 20,000 years linked to high-latitude surface temperature. Nature 330:35–40CrossRefGoogle Scholar
  4. Broecker WS (1991) The great ocean conveyor belt. Oceanography 4:79–87Google Scholar
  5. Bryan F (1986) High-latitude salinity effects and interhemispheric thermohaline circulations. Nature 323:301–304CrossRefGoogle Scholar
  6. Bryan K, Lewis LJ (1979) A water mass model of the world ocean. J Geophys Res 84:2503–2517CrossRefGoogle Scholar
  7. DeVries P, Weber SL (2005) The Atlantic fresh water budget as a diagnostic for the existence of a stable shut down of the meridional overturning circulation. Geophys Res Lett 32. doi: 10.1029/2004GL021450
  8. Dijkstra HA (2007) Characterization of the multiple equilibria regime in a global ocean model. Tellus 59a:695–705Google Scholar
  9. Dijkstra HA (2008) Scaling of the Atlantic meridional overturning in a global ocean model. Tellus 60a:749–760Google Scholar
  10. Fuerst JJ, Levermann A (2011) Minimal model of a wind- and mixing-driven overturning—threshold behaviour for both driving mechanisms. Clim Dyn 37. doi: 10.1007/s00382-011-1003-7
  11. Ganachaud A, Wunsch C (2003) Large scale ocean heat and freshwater transports during the world ocean circulation experiment. J Clim 16:696–705CrossRefGoogle Scholar
  12. Gent PR, McWilliams JC (1990) Isopycnal mixing in ocean general circulation models. J Phys Oceanogr 20:150–155CrossRefGoogle Scholar
  13. Gerdes R, Köberle C, Willebrand J (1991) The influence of numerical advection schemes on the results of ocean general circulation models. Clim Dyn 5:211–226CrossRefGoogle Scholar
  14. Gregory JM, Saenko OA, Weaver AJ (2003) The role of the Atlantic freshwater balance in the hyteresis of the meridional overturning circulation. Clim Dyn 21:707–717. doi: 10.1007/s00382-003-0359-8 CrossRefGoogle Scholar
  15. Griesel A, Morales-Maqueda MA (2006) The relation of meridional pressure gradients to North Atlantic deep water volume transport in an ocean general circulation model. Clim Dyn 26:781–799CrossRefGoogle Scholar
  16. Hofmann H, Rahmstorf S (2009) On the stability of the Atlantic meridional overturning circulation. PNAS 106:20584–20589CrossRefGoogle Scholar
  17. Hughes TMC, Weaver AJ (1994) Multiple equilibria of an asymmetric two-basin ocean model. J Phys Oceanogr 24:619–637CrossRefGoogle Scholar
  18. Huisman SE, den Toom M, Dijkstra HA (2010) An indicator of the multiple equilibria regime of the Atlantic meridional overturning circulation. J Phys Oceanogr 40:551–567CrossRefGoogle Scholar
  19. Kalnay E, Kanamitsu M, Kistler R, Collins W, Deaven D, Gandin L, Iredell M, Saha S, White G, Woollen J, Zhu Y, Leetmaa A, Reynolds R (1996) The NCEP/NCAR 40-year re-analysis project. Bull Am Meteor Soc 77:437–471CrossRefGoogle Scholar
  20. Levermann A, Fuerst JJ (2010) Atlantic pycnocline theory scrutinized using a coupled climate model. Geophys Res Lett 37. doi: 10.1029/2010GL044180
  21. Levermann A, Griesel A (2004) Solution of a model for the oceanic pycnocline depth: scaling of overturning strength and meridional pressure difference. Geophys Res Lett 31. doi: 10.1029/2004GL020678
  22. Manabe S, Stouffer RJ (1988) Two stable equilibria of a coupled ocean-atmosphere model. J Clim 1:841–866CrossRefGoogle Scholar
  23. Manabe S, Stouffer RJ (1999) Are two modes of thermohaline circulation stable?. Tellus 51A:400–411Google Scholar
  24. Pacanowski R (1995) MOM2 Documentation user’s guide and reference manual: GFDL Ocean Group Technical Report 3, 3rd edn. NOAA, GFDL, PrincetonGoogle Scholar
  25. Rahmstorf S (1996) On the freshwater forcing and transport of the Atlantic thermohaline circultion. Clim Dyn 12:799–811CrossRefGoogle Scholar
  26. Rahmstorf S (2002) Ocean circulation and climate during the past 120,000 years. Nature 419:207–214CrossRefGoogle Scholar
  27. Rahmstorf S, Willebrand J (1995) The role of temperature feedback in stabilizing the thermohaline circulation. J Phys Oceanogr 25:787–805CrossRefGoogle Scholar
  28. Rooth C (1982) Hydrology and ocean circulation. Prog Oceanogr 11:131–149CrossRefGoogle Scholar
  29. Saenko OA, Weaver AJ, Gregory JM (2003) On the link between the two modes of the ocean thermohaline circulation and the formation of global-scale water masses. J Clim 16:2797–2801CrossRefGoogle Scholar
  30. Sarnthein M, Winn K, Jung SJA, Duplessy JC, Labeyrie L, Erlenkeuser H, Ganssen G (1994) Changes in east Atlantic deepwater circulation over the last 30,000 years: eight time slice reconstructions. Paleoceanography 9:209–267CrossRefGoogle Scholar
  31. Sijp WP, England MH (2006) Sensitivity of the Atlantic thermohaline circulation and its stability to basin- scale variations in vertical mixing. J Clim 19:5467–5478CrossRefGoogle Scholar
  32. Sijp WP, England MH, Gregory JM (2011a) Precise calculations of the existence of multiple AMOC equilibria in coupled climate models part I: equilibrium states. J Clim (Accepted)Google Scholar
  33. Sijp WP, Gregory JM, Tailleux R, Spence P (2011b) The key role of the western boundary in linking the amoc strength to the north-south pressure gradient. J Phys Oceanogr (In Revision)Google Scholar
  34. Smith RS, Gregory JM, Osprey A (2008) A description of the famous (version xdbua) climate model and control run. Geosci Model Dev 1:53–68CrossRefGoogle Scholar
  35. Stommel H (1961) Thermohaline convection with two stable regimes of flow. Tellus 13:224–230CrossRefGoogle Scholar
  36. Talley LD (2008) Freshwater transport estimates and the global overturning circulation: Shallow, deep and throughflow components. Prog Oceanogr 78:257–303CrossRefGoogle Scholar
  37. Thorpe RB, Gregory JM, Johns TC, Wood RA, Mitchell JFB (2001) Mechanisms determining the Atlantic thermohaline circulation response to greenhouse gas forcing in a non-flux-adjusted coupled climate model. J Clim 14:3102–3116CrossRefGoogle Scholar
  38. Vellinga M, Wood RA (2002) Global climatic impacts of a collapse of the Atlantic thermohaline circulation. Clim Change 54:251–267CrossRefGoogle Scholar
  39. Weaver AJ, Eby M, Wiebe EC, co authors (2001) The UVic Earth System Climate Model: model description, climatology, and applications to past, present and future climates. Atmosphere-Ocean 39:1067–1109CrossRefGoogle Scholar
  40. Zalesak ST (1979) Fully multidimensional flux-corrected transport algorithms for fluids. J Comput Phys 31:335–362CrossRefGoogle Scholar

Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  1. 1.Climate Change Research Centre (CCRC)University of New South WalesSydneyAustralia

Personalised recommendations