Multiple Equilibria and Abrupt Transitions in Arctic Summer Sea Ice Extent - Arctic Sea Ice Decline: Observations, Projections, Mechanisms, and Implications - page 170

Held, H., and T. Kleinen (2004), Detection of climate system bi-
furcations by degenerate fingerprinting, Geophys. Res. Lett. , 31 ,
l23207, doi:10.1029/2004Gl020972.
Hibler, W. D. (1979), A dynamic thermodynamic sea ice model, J.
Phys. Oceanogr. , 9 , 815-846.
Holland, M. M., and C. M. Bitz (2003) Polar amplification of cli-
mate change in coupled models, Clim. Dyn. , 21 , 221-232.
Holland, M. M., C. M. bitz, and b. Tremblay (2006a), Future
abrupt transitions in the summer Arctic sea ice, Geophys. Res.
Lett. , 33 , l23503, doi:10.1029/2006Gl028024.
Holland, M. M., C. M. bitz, E. C. Hunke, W. H. liscombe, and J.
L. Schramm (2006b), Influence of the sea ice thickness distribu-
tion on polar climate in CCSM3, J. Clim. , 19 , 2398-2414.
Intergovernmental Panel on Climate Change (2001), Climate
Change 2001: The Scientific Basis: Contribution of Working
Group I to the Third Assessment Report of the Intergovernmen-
tal Panel on Climate Change , edited by J. T. Houghton et al.,
Cambridge Univ. Press, Cambridge, U. K.
Kleinen, T., H. Held, and G. Petschel-Held (2003) The potential
role of spectral properties in detecting thresholds in the Earth
system: Application to the thermohaline circulation, Ocean
Dyn. , 53 , 53-63.
lindsay, R. W., and J. Zhang (2005), The thinning of Arctic sea
ice 1988--2003: Have we passed a tipping point?, J. Clim. , 18 ,
4879-4894.
Manabe, S., and R. J. Stouffer (1999), Are two modes of thermoha-
line circulation stable?, Tellus, Ser. A , 51 , 400-411.
Maykut, G. A., and N. Untersteiner (1971), Some results from a
time-dependent thermodynamic model of sea ice, J. Geophys.
Res. , 76 , 1550-1575.
Monahan, A. H. (2002a), Stabilization of climate regimes by noise
in a simple model of the thermohaline circulation, J. Phys. Ocea-
nogr. , 32 , 2072-2085.
Monahan, A. H. (2002b), Correlation effects in a simple stochastic
model of the thermohaline circulation, Stochastics Dyn. , 2 , 437-462.
North, G. R. (1975), Analytical solution to a simple climate model
with diffusive heat transport, J. Atmos. Sci. , 32 , 1301-1307.
North, G. R. (1984), The small ice cap instability in diffusive cli-
mate models, J. Atmos. Sci. , 41 , 3390-3395.
Olbers, D. (2001), A gallery of simple models from climate physics,
in Stochastic Climate Models, Prog. Probab. , vol. 49, edited by P.
Imkeller and J.-S. von Storch, pp. 3-63, birkhäuser, boston, Mass.
Overpeck, J. T., et al. (2005), Arctic system on trajectory to new,
seasonally ice-free state, Eos Trans. AGU , 86 (34), 309.
Polyakov, I. V., et al. (2005), One more step toward a warmer Arctic,
Geophys. Res. Lett. , 32 , l17605, doi:10.1029/2005Gl023740.
Rahmstorf, S. (1995), bifurcations of the Atlantic thermohaline
circulation in response to changes in the hydrological cycle, Na-
ture , 378 , 145-148.

Rahmstorf, S. (1999), Rapid transitions of the thermohaline ocean
circulation—A modelling perspective, in Reconstructing Ocean
History: A Window Into the Future , edited by F. Abrantes and A.
C. Mix, pp. 139-149, Kluwer Acad., New york.
Rigor, I. G., and J. M. Wallace (2004), Variations in the age of
Arctic sea-ice and summer sea-ice extent, Geophys. Res. Lett. ,
31 , l09401, doi:10.1029/2004Gl019492.
Sayag, A., E. Tziperman, and M. Ghil (2004), Rapid switch-like
sea ice growth and land ice-sea ice hysteresis, Paleooceanogra-
phy , 19 , PA1021, doi:10.1029/2003PA000946.
Sorteberg, A., V. Kattsov, J. E. Walsh, and T. Pavlova (2007), The
Arctic surface energy budget as simulated with the IPCC AR4
AOGCMs, Clim. Dyn. , 29 , 131-156.
Stocker T. F., and D. G. Wright (1991), Rapid transitions of the
ocean's deep circulation induced by changes in the surface water
fluxes, Nature , 351 , 729-732.
Stommel, H. (1961), Thermohaline convection with two stable re-
gimes of flow, Tellus , 13 , 224-230.
Stroeve, J. C., M. C. Serreze, F. Fetterer, T. Arbetter, W. Meier,
J. Maslanik, and K. Knowles (2005), Tracking the Arctic's shrink-
ing ice cover: Another extreme September minimum in 2004,
Geophys. Res. Lett. , 32 , l04501, doi:10.1029/2004Gl021810.
Stroeve J., M. M. Holland, W. Meier, T. Scambos, and M. Serreze
(2007), Arctic sea ice decline: Faster than forecast, Geophys.
Res. Lett. , 34 , l09501, doi:10.1029/2007Gl029703.
Taylor, P. D., and D. l. Feltham (2005), Multiple stationary solu-
tions of an irradiated slab, J. Cryst. Growth , 276 , 688-697.
Thorndike, A. S. (1992), A toy model linking atmospheric thermal
radiation and sea ice growth, J. Geophys. Res. , 97 , 9401-9410.
Titz, S., T. Kuhlbrodt, S. Rahmstorf, and U. Feudel (2002) On
freshwater-dependent bifurcations in box models of the inter-
hemispheric thermohaline circulation, Tellus, Ser. A , 54 , 89-98.
von Storch, H., and F. W. Zwiers (1999), Statistical Analysis in
Climate Research , 484 pp., Cambridge Univ. Press, New york.
Winton, M. (2006), Does Arctic sea ice have a tipping point?, Geo-
phys. Res. Lett. , 33 , l23504, doi:10.1029/2006Gl028017.
Zhang, x., and J. E. Walsh (2006), Toward a seasonally ice-cov-
ered Arctic Ocean: Scenarios from the IPCC AR4 model simula-
tions, J. Clim. , 19 , 1730-1747.

M. M. Holland, National Center for Atmospheric Research,
boulder, CO 80307-3000, USA.
W. Merryfield, Canadian Centre for Climate Modeling and
Analysis, University of Victoria, P.O. box 1700, Victoria, bC
V8W 2Y2, Canada. ([e-mail])
A. H. Monahan, School of Earth and Ocean Sciences, University
of Victoria, Victoria, bC V8W 3P6, Canada.