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system through thresholds. Model validation includes repli-
cating observed features of the D-O time series over the last
100 kyr and corroborating that key results are consistent
across models. To serve as a guide into climate behavior
beyond the scope of the conceptual models, we use the
global atmosphere-ocean-ice coupled climate model of inter-
mediate complexity ECBILT-CLIO [Opsteegh et al., 1998;
Goosse et al., 2002]. See Appendix A for a discussion of
ECBILT-CLIO
retreats. Figure 2 shows an example of this, which is com-
mon to any other time interval and boundary condition as
long as insolation forcing is kept constant, and D-O-like
fluctuations occur. Note that the water column during the
time preceding all D-O-like abrupt warming events is warm
and salty at depth, while colder and fresher (and lighter) at
shallow depths. As shown, ECBILT-CLIO and a much sim-
pler box model [Colin de Verdiere et al., 2006] reproduce the
same conditions. One possible interpretation is that under
such preconditioning, the water column becomes convec-
tively unstable, with double-diffusion mixing leading to
abrupt salt and heat rise, which transforms the stored poten-
tial energy of the top-heavy water column into kinetic energy
[Stern, 1975], while vigorous convection ensues. Note that in
Figure 2, the retreat of sea ice begins soon after the deep
ocean reaches what will be its maximum temperature. In the
actual ocean, this could be the time at which the water
column overturns and North Atlantic Deep Water is formed.
This apparent causal relationship (more about this in section
4) between warming of deep waters and sea ice retreat
appears important and should be testable, for instance, by
investigating deep ocean paleotemperature proxies in the
Arctic or the change in mean ocean temperature since the
beginning of Arctic sea ice retreat in the 1980s. These are
also the times, just before an abrupt warming episode, when
Heinrich events [Heinrich, 1988; Broecker et al., 1992] are
likely to occur. The sequence of peak warming and sudden
cooling of the deeper ocean near these times may shed some
light on the mechanism that accompanies these anomalous
detritus deposits [Bond et al., 1993; Rashid and Boyle,
2007].
Millennial-scale free oscillations in ocean temperature and
salinity due to the interplay of convective instability and
turbulent mixing has long been known to theoretically exist
[Bryan, 1986; Winton, 1993; Haarsma et al., 2001; Sakai
and Peltier, 1997], so the fact that ECBILT-CLIO produces
internal, unforced thermohaline oscillations or hesitations
(Figure 2) is not necessarily surprising, nor is it surprising
that under certain conditions (for instance, if the full ice sheet
topography is included), D-O-like oscillations get sup-
pressed [e.g., Friedrich et al., 2010], as discussed in Appen-
dix A. Of course, not all Earth models of intermediate
complexity (EMICs) produce identical results. We per-
formed numerous experiments with the University of Victo-
ria
S results.
The chapter is organized as follows: Section 2 describes
conditions under which climate models simulate bistable
climates that produce D-O-like warming events. Section 3
discusses sea ice extent and mean ocean temperature (the
main variables this study focuses on); section 4 describes
the Langevin and van der Pol models; section 5 describes the
combined use of simpli
'
ed models, and a discussion of the
implications of the modeling results is given in section 6. All
models used are described in detail in Appendix A.
2. BISTABLE CLIMATES
Our modeling strategy involves the combined use of cli-
mate models to capture some essential physics of the climate
response. The most basic of the simpli
ed models we use
that describes bistability is a nonlinear stochastic Langevin
equation that serves as foundation for the more elaborate,
“
SIO. We also use the Earth model of intermediate
complexity ECBILT-CLIO, which can sustain D-O-like cli-
mate fluctuations [Schulz et al., 2007; Goosse et al., 2002;
Haarsma et al., 2001] that can be interpreted as a bistable
climate system that transitions at random between two stable
states [Stommel, 1961; Lorenz, 1976]. In Appendix A (Figure
A1) we show results of modeling experiments performed for
time intervals of 10
noisy
”
20 kyr, allowing ECBILT-CLIO code to
produce its built-in responses for a set of boundary condi-
tions that simulates mean climates from preindustrial (PI) to
Last Glacial Maximum (LGM).
-
3. SEA ICE EXTENT AND OCEAN TEMPERATURE
DURING ABRUPT CLIMATE CHANGE
Sea ice extent is known to be an important variable in the
study of abrupt climate change because the rapid response of
floating ice to temperature change and insolation could ex-
plain the abruptness of the D-O, and its role as ocean
s heat
insulator could explain the warming of the covered ocean
that eventually drives its retreat [e.g., Saltzman, 2002]. In
fact, modeling results to be discussed indicate that deep
ocean temperature (below ~500 m) interacts with sea ice
extent whereby the ocean begins to warm up soon after sea
ice extent reaches its maximum and cools off as sea ice
'
s ESCM model that consistently exhibited D-O-like
oscillations but with longer periods (~5000 years) and weaker
ocean temperature jumps (1K as opposed to 3K in ECBILT-
CLIO) under the same boundary conditions. It is not a simple
matter to decide which model better captures a semblance of
the actual climate. Though we consider this an unresolved
issue, the simple box-type models that produce millennial
'
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