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larger values of
s
gn
stochastic resonance occurs, as shown in Fig.
4.28
(c). We note that
the periodicity of these fluctuations is imposed by the period of the external forcing.
Other authors (
Pelletier
,
2003
) argued that the observed 100,000-yr periodicity is
not imposed by a periodic forcing but it is inherent in the dynamics, whereas noise
enhances the occurrence of 100,000-yr fluctuations through a
coherence-resonance
mechanism (see Chapter 3).
4.8.2 Fluctuations in the glacial climate: An effect of stochastic
or coherence resonance?
Stochastic resonance was recently invoked (
Alley et al.
,
2001
;
Ganopolski and Rahm-
storf
,
2002
;
Braun et al.
,
2005b
;
Ditlevsen et al.
,
2005
) to explain the occurrence
of temporary and abrupt warming episodes - known as
Dansgaard-Oeschger (DO)
events
- in the course of the last glacial period (100-10 kyr before the present). Alter-
native mechanisms based on the coherence-resonance theory have also been proposed
(
Timmermann et al.
,
2003
).
Ice-core records indicate that the waiting times between two consecutive DO
episodes are clustered around 1500 yr, and - with lower probability - around 3000
and 4500 yr (
Alley et al.
,
2001
), as shown in Fig.
4.29
(e). The occurrence of DO
events in 1500-yr cycles and in cycles with periods that are integer multiples of
1500 yr is suggestive of a stochastic-resonance mechanism (see Chapter 3). How-
ever, in this case stochastic resonance occurs in a system that is slightly different
from those presented in Chapter 3. In fact, in this complex system the detection of
stochastic resonance requires simulations with global-climate models with several
state variables and parameters, rather than simplified models with one differential
equation (
Ganopolski et al.
,
1998
;
Ganopolski and Rahmstorf
,
2002
;
Timmermann
et al.
,
2003
). Moreover, in this case the underlying deterministic dynamics are not
bistable (
Ganopolski and Rahmstorf
,
2001
). In fact, while under present-day climate
conditions, the Atlantic Ocean theormohaline circulation - a major contributor to the
regional heat budget - has two stable states, bistability did not exist under glacial
climate conditions (
Ganopolski and Rahmstorf
,
2001
). The glacial Atlantic Ocean
circulation used to have only one stable mode, known as the cold conveyor belt (sta-
dial conditions). Warm DO events occurred as perturbations of the “cold” climate
conditions, and were presumably triggered by small salinity changes in the North
Atlantic. Each event involved only a temporary shift to the unstable warm circulation
state, and included three distinctive phases: abrupt warming by about 10
◦
C, slow
cooling, and abrupt cooling to the cold stadial conditions.
Thus the glacial Atlantic behaved like an excitable system and could have exhib-
ited either coherence-resonant or stochastic-resonant behavior, depending on whether
the freshwater inflow was perturbed only with noise or also with periodic forcing.
Using global-climate simulations,
Ganopolski and Rahmstorf
(
2002
) showed that, in
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