Environmental Engineering Reference
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