Environmental Engineering Reference
In-Depth Information
complex communities are often found to be stable (e.g.,
Polis
,
1991
;
Goldwasser and
Roughgarden
,
1993
), it can be argued that community composition is unlikely to be
random. In fact, natural selection is expected to play a role in determining how species
interact within a community.
4.8 Stochastic resonance and coherence in environmental processes
The concept of stochastic resonance was first formulated (
Benzi et al.
,
1982a
,
1982b
)
to explain the emergence of periodic fluctuations in climate dynamics in the presence
of relatively weak periodic drivers. Typical examples include the 100-kyr periodicity
observed in climate-change episodes (
Benzietal.
,
1982b
), the periodic fluctuations in
the Holocene thermohaline circulation (
Velez-Belchi et al.
,
2001
), and the periodicity
in the occurrence of Dansgaard-Oeschger (DO) events (i.e., short and abrupt warming
episodes) during the last glaciation (
Alley et al.
,
2001
;
Ganopolski and Rahmstorf
,
2002
). Coherence resonance was recently invoked to explain species coexistence and
biodiversity (
Lai and Liu
,
2005
) and regular random fluctuations in predator-prey
systems (
Sieber et al.
,
2007
).
4.8.1 The Benzi-Parisi-Sutera-Vulpiani climate-change model
The notion of stochastic resonance was introduced by
Benzi et al.
(
1982a
),
1982b
)
to study periodical changes in the Earth's climate observed in palaeoclimate records
(
Mason
,
1976
).
Benzi et al.
(
1982a
) developed the stochastic-resonance framework to
show how the 100,000-yr periodicity observed in climate fluctuations may result from
the combined effect of a weak (deterministic) astronomic forcing and background
environmental noise in a complex, nonlinear system with internal feedbacks. The
synergism between the weak periodic forcing and a noise of suitable intensity would
be able to cause organized periodic fluctuations in the climate system, which would
not appear in the absence of noise. Thus noise would induce order and regularity in
these long-term climate dynamics.
Benzi et al.
(
1982b
) modified the Budyko-Sellers model (
Budyko
,
1969
;
Sellers
,
1969
) of the Earth's energy balance:
c
d
T
d
V
(
T
)
d
T
d
t
=−
=
R
in
−
R
out
,
(4.70)
where
c
is the active thermal inertia of the Earth system,
T
is the Earth's temperature,
V
(
T
) is the potential function associated with the dynamics of
T
,
R
in
is the incoming
solar radiation, and
R
out
is the outgoing (radiated and reflected) radiation. The incom-
ing radiation is affected by periodical astronomic forcing, whereas outgoing radiation
is the sum of reflected [
α
(
T
)
R
in
] and long-wave [
E
(
T
)] radiation:
R
in
=
Q
[1
+
a
cos(
ω
t
)]
,
R
out
=
α
(
T
)
R
in
+
E
(
T
)
,
(4.71)
Search WWH ::
Custom Search