Multiple Equilibria and Abrupt Transitions in Arctic Summer Sea Ice Extent - Arctic Sea Ice Decline: Observations, Projections, Mechanisms, and Implications - page 168

dom forcing, (2) examine sensitivity to various parameters,
and (3) obtain an analytical description of the equilibria and
their stability.
It was found in section 3.3 that multiple stable equilibria
exist for physically relevant values of the parameters, in-
cluding those representative of CCSM3. It is thus tempting
to speculate that transitions between equilibria triggered by
OHT increases play a key role in the abrupt transitions in
CCSM3. However, in the numerical experiments described
in section 3.4.1 and illustrated in Plate 1, when OHT fluctua-
tions are as large as in CCSM3, the abrupt transitions occur
primarily as a consequence of the fluctuations themselves,
together with the increased sensitivity of sea ice to pertur-
bations as summer ice extent decreases. Multiple equilibria
play a larger role in abrupt transitions when OHT fluctua-
tions are smaller.
These results suggest that the physical processes identified
by HbT as being associated with abrupt sea ice transitions
in CCSM3 are, in fact, sufficient to trigger such behavior.
However, a significant caveat is that behavior following
abrupt transitions is sensitive to parameterization changes,
described in section 4, that may represent more plausibly the
effect of complete seasonal loss of ice cover on ocean short-
wave absorption. Abrupt transitions then lead to a sudden
perennial disappearance of ice cover that is strongly hyster-
etic. Such behavior is reminiscent of the small ice cap insta-
bility that occurs in certain other simplified representations
of sea ice but is not seen in CCSM3.
This case study thus illustrates both some of the prom-
ises and potential pitfalls of imposing major simplifications
in order to study fundamental climate system behavior. On
one hand, as climate models become more complex, a more
complete and detailed simulation of the climate system is
produced. Arguably, this may not by itself enable simulated
phenomena to be fundamentally understood; for this pur-
pose, simplified models and conceptual frameworks can pro-
vide valuable tools [ Held , 2005]. On the other hand, while
such simplifications may enable solving for and identifying
key influences on climate system phenomena (analytically
in some cases as here), results may be sensitive to which
processes are included and how the included processes are
represented, as, for example, in box models of ocean circula-
tion and simple conceptual models of ENSO [e.g., Olbers ,
2001].

Figure 18. Time series of ocean shortwave absorption with OHT
forcing as in Figure 17 under section 3 parameterizations (solid
curve) versus section 4 parameterizations (dashed curve).

in Figure 17 between behavior under the two shortwave
parameterizations.
Whether an abrupt loss of perennial ice can, in fact, occur
in a climate model was investigated by Winton [2006], who
found that this phenomenon does occur in one model (Max
Planck Institute ECHAM5), though not in CCSM3.

5. DISCUSSION AND CONClUSIONS

by quantifying in a simple manner three effects identi-
fied by HBT as contributing crucially to abrupt declines in
summer Arctic sea ice extent in CCSM3 21st century cli-
mate simulations, a nonlinear set of equations (6) - (8) was
obtained that appears able to reproduce some aspects of the
CCSM3 results. The key nonlinearity is the inverse depend-
ence of open water formation on winter ice thickness in (7),
whereas the impact of this effect on the following winter's
ice thickness is crucially enabled by the ice-albedo feedback
term in (6), which serves as an amplifier; if the coefficient b
in this expression is sufficiently large, then abrupt disappear-
ances of summer ice cover can occur under infinitesimal in-
creases in OHT. This is in contrast to the SICI phenomenon
discussed in section 2.1, for which albedo contrast provides
the essential nonlinearity and the minimum size of a viable
ice cap is determined by a length scale characterizing dif-
fusive atmospheric heat transport.
The main utility of the approach outlined here is its ex-
treme simplification: to the extent that the most important
physical processes are plausibly represented, it enables the
phenomenology of abrupt transitions to be examined in a
context removed from the massive computational expendi-
ture involved in running and analyzing results from a com-
prehensive climate model. This reduction has enabled us to
(1) obtain statistics encompassing many realizations of ran-

APPENDIx A: STRUCTURE AND STAbIlITy OF
MUlTIPlE EqUIlIbRIA

To obtain equilibria T e and A e as functions of H , (6) - (8)
are first combined to obtain closed expressions for T e , given
by (9a) and (10a). The quadratic equation (9a) has solutions