Sensitivity of Arctic Sea Ice Thickness to Intermodel Variations in the Surface Energy Budget - Arctic Sea Ice Decline: Observations, Projections, Mechanisms, and Implications - page 75

thickness and concentration, such as cloud radiative forc-
ing, snow cover, melt pond fraction, upper ocean stability,
surface wind stress, etc. While consideration of these inputs
and their uncertainties is clearly necessary, their impact on
thickness depends on the intrinsic sensitivity of thickness to
errors in inputs. furthermore, the intrinsic sensitivity deter-
mines the extent to which incremental improvement in the
inputs will lead to better thickness simulations.
In this chapter, we examine the intrinsic sensitivity of
sea ice thickness to errors in surface energy fluxes using
the 20c3M simulation archive and a diagnostic thermody-
namic equation. our goal is to describe the sensitivity in the
simplest possible terms, foregoing as much model-specific
complexity as possible to achieve an understanding in terms
of basic physical principles applicable to all climate models.
In this simple analysis, the behavior of thickness sensitivity
can be understood as a consequence of the inverse relation-
ship between thickness and summertime net energy gain, so
that the thickness error associated with an error in, say, in-
solation is strongly dependent on the true value of the sum-
mertime energy gain. this result is analogous to the global
temperature sensitivity to co 2 doubling found by Roe and
Baker [2007] [see also Bitz , this volume], in which the in-
verse relationship between temperature sensitivity and net
climate feedback leads to a long-tailed distribution of tem-
perature sensitivity, or a poorly constrained upper bound on
global warming.
further motivation for this research comes from the is-
sue of model credibility. the credibility of climate model
projections of Arctic sea ice decline is often judged by the
models' ability to simulate present-day sea ice conditions.
While success in present-day simulation is a logical crite-
rion, it is possible that successful simulations have been
achieved through nonphysical “tuning” which masks severe
model physics deficiencies. In that case, simulation success
confers a false confidence in future projections, an undesir-
able outcome when projections are used as input for policy
decisions. As discussed by Eisenman et al. [2007] (herein-
after referred to as EuW) [see also DeWeaver et al. , 2008]
(hereinafter referred to as dHH), nonphysical tuning could
be manifested as an incompatibility between the intermodel
ranges of thickness and surface energy fluxes. According to
EuW's calculations, the ensemble spread of 40 W m -2 in
downwelling longwave fluxes found in the 20C3M ensemble
should produce an ensemble sea ice thickness spread which
greatly exceeds the actual spread. they offer this discrep-
ancy as evidence that nonphysical tuning of sea ice albedo
has been used to artificially compress the spread of thickness
values. In our analysis, the ensemble ranges of thickness
and surface energy flux are inherently compatible, without
the need for nonphysical tuning. of course, the simplifying

assumptions made in the diagnostic equation preclude a de-
finitive judgment of state-of-the-art climate models. Yet it is
reassuring that the simple calculation can capture the sensi-
tivity of the 20c3M ensemble in an approximate sense.
the remainder of the chapter is divided into four sections.
Section 2 lays out the theoretical framework of the diagnos-
tic analysis and shows how energy balance and surface flux
continuity can be used to obtain an equation for sea ice thick-
ness, which is used in section 3 to reconcile the discrepancy
between flux and thickness spread found by EUW. Section 4
uses the equation diagnostically to relate the spread of thick-
ness in the 20c3M ensemble to the corresponding spread
in surface fluxes and shows that the flux-derived thickness
spread is consistent with the actual spread. Surface fluxes for
the ensemble are compared with available observations, and
the spread in the summertime energy balance is found to be
strongly related to albedo and surface temperature. conclu-
sions follow in section 5.

2. tHEorEtIcAl frAMEWork

the diagnosis presented here and by EuW is based on
a variant of Thorndike 's [1992] (hereinafter referred to as
t92) simple model, shown schematically in figure 1. the
ice is represented as a motionless slab with thickness h , sur-
face temperature T (in celsius degrees), and bottom tem-
perature 0 ° c, taken as the approximate freezing temperature
of seawater. the year is partitioned into ice growth and ice
melt seasons of length τ G and τ M , respectively, with no inso-
lation during the growth season and a constant mean insola-
tion during the melt season (a square-wave seasonal cycle
of insolation). T = 0 during the melt season and T during
ice growth satisfies a heat conduction equation in which the
net surface heat loss via longwave radiation is balanced by
upward conductive heat flux through the ice.

Figure 1. Schematic depiction of sea ice and energy fluxes for
equations (1), (2), and (3) in sections 2 and 3.