Sensitivity of Arctic Sea Ice Thickness to Intermodel Variations in the Surface Energy Budget - Arctic Sea Ice Decline: Observations, Projections, Mechanisms, and Implications - page 78

to-model variation in surface fluxes, which, in turn, should
produce an intermodel spread of h values approximated by
the above formula (for simplicity we consider the impact of
annual mean flux errors, although flux errors and thickness
sensitivity are expected to have strong seasonality). In an
unbiased ensemble in which the ensemble mean values of W
and S are close to their real-world counterparts, (3) expresses
the expected relationship between flux errors and thickness
errors.
EuW use (3) to estimate the ensemble spread in h which
should occur as a result of cloud-induced longwave flux
errors, which they estimate to be about df = ±20 W m -2 .
Assuming t M = t G and ensemble mean S = 22 W m -2 and
W = -162 W m -2 (values taken from t92), this range implies
an h range from 1 to 39 m, a full order of magnitude larger
than the range of 1 to 4 m which they find in the spread
of mean Arctic sea ice thickness over the 20c3M coupled
model ensemble. to account for this order of magnitude dis-
crepancy, they propose that modelers must be adjusting S by
tuning sea ice albedo. following t92, they use F SW ¯ = 100 W
m -2 so that with F SW = (1- a) F SW ¯ an albedo decrease of 0.1
yields a 10 W m -2 increase in S . thus, a mean thickness of
39 m could be corrected to 6 m through a decrease of 0.1 in
surface albedo. If modelers apply these albedo adjustments
to avoid excessive thickness, the spread in h is compressed
through a nonphysical relationship between cloud-induced
longwave flux and sea ice albedo. Such spread compression
is clearly quite misleading if models are evaluated according
to their ability to produce a reasonable mean Arctic sea ice
thickness in the present-day climate.
fortunately, the order-of-magnitude discrepancy can
be resolved by considering the different lengths of the ice
growth and ice melt seasons. Melting in the 20c3M ensem-
ble, much like in reality, occurs only from May to August
so that t G / t M » 2. to maintain the values of T G = -30.8°c
and h = 2.8 m assumed by EuW (following t92) with a
growth season that is twice the length of the melt season
would require an average melt season surface flux S = - kT G /
h ×(t G /t M ) of 44 W m -2 . With S = 44 W m -2 , W = -162 W m -2 ,
and d F = ±20 W m -2 , (3) yields a thickness range of 1 to 6
m, in qualitative agreement with the actual ensemble spread.
thus, there is no need to assume a nonphysical relationship
between longwave cloud forcing and sea ice albedo to rec-
oncile the ranges of h and d F , provided that the ensemble
mean S value is close to 44 W m -2 .
for the growth season ( W ) and melt season ( S ) flux values
assumed here, much of the ice thickness spread in h implied
by (3) comes from the variation of the flux error (d F ) in the
denominator, the expected spread in h approaching infinity
when d F approaches - S . This flux error causes a singular-
ity because it reduces the summertime energy gain to zero,

which implies zero wintertime conductive heat loss in (1)
resulting in infinite thickness. Thus, the ensemble mean net
summer flux S is the critical factor in determining the range
of h values corresponding to the ensemble range of flux er-
rors, at least in this simple diagnostic analysis.

4. 20c3M SurfAcE EnErGy fluxES And
flux-dErIVEd tHIcknESS

4.1. Ensemble Spread of Flux-Derived Thickness

With this insight, we consider the multimodel 20c3M en-
semble, applying a modified version of the simple model to
relate the spread in h to the ensemble spread in surface fluxes.
We calculate a diagnostic thickness h D for each model using
area-averaged fluxes and temperatures for grid points north
of 70°n in which 1980-1999 climatological September sea
ice fraction for that model is at least 85%. the diagnostic
thickness equation is derived from (1) and (2) but includes a
complete surface energy budget:

h D = - kT G ( t G / t M )
S

,

(4)

where

S º ( F SW + F LW + F SL ) M + R (t G + t M )/t M .

(5)

F SL is the sum of latent and sensible heat flux from the surface
and R is the annual mean energy budget residual (calculated
as minus the annual mean sum of surface fluxes), including
ocean heat flux convergence, energy transport by ice motion,
and any error in the model budgets (variables given in table
1). The presumption in (1) is that the net energy flux from
the ice is negative (out of the ice), while (2) is an annual
mean budget in which S is a mean over the months when (1)
does not apply, i.e., when the surface flux is positive. Thus
( ) M is the average for May, June, July, and August (MJJA),
the months of positive surface flux for all but two models
(models 1 and 2 in figure 3a, discussed further in section
4.2; similar results were obtained using a JJA average). If
desired, an equation analogous to (3) relating thickness to
the ratio of summer and winter energy fluxes can be formed
by combining (5) with an energy budget equation like (2) but
including all surface fluxes and the budget residual R in (5).
However, this equation is unnecessarily complicated, since
the spread in (1) is determined primarily by the spread in Ŝ ,
as shown below.
figure 3a compares h D with the coupled model simulated
1980-1999 mean ice thickness over the same grid points.
Model output is obtained from the Program for climate