What Is the Trajectory of Arctic Sea Ice? - Arctic Sea Ice Decline: Observations, Projections, Mechanisms, and Implications - page 172

We analyze the trajectory of Arctic sea ice from two mod-
els. One is a retrospective coupled ice-ocean model that as-
similates sea ice concentration data and is run for the years
1958-2005. Using the output of this model, we construct
a pair of equations for the evolution of thin ice and thick
ice that exhibits two stable annual cycles: one with ice-free
summers and one with sea ice year-round. The second model
is a coupled global general circulation climate model that
is forced with increasing greenhouse gas and aerosol con-
centrations and is run for the years 1870-2099. This model
attains ice-free summers by the second half of the 21st cen-
tury. We use these models to contrast the influence of exter-
nal forcing versus internal dynamics. We end with a brief
discussion of tipping points and the transition from one state
to another.

Table 2. CCSM3 Sea Ice Thickness Bins
Bin Lower

Limit (m)

Upper
Limit (m)

Designation

0 0.00 0.00 open water

1 >0.00 0.65 thin ice

2 0.65 1.39 thin ice

3 1.39 2.47 thick ice

4 2.47 4.57 thick ice

5 4.57 infinity thick ice

pole displaced over Greenland. The model assimilates open-
ocean sea surface temperature (SST) data using a nudging
method with a 15-day time constant, and sea ice concentra-
tion data using a nudging method that emphasizes the ice
extent and minimizes the effect of observational errors in
the interior of the pack ice [ Lindsay and Zhang , 2006]. The
assimilated data (HadISST [ Rayner et al. , 2003]) consists
of monthly averaged values on a 1 o grid. The effect of the
assimilation of total ice concentration is that the sum of the
model ice concentrations over all the bins (g 1 + … + g 7 ) is
constrained to match (approximately) the observations. The
assimilation of ice concentration also improves the modeled
ice thickness compared to submarine and moored upward
looking sonar data [ Lindsay and Zhang , 2006]. Thus the
PIOMAS ice concentration and ice thickness are in reason-
able agreement with observations. The model is run for 48
years (1958-2005), forced with daily fields of 10 m surface
wind velocities, 2 m air temperature and humidity, precipi-
tation, and downwelling longwave and shortwave radiative
fluxes. These are obtained from the ERA-40 reanalysis for
1958-2001, and from the ECMWf operational analysis for
2002-2005. The daily sea ice thickness distributions com-
puted by the model are then temporally averaged over each
month, and spatially averaged over 6.6 × 10 6 km 2 of the cen-
tral Arctic Ocean shown in figure 1. Thus the end result is
one sea ice thickness distribution (with seven bins) for each
month, 1958 through 2005.
The second model used in this study is the Community
Climate System Model version 3.0 (CCSM3) [ Collins et al. ,
2006]. It is a state-of-the-art fully coupled climate model
composed of four separate models simultaneously simulat-
ing the Earth's atmosphere, ocean, land surface, and sea ice.
The sea ice model has five ice thickness categories plus open
water (Table 2), and a nominal 1 o grid with the pole displaced
over Greenland. The ocean model (POP) is the same as that
used in PIOMAS. The 20th century simulation is forced with
observed CO 2 , CH 4 , nO 2 , solar variability, volcanic sulfate
aerosols, and industrial aerosols. The 21st century simulation
is an Intergovernmental Panel on Climate Change Special

2. MODELS

The first model used in this study is the Pan-Arctic Ice-
Ocean Modeling and Assimilation System (PIOMAS), which
has been used in a wide range of retrospective climate studies
[ Zhang and Rothrock , 2005]. It is based on the parallel ocean
and ice model of Zhang and Rothrock [2003]. It consists of
the Parallel Ocean Program (POP) ocean model developed at
Los Alamos national Laboratory coupled to a multicategory
ice thickness and enthalpy distribution sea ice model [ Zhang
and Rothrock , 2001; Hibler , 1980]. The POP model is a
Bryan-Cox-Semtner type ocean model [ Bryan , 1969; Cox ,
1984; Semtner , 1976] with numerous improvements. The
sea ice model consists of five main components: (1) a mo-
mentum equation that determines ice motion, (2) a viscous-
plastic rheology that determines the internal ice stress, (3) a
heat equation that determines ice temperature profiles and
ice growth or decay, (4) an ice thickness distribution equa-
tion that conserves ice mass, and (5) an enthalpy distribution
equation that conserves ice thermal energy. The model has
seven ice thickness categories plus open water (Table 1), and
a latitude/longitude grid with mean spacing 22 km, with the

Table 1. PIOMAS Sea Ice Thickness Bins
Bin

Lower
Limit (m)

Upper
Limit (m)

Designation

0 0.00 0.10 open water

1 0.10 0.66 thin ice

2 0.66 1.93 thin ice

3 1.93 4.20 thick ice

4 4.20 7.74 thick ice

5 7.74 12.74 thick ice

6 12.74 19.31 thick ice

7 19.31 27.51 thick ice