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from free drift by allowing nonzero ice pressure under converging conditions but,
like free drift, offers no resistance to divergence or shear (Flato and Hibler,
1992
).
The Hibler (
1979
) model uses a viscous-plastic constitutive law, which relates the
strength of the ice interaction to a thickness distribution. This basic formulation,
which still finds wide use, allows the ice strength to be greater in regions of ice con-
vergence and weaker in regions of divergence. Other formulations include the mod-
ified Coulombic law described by Hibler, P. Heil, and V. Lytle (
1998
) and Hibler
and E. Schulson (
2000
).
Snow cover is not included explicitly in the Hibler (
1979
) model; the effects of
snow cover are approximated by setting the ice surface albedo to that of snow when
the surface temperature is below freezing and to that of snow-free ice when the sur-
face is at the melting point. J. Walsh, Hibler, and B. Ross (
1985
) include treatments
of “thick” ice and snow using seven thickness levels. In most sea ice models, heat
calculated via the energy balance is used to melt all of the snow before it is used to
melt ice at the upper surface.
The field of ice-ocean modeling has quickly grown. Such models couple a
dynamic-thermodynamic ice model of the Hibler variety with ocean models of
varying complexity. The first ice-ocean model was that of Hibler and F. Bryan
(
1987
), which coupled the Hibler ice model to the Bryan-Cox multilevel ocean
model (Bryan,
1969
). Other early efforts include A. Semtner (
1987
), G. Fleming
and Semtner (
1991
) and S. Riedlinger and R. Preller (
1991
).
The study of Zhang, Rothrock, and Steele (
2000
) is a good example of the appli-
cation of an ice-ocean model. They examined the response of Arctic sea ice to forc-
ing by the North Atlantic Oscillation (NAO; see
Chapter 11
). The model had a hor-
izontal resolution of 40 km, with twenty-one ocean levels and twelve ice thickness
categories. The model was forced by winds, SAT, specific humidity, and longwave
and shortwave radiation fluxes.
Figure 9.9
shows simulated annual mean ice velocity and mean sea level pressure
fields for the two periods (1979-1988 and 1989-1996), along with corresponding
ice velocity anomaly fields. These two decades characterize the generally low and
high index phases of the NAO, respectively (see
Chapter 4
). Readily seen are large
differences in the shape and intensity of the Beaufort Gyre and Transpolar Drift
Stream. Note the strongly cyclonic anomaly during the high NAO phase (1989-
1996) and the implied increase in the Fram Strait outflow.
Figure 9.10
gives simu-
lated fields of mean annual ice thickness for the two periods and the difference field.
Observations show a pattern of thicker ice off the Canadian Archipelago and north
Greenland coast and thinner ice on the Siberian side of the Arctic (
Figure 7.6
). The
model captures this basic pattern, but over both decades gives unrealistically large
thicknesses along the Alaskan coast. However, useful information is provided by the
difference fields - the model results suggest a general tendency for the ice under the
persistently positive NAO phase of 1989-1996 to have been thinner in the eastern
Arctic and thicker in the western Arctic. These findings support arguments by G.
Holloway and T. Sou (
2002
) that at least part of the observed thinning of the peren-
nial ice cover the central Arctic Ocean in the 1990s as assessed from submarine