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Lena
MacKenzie
100
100
CHASM
NOAH
CLM
VIC
ECMWF
80
80
60
60
40
40
20
20
0
0
J
FM
A
M
J
J
A
SOND
J
FM
A
M
J
J
A
SOND
Ob
Yenesi
100
100
80
80
60
60
40
40
20
20
0
0
J
FM
A
M
J
J
A
SOND
J
FM
A
M
J
J
A
SOND
Figure 9.8. Monthly mean evapotranspiration (mm per month, positive upwards in
this figure) for the four major Arctic-draining watersheds (the Lena, the Mackenzie,
the Ob, and the Yenesi) from five land surface models driven by data from the ERA-
40 atmospheric reanalysis for the 1980-2001 period (from Slater et al., 2007 , by
permission of AGU).
model (dynamic meaning that ice motion is simulated) is that of Parkinson and
Washington ( 1979 ). Four vertical layers are represented within each grid cell: a
mixed layer ocean, an ice layer, a snow layer, and an atmospheric boundary layer. At
the ice-ocean interface, ocean currents provide water stress and a constant dynamic
topography (recall that because of density variations, the ocean surface is not
entirely flat). A constant ocean heat flux is also used. Atmospheric heat fluxes and
surface stresses are applied at the air-ice interface. Ice dynamics is treated as free
drift (see Chapter 7 ). The basic Parkinson and Washington ( 1979 ) thermodynamics
approach is still widely used.
Hibler ( 1979 ) developed the first widely used dynamic-thermodynamic model
which included the effects of internal ice stress (floe-to-floe interactions). The
model, driven by observed winds and near surface air temperature, was able to
reproduce observed patterns of ice drift and ice thickness. The model incorporates
the equations of continuity for ice thickness and concentration. In early versions of
the model, ice growth rates were prescribed. Hibler ( 1980 ) subsequently developed
formulations whereby the growth rates are calculated from a heat budget; Hibler
also included a variable ice thickness distribution model.
All dynamic-thermodynamic models of the Hibler variety contain a constitutive
law, which relates the ice deformation to the forces applied. A variety of formula-
tions have been examined. For example, the “cavitating fluid” approximation differs
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