## The momentum balance

Detailed reviews of sea ice dynamics and kinematics are given by Thorndike (1986) and Hibler (1986). The motion of sea ice can be described by a momentum balance:

The term on the left side is the time change in momentum (i.e. acceleration), where m is the ice mass per unit area and U is the ice velocity. The first term on the right side is the stress due to the Coriolis force, where f is the Coriolis parameter and k is a unit vector normal to the surface. Ta and Tw are air and water stresses, and F is the internal ice stress, which describes floe-to-floe (ice) interaction. The final term, mgVH describes ocean tilt, where H is the dynamic height of the sea surface and g is gravitational acceleration (because of regional density variations in the ocean, the ocean surface is not flat, and this has to be accounted for in the momentum balance).

The relative magnitudes of the momentum balance terms vary seasonally and spatially. The dominant terms, however, are the air and water stresses, the Coriolis force, and ice interaction (Hibler, 1986). While ice interaction can be large in winter and near coasts, in summer and away from coasts the term is often small. In these situations it is appropriate to consider the pack ice to be in a state of "free drift" (McPhee, 1980).

Nansen (1902) was the first to observe that on a day-to-day basis the pack ice generally moves at about 2% of the surface wind speed and 30° to the right of the wind velocity vector. Zubov (1945) made similar observations. Using data from the Arctic Ice Dynamics Joint Experiment and the IABP, Thorndike and Colony (1982) developed a linear regression model to show that away from coasts typically 70% of the variance in ice motion at daily to monthly time scales is explained by the local surface geostrophic wind. On average, the ice moves 8° to the right of the geostrophic wind direction and at 0.008 of its speed. However, strong seasonality occurs in the mean drift angle, ranging from 5° in winter to 18° in summer. In turn, the wintertime scaling factor is approximately 0.007, increasing in summer to about 0.011. Serreze et al. (1989), using a longer data record, obtained similar results.

Seasonal variations in the characteristics of ice drift, such as observed by Serreze et al. (1989), are in part attributable to changes in the magnitude of the internal ice stress term. While the inclusion of internal stresses does not generally destroy the linear relationship between ice velocity (U) and the geostrophic wind (G), it is manifested by a change in the ratio | U | /1G | and the turning angle (Moritz, 1988). Typically, both are reduced. The stability of the atmosphere also has an impact (Thorndike and Colony, 1982). Given the same geostrophic wind, increased low-level stability in winter acts to reduce the surface wind stress and to increase the turning angle between the geostrophic wind and the wind stress vector (Albright, 1980).

On annual and longer time scales, variations in ice motion are approximately 50% wind driven and 50% current driven. Because winds are highly variable, their forcing tends to cancel out on longer time scales, so that relatively steady current effects play a stronger role.

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