A random discontinuous model of sea ice motion

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Abstract
The rate at which the sea ice pack spreads apart, exposing the warm ocean to the cold atmosphere, controls the air‐sea heat exchange in the Arctic and the production of ice mass. The rate of spreading, or opening, can be estimated from observations of ice motion, using a model of the ice pack which accounts for the random manner in which the ice is broken into rigid pieces. In a region intersected by many cracks, some cracks will typically be opening while others are closing. In this case the total of the openings will exceed the average divergence of the region. A few measurements of the ice motion cannot resolve the openings at each crack, so that any estimate of opening will be accompanied by estimation errors. The random model adopted here imagines the leads to be distributed according to the Poisson distribution and the relative displacements at any crack to be Gaussian. Under these assumptions it is determined how the total opening is related to the average deformation, and how this relationship depends on the size of the region and on the number of points used to determine the average deformation.

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