The thickness variable in sea-ice models

The thickness distribution function is considered a fundamental state variable for sea-ice. However, certain assumptions are implicit in its use. Based largely on observations, we estimate upper and lower bounds on the spatial scale for which the usual interpretation of the thickness distribution function is valid. These scales turn out to be similar to 200 km and similar to 10 km respectively for central Arctic conditions, although the upper bound is expected to decrease near coastlines and open-water boundaries. At scales larger than the upper bound real geophysical variations of the thickness distribution occur, violating the assumption of homogeneity. At scales smaller than the lower bound, the distribution function is not sufficiently well sampled to ensure that it varies smoothly in space.