Measuring the sea ice floe size distribution

Abstract

Sea ice is broken into floes whose diameters range from meters to a hundred kilometers. This fragmentation affects the resistance of the ice cover to deformation and the melting at floe sidewalls in summer. Floes are broken by waves and swell near the ice edge and, throughout the pack, by isostatic imbalances, thermal cracking, winds, and currents. In winter, they are welded together by freezing. Floe size can be measured by several properties p , for instance, area or mean caliper diameter. Two definitions of floe size distribution seem useful: F ( p ), the fraction of area covered by floes no smaller than p ; and N ( p ), the number of floes per unit area no smaller than p . F ( p ) can be measured by sets other than areas, such as the fraction of a line or of a point set covered by floes no smaller than p . If N behaves like ρ α for small ρ, where ρ is mean caliper diameter, α must be greater than −2 so that the small floes occupy finite area. If −2<α<−1, the perimeter of small floes is infinite. Several summertime distributions have been measured. On a log‐log graph their slopes (local values of α) range from −1.7 to −2.5. One distribution follows a power law; the others have steeper slopes for larger floes and more gradual slopes for smaller floes. Another sampling strategy is to measure the lengths of line segments on floes. The distribution of these chord lengths is equivalent to the distribution of floe diameters. The variance of an estimate of the fraction g of area covered by floes in any size range is g (1 ‐ g ) K −1 , where K is the equivalent number of independent samples. K can be found from the autocovariance of the indicator function for the chosen size range. For line sampling of a narrow range of floe diameters, K is the ratio of the sample length to the floe diameter.