Power Scaling and Seasonal Changes of Floe Areas in the Arctic East Siberian Sea

Abstract

The cumulative number versus floe area distribution of seasonal sea floes from six satellite images of the Arctic Ocean during the summer breakup and melting is fit by two scale-invariant power law scaling regimes for floe areas ranging from 30 to 28,400,000 m2. Scaling exponents, β, for larger floe areas range from −0.6 to −1.0 with an average of −0.8. Scaling exponents, β, for smaller floe areas range from −0.3 to −0.6 with an average of −0.5. The inflection point between the two scaling regimes ranges from 283 × 102 to 4850 × 102 m2 and generally moves from larger to smaller floe areas through the summer melting season. The stability of the power scaling results is demonstrated for two of the images by dividing each in half and analyzing each half separately, with the result that the scaling exponents and the size of the inflection points are nearly the same for each half as for the whole image. We propose that the two scaling regimes and the inflection between them are established during the initial breakup of sea ice solely by the process of fracture. The distributions of floe size regimes retain their scaling exponents as the floe pack evolves from larger to smaller floe areas from the initial breakup through the summer season, due to grinding, crushing, fracture, and melting. The scaling exponents for floe area distribution are in the same range as those reported in previous studies of Arctic floes and for the single scaling exponents found for crushed and ground geologic materials including streambed gravel, lunar debris, and artificially crushed quartz. The single scaling exponent found for fault gouge falls below the range for floes possibly because the fracturing and grinding process in fault gouge takes place under high confining pressure. A probabilistic model of fragmentation is proposed that generates a single power law scaling distribution of fragment size.