Power Scaling and Seasonal Evolution of Sea-Ice Floe Area Distribution in the Weddell Sea, Antarctica

The size distribution of sea-ice floes and its evolution during the Antarctic summer season and a model of fragmentation that generates a power scaling distribution of fragment sizes are the subject of this study. This topic is of relevance to marine vessels that encounter floes, to the calculation of sea ice albedo, to the determination of Antarctic heat exchange which is strongly influenced by ice concentrations and the amount of open water between floes, and to photosynthetic marine organisms which are dependent upon sunlight penetrating the spaces between floes.

Floe areas ranging from 7 x 10⁴ to 200,000 x 10⁴ m² were measured using ArcGIS to analyze images from NASA'S Landsat 7 satellite. The cumulative number versus floe area distribution of seasonal ice floe from four images in the Weddell Sea during the summer breakup and melting (November-February) are well fit by two scale-invariant power scaling regime. Scaling exponents for larger floe areas range from -1.5 to -1.7 with an average of -1.6. Scaling exponents for smaller floe areas range from -0.8 to -0.9 with an average of -0.85. The inflection point between the two scaling regimes range from 68 x 10⁶ m² to 155 x 10⁶ m² and generally moves from larger to smaller floe areas through the summer season.

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 distribution 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 slightly larger than those reported by Geise, Barton, and Tebbens (2016) for Arctic floes; larger floe areas -.06 to -1.0 and smaller floe areas -0.3 to -0.6. The scaling exponents for floe area distribution in the Weddell Sea are similar to those reported in previous studies; -1.4, Lensu (1990); and -1.4 to -1.8, Toyota, Haas, and Tamura (2011) for single power scaling regimes; and -0.9 and -1 to -2 for two power scaling regimes, Steer, Worby, and Heil (2008).

A probabilistic model for fragmentation, presented in Geise, Barton, and Tebbens (2016), which generates a power scaling distribution of fragment size is applicable to our study.