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Prognostic floe size distributions are being integrated into the next generation of large-scale sea ice models (Bennetts et al., 2017; Horvat and Tziperman, 2015; Roach et al., 2018a; Zhang et al., 2015, 2016). Early results show that the floe size distribution affects ice concentration and volume close to the ice edge in the marginal ice zone, where ocean waves regulate floe sizes and floes are generally the smallest, meaning they are prone to melting in warmer seasons (Steele, 1992). However, at present the only field data available to validate and improve the models are empirical distributions derived for pack ice spanning several orders of magnitude (Toyota et al., 2016) and none resolve floes below the metre scale.

The break up of pack ice often resembles fractal behaviour similar to many brittle materials (Gherardi and Lagomarsino, 2015). It has been argued that the exceedance probability of the characteristic floe size, D, expressed as the number of floes, follows a power law N(D)∝D-α, where the scaling exponent is α=2 if a fractal behaviour is assumed (Rothrock and Thorndike, 1984).

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Most of the previous observations of the floe size distribution in the marginal ice zone (noting that no observations are in pancake ice conditions) conform to a truncated power law (Stern et al., 2018), with the α value varying among studies depending on season, distance from the ice edge and a range of measured diameters. Some observations of floe size distributions have been interpreted using a split power law (Toyota et al., 2016), with a mild slope for smaller floes and a steeper one for larger floes. In most cases, the sharp change in slope is an artefact due to finite size effects (Stern et al., 2018), although in few instances the split power law behaviour might be consistent with the data (Stern et al., 2018). The truncated power law cannot explain two different slopes in the probability density function n(D), suggesting that different mechanisms might in fact govern the distributions for small and large floes (Steer et al., 2008).

The power law behaviour has been verified for most cases but its universality has not been demonstrated yet (Horvat and Tziperman, 2017). Scaling parameters are typically estimated on the log-log plane with a least square fit, which leads to biased estimates of α, and, as noted by Stern et al. (2018), without rigorous goodness-of-fit tests. In comparison, Herman et al. (2018) examined the size distribution of floes under the action of waves in controlled laboratory experiments, by analysing the probability density function n(D), which revealed a fractal response due to an arbitrary strain (a power law) superimposed on a Gaussian break-up process induced by the waves. The interplay of these mechanisms is hidden in the floe number exceedance probability.

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Existing observations do not provide quantitative descriptions of the floe size distribution for pancake ice floes, which form from frazil ice under the continuous action of waves and thermodynamic freezing processes (Roach et al., 2018b; Shen et al., 2004). This is important, for example, during the Antarctic winter sea ice expansion, when hundreds of kilometres of ice cover around the Antarctic continent is composed of pancake floes of roughly circular shape and characteristic diameters of 0.3-3 m (Worby et al., 2008). Pancake floes represent most of the Antarctic sea ice annual mass budget (Wadhams et al., 2018). Moreover, in the Arctic, pancakes are becoming more frequent than in the past due to the increased wave intensity associated with the ice retreat (Roach et al., 2018b; Wadhams et al., 2018).

Shen and Ackley (1991) reported pancake floe sizes from aerial observations collected during the Winter Weddell Sea Project (July 1986), showing that pancake sizes increase with distance from the ice edge, from 0.1 m in the first 50 km up to ≈1 m within 150 km from the edge (but without investigating the floe size distribution). They attributed this to the dissipation of wave energy with distance to the ice-covered ocean and proposed a relationship between wave characteristics, mechanical ice properties and pancake size (Shen et al., 2004). More recently, Roach et al. (2018b) used camera images acquired from SWIFT buoys deployed in the Beaufort Sea (Sea State cruise, October-November 2015) to quantify the lateral growth of pancakes and their welding. A correlation between wave properties and the size of relatively small pancakes (up to 0.35 m) was confirmed.

To our knowledge, the pancake floe size distribution has yet to be characterized, noting that, although Parmiggiani et al. (2017) developed an algorithm for pancake floe detection, they did not provide a quantitative indication of the shape and size of the floes. Here, a new set of images from the Antarctic marginal ice zone is used to measure the shape of individual pancakes to infer their size distribution.

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