On reconciling disparate studies of the sea-ice floe size distribution

Abstract

The size distribution of sea-ice floes is an important descriptor of the sea-ice cover. Most studies report that floe sizes follow a power-law distribution over some size range, but the power-law exponents often differ substantially. Other studies report two power-law regimes over different size ranges, or more complicated behavior. We review the construction of power-law floe size distributions and compare the results of previous studies. Differences between studies may be due to spatial and temporal variability of the floe size distribution, sampling variability, inadequacy of the power-law model, or flaws in the mathematical analysis. For a power-law model, the most accurate method for determining the exponent from data is Maximum Likelihood Estimation; least-squares methods based on log-log plots of the data yield biased estimates. After calculating the power-law exponent from data, a goodness-of-fit test should be applied to determine whether or not the power-law model actually describes the distribution of the data. These analysis principles have been described in the literature but have not generally been applied to floe size distributions. Numerical ice-ocean models are beginning to simulate the floe size distribution, which should give further insight into the interpretation of observational studies.