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. We explore several statistical properties of the observed and simulated Arctic sea-ice lead fraction, as well as the statistics of simulated Arctic ocean–atmosphere heat fluxes.First we show that the observed lead fraction in the Central Arctic has a monofractal spatial scaling, which we relate to the multifractal spatial scaling present in sea-ice deformation rates.We then show that the relevant statistics of the observed lead fraction in the Central Arctic are well represented by our model, neXtSIM.Given that the heat flux through leads may be up to 2 orders of magnitude larger than that through unbroken ice, we then explore the statistical properties (probability distribution function – PDF – and spatial scaling) of the heat fluxes simulated by neXtSIM.We demonstrate that the modelled heat fluxes present a multifractal scaling in the Central Arctic, where heat fluxes through leads dominate the high-flux tail of the PDF. This multifractal character relates to the multi- and monofractal character of deformation rates and the lead fraction. In the wider Arctic, the high-flux tail of the PDF is dominated by an exponential decay, which we attribute to the presence of coastal polynyas.Finally, we show that the scaling of the simulated lead fraction and heat fluxes depends weakly on the model resolution and discuss the role sub-grid-scale parameterisations of the ice heterogeneity may have in improving this result.

On the statistical properties of sea-ice lead fraction and heat fluxes in the Arctic