Critical percolation threshold restricts late-summer Arctic sea ice melt pond coverage

Abstract

During the summer, vast regions of Arctic sea ice are covered by meltwater ponds that significantly lower the ice reflectivity and accelerate melting. Ponds develop over the melt season through an initial rapid growth stage followed by drainage through macroscopic holes. Recent analysis of melt pond photographs indicates that late-summer ponds exist near the critical percolation threshold, a special pond coverage fraction below which the ponds are largely disconnected and above which they are highly connected. Here, we show that the percolation threshold, a statistical property of ice topography, constrains pond evolution due to pond drainage through macroscopic holes. We show that it sets the approximate upper limit and scales pond coverage throughout its evolution after the beginning of drainage. Furthermore, we show that the rescaled pond coverage during drainage is a universal function of a single non-dimensional parameter, $\eta$, roughly interpreted as the number of drainage holes per characteristic area of the surface. This universal curve allows us to formulate an equation for pond coverage time-evolution during and after pond drainage that captures the dependence on environmental parameters and is supported by observations on undeformed first-year ice. This equation reveals that pond coverage is highly sensitive to environmental parameters, suggesting that modeling uncertainties could be reduced by more directly parameterizing the ponds' natural parameter, $\eta$. Our work uncovers previously unrecognized constraints on melt pond physics and places ponds within a broader context of phase transitions and critical phenomena. Therefore, it holds promise for improving ice-albedo parameterizations in large-scale models.