Transition in the fractal geometry of Arctic melt ponds

Abstract

Abstract. During the Arctic melt season, the sea ice surface undergoes a remarkable transformation from vast expanses of snow covered ice to complex mosaics of ice and melt ponds. Sea ice albedo, a key parameter in climate modeling, is determined by the complex evolution of melt pond configurations. In fact, ice-albedo feedback has played a major role in the recent declines of the summer Arctic sea ice pack. However, understanding melt pond evolution remains a significant challenge to improving climate projections. By analyzing area-perimeter data from hundreds of thousands of melt ponds, we find here an unexpected separation of scales, where pond fractal dimension D transitions from 1 to 2 around a critical length scale of 100 m 2 in area. Pond complexity increases rapidly through the transition as smaller ponds coalesce to form large connected regions, and reaches a maximum for ponds larger than 1000 m 2 , whose boundaries resemble space-filling curves, with D ≈ 2. These universal features of Arctic melt pond evolution are similar to phase transitions in statistical physics. The results impact sea ice albedo, the transmitted radiation fields under melting sea ice, the heat balance of sea ice and the upper ocean, and biological productivity such as under ice phytoplankton blooms.

Ising model for melt ponds on Arctic sea ice

“…Within this data set, we further exclude both the smaller ponds with A<15 m 2 which are affected by the discreteness of the lattice, and the larger ponds with A>400 m 2 which are subject to substantial sampling variability because of their rareness. Figure 3(c) compares our Ising model D(A) function (thin solid black curve) with the observed fractal dimension dependence on area for real melt ponds (thick gray data curve) [12]. The model thin black curve is a best fit to the data points in the (A, P)-plane for model ponds, as in [16].…”

“…Area-perimeter analysis of images of melt ponds from SHEBA as well as the 2005 Healy-Oden Trans Arctic Expedition (HOTRAX) has shown that as the ponds grow and coalesce into much larger connected structures they display a transition in fractal geometry [12], evolving from simple Euclidean shapes into complex, selfsimilar regions whose boundaries behave like space-filling curves. The fractal dimension of the boundary curves transitions from 1 to about 2 around a critical area of about 100 m 2 .…”

Object-based detection of Arctic sea ice and melt ponds using high spatial resolution aerial photographs

“…Third, the color of melt ponds may vary between light turquoise and dark blue and are all considered in this paper as melt ponds, since their albedos definitely differ from those ponds that melt through to the ocean's surface so that seawater enters the ponds. Previous studies sometimes labeled these melt holes as deep melt ponds based on directional derivative of the color intensity (Hohenegger et al, 2012), or label them as open water (Lu et al, 2010;Perovich et al, 2002;Renner et al, 2013). Since the albedos of these melt holes are essentially equivalent to sea water, we classify them as open water in this paper.…”

“…Second, pond-like features are often present at the edges of sea ice (i.e., submerged ice) due to the lateral melting or edge erosion of ice, or break-up melt ponds, but previous methods simply ignored these features or combined them with melt ponds (Hohenegger et al, 2012;Inoue et al, 2008;Lu et al, 2010). Third, the color of melt ponds may vary between light turquoise and dark blue and are all considered in this paper as melt ponds, since their albedos definitely differ from those ponds that melt through to the ocean's surface so that seawater enters the ponds.…”

The Effect of Melt Pond Geometry on the Distribution of Solar Energy Under First‐Year Sea Ice

“…Over the course of the melt season, ponds of melt water develop on surface of Arctic sea ice and constitute a significant fraction of the sea ice area, particularly for first-year sea ice (Fetterer & Untersteiner, 1998;Polashenski et al, 2012Polashenski et al, , 2017Rösel et al, 2012). Their geometry becomes more complex, with a transition in fractal dimension as pond area grows (Hohenegger et al, 2012).…”