Simple Rules Govern the Patterns of Arctic Sea Ice Melt Ponds

Climate change, amplified in the far north, has led to rapid sea ice decline in recent years. In the summer, melt ponds form on the surface of Arctic sea ice, significantly lowering the ice reflectivity (albedo) and thereby accelerating ice melt. Pond geometry controls the details of this crucial feedback; however, a reliable model of pond geometry does not currently exist. Here we show that a simple model of voids surrounding randomly sized and placed overlapping circles reproduces the essential features of pond patterns. The only two model parameters, characteristic circle radius and coverage fraction, are chosen by comparing, between the model and the aerial photographs of the ponds, two correlation functions which determine the typical pond size and their connectedness. Using these parameters, the void model robustly reproduces the ponds’ area-perimeter and area-abundance relationships over more than 6 orders of magnitude. By analyzing the correlation functions of ponds on several dates, we also find that the pond scale and the connectedness are surprisingly constant across different years and ice types. Moreover, we find that ponds resemble percolation clusters near the percolation threshold. These results demonstrate that the geometry and abundance of Arctic melt ponds can be simply described, which can be exploited in future models of Arctic melt ponds that would improve predictions of the response of sea ice to Arctic warming.

Figure 1

(a) A photograph of melt ponds taken on August 7, 1998 during the SHEBA mission. (b) A binarized version of the same image. (c) A void model with a typical circle radius of $r_0=1.8\mathrm{m}$, and a coverage fraction of $\rho =0.31$.

Figure 2

(a) An example of the two-point correlation function $C(l)$ for melt ponds shown on a semilog plot. Dashed black lines represent fits to a small length scale exponential and a large length scale exponential. The inset shows $C(l)$ before and after a fit to the large length scale exponential has been subtracted. (b) A comparison between the two-point correlation function for ponds from 1998 and 2005 (circles), and the void model (dashed line). Ponds on all dates show a similar scale matched by the void model using $r_0=1.8\mathrm{m}$. (c) A comparison between the cluster correlation function $g(l)$ for August 7, 1998 (red circles), August 14, 2005 (yellow circles), and the void model using the same $r_0$ as in panel (b) (black dashed lines). Both model lines use $\rho =0.31$, and the difference between them is due only to differing simulated image sizes. The image size for 1998 is indicated by a red arrow and the image size for 2005 is indicated by a yellow arrow. The fact that the exponential cutoff is set by the image size indicates that the ponds are roughly at the percolation threshold. The inset shows an independent estimation of the percolation threshold. Red points show the probability of finding a spanning cluster in the void model implemented on a grid the same size and resolution as the SHEBA images. The probability of finding a spanning cluster increases from 0 to 1 between $\rho =0.28$ and $\rho =0.31$.

Figure 3

(a) A comparison between the fractal dimension of pond boundaries for different dates after pond drainage from 1998 (red curves), 2005 (yellow curve), and the void model with $r_0$ and $\rho$ the same as in Fig 2 (black dashed curve). Examples of ponds (below the curve) and voids (above the curve) of various sizes are also shown. (b) Size distribution for ponds on August 7, 1998 (red dots), ponds on August 14, 2005 (yellow dots), and the void model (black dashed line).