How many parameters are needed to represent polar sea ice surface patterns and heterogeneity?

Abstract. Sea ice surface patterns encode more information than can be represented solely by the ice fraction. The aim of this paper is thus to establish the importance of using a broader set of surface characterization metrics and to identify a minimal set of such metrics that may be useful for representing sea ice in Earth system models. Large-eddy simulations of the atmospheric boundary layer over various idealized sea ice patterns, with equivalent ice fractions and average floe areas, demonstrate that the spatial organization of ice and water can play a crucial role in determining boundary layer structures. Thus, various methods used to quantify heterogeneity in categorical lattice-based spatial data, such as those used in landscape ecology and Geographic Information System (GIS) studies, are employed here on a set of recently declassified high-resolution sea ice surface images. It is found that, in conjunction with ice fraction, patch density (representing the fragmentation of the surface), the splitting index (representing variability in patch size), and the perimeter–area fractal dimension (representing the tortuosity of the interface) are all required to describe the two-dimensional pattern exhibited by a sea ice surface. For surfaces with anisotropic patterns, the orientation of the surface relative to the mean wind is also needed. Finally, scaling laws are derived for these relevant landscape metrics, allowing for their estimation using aggregated spatial sea ice surface data at any resolution. The methods used in and the results gained from this study represent a first step toward developing further methods for quantifying variability in polar sea ice surfaces and for parameterizing mixed ice–water surfaces in coarse geophysical models.