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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 surface patterns, with equivalent ice fraction and average floe area, demonstrate that the spatial organization of ice and water can play a crucial role in determining boundary-layer structure. Thus, different methods to quantify heterogeneity in categorical lattice spatial data, such as those done in landscape ecology and Geographic Information System (GIS) studies, are used here on a set of high-resolution, recently-declassified sea ice surface images. It is found that, in conjunction with ice fraction, the patch density (representing the fragmentation of the surface), the splitting index (representing the variability in patch size), and 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. Furthermore, for surfaces with anisotropic patterns, the orientation of the surface relative to the mean wind is needed. Furthermore, scaling laws are derived for these relevant landscape metrics to estimate them from aggregated spatial sea ice surface data at any resolution. The methods used and results gained from this study are a first step towards further development of methods to quantify the variability of non-binary surfaces, and for parameterizing mixed ice-water surfaces in coarse geophysical models.