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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. 

Arctic amplification (AA) is a coupled atmosphere-sea ice-ocean process. This understanding has evolved from the early concept of AA, as a consequence of snow-ice line progressions, through more than a century of research that has clarified the relevant processes and driving mechanisms of AA. The predictions made by early modeling studies, namely the fall/winter maximum, bottom-heavy structure, the prominence of surface albedo feedback, and the importance of stable stratification have withstood the scrutiny of multi-decadal observations and more complex models. Yet, the uncertainty in Arctic climate projections is larger than in any other region of the planet, making the assessment of high-impact, near-term regional changes difficult or impossible. Reducing this large spread in Arctic climate projections requires a quantitative process understanding. This manuscript aims to build such an understanding by synthesizing current knowledge of AA and to produce a set of recommendations to guide future research. It briefly reviews the history of AA science, summarizes observed Arctic changes, discusses modeling approaches and feedback diagnostics, and assesses the current understanding of the most relevant feedbacks to AA. These sections culminate in a conceptual model of the fundamental physical mechanisms causing AA and a collection of recommendations to accelerate progress towards reduced uncertainty in Arctic climate projections. Our conceptual model highlights the need to account for local feedback and remote process interactions within the context of the annual cycle to constrain projected AA. We recommend raising the priority of Arctic climate sensitivity research, improving the accuracy of Arctic surface energy budget observations, rethinking climate feedback definitions, coordinating new model experiments and intercomparisons, and further investigating the role of episodic variability in AA.