Toward less subjective metrics for quantifying the shape and organization of clouds

Abstract. As clouds sizes and shapes become better resolved by numerical climate models, objective metrics are required to evaluate whether simulations satisfactorily reflect observations. However, even the most recent cloud classification schemes rely on quite subjectively defined visual categories that lack any direct connection to the underlying physics. The fractal dimension of cloud fields has been used to provide a more objective footing. But, as we describe here, there are a wide range of largely unrecognized subtleties to such analyses that must be considered prior to obtaining meaningfully quantitative results. Methods are described for calculating two distinct types of fractal dimension: an individual fractal dimension D_i representing the roughness of individual cloud edges, and an ensemble fractal dimension D_e characterizing how cloud fields organize hierarchically across spatial scales. Both have the advantage that they can be linked to physical symmetry principles, but D_e is argued to be better suited for observational validation of simulated collections of clouds, particularly when it is calculated using a straightforward correlation integral method. A remaining challenge is an observed sensitivity of calculated values of D_e to subjective choices of the reflectivity threshold used to distinguish clouds from clear skies. We advocate that, in the interests of maximizing objectivity, future work should consider treating cloud ensembles as continuous reflectivity fields rather than collections of discrete objects.