The Ensemble Fractal Dimension of Clouds

A rich history of examining atmospheric phenomena through the lens of scale invariance has provided manyinvaluable insights into Earth's climate. One particular success has been the fractal analysis of clouds,which tells us how the boundary between cloudy and clear air scales with measurement resolution using thefractal dimension. While the fractal dimension of individual clouds is well established, there is a distinctfractal dimension that applies to the total cloud perimeter (summed over all clouds) that has been neglected.Furthermore, a recent theoretical framework (Garrett et. al. 2018) elevates the total cloud perimeter to oneof the primary control knobs on the mean cloud state, providing important constraints on climatic cloudfeedback.

Despite the potential of this framework, the total cloud perimeter scaling law is unknown. Herein wepropose a physically-motivated scaling law based on a similarity assumption. We then measure the totalcloud perimeter using several geostationary and polar-orbiting satellites with varying resolutions.