Uncovering the fractal nature of water vapor distribution above the surface of the earth

Abstract

Fractals have been at the heart of geophysical and geospatial studies in the recent past. We explore the fractal character of water vapor distributions above the surface of the Earth as a function of both image resolution (number of pixels) and moisture content percentile and study the emergent scaling properties. The percolation phenomena associated with the vapor distribution clusters has been studied for both the cases. For our analysis, computational methods and algorithms have been used to derive the physically relevant quantities such as fractal dimension, number of clusters, and size of the largest cluster. The box counting method, used to calculate the fractal dimension, unravels a potential multi-fractal character of the data. We also test the applicability of Korcak’s law on our system and determine the quality of the fit using the Kolmogorov–Smirnov statistic. We show that the fractal character of the distribution is exact as a function of image resolution and approximate in some regimes as a function of the vapor percentile.