Mapping cumulus clouds to scale invariant rough surfaces

TL;DR

This paper explores the connection between cumulus clouds and self-similar rough surfaces, analyzing their statistical properties and revealing their unconventional non-Gaussian self-affine nature, which challenges existing hyper-scaling relations.

Contribution

It establishes a novel link between cloud structures and scale-invariant rough surfaces, demonstrating their non-Gaussian, self-affine characteristics through detailed statistical analysis.

Findings

The cloud surface is a non-Gaussian self-affine random surface.

It violates Kondev hyper-scaling relations.

The study connects cloud thickness to intensity fluctuations.

Abstract

Motivated by a recent observation on the self-organized criticality of cumulus clouds (Phys. Rev E 103, 052106, 2021) we study their connection to self-similar rough surfaces, in which $f\equiv \log I$ plays the role of the main field, where $I$ is the intensity of the received visible light. By simulating the light scattering based on a coarse-grained phenomenological model in a two-dimensional cloud, we argue the possible connection of $I$ to the actual cloud thickness. Although in the vertical incident light $f$ is proportional to the cloud thickness, in the general case it is complected. We study the statistical properties of observational data for $f$ with a focus on the conventional exponents of this scale-invariant rough surface. By calculating the roughness exponents, and comparing them with other exponents like the fractal dimension of loops, the distribution function of the radius of gyration and loop lengths, and the exponent of the green function, we prove that this surface is unconventional in the sense that it is the non-Gaussian self-affine random surface which violates the Kondev hyper-scaling relations.