Simulating cumulus clouds based on self-organized criticality

Recently it was shown that self-organized criticality is an important component of the dynamics of cumulus clouds (Najafi et al., 2021). Here we introduce a new algorithm to simulate cumulus clouds in two-dimensional square lattices, based on two important facts: the cohesive energy of wet air parcels and a sand-pile-type diffusion of cloud segments. The latter is realized by considering the evaporation/condensation of air parcels in various regions of the cloud, which enables them to diffuse to the neighboring regions. The results stemming from this model are in excellent agreement with observations reported in the above-cited paper, in which the exponents were determined for two-dimensional earth-to-sky RGB cloud images. The exponents obtained at the lowest condensation level in our model are consistent with the exponents observed in nature. We find that the cloud fields obtained from our model are fractal, with the outer perimeter having a fractal dimension of Df=1.25±0.01. Furthermore, the distributions of the radius of gyration and the loop length follow a power-law function with exponents τr=2.3±0.1 and τl=2.1±0.1, respectively. The loop Green function is found to be logarithmic with the radius of gyration of the loops following the observational results. The winding angle statistic of the external perimeter of the cloud field is also analyzed, showing an exponent in agreement with the fractal dimension, which may serve as the conformal invariance of the system.