Simulating Cumulus Clouds based on Self-Organized Criticality

Recently it was shown that self-organized criticality is an important ingredient of the dynamics of cumulus clouds (Physical Review E, 103(5), p.052106, 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 sandpile-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 the observational results reported in the above-cited paper, where the exponents have been obtained for the two-dimensional earth-to-sky RGB images of clouds. The exponents that are obtained at the lowest condensation level in our model are consistent with the observational exponents. We observed that the cloud fields that we obtain from our model are fractal, with the outer perimeter having a fractal dimension of $D_f = 1.25 \pm 0.01$. Furthermore, the distributions of the radius of gyration and the loop length follow a power-law function with exponents $τ_r = 2.3 \pm 0.1$ and $τ_l = 2.1 \pm 0.1$, 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.