  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 $\tau_r = 2.3 \pm 0.1$ and $\tau_l = 2.1 \pm 0.1$,
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.
