This work presents an analytical investigation for a Self-Organized Criticality abelian model that describes basic properties of rainfall phenomena. The knowledge of the exact solution for the probability that a site topples when mass is added to any other site of the lattice leads to a large number properties of the model, including the exponent of the power law that describes presence of the events as function of their magnitude. It is shown that the model belongs to the same universality class of a first model proposed by Dhar and Ramaswamy (DR). However, for finite size lattices, it is found that its exponent is larger than that one for the DR model.
