A stochastic model for making artificial rain using aerosols

In this paper, a nonlinear deterministic mathematical model along with its stochastic version for artificial rain is proposed and analyzed. We have considered three dynamical variables in the modeling process; namely (i) density of cloud droplets, (ii) density of raindrops, and (iii) concentration of mixture of conducive aerosols. It is assumed that the cloud droplets are continuously formed in the atmosphere at a constant rate but its conversion into raindrops does not take place in the same proportion. The artificially introduced aerosols increase the rate of formation of raindrops from cloud droplets. These aerosols are introduced in the regional atmosphere at a rate proportional to the density of cloud droplets. The proposed model is analyzed using stability theory of differential equations in deterministic as well as stochastic environment. Numerical simulation is performed to see the effect of important parameters on the process leading to rainfall.