Studying the effectiveness of cloud seeding on enhancing precipitation

Lack of rain is one of the problems that faces countries around the world. Not only seeking solutions, but also improving these solutions is always on the agenda of these countries. Cloud seeding process is considered one of the effective solution to increase artificial rainfall. This research constructed a mathematical model that simulate the dynamics of the process. The assumption on which the model is based is to introduce a conducive mixture of aerosol chemicals into the environment at a rate proportional to the water vapor formation density rather than being introduced continuously into the atmosphere. The constant induction of the aerosol chemical, when the atmosphere lacks sufficient vapor densities, wastes the chemical, which adds more expenses to the process and pollutes the environment. Hence, our assumption takes into consideration avoiding polluting the environment with the constant induction of the aerosol chemical, avoiding wasting the conducive mixture when the atmosphere lacks vapor density, and reducing the expenses of the process. The theoretical analysis of the model reveals the existence of one critical point. On the other hand, the linear stability analysis, with the aid of Descartes’ rule of signs, confirmed the local asymptotic stability of this point. Global stability is also discussed via Lyapunov’s stability theory, and sufficient conditions were obtained. Finally, the numerical simulations conducted supported the analytical findings.