Effects of aerosols in making artificial rain: a modeling study

Abstract

Rain is an important phenomenon occurring in nature. Nowadays, in some places across the world, less amount of rain is observed, which affects human population in several ways, like shortage of drinking water, less production from agriculture fields, increase in pollution level, etc. Keeping this point in view, in this paper, a mathematical model for making artificial rain is proposed and analyzed. In the modeling process, it is assumed that water vapors are continuously formed in the atmosphere and are not condensed enough to form clouds. Further, it is assumed that aerosols (mixture of two or more) are introduced in the atmosphere to increase the process of nucleation of cloud droplets from water vapors and changing them into raindrops. The qualitative analysis of the proposed model is presented using stability theory of differential equations. It is found that model exhibits only one nonnegative equilibrium. The sufficient conditions for stability of the equilibrium have been obtained. Numerical simulation is carried out to see the effect of key parameters on the process leading to rainfall.