Modeling the impact of air and water pollutants emitted from industries on rainfall

Rainfall regulates the hydrological cycle on the planet Earth, sustains our ecological system, and provides fresh water to all living beings. In the recent past, a deterioration in rainfall has been observed due to the increased level of pollutants emitted by industries in the environment. The presence of these industrial pollutants in the environment affects the processes of evaporation, condensation, and nucleation, requisite in forming cloud droplets and raindrops. In formulating the model, we categorize the total emissions of industrial pollutants into surface water pollutants and atmospheric pollutants in the environment to assess their effect explicitly on rainfall. We presume the natural formation rate of cloud droplets as a decreasing function of surface water pollutants. It is further assumed that the density of cloud droplets decreases due to atmospheric pollutants; and the surface water pollutants in regional water bodies increase due to the leaching of atmospheric pollutants during rainfall. To analyze the formulated model system, we use the qualitative theory of differential equations. The equilibrium solution is obtained, and its stability properties are discussed. The numerical analysis is performed to substantiate the analytically obtained results of the formulated mathematical model. The obtained results clearly show that industrial pollutants emitted into the environment exert a negative impact on rainfall.