A Mathematical Model to Unravel the Acid Rain Impact on the Growth of Plant Biomass

Abstract

Acid rain, characterized by precipitation containing acidic components such as sulphuric and nitric acid, poses a serious environmental threat. It is caused by the release of acid-forming gases from sources such as vehicular exhaust, industrial emissions, fossil fuel combustion, and volcanic eruptions. Acid rain has detrimental effects on ecosystems, particularly on plant biomass. This study presents a nonlinear six-dimensional mathematical model designed to analyze the impact of acid rain on plant growth. The model examines interactions between key factors, including human population growth, acid-forming gases, atmospheric water droplets, acid rain, and plant biomass uptake. The logistic growth models are applied to both the human population and the plant biomass, with stability analysis conducted to assess the behaviour of model equilibria. The results of the model show a direct relation between the growth of human population and the increased level of acid forming gases emitted from various sources resulting in the formation of acid rain. When acid rain is uptaken by the plant species, it adversely affects the growth of plant biomass. This disruption has a significant impact on the ecosystem, which may lead to a decrease in plant diversification. Further, it is shown that the plant biomass may become extinct if the amount of acid rain keeps on increasing. In order to evaluate the sensitivity of model solutions with respect to major parameters of the system, a simple differential sensitivity analysis has also been performed. Furthermore, numerical simulation has been conducted in order to corroborate the findings obtained through model analysis.

Keywords: acid forming gases, acid rain, numerical simulation, plant biomass, sensitivity analysis