Modeling The Effects Of Global Climate Change And Decreasing Forest Cover On Seasonal Rainfall

Abstract

In this research work we develop a mathematical model that describe the e_ects of global climate change and decreasing of forest cover on seasonal rainfall. Here, we assume that global tempera- ture, the amount of forest cover and the amount of rainfall are related. A non linear di_erential equation model was developed and analyzed using the stability theory of ordinary di_erential equations. Both local and global stability was studied using linearizing and lyapunov function approach respectively. The rise in global temperature was represented by energy balance equation and the decline in forest area was represented by logistic equations. Rainfall is, however, rep- resented as a periodic function; hence, second order di_erential equation, of which the solution is periodic, is used to represent the rate of change in the amount of rainfall. From the obtained results, it is inferred that the decreasing in the amount of forest cover and the rise in global tem- perature a_ects the uctuation of rainfall. Furthermore, the amount of rainfall is directly depend on the amount of forest cover. Numerical simulations are carried out to verify the analytical re- sults and con_rm this results. We also concluded that in order to avoid the uctuation of rainfall, e_orts should be made to limit the deforestation and releasing green house gases into atmosphere.