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Computational Ecology and Software, 2020, 10(1): 1-14
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Article

Modeling the dynamics of methane emission from rice paddies and livestock populations and its effects on global warming: A comparison of model with data

Shyam Sundar1, Ashish Kumar Mishra1, Ram Naresh2, J. B. Shukla3
1Pranveer Singh Institute of Technology, Kanpur, India
2School of Basic Sciences, Harcourt Butler Technical University, Kanpur, India
3Innovative Internet University for Research (A Think Tank), Kanpur-208017, India

Received 31 December 2019;Accepted 9 January 2020;Published 1 March 2020
IAEES

Abstract
The rice paddies and livestock populations are the largest anthropogenic sources of methane emissions in the atmosphere causing global warming. In this paper, a nonlinear mathematical model is proposed and analysed to study the effect of methane emissions on global warming by considering four dependent variables, namely, the cumulative biomass density of rice paddies, the cumulative density of livestock populations, the atmospheric concentration of methane emitted from rice paddies, livestock populations as well as natural sources and the average global warming temperature of near earth's atmosphere. In the modeling process, it is assumed that both the cumulative densities of rice paddies and livestock populations follow logistic models with their respective growth rates and carrying capacities. The livestock populations are assumed to be partially dependent on rice paddies for food. Further, the livestock populations are assumed to be harvested for meat and leather. The growth rate of methane concentration in the atmosphere is assumed to be proportional to the cumulative density of rice paddies as well as of livestock populations. This growth rate also increases with a constant rate from natural sources but it decreases with a rate proportional to its concentration in the atmosphere due to various factors. The growth rate of global warming temperature is assumed to be proportional to the increased level of methane concentration in the atmosphere from its equilibrium value. It is also assumed that this temperature decreases with a rate proportional to its enhanced level from its equilibrium value caused by various natural factors such as rain fall, reforestation, etc. The model is analyzed by using stability theory of ordinary differential equations and computer simulation. The analysis shows that as the emissions of methane from rice paddies and livestock populations increase, the global warming temperature increases considerably from its equilibrium level. The percentage increase in global warming temperature with the corresponding increase in methane concentration is determined from the model and compared with the available data in the literature. The comparison is found to be very satisfactory. The numerical simulation confirms this result.

Keywords mathematical model;methane;rice paddies;livestock populations;global warming;stability analysis.


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