A mathematical model to study the dynamics of carbon capture in forest plantations

Abstract

Fast-growing forest plantations play an important role in reducing global warming and have great potential for carbon capture. In this study, we aimed to model the dynamics of carbon capture in fast-growing plantations. A mathematical model is proposed consisting of a tridimensional nonlinear system. The variables involved are the amount of living biomass, the intrinsic growth of biomass, and the burned area by forestry fire. The environmental humidity is also considered, assumed as a parameter by simplicity. The solutions of the model are approximated numerically by the Runge-Kutta fourth-order method. Once the equilibria of the model have been obtained and its local stability determined, the analysis of the model reveals that the living biomass, as well as the stored carbon, decreases in each harvest cycle as a consequence of the negative effects of fire on soil properties. Furthermore, the model shows that the maximum area burned is attained always after the maximum volume of biomass is obtained. Numerical simulations show that the model solutions are reasonable for the growth dynamics of a plantation, from a theoretical perspective. The mathematical results suggest that a suitable optimal management strategy to avoid biomass losses in the successive regeneration cycles of the plantation is the prevention of fires together with soil fertilization, applied to fast-growing plantations.