Mathematical modeling of forest ecosystems by a reaction-diffusion-advection system: impacts of climate change and deforestation.

We present an innovative mathematical model for studying the dynamics of forest ecosystems. Our model is determined by an age-structured reaction-diffusion-advection system in which the roles of the water resource and of the atmospheric activity are considered. The model is abstract but constructed in such a manner that it can be applied to real-world forest areas; thus it allows to establish an infinite number of scenarios for testing the robustness and resilience of forest ecosystems to anthropic actions or to climate change. We establish the well-posedness of the reaction-diffusion-advection model by using the method of characteristics and by reducing the initial system to a reaction-diffusion problem. The existence and stability of stationary homogeneous and stationary heterogeneous solutions are investigated, so as to prove that the model is able to reproduce relevant equilibrium states of the forest ecosystem. We show that the model fits with the principle of almost uniform precipitation over forested areas and of exponential decrease of precipitation over deforested areas. Furthermore, we present a selection of numerical simulations for an abstract forest ecosystem, in order to analyze the stability of the steady states, to investigate the impact of anthropic perturbations such as deforestation and to explore the effects of climate change on the dynamics of the forest ecosystem.

Impact of land-cover change in the southern Amazonia climate: a case study for the region of Alta Floresta, Mato Grosso, Brazil.

The transformation of forest into pastures in the Brazilian Amazon leads to significant consequences to climate at local scale. In the region of Alta Floresta (Mato Grosso, Brazil), deforestation has been intense with over half the forests being cut since 1970. This article first examines the evolution of precipitation observed in this region and shows a significant trend in the decrease in total precipitation especially at the end of the dry season and at the beginning of the rainy season. The study then compares the temperatures measured in cleared and forested sectors within a reserve in the area of Alta Floresta (Mato Grosso, Brazil) between 2006 and 2007. The cleared sector was always hotter and drier (from 5% to 10%) than the forested area. This difference was not only especially marked during the day when it reached on average 2°C but also seemed to increase during the night with the onset of the dry season (+0.5°C). The Urban Heat Island effect is also evident especially during the night and in the dry season.