Abstract
For the tipping elements in the Earth’s climate system, the most important issue to address is how stable is the desirable state against random perturbations. Extreme biotic and climatic events pose severe hazards to tropical rainforests. Their local effects are extremely stochastic and difficult to measure. Moreover, the direction and intensity of the response of forest trees to such perturbations are unknown, especially given the lack of efficient dynamical vegetation models to evaluate forest tree cover changes over time. In this study, we consider randomness in the mathematical modelling of forest trees by incorporating uncertainty through a stochastic differential equation. According to field-based evidence, the interactions between fires and droughts are a more direct mechanism that may describe sudden forest degradation in the south-eastern Amazon. In modeling the Amazonian vegetation system, we include symmetric α-stable Lévy perturbations. We report results of stability analysis of the metastable fertile forest state. We conclude that even a very slight threat to the forest state stability represents L´evy noise with large jumps of low intensity, that can be interpreted as a fire occurring in a non-drought year. During years of severe drought, high-intensity fires significantly accelerate the transition between a forest and savanna state.
Highlights
Tipping elements (TEs) are subsystems of the Earth’s climate system, at least subcontinental in scale, which are characterized by a critical control value, called the tipping point, beyond which even small perturbations of the system may lead to drastic qualitative changes in the system’s features and behaviour[1]
We are interested in performing a stability analysis of the current fertile forest state against stochastic perturbations[2]
To carry out the stability analysis, we study three quantities that provide information on the dynamical behaviour of the system and are appropriate for this type of analysis
Summary
Tipping elements (TEs) are subsystems of the Earth’s climate system, at least subcontinental in scale, which are characterized by a critical control value, called the tipping point, beyond which even small perturbations of the system may lead to drastic qualitative changes in the system’s features and behaviour[1]. A coupled approach combining dendrochronology and ecophysiology has been used by Bréda et al.[8] to illustrate how some extreme events affect forest ecosystems and to provide various management guidance in order to moderate extreme drought and control selective mortality Another attempt to clarify this subject has been made by Rammig et al.[9] and consists in estimating the risk of Amazonian forest dieback by using weighted rainfall projections from general circulation models to create probability density functions of future forest biomass changes. Models from catastrophe theory with bifurcation points proposed for the switch between forest cover and the alternative stable state of grassland are deterministic systems, even though the deterministic nature of these systems does not make them predictable, their future behavior is fully determined by their parameters and initial conditions, with no random elements involved These extreme events and their local effects, are extremely stochastic in nature and are difficult to measure
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