Developing strategies to prevent collapse of the Amazon rainforest

Lead Research Organisation: University of Exeter
Department Name: Mathematics

Abstract

By generating its own rainfall regionally and suppressing occurrence of wildfires locally, the Amazon rainforest promotes the conditions required for its own stability. Hence, removal of forest reduces the stability of the remaining forest. Studies estimate that a 20-25% deforestation combined with climate change could induce a large scale collapse of the remaining forest to tropical savanna. This would cause a loss of much of its 10% share of global biodiversity, disrupt the regional water cycle and further accelerate global climate change. The current amount of deforestation is 17%, with recent droughts seen as possible first signs of an approaching collapse.
Rapid state shifts that are disproportionate to the driving changes in conditions are commonly called tipping points. Identification and classification of tipping points is based on the analysis of governing equations. Yet, one can only obtain these equations by taking a so-called mean-field approximation, which expresses the system's dynamics in terms of the means of its macro-scale quantities (such as forest cover fraction).
This works when the number of system units (such as plant patches) is large, the environmental conditions are approximately spatially homogeneous, and random influences average out, making fluctuations small. In an ecosystem such as the Amazon rainforest these assumptions are violated: spreading processes such as plant dispersal or fire can generate large fluctuations and environmental conditions (such as rainfall patterns) are often highly heterogeneous.
This project will introduce a method that can extract tipping criteria from simulations of large systems of coupled units with random interactions, even when the model is heterogeneous or the assumptions behind mean field approximations break down (at so-called continuous phase transitions).
The method runs the simulations in a non-conventional way by introducing artificial feedback control and then extracting information about the original uncontrolled system from observations of the controlled system.
This new approach will be developed and tested on probabilistic cellular automata. We will then apply the new method to a model of the Amazon rainforest with realistic heterogeneities (including climatic gradients, soil quality and human impact). We will study its tendency to collapse under various deforestation scenarios and determine which reforestation strategies would be required for prevention of or recovery from collapse.

Publications

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Falkena S (2021) A delay equation model for the Atlantic Multidecadal Oscillation in Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

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Panagiotopoulos I (2023) Continuation with Noninvasive Control Schemes: Revealing Unstable States in a Pedestrian Evacuation Scenario in SIAM Journal on Applied Dynamical Systems

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Wang A (2023) Time Series Analysis and Modeling of the Freezing of Gait Phenomenon in SIAM Journal on Applied Dynamical Systems

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Wuyts B (2023) Emergent structure and dynamics of tropical forest-grassland landscapes. in Proceedings of the National Academy of Sciences of the United States of America

 
Description A joint manuscript with Bert Wuyts, Emergent structure and dynamics of tropical forest-grassland landscapes, develops a landscape-scale balance of forest area change. It helps identify which parts of the landscape are best targeted for conservation or restoration to avert forest dieback.
Exploitation Route Next step is analysis of landscapes from satellite data.
Sectors Environment

 
Description Collaboration with Joseph Paez Chavez on piecewise smooth systems and control 
Organisation Escuela Superior Politécnica del Litoral
Country Ecuador 
Sector Academic/University 
PI Contribution Contribution to joint papers with Zhi Zhang, Yang Liu
Collaborator Contribution Contribution to joint papers with Zhi Zhang, Yang Liu
Impact Two joint papers: Zhi Zhang, Joseph Páez Chávez, Jan Sieber, Yang Liu, Controlling coexisting attractors of a class of non-autonomous dynamical systems, Physica D: Nonlinear Phenomena,Volume 431, 2022, 133134, ISSN 0167-2789, doi:10.1016/j.physd.2021.133134. Zhang, Z., Páez Chávez, J., Sieber, J. et al. Controlling grazing-induced multistability in a piecewise-smooth impacting system via the time-delayed feedback control. Nonlinear Dyn 107, 1595-1610 (2022), doi:10.1007/s11071-021-06511-2
Start Year 2020
 
Description Simos Gerasimidis (University of Masachussetts, Amherst, US) 
Organisation University of Massachusetts Amherst
Country United States 
Sector Academic/University 
PI Contribution Joint editors of Theme Issue in Philosophical Transactions of the Royal Society A on "Probing and Dynamics of Shock Sensitive Shells"
Collaborator Contribution Joint editors of Theme Issue in Philosophical Transactions of the Royal Society A on "Probing and Dynamics of Shock Sensitive Shells"
Impact Outcome will be Theme Issue in Philosophical Transactions of the Royal Society A. Disciplines involved are Engineering, Mathematics, Physics.
Start Year 2021