Finding Positive Feedback Loops in Environmental Models: A Mathematical Investigation
Abstract
Dynamics of most earth and environmental systems are generally governed by interactions between several hydrological (e.g., soil moisture and precipitation), geological (e.g., and erosion), geochemical (e.g., nutrient loading), and atmospheric (e.g., temperature) processes which operate on a range of spatio-temporal scales. These interactions create numerous feedback mechanisms with complex behaviours, and their understanding and representation can vary depending on the scale in space and/or time at which the system is analyzed. One of the most crucial characteristics of such complex systems is the existence of positive feedback loops. The presence of positive feedbacks may increase complexity, accelerate change, or trigger multiple stable states in the underlying dynamical system. Furthermore, because of the inherent non-linearity, it is often very difficult to obtain a general idea of their complex dynamics. Feedback loops in environmental systems have been well recognized and qualitatively discussed. With a quantitative/mathematical view, in this presentation, we address the question of how the positive feedback loops can be identified/implemented in environmental models. We investigate the nature of different feedback mechanisms and dynamics of simple example case studies that underlie fundamental processes such as vegetation, precipitation and soil moisture. To do this, we apply the concept of "interaction graph" from mathematics which is built from the Jacobian matrix of the dynamical system. The Jacobian matrix contains information on how variations of one state variable depends on variations of other variables, and thus can be used to understand the dynamical possibilities of feedback mechanisms in the underlying system. Moreover, this study highlights that there are some situations where the existence of positive feedback loops can cause multiple stable states, and thereby regime shifts in environmental systems. Systems with multiple stable states are usually characterized by having limited resilience, because an increase in the variance of external forcing can lead to an abrupt and often irreversible change. Results and insights gained through this study can help to develop improved models with increased realism, particularly when facing climate change and new extremes.
- Publication:
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AGU Fall Meeting Abstracts
- Pub Date:
- December 2016
- Bibcode:
- 2016AGUFMNG32A..07S
- Keywords:
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- 9820 Techniques applicable in three or more fields;
- GENERAL OR MISCELLANEOUSDE: 3238 Prediction;
- MATHEMATICAL GEOPHYSICSDE: 4410 Bifurcations and attractors;
- NONLINEAR GEOPHYSICSDE: 4430 Complex systems;
- NONLINEAR GEOPHYSICS