Burgers Lecture : Concepts of dynamical systems theory in environmental science

The dynamics of our environment are, in general, characterized by complex patterns which evolve in space and time, such as circulation patterns in the oceans, weather patterns in the atmosphere and biodiversity patterns in the biosphere. The methodology of dynamical systems theory is focused, on the one hand, on characterizing spatio-temporal patterns and, on the other hand, on studying transitions between such patterns when environmental parameters or forcings are varied. We will discuss several approaches originating from dynamical systems theory and their extension to in environmental science. As one example, we will demonstrate how the concept of Lagrangian Coherent Structures and Finite Time/Size Lyapunov Exponents can be used to study the organization of ocean flows and its impact on marine biology. Furthermore, we will examine the notion of tipping points and their relation to transitions between patterns, e.g. alternative states of vegetation in arid areas, species dominance in oceans, and lakes and sediments in the context of climate change. However, tipping points can also correspond to switches between states due to changing long-term trends or changing variability. Climate change is not only related to changes in mean value like, for example, the increase of mean temperatures in the ocean and atmosphere, but also to a variation of the characteristics of fluctuations (noise) with, for example, an increasing number of extreme events. We will discuss various examples from different fields of environmental science to shed some light on the study of conceptual models using dynamical systems theory to understand basic principles of transitions in the earth system resulting from changing environmental conditions and the challenges to identify those transitions in complex models and natural systems.