Dynamical systems theory is an extremely powerful framework for understanding the behavior of complex systems. Its concepts apply to many scientific fields, and hence its language provides a multidisciplinary and unifying communication tool. The theory provides a systematic approach for assessing the sensitivity of a mathematical model of a particular phenomenon to changes in parameters and initial conditions. As such, it finds application in stability problems, transition behavior and predictability studies. In addition, techniques and concepts from dynamical systems theory have led to the development of a diverse set of nonlinear methods of time series analysis.

For many phenomena, existing models cannot resolve all relevant spatial and temporal scales, and hence small-scale features are often represented as ‘noise’. As a result of the increase in computational power, solutions of the resulting stochastic partial differential equations are now within reach. Although stochastic dynamical systems are difficult to deal with, in recent years, the theory of stochastic dynamical systems has matured and is ready to be applied to many scientific areas.

This book developed from a course on climate dynamics that I taught at Colorado State University in 2005 and a course on stochastic climate models that I taught at Utrecht University in 2008. My main motivation in writing this book was to provide both an introduction into stochastic dynamical systems theory and to show the application of these methods to problems in climate dynamics.