A general perspective of extreme events in weather and climate

One of the most important problems in meteorology, physical oceanography, climatology, and related fields is the understanding and dynamical description of multi-scale interactions. Multi-scale interactions are closely related to extreme events in climate and, therefore, of great practical importance. Here an extreme event is defined in terms of the non-Gaussian tail (sometimes also called a weather or climate regime) of the data’s probability density function (PDF), as opposed to the definition in extreme value theory, where the statistics of time series maxima (and minima) in a given time interval are studied. The non-Gaussian approach used here allows for a dynamical view of extreme events in weather and climate, going beyond the solely mathematical arguments of extreme value theory. Extreme events are by definition scarce, but they can have a significant impact on people and countries in the affected regions. Understanding extremes has become an important objective in weather/climate variability research because weather and climate risk assessment depends on knowing the tails of PDFs. In recent years, new tools that make use of advanced stochastic theory have evolved to evaluate extreme events and the physics that govern these events. Stochastic methods are ideal to study multi-scale interactions and extreme events because they link vastly different time and spatial scales. One theory attributes extreme anomalies to stochastically forced dynamics, where, to model nonlinear interactions, the strength of the stochastic forcing depends on the flow itself (multiplicative noise). This closure assumption follows naturally from the general form of the equations of motion. Because stochastic theory makes clear and testable predictions about non-Gaussian variability, the multiplicative noise hypothesis can be verified by analyzing the detailed non-Gaussian statistics of atmospheric and oceanic variability. This review paper discusses the theoretical framework, observational evidence, and related developments in stochastic modeling of extreme events in weather and climate.