Stochastic Models of Climate Extremes: Theory and Observations

One very important topic in climatology, meteorology, and related fields is the detailed understanding of extremes in a changing climate. There is broad consensus that the most hazardous effects of climate change are due to a potential increase (in frequency and/or intensity) of extreme weather and climate events. Extreme events are by definition rare, but they can have a significant impact on people and countries in the affected regions. Here an extreme event is defined in terms of the non-Gaussian tail (occasionally 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. Because weather and climate risk assessment depends on knowing the tails of PDFs, understanding the statistics and dynamics of extremes has become an important objective in climate research. Traditionally, stochastic models are extensively used to study climate variability because they link vastly different time and spatial scales (multi-scale interactions). However, in the past the focus of stochastic climate modeling hasn’t been on extremes. Only in recent years new tools that make use of advanced stochastic theory have evolved to evaluate the statistics and dynamics of extreme events. 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 chapter discusses the theoretical framework, observational evidence, and related developments in stochastic modeling of weather and climate extremes.