Large deviation theory, extreme events and abrupt changes in the climate system*

In the climate system, many events of primarily importance, for instance rare extreme events or rare transitions between climate attarctors can not be studied with conventional approaches, because they are too rare and the realisitc models are too complex. We will discuss several new algorithms and new theoretical approaches based on large deviation theory, where huge progress have been made to compute such rare events. We discuss results for the study of extreme heat waves and abrupt climate changes. We will delineate a research program in order for these approaches to be used with the most realistic models in the future in order to pave the way of a quantitative science of rare climate events.