Prediction of Extreme Events
We discuss concepts for the prediction of extreme events based on time series data. We consider both probabilistic forecasts and predictions by precursors. Probabilistic forecasts employ estimates of the probability for the event to follow, whereas precur
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Abstract. We discuss concepts for the prediction of extreme events based on time series data. We consider both probabilistic forecasts and predictions by precursors. Probabilistic forecasts employ estimates of the probability for the event to follow, whereas precursors are temporal patterns in the data typically preceeding events. Theoretical considerations lead to the construction of schemes that are optimal with respect to several scoring rules. We discuss scenarios for which, in contrast to intuition, events with larger magnitude are better predictable than events with smaller magnitude.
Keywords: Extreme events, Forecasting, Scoring rules, Receiver operating characteristic, Precursor
1 Prediction of Events Geophysical processes are characterized by complicated time evolutions which are generally aperiodic on top of potential seasonal oscillations and exhibit large fluctuations. This applies to all processes related to or caused by the atmosphere, but also is true for geological processes. The prediction of extreme events is of particular interest due to their usually large impact on human life, as exemplified by earthquakes, storms, or floods. For many of such processes no detailed physical models and also no useful observations to put into such models are available, such that their prediction is very often a time series task. But even in much more favorable situations where sophisticated models, sophisticated observations, and hence model based forecasts exist, extreme events pose challenges. Due to its immense relevance in all aspects of daily life, the weather has been subject to forecasts for centuries, on various levels of sophistication. Weather predictions are nowadays generated on a daily basis with the involvement of an enormous body of scientific results and computational resources. This type of prediction is different though from the prediction of extreme events in one specific aspect: Weather predictions are designed to
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perform well under a large variety of “typical” situations, most of which are not extreme in any sense. Hence, a prediction scheme which works excellently on average might completely fail in rare but extreme situations. Indeed, there have been situations in recent years where public warnings of extreme weather situations turned out to be inadequate, such as with the Great Strom of October 15/16, 1986 in South England [1, 2] or the extreme precipitation event in Saxony on 12/13 August, 2002, leading to floodings of the river Elbe and its tributories. Both events were misplaced or overlooked by medium range weather forecasts [3]. In this chapter, we discuss the predictability and prediction schemes for extreme events, based exclusively on time series analysis. We are not employing any prior knowledge about physical processes or models for the phenomenon under study, but rely only on recordings of past data. For weather prediction over lead times larger than a few hours, this approach would not be too reasonable, as the atmospheric phenomena governing the evolution
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