Abstract
Rare weather and climate events, such as heat waves and floods, can bring tremendous social costs. Climate data is often limited in duration and spatial coverage, and so climate forecasting has often turned to simulations of climate models to make better predictions of rare weather events. However very long simulations of complex models, in order to obtain accurate probability estimates, may be prohibitively slow. It is an important scientific problem to develop probabilistic and dynamical techniques to estimate the probabilities of rare events accurately from limited data. In this paper we compare four modern methods of estimating the probability of rare events: the generalized extreme value (GEV) method from classical extreme value theory; two importance sampling techniques, geneaological particle analysis (GPA) and the Giardina-Kurchan-Lecomte-Tailleur (GKLT) algorithm; as well as brute force Monte Carlo (MC). With these techniques we estimate the probabilities of rare events in three dynamical models: the Ornstein-Uhlenbeck process, the Lorenz ’96 system and PlaSim (a climate model). We keep the computational effort constant and see how well the rare event probability estimation of each technique compares to a gold standard afforded by a very long run control. Somewhat surprisingly we find that classical extreme value theory methods outperform GPA, GKLT and MC at estimating rare events.
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Acknowledgements
We warmly thank Frank Lunkeit at Universität Hamburg for very helpful discussions and advice concerning PlaSim. MN was supported in part by NSF Grant DMS 1600780.
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Carney, M., Kantz, H., Nicol, M. (2020). Analysis and Simulation of Extremes and Rare Events in Complex Systems. In: Junge, O., Schütze, O., Froyland, G., Ober-Blöbaum, S., Padberg-Gehle, K. (eds) Advances in Dynamics, Optimization and Computation. SON 2020. Studies in Systems, Decision and Control, vol 304. Springer, Cham. https://doi.org/10.1007/978-3-030-51264-4_7
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DOI: https://doi.org/10.1007/978-3-030-51264-4_7
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