  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 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, genealogical 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.
