Analysis and Simulation of Extremes and Rare Events in Complex Systems

点击翻译按钮获取中文摘要

It is vital to be able to accurately predict the probability of rare and extreme events, such as heatwaves and hurricanes, in particular from climate models and climate data. Better techniques to estimate the probability of rare events and extremes are of obvious benefit to society, and will lead to better planning for floods, heatwaves, and other exigencies. Prediction from computer simulations or from real world data is an extremely challenging task. Brute force simulations by computer are often not feasible; the number of computer simulations it requires to obtain accurate estimates of the probability and form of rare events is too high for this to be a useful method in practice. In addition to this, we typically lack sufficient data to make confident predictions about rare events and extremes from climate records. Two strands of research will be developed. First, to develop a rigorous understanding of a technique from probability called importance sampling in simple mathematical models with the aim to have a firm foundation for their implementation in more realistic and complicated climate models. Importance sampling in a sense makes rare events less rare and allows reliable estimates of rare events in situations where brute force simulations are not feasible. Second, a statistical technique called extreme value theory will be developed in order to allow better estimates of the probabilities of the duration of extremes, such as heatwaves, from climate models and data.The Principal Investigators will develop a technique from importance sampling called genealogical particle analysis to speed up sampling by making rare events more common. The steps enabling the speedup may be tracked and accounted for to obtain more accurate estimates of rare events with less computational effort. Extreme value theory for physical observables such as temperature, wind velocity and energy for climate models will be developed and tested on simple climate models and extended to determine the probability of the duration of extremes, such as heatwaves, from time series data. Clustering algorithms based on information theory will be developed to sort data from spatially distinct sites to amplify the data available to better predict, for example, heatwaves and cold spells. The investigation will be in part theoretical, numerical and data analytic. Progress in this area would significantly improve our conceptual understanding of rare events and extremes in complex systems such as the climate and our ability to predict their behavior. The investigators past work on extreme value theory has been recognized and cited by meteorologists; it has detailed how extreme value theory should be applied to deterministic models. The current research will be at the interface of applications and of general interest to scientists modeling complex systems. In addition, the project will provide excellent training in probabilistic techniques and data analysis for the graduate students involved in the research.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.