CMG: Multivariate Nonstationary Spatial Extremes in Climate and Atmospherics

本项目将发展各种方法，在观测和气候模式模拟中估计极端天气和气候事件发生的可能性。极端情况是指在特定时间段内预计只会发生一次的事件的强度，比如百年一遇的洪水的规模。极端情况对于大坝和防洪堤等基础设施项目的规划至关重要。但是极端事件的重现时间很难从仪器记录的相对较短的时间内估计出来。由于气候变化导致的数据的长期趋势使给定返回时间的预期极值的计算进一步复杂化，这与传统统计所基于的平稳性假设相矛盾。除了这些时间问题之外，极端事件研究的长期数据只能在特定地点获得，而对极端值可能性的估计需要在较大的中间区域进行。在这个项目下进行的工作将发展统计技术，以克服时间上的非平稳和空间上的稀疏所带来的困难。本文将引入三种新的框架来表征极值：(1)观测值的非参数多元空间dirichlet混合模型；(2)估计多元空间极值的贝叶斯非参数函数数据分析；(3)混合模型，其边际具有空间变化参数的广义极值（GEV）分布，即使在考虑空间变化参数后，观测值也具有空间相关性。这项研究将根据最近（1970-2000年）的观测和气候模式模拟，绘制温度极值的空间图。这项研究将引起包括统计学家、气候学家和资源管理人员在内的广大受众的兴趣。这项工作的动机之一是确定在不断变化的气候中极端事件的频率将如何变化。气候变化通常用大区域平均长期平均值的变化来表示，但与极端事件变化相关的不利影响，如热浪发生的增加，可能比平均值的变化带来更大的挑战。此外，对极端事件的规划通常是根据过去极端事件的发生情况来进行的，但是在不断变化的气候中，预测极端事件发生的可能性将需要像这里所开发的新技术。

This project will develop methods to estimate the likelihood of extreme weather and climate events, both in observations and in climate model simulations. Extremes, expressed as the magnitude of an event that is only expected to occur once in a given time period, such as the size of the 100-year flood, are central to planning for infrastructural projects like dams and levees. But return times for extreme events are difficult to estimate from the relatively short time period available from the instrumented record. The calculation of expected extreme values for a given return time is further complicated by long-term trends in the data due to climate change, which contradict the stationarity assumption on which traditional statistics is predicated. Beyond these temporal issues, long-term data for extreme event studies is only available at specific locations, while estimates of extreme value likelihood are desired over the large intervening regions. The work conducted under this project will develop statistical techniques to overcome the difficulties presented by nonstationarity in time and sparseness in space. Three new frameworks will be introduced to characterize extremes: (1) Nonparametric multivariate spatial Dirichlet-type mixture models for the observations, (2) Bayesian nonparametric functional data analysis to estimate multivariate spatial extremes, and (3) Mixture models, with marginals that have generalized extreme value (GEV) distributions with spatially varying parameters and the observations are spatially-correlated even after accounting for the spatially varying parameters. The research will produce spatial maps of extreme values for temperature, both from observations and climate model simulations of the recent past (1970-2000).The research will be of interest to a large audience including statisticians, climatologists, and resource managers. One motivation for the work is the problem of determining how the frequency of extreme events will change in a changing climate. Climate change is usually expressed in terms of changes in long-term means averaged over large regions, but the adverse impacts associated with changes in extremes, such as increases in the occurrence of heat waves, can pose greater challenges than changes in means. In addition, planning for extreme events is usually conducted based on past occurrences of extremes, but new techniques such as the ones developed here will be required to anticipate the likelihood of extremes in a changing climate.