ATD: Collaborative Research: A Geostatistical Framework for Spatiotemporal Extremes

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Extreme weather events such as heat waves, drought, and intense precipitation can cause drastic losses and disruptions to the U.S. economy and natural systems. There is abundant evidence that the frequency and magnitude of such extremes are increasing, making it critical to better understand the spatiotemporal distributions of the extreme events and to develop efficient statistical tools to model the spatiotemporal trends and the associated uncertainties. In this research the investigators will develop a systematic, statistical approach to study certain new and challenging directions in extremes of random fields with applications in statistics, geography, geographic information science (GIScience) and climate sciences. Random fields are playing increasingly important roles in statistics and geosciences, due to their extensive applications as spatiotemporal models, where many problems involve dependent data at spatial and temporal locations.The project will also provide research training to students. Specifically, the investigators will develop methods to obtain the exact probability distributions of peak heights for smooth Gaussian and related non-Gaussian random fields such as chi-squared, t and F fields. For the nonstationary case, since the peak height distribution varies at different locations, a new concept on regional peak height distribution will be investigated. The investigators will also study the spatial distribution of peaks, which characterizes the probability to observe peaks in certain domains. This will provide valuable methods to estimate and predict the chances of extreme events in specific regions. The developed peak height distributions will be employed in multiple testing of local maxima (particularly in computing p-values) for detecting peaks for signals embedding in nonstationary Gaussian noises or non-Gaussian noises. Moreover, the investigators will extend the proposed methods for structural change detections of linear models by investigating the links between change points and peaks. The project developments will be evaluated in domain applications with national priority: characterizing and modeling of extreme heat events and land surface changes. This proposed research will integrate interdisciplinary tools from probability, statistics, geometry and GIScience to develop desired theoretical results and statistical methods, and will create synergy with related disciplines such as climate sciences, environmental sciences and social sciences.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.