Projecting Flood Frequency Curves Under a Changing Climate Using Spatial Extreme Value Analysis

人们常常用平均数来描述气候变化，但它在极端事件中表现得最为明显。特别是，国际气候变化专门委员会最近的第六次评估警告说，未来几十年极端洪水事件的可能性和规模都将增加。了解这些变化的时空变异性对减轻其影响至关重要。然而，目前的空间极值分析方法在建模灵活性和计算能力方面受到限制，因此需要进行方法学工作来分析美国各地的极端事件。因此，在本项目中，研究人员将开发新的空间极值分析方法和计算工具，并将其应用于气候变化下的洪水风险预测。项目小组由一个跨学科的统计学家和水文学家小组组成，以实现这些雄心勃勃的目标，并确保将结果传播给适当的社区。该分析结合了50年来美国地质调查局提供的数百个仪表的年度最大流量观测，以及在不同气候情景下产生的CMIP6气候模式输出。该分析将提供洪水风险预期变化的高分辨率地图和当地洪水频率曲线，为水利基础设施项目提供信息。该项目的一个亮点是举办一个研讨会，通过鼓励分享洪水风险预测的想法、方法和解决方案，促进统计学家和水文学家之间的协同作用，并帮助制定统计学家和水文学家共享的共同语言，以实现跨学科知识的成功转移。总体目标是提高美国对极端洪水事件的恢复能力。该项目将在空间极值分析和水文学两方面取得重大进展。研究人员将采用两种方法，分别利用分布式计算、机器学习和人工智能的最新发展来改进空间极值分析的计算。空间极值的计算具有挑战性，因为最常见的模型是最大稳定过程，该模型给出了一个难以处理的似然函数，因此不利于最大似然或贝叶斯分析的直接应用。为了克服这一困难，本项目将开发一种分而治之的方法，即按次区域分别分析数据，然后使用广义矩法技术将结果结合起来。结果表明，该程序具有理想的理论性质，并提供了大量的性能增益比最先进的方法。该项目还在贝叶斯框架下开发了一种新的方法，该方法是不确定性量化的首选方法。该方法将难以处理的似然函数分解为一系列更简单的函数，并使用深度学习分布回归逼近这些更简单的函数。这种近似可以任意精确地满足与空间位置数量成线性比例的计算要求，从而促进对大型数据集的分析。该项目以分析美国各地的洪水频率曲线为高潮。与现有方法相比，利用空间极值分析借鉴了跨空间的信息，提高了对小概率的估计，并估计了多个地点同时经历极端事件的概率。该项目将开发用于极值分析的新软件，并培养两名研究生，研究水文学极值分析的理论、计算和应用，重点是跨学科合作。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

Climate change is often described in terms of the mean, but it will be felt most acutely in terms of extreme events. In particular, the International Panel of Climate Change’s recent Sixth Assessment warns of an increase in the likelihood and magnitude of extreme flooding events in upcoming decades. Understanding the spatiotemporal variability of these changes is critical to mitigating their impact. However, current methods for spatial extreme value analysis are limited in their modeling flexibility and computational capabilities, and thus methodological work is required to analyze extreme events across the United States. Therefore, in this project, the investigators will develop new methodological and computational tools for spatial extreme value analysis and apply them to forecasting flood risk under a changing climate. The project team is comprised of an interdisciplinary group of statisticians and hydrologists to accomplish these ambitious objectives and ensure that the results are disseminated to the appropriate communities. The analysis combines fifty years of annual maximum streamflow observations at hundreds of gauges provided by the United States Geological Survey with CMIP6 climate model output produced under different climate scenarios. This analysis will provide high-resolution maps of anticipated change in flood risk and local flood frequency curves to inform water infrastructure projects. A highlight of the project is a workshop that will foster synergy between statisticians and hydrologists by encouraging the sharing of ideas, approaches and solutions to flood risk prediction, and aid in the formulation of a common language shared by statisticians and hydrologists for successful transfer of knowledge across disciplines. The overall objective is to improve resiliency to extreme flooding events in the United States.This project will result in major advances in both spatial extreme value analysis and hydrology. The investigators will pursue two methods that exploit recent developments in distributed computing, machine learning and artificial intelligence, respectively, to improve computation for spatial extreme value analysis. Computation for spatial extremes is challenging because the most common model is the max-stable process, and this model gives an intractable likelihood function and is thus not conducive to direct application of maximum likelihood or Bayesian analysis. To overcome this difficulty, this project will develop a divide-and-conquer method that analyzes data separately by subregion and then combines the results using generalized method of moments techniques. It is shown that this procedure has desirable theoretical properties and gives substantial performance gain over state-of-the-art methods. The project also develops a new method under the Bayesian framework that is preferred for uncertainty quantification. The new method decomposes the intractable likelihood function into a sequence of simpler functions, and uses deep-learning distribution regression to approximate these simpler functions. This approximation can be arbitrarily precise with computational requirements that scale linearly with the number of spatial locations, facilitating analysis of large datasets. The project culminates with the analysis of flood-frequency curves across the US. Compared to current methods, by using spatial extreme value analysis the analysis borrows information across space to improve estimation of small probabilities and estimate the probability of multiple locations simultaneously experiencing an extreme event. This project will produce new software for extreme value analysis and also train two graduate students in theoretical, computational and applied extreme value analysis in hydrology with a strong emphasis on interdisciplinary collaboration.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.