Fingerprinting Methods for Detection and Attribution of Changes in Climate Extremes with Spatial Estimating Equations

极端气候变化对自然和人类系统的影响往往比气候平均状态的变化更为严重。然而，由于数据稀少、信噪比低和极端事件的独特特征，对气候极端事件变化的检测和可能原因的归因研究远少于对气候平均状态变化的检测。最佳指纹法是检测和归因气候平均状态变化的标准方法，但对极端气候变化没有令人满意的模拟。该项目旨在缩小这一差距，方法是开发一种类似于最佳指纹法的方法，利用空间估计方程以高功率探测和归因于极端气候的变化。该项目在统计和气候研究方面具有跨界影响。极值分析的最优指纹方法在气候研究中有着广泛的应用和影响。这些方法的应用将提高公众对可能的气候变化及其对环境和社会影响的认识。在R系统严格质量控制下的开源软件实施不仅将使气候变化领域的从业人员能够广泛使用这些方法，而且还将使它们公开供公众审查，这两者对于理解气候极端变化和归因于可能的原因都很重要。该项目的目的是：（1）为空间估计方程建立推论，作为极端气候变化的指纹方法的模拟; 2）推导出具有空间和时间依赖的测量误差的空间估计方程; 3）确定和归因全球陆地区域尺度极端温度和北美极端降水的变化;（4）开发一个开放源码、高质量和用户友好的软件包，并与拟议的方法配套。空间估计方程将通过组合所有站点的边缘广义极值分布的得分方程来构建，而不指定空间依赖性。控制效率的组合权重将基于工作协方差矩阵或多个矩阵的倒数，每个矩阵将一个研究中心的评分与附近研究中心的评分进行对比。空间和时间相关的测量误差将接近与模拟外推方法，其中的模拟步骤将由随机归一化对比度的方法来处理，以保持相关结构。这些方法将用于检测和归因于多种外力作用下极端温度的变化和单一外力作用下极端降水的变化。该项目涵盖了气候研究界在检测和归因于极端气候变化方面的统计挑战。直到最近，由于大量观测数据和气候模型模拟，才有可能对极端现象进行重点关注。所提出的方法推进统计学知识的发展：1）有效的空间估计方程的推论，主要集中在边际回归系数，和2）测量误差模型与空间和时间相关的测量误差。这些方法为极值分析提供了最佳指纹方法的密切模拟。在探测和归因方面的应用增进了对极端温度和极端降水变化的可能原因的了解。

Changes in climate extremes often influence natural and human systems with more severe consequences than changes in climatic mean states. Detection of changes in climate extremes and attribution to possible causes, however, are much less studied than the counterpart in climatic mean states due to sparsity of data, low signal noise ratio, and the unique features of extremes. The optimal fingerprint method, which is standard in detection and attribution of changes in climatic mean states, has no satisfactory analog for changes in climate extremes. This project aims to close this gap by developing a close analog of the optimal fingerprint method for detection and attribution of changes in climate extremes with high power using spatial estimating equations. The project has cross-boundary impact in both statistics and climate research. The optimal fingerprinting method for extreme value analysis has wide applications and impact on climate research. Applications of the methods will increase the public awareness of the possible climate changes and their impact on environment and society. The open source software implementation under the strict quality control of the R system will not only make the methods widely accessible to practitioners in climate change, but also make them openly available for public scrutiny, both of which are important in understanding changes in climate extremes and attributing to possible causes.Specifically, the project aims to 1) develop inferences for spatial estimating equations as an analog of the fingerprint method for changes in climate extremes; 2) develop inferences for spatial estimating equations with measurement errors that are spatially and temporally dependent; 3) identify and attribute changes in extreme temperature at the regional scale for global lands and in extreme precipitation in North America; and 4) develop an open-source, high-quality, and user-friendly software package accompanying the proposed methodologies. The spatial estimating equations will be constructed by combining the score equations of the marginal generalized extreme value distributions at all sites, without specification of the spatial dependence. The combining weight that controls the efficiency will be based on the inverse of a working covariance matrix or multiple matrices each of which contrasts the score at a site with those from sites nearby. The spatially and temporally dependent measurement errors will be approached with the simulation extrapolation method, the simulation step of which will be handled by a random normalized contrasts approach to preserves the dependence structure. The methods will be applied to detection and attribution of changes in extreme temperature with multiple external forcings and in extreme precipitation with a single forcing. This project embraces the statistical challenges in detection and attribution of changes in climate extremes from the climate research community. The focus on extremes was made possible only recently by the large amount of observed data and climate model simulations. The proposed methods advance knowledge in statistics with the development of 1) efficient spatial estimating equations for inferences with primary focus on marginal regression coefficients, and 2) measurement error models with spatially and temporally dependent measurement error. These methods offer a close analog of the optimal fingerprint method for extreme value analysis. Applications in detection and attribution advance knowledge about the possible causes of changes in extreme temperature and extreme precipitation.