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.
