Collaborative Research: P2C2--Derivation of Ensemble and Joint-Variable Climate Field Reconstructions of the Common Era Using New Random Field Methods

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The project generally aims to explore climate field reconstructions (CFRs) to target spatial patterns of climate variability that may aid in more artful characterizations of climate dynamics than the more widely available reconstructions of single indices (e.g. Northern Hemisphere means). An increasing number of CFRs are emerging that span the last several millennia over regional and global spatial scales. This situation allows for an extensive evaluation of different CFRs and new cutting-edge studies to improve CFR methods. The research involves novel statistical research in an area of climate science that presents important statistical challenges, thereby fostering potential intellectual advancement across the fields of math and physical science.The specific goal of this project is to provide a rigorous and comprehensive statistical assessment of CFRs by pursuing a nonparametric approach to jointly evaluate the first and second moments of two dependent spatio-temporal random fields based on functional data analysis. Bayesian hierarchical models that incorporate the skill assessment of each climate field reconstruction (CFR) are expected to integrate the strengths of individual CFRs and climate models into a single coherent reconstruction. These developments will significantly benefit the understanding of the spatio-temporal characteristics of different CFRs and the advancement of new and powerful CFR methodologies. Formal statistical tests will specifically be developed to determine the difference between two CFRs in terms of their first and second moments jointly, or of their eigenvalues and eigenfunctions jointly. The tests will yield a systematic assessment of the discrepancies across widely employed CFRs, which will be in turn used to integrate different CFRs. Multivariate spatial copula models will also be developed that could account for non-stationary teleconnections to reconstruct the spatially varying bivariate distribution of temperatures and precipitation given proxy data. No large-scale CFR methodology has attempted to account for both teleconnection non-stationarity and the multivariate nature of climate and proxies, making the inclusion of these features into a reconstruction methodology a potential major advance. The project will foster fundamental collaborations between statisticians and climate scientists thereby laying the foundation for more interdisciplinary research. The project will engage undergraduate students in many aspect of the scientific research.