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

该项目的总体目标是探索气候场重建(CFR)，以确定气候变异性的空间模式，这可能有助于更巧妙地刻画气候动态，而不是更广泛使用的单一指数重建(例如北半球平均值)。越来越多的CFR正在出现，它们跨越了过去几千年的区域和全球空间范围。这种情况允许对不同的CFR进行广泛的评估，并进行新的尖端研究以改进CFR方法。这项研究涉及气候科学领域的新统计研究，该领域提出了重要的统计挑战，从而促进了数学和物理科学领域的潜在智力进步。该项目的具体目标是通过采用非参数方法来联合评估基于函数数据分析的两个独立时空随机场的一阶矩和二阶矩，从而提供严格和全面的CFRs统计评估。贝叶斯分层模型结合了对每个气候场重建(CFR)的技能评估，预计将把单个CFR和气候模型的优点整合到一个连贯的重建中。这些进展将大大有助于理解不同CFR的时空特征，并推动新的、强大的CFR方法的发展。将专门制定正式的统计检验，以确定两个CFR之间的差异，包括它们的一阶矩和二阶矩，或者它们的特征值和特征函数的联合差异。这些测试将对被广泛使用的CFR之间的差异进行系统评估，这反过来将被用于整合不同的CFR。还将开发能够解释非平稳遥相关的多变量空间Copula模型，以重建给定替代数据的温度和降水在空间上变化的双变量分布。没有一种大规模的CFR方法试图解释遥相关的非平稳性以及气候和指标的多变量性质，这使得将这些特征纳入重建方法成为一项潜在的重大进步。该项目将促进统计学家和气候科学家之间的基础合作，从而为更多跨学科研究奠定基础。该项目将吸引本科生参与多方面的科学研究。

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.