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），以针对气候变率的空间格局，这可能有助于比更广泛使用的单一指数重建（例如北方平均值）更巧妙地描述气候动态。 在区域和全球空间尺度上，跨越过去几千年的气候变化框架正在出现越来越多。 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，提出了重要的统计挑战，该项目的具体目标是通过追求非参数方法来联合评估两个相关空间的一阶矩和二阶矩，从而提供对CFRs的严格和全面的统计评估。基于函数数据分析的时间随机场。 贝叶斯层次模型，包括每个气候场重建（CFR）的技能评估，预计将整合到一个单一的连贯重建个别的CFR和气候模型的优势。这些发展将大大有利于理解不同CFR的时空特性和新的和强大的CFR方法的进步。将专门开发正式的统计测试，以确定两个CFR之间的差异，在其第一和第二时刻联合，或其特征值和特征函数联合。 这些测试将对广泛采用的CFRs之间的差异进行系统评估，进而用于整合不同的CFRs。还将开发多变量空间copula模型，这些模型可以解释非平稳遥相关，以根据代用数据重建温度和降水量在空间上变化的双变量分布。 没有大规模的CFR方法试图解释遥相关非平稳性和气候和代理的多变量性质，使这些功能纳入重建方法的一个潜在的重大进步。该项目将促进统计学家和气候科学家之间的基本合作，从而为更多的跨学科研究奠定基础。该项目将吸引本科生参与科学研究的许多方面。

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.