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（CFRs），以确定气候变率的空间格局，这可能比更广泛使用的单一指数重建（如北半球平均值）更有助于更巧妙地表征气候动力学。在过去的几千年里，在区域和全球空间尺度上出现了越来越多的cfr。这种情况允许对不同的CFR进行广泛的评估，并进行新的前沿研究以改进CFR方法。这项研究涉及气候科学领域的新颖统计研究，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。本项目的具体目标是在功能数据分析的基础上，通过采用非参数方法联合评估两个相关时空随机场的第一和第二矩，为CFRs提供严格和全面的统计评估。结合每个气候场重建（CFR）技能评估的贝叶斯层次模型有望将单个气候场重建和气候模型的优势整合到单个连贯的重建中。这些研究成果将有助于进一步认识不同类型CFR的时空特征，并促进新的、强大的CFR研究方法的发展。将专门开发正式的统计检验，以确定两个CFRs在其第一阶矩和第二阶矩方面的差异，或其特征值和特征函数之间的差异。这些测试将产生对广泛使用的CFRs之间差异的系统评估，这将反过来用于整合不同的CFRs。还将开发多元空间耦合模型，该模型可以解释非平稳遥相关，以重建给定代理数据的温度和降水的空间变化双变量分布。没有大型CFR方法试图同时考虑远相关的非平稳性和气候和代用物的多变量性质，这使得将这些特征纳入重建方法可能是一项重大进展。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.