CMG Collaborative Research: Efficient high dimensional Bayesian methods for climate field reconstruction

CMG 合作研究：气候场重建的高效高维贝叶斯方法

• 批准号: 1025464
• 负责人: Julien Emile-Geay
• 金额: $ 21.4万
• 依托单位: University of Southern California
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2010
• 资助国家: 美国
• 起止时间: 2010-10-01 至 2015-09-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1025464&HistoricalAwards=false
• 关键词: CMG; Collaborative; Research; Efficient; dimensional

Paleoclimate reconstructions aim to recreate past climates and are critical in assessing how modern day temperatures (and other climate variables) are anomalous in a millennial context. Most of the methods available in the literature give consolidated estimates of climate variables over the past millennium and beyond. It is widely recognized that changes in climate differ by spatial location; for example, estimated changes in temperature, and variability thereof, between the tropics and the polar regions are different. Obtaining a detailed understanding of such phenomena requires developing methodology for paleoclimate reconstructions that are spatially disaggregated, with uncertainty quantifications of estimated past climate. Spatially disaggregate paleoclimate reconstructions are fundamentally high dimensional statistical problems, with unique challenges imposed by the geosciences context. In particular, paleoclimate reconstruction rely on relating climate variables to proxy variables (such as tree rings, ice cores etc..). The project will lay the theoretical foundation for high dimensional paleoclimate reconstructions using modern day statistical methods. As a concrete application the project will reconstruct global past climates at a spatially disaggregated levels for the past millennium, and also attach confidence statements to these reconstructions. The proposed work entails a collaboration between the mathematical and geo-sciences to solve a scientific problem at the interface of both fields. The methods developed during the project also have broad applications in other fields, such as genomics, where relationships between genes in a high dimensional context are often studied.Climate field reconstructions are inherently multivariate inference problems (e.g., spatial data on a large grid are required), rely on noisy input data, and are often so high-dimensional that the data dimension is close to or exceeds the sample size, resulting in ill-posed or rank-deficient estimation problems. In this context high dimensional mean and covariance estimation is often at the center of the inferential problem. Furthermore, meaningful solutions to such problems require a reliable knowledge of the uncertainty in estimated model parameters. The need for a rigorous quantification of uncertainties has recently spurred much interest in Bayesian methods for climate reconstruction, usually based on Markov Chain Monte Carlo (MCMC) sampling techniques. The latter pose two major issues, as: (1) there is no guarantee that posterior samples are generated from the required distribution (convergence issue); (2) they rely on computationally-heavy algorithms which limit their applicability (efficiency, scalability and applicability). We propose to overcome both limitations by using a flexible but high dimensional Bayesian approach that leads to closed-form solutions for posterior quantities, hence alleviating much of the computational burden. Convergence issues will be addressed first, and dimensionality reduction will subsequently be implemented by exploiting the rich theory of Markov Random fields. The outcome of the theoretical component of the project will be the construction of novel and sound, efficient high-dimensional Bayesian algorithms tailor-made for climate field reconstruction problems. These new statistical tools will then be applied to the reconstruction of global and regional temperature fields from heterogeneous geological proxies (tree rings, ice cores, speleothems, corals, sediments) over the Common Era, and new analysis of instrumental surface temperature and sea-level pressure. The solutions will be accompanied by credible intervals, and promises to yield new insights into natural climate variability at global scales.

古气候的重建旨在重现过去的气候，并且在评估现代温度（和其他气候变量）在千禧一代的情况下如何异常。文献中可用的大多数方法给出了过去千年及以后的气候变量的综合估计。人们普遍认为，气候变化因空间位置而有所不同。例如，热带地区和极地区域之间的温度变化及其变异性变化是不同的。获得对这种现象的详细理解，需要开发用于在空间分类的古气候重建的方法，并具有对过去气候的估计的不确定性量化。在空间上，古气候重建是从根本上是高维统计问题，而地球科学背景施加的独特挑战。特别是，古气候重建依赖于将气候变量与代理变量（例如树环，冰芯等）相关联。该项目将使用现代统计方法为高维古气候重建奠定理论基础。作为具体应用，该项目将在过去千年的空间分类水平上重建全球过去的气候，并将信心陈述附加到这些重建中。拟议的工作需要在数学和地理界之间进行合作，以在两个领域的界面上解决科学问题。项目期间开发的方法在其他领域（例如基因组学）也有广泛的应用，在高维环境中基因之间的关系经常被研究。气候现场重建是固有的多变量推理问题，例如，在大网格上的空间数据（需要大量的网格上的空间数据），通常依赖于噪声的数据，并且超出了较高的数据范围，或者是近距离的范围，并且是近距离的范围，以至于尺寸均匀地构建了尺寸，以至于以上是较高的。排名不足的估计问题。在这种情况下，高维平均值和协方差估计通常是推论问题的中心。此外，解决此类问题的有意义的解决方案需要对估计模型参数中不确定性的可靠知识。对不确定性进行严格量化的需求最近促使人们对贝叶斯方法进行气候重建的兴趣，通常基于马尔可夫链蒙特卡洛（MCMC）采样技术。后者提出了两个主要问题，因为：（1）不能保证从所需的分布（收敛问题）产生后样本； （2）他们依赖于限制其适用性（效率，可扩展性和适用性）的计算算法。我们建议通过使用灵活但高维的贝叶斯方法来克服这两种局限性，从而导致后量的封闭式解决方案，从而减轻大部分计算负担。收敛问题将首先解决，并通过利用马尔可夫随机领域的丰富理论来降低维度的降低。该项目的理论组成部分的结果将是构建新颖，声音，高效的高维贝叶斯算法，以量身定制为气候现场重建问题。然后，这些新的统计工具将应用于在共同时代的异质地质代理（树环，冰芯，棘突，尖峰，珊瑚，沉积物）以及对工具表面温度和海平面压力的新分析中的全球和区域温度场的重建。该解决方案将伴随可靠的间隔，并承诺将对全球尺度上自然气候变异性产生新的见解。