The Argo Data and Functional Spatial Processes

该项目侧重于受Argo数据集启发和激励的研究问题。这些数据是多国Argo项目的成果，该项目自2007年以来一直在监测开放海洋（大西洋、印度洋和太平洋）的温度和盐度。它包括温度/盐度剖面——在一个密集的压力水平网格上测量——从海平面以下0到2000米的上层海洋。目前，Argo项目运行着大约4000个自主浮子，这些浮子在覆盖所有公海的空间网格上不断地对这种类型的功能数据剖面进行采样。由此产生的丰富的由空间和时间索引的函数值数据集已成为海洋学和气候科学基础科学研究的主要资源。在这个项目中，合作项目负责人和他们的研究团队，以及合作的海洋学家，将专注于开发最先进的统计理论和方法，以及成熟的算法实现，以帮助解决Argo项目的科学挑战。这项研究还将对基本的统计理论和方法以及更广泛地对其他科学领域的复杂时空数据的建模和分析产生影响。研究生资助将用于极值理论的研究。现有的空间统计理论和方法主要集中在具有平稳结构的标量数据上。具有时空变化的非平凡依赖结构的函数值数据提出了新的理论和方法挑战。近年来，功能空间数据领域稳步发展，但理论与应用之间仍存在巨大差距。例如，科学文献中对Argo数据的现有分析仍然侧重于使用传统的空间统计方法一次处理一个压力水平。合作pi计划开发一个适用于Argo数据分析的函数值随机场模型的综合框架。这一框架将通过将海洋温度和盐度视为连续压力水平范围的函数，为解决这一问题提供原则性的方法。函数均值和协方差的估计量将与它们的不确定性一起发展。通过交叉验证计算估计量和最优平滑参数的重要实际挑战将使用新的算法和可扩展的实现来解决。该研究还将解决基本的函数克里格问题，即由空间和时间索引的函数值数据的最优预测。这将涉及发展一种新的统计范式，它将连接两个领域：功能数据分析和空间统计。一个核心问题是引入符合目标的新模型，为此，一个很好的起点是将空间统计中的内在静止模型理论扩展到功能空间过程的背景下。该计划将包括对构建足够和灵活的模型所需的此类过程的结构和表示的研究。这将随后通过切线场概念的推广来研究局部本质平稳的功能空间过程。将开发具体的模型、估算器及其在Argo项目中的应用，为更广泛的科学界提供新的工具和数据产品。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

The project focuses on research problems inspired and motivated by the Argo data set. The data is the product of the multi-national Argo project that has been monitoring the temperature and salinity of the open oceans (Atlantic, Indian, and Pacific) since 2007. It consists of temperature/salinity profiles -- measurements over a dense grid of pressure levels -- of the upper ocean layer from 0 through 2,000 meters below the surface. Currently, the Argo project operates around 4,000 autonomous floats, which continuously sample such type of functional data profiles over a spatial grid covering all open oceans. The resulting rich collection of function-valued data indexed by space and time has been a major resource for basic scientific research in oceanography and climate science. In this project, the co-PIs and their research team, along with collaborating oceanographers, will focus on producing state-of-the-art statistical theory and methodology along with full-fledged algorithmic implementations to help address the scientific challenges of the Argo project. The research will also have an impact on fundamental statistical theory and methodology as well as, more broadly, on modeling and analysis of complex space-time data in other scientific domains. The graduate student support will be used for research on extreme value theory. The existing theory and methodology of spatial statistics has largely focused on scalar data with stationary structure. Function-valued data with non-trivial dependence structure that varies in space and time pose novel theoretical and methodological challenges. Recently, the field of functional spatial data has seen a steady development but there remains a huge gap between theory and applications. For example, the existing analysis of the Argo data in the scientific literature is still focused on treating one pressure-level at a time using conventional spatial statistics methods. The co-PIs plan to develop a comprehensive framework of function-valued random field models that is suitable for the analysis of the Argo data. This framework will provide a principled approach to the problem by treating ocean temperature and salinity as functions of a continuous range of pressure levels. Estimators for the functional mean and covariance will be developed along with their uncertainties. Important practical challenges on computing the estimators and optimal smoothing parameters through cross-validation will be addressed using novel algorithms and scalable implementations. The research will also address the fundamental functional kriging problem, i.e., the optimal prediction of function-valued data indexed by space and time. This will involve the development of a new statistical paradigm that bridges the two fields: functional data analysis and spatial statistics. A core issue is the introduction of new models that are amenable to the objective, for which a good starting point is extending the theory of intrinsically stationary models in spatial statistics to the context of functional spatial processes. This program will involve research on the structure and representation of such type of processes required to build adequate and flexible models. This will be followed by studying functional spatial processes that are locally intrinsically stationary through a generalization of the notion of tangent field. Concrete models, estimators and their applications to the Argo project will be developed, resulting in new tools and data products for the broader scientific community.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.