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.
