Collaborative Research: Theory and Methods for Highly Multivariate Spatial Processes with Applications to Climate Data Science

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Geophysical, environmental and ecological datasets often include many variables observed over a set of irregular geographical locations. While spatial datasets are increasing in size, they are also increasing in complexity with many variables being simultaneously observed, recorded, modeled or derived. Current methods in spatial statistics are unable to cope with such highly multivariate datasets; this research addresses this gap in statistical science, aiming to establish a new framework for multivariate spatial models. The testbed for the new framework is in the field of climate data science. Understanding of the Earth system relies on coupled physical models that represent the dynamic evolution of the atmosphere, ocean, land use, rivers, glaciers and other processes. These models have led to vast amounts of climate model data that severely constrain storage resources. Moreover, statistical emulators are increasingly common and desirable alternatives to running complex physical models directly. Development and validation of compression and emulation algorithms require understanding and maintaining complex dependencies between physical variables, but current tools are univariate or pairwise-based. This research will provide statistical guidance for climate data science applications.This project focuses on a modeling framework for multivariate spatial processes, and relies on new theory incorporating graphical models in multiscale multivariate spatial process representations. Moreover, many multivariate datasets exhibit non-Gaussian behavior. A companion thrust of this work is in introducing and exploring empirical likelihood techniques for large multivariate spatial processes. Finally, the proposed models and estimation frameworks will be applied to a climate dataset from the Community Atmosphere Model.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.