Spatial-temporal models and methods for big nonstationary multivariate

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High dimensional statistical problems are prevalent in the environmental sciences, particularly in soil, atmospheric, and oceanic data applications. In these cases the processes of interest are inherently nonlinear and dynamic. Different sources of information for these systems include spatial observational data as well as physics and chemistry based numerical models. Over the past decade there has been an increase in the amount of available real-time geographic information as well as advances in the sophistication and resolution of deterministic atmospheric and oceanic models. A broad class of spatial-temporal models is developed for multivariate processes on Euclidean spaces and the sphere to explain the variability and the cross-dependency between different variables. This general class of models goes beyond standard assumptions, in particular of stationarity. The properties of the proposed methods, as well as the asymptotic properties of the estimates are studied. Likelihood approximation methods for massive spatial data are presented to efficiently implement the proposed statistical models. The proposed framework and models are used to better model soil pollution, air pollution, and wind fields. These high spatial resolution wind fields are used to predict energy production from windmills, they are also the primary forcing for numerical forecasts of the coastal ocean response to force winds such as the height of the storm surge and the degree of coastal flooding. The goal is to obtain more accurate estimation of wind fields over land and water to improve the quality of storm surge forecasts, and wind energy.The most important scientific contributions of this research project are: the introduction of flexible spatial models on the sphere for prediction and estimation of environmental spatial processes observed over larger regions on the Earth's surface; methods for likelihood approximation of big spatial temporal lattice data in general situations; general and flexible models for spatial prediction of multivariate environmental processes on spatial lattices, introducing the concept of conditional correlation in spatial lattice models; and advanced methods for spatial prediction and estimation in the presence of massive data from observations and physical and chemistry models. In these cases the processes of interest are inherently nonlinear and dynamic. Different sources of information for these systems include observational data as well as physics-based numerical models. Over the past decade there has been an increase in the amount of available real-time observations as well as advances in the sophistication and resolution of deterministic chemistry, atmospheric and oceanic models. Our methodology will provide more accurate representation and prediction of the underlying space-time process of interest. Through our collaborative work, we will help the enhancement of science by implementing these methods to hurricane wind fields and to weather and air and soil pollution to improve weather and air/soil quality mapping. The investigators will disseminate broadly the methods proposed here to enhance mathematical and scientific understanding. The PI will offer short courses in Spanish in Hispanic countries to broaden the participation of underrepresented geographic and ethnic groups. A course in advanced spatial statistics methods will be taught by the PI, and the new statistical methods proposed here will be introduced to the students. The investigators will continue their efforts to broaden the participation of minorities and women in Sciences and the PI through this project will continue her involvement on K-12 educational efforts, through the Kenan Fellows for Curriculum and Leadership Development Program and the Science House at NCSU.