Global Non-Gaussian Stochastic Partial Differential Equation Models for Assessing Future Health of Ecohydrologic Systems

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In recent decades, the dramatic increase of computational power, coupled with technological advances in portable and remote sensing devices has exponentially increased the volume, variety and velocity of data, facilitating new scientific and engineering breakthroughs. This project focuses on global spatio-temporal data, a data type highly affected by this Big Data revolution and aims to develop a new global dynamical model for processes monitored at high resolution in time (daily or hourly). The application will focus on the occurrence and intensity of rainfall, and the model will be applied to assess risks faced by diverse hydrologic systems, including lakes, wetlands, and the surface/groundwater interaction zone. The proposed global statistical model will be flexible enough to explain floods and drought events governed by large scale atmospheric/oceanic patterns (for example, the El Niño Southern Oscillation) that a local model could miss. This application will focus on four regions in the continental USA known to be sensitive to precipitation events. Outreach activities at different levels, from lectures to high school students to events for the local community, are planned to increase awareness on the value of healthy hydrological systems, and a computer program will allow users to explore which areas in the United States are at higher risk of floods and droughts. The graduate student support will be used on interdisciplinary research and writing codes. Models for global data represent a theoretical challenge, as there are restrictions in defining valid processes over the sphere and time. Practical and computational challenges also exist as these models must be both flexible enough to capture non-trivial data structure across the globe, and be able to fit the extremely large size of modern data sets (billions of points). A latent Gaussian model for global spatio-temporal data is proposed, which will control the spatial dependence by a Stochastic Partial Differential Equation with an operator able to capture non-stationarity with a local tensor deformation, and changing behavior across land and ocean to allow for a smooth transition across the two domains. The model will be solved with a finite volume approach which will guarantee sparsity of the precision matrix in the latent process, thus allowing scalability for extremely large data sets. The application will address the critical issue in hydrology of the assessment of the uncertainty in future health of ecohydrological systems. Global simulations of daily precipitation and a mass conservation equation will provide estimates of the future risk to droughts and floods in four regions in the United States.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.