Multivariate space-time models and methods to combine large disparate spatial data and numerical models

North Carolina State University, Raleigh NC

Investigators

Abstract

Multivariate space-time models and methods to combine large disparate spatial data and numerical models Multivariate spatial-temporal statistical problems are prevalent in the environmental sciences, particularly in atmospheric and oceanic data applications. In many 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 availability of real-time observations as well as advances in the sophistication and resolution of deterministic atmospheric and oceanic models. A modeling framework to combine numerical models and observations is proposed, this framework allows for estimation of a multivariate statistical model for the data as well as parameters of physically-based deterministic models, while accounting for potential additive and multiplicative bias in the observed data. A broad class of multivariate spatial-temporal models is developed to explain the variability in the multivariate space-time data, as well as the cross-dependency between different variables. This general class of models goes beyond the standard assumptions of symmetry, separability and stationarity of the covariance function, and an extension to non-Gaussian processes is presented. Storm surge is the onshore rush of seawater associated with hurricane winds and can lead to loss of property, billion of dollars in damage, and large number of fatalities. Numerical ocean models are used to determine when and where to send evacuation warnings and recovery units to affected areas. One of the main inputs to the ocean models is the surface wind field, which is calculated based on a physical model. Currently, physical wind measurements from buoys and satellites are not used to forecast storm surge. The proposed statistical framework and models are used to better model hurricane surface wind fields by supplementing the physics-based model output with wind information from buoys and satellites. Statistical multivariate space-time modeling is used to combine these data to make predictions. Statistical models have proven to be an essential tool in the environmental sciences to describe complex spatial and temporal behavior of physical processes. Statistical models also allow for prediction of the underlying spatial-temporal processes at new locations and times. Through collaborations between scientists and statisticians, it is anticipated that the new statistical models and methods presented in this proposal for multivariate space-time processes will enhance science by improving ocean coastal prediction, and by introducing new methodology to analyze massive datasets. The investigators will use part of the funds to travel and disseminate broadly the methods proposed here to enhance mathematical and scientific understanding. The principal investigator will give some talks and short courses in Hispanic countries to broaden the participation of underrepresented geographic and ethnic groups. The investigators will continue their efforts to broaden the participation of minorities and women.