Spatio-temporal models with time-varying spatial model error for environmental processes

Abstract

[ACCESS RESTRICTED TO THE UNIVERSITY OF MISSOURI AT AUTHOR'S REQUEST.] Environmental processes exhibit uncertainty in the spatial and temporal domains. Often, mechanistic forecast models, such as weather forecasting systems, may not necessarily match the observed data, resulting in the need for a stochastic error term. This is common in the context of data assimilation, where one seeks to blend observations and mechanistic (deterministic) models to create complete spatio-temporal fields and their uncertainty. The observation and state-process error covariances play important roles in the development and implementation of such data assimilation models. However, the mechanistic models in this framework depend on approximations that may fail under certain real-world conditions. These models may be inadequate for various reasons, such as the need for parameters to vary through time and/or space, incomplete knowledge of the process, improper assumptions, such as temporal stationarity, or incomplete data. As such, spatio-temporal structure may exist in the resulting misfit error process. Thus, the evolution of spatial covariances may be nonstationary in time. Because of the complexities involved in characterizing these error processes, Bayesian hierarchical models (BHMs) provide an appropriate framework for modeling time-varying covariances through appropriate decompositions of the spatial covariance matrix. In this dissertation, we develop models that account for the evolution of time-varying covariance matrices in dynamical spatio-temporal models.