Development of Novel Bayesian Models of Environmental Systems with Application to the Prairie Wetlands of North America

Abstract

This dissertation is primarily concerned with the development and application of statistical models for analyzing ecological and hydrological data. A key technical achievement contained within is the deployment of Markov chain Monte Carlo methods leveraging log posterior gradients for dramatically speeding up inference for hybrid empirical-mechanistic models as well as for analyses of large ecological datasets. In order to utilize such methods, the environmental models had to be implemented in automatic differentiation frameworks originally designed for optimization of deep neural networks. These models are highly challenging to use with previously existing methods such as the Gibbs sampler and random walk Metropolis sampling. These findings enable the enumeration and estimation of an enormous variety of new models spanning a range of process specificities from purely empirical to purely mechanistic forms, all within the same coherent joint parameter estimation framework. Additionally, these methods were employed in an analysis of ongoing changes in hydrology in the Prairie Pothole Region of North America (PPR). Key contributions from this analysis include the identification of a major structural shift in the number and geometry of ponds and wetlands in the PPR likely exacerbated by shifts in agricultural practices. Observational data from this region were used to develop and assess the performance of the first Bayesian model of upland-embedded wetland water volumes. The utility of this approach is shown by conducting inference of model parameters using biased and highly noisy calibration data derived from remote sensing.