| Fluvial sediment transport is a process that has long been important in managing water resources. While we intuitively recognize that increased flow amounts to increased sediment discharge, there is still significant uncertainty in the details. Because sediment transport---and in the context of this dissertation, bed load transport---is a strongly nonlinear process that is usually modeled using empirical or semi-empirical equations, there exists a large amount of uncertainty around model parameters, predictions, and model suitability. The focus of this dissertation is to develop and demonstrate a series of physically---and statistically-based sediment transport models that build on the scientific knowledge of the physics of sediment transport while evaluating the phenomenon in an environment that leads us to robust estimates of parametric, predictive, and model selection uncertainty. The success of these models permits us to put theoretically and procedurally sound uncertainty estimates to a process that is widely acknowledged to be variable and uncertain but has, to date, not developed robust statistical tools to quantify this uncertainty. This dissertation comprises four individual papers that methodically develop and prove the concept of Bayesian statistical sediment transport models. A simple pedagogical model is developed using synthetic and laboratory flume data---this model is then compared to traditional statistical approaches that are more familiar to the discipline. A single-fraction sediment transport model is developed on the Snake River to develop a probabilistic sediment budget whose results are compared to a sediment budget developed through an ad hoc uncertainty analysis. Lastly, a multi-fraction sediment transport model is developed in which multiple fractions of laboratory flume experiments are modeled and the results are compared to the standard theory that has been already published. The results of these models demonstrate that a Bayesian approach to sediment transport has much to offer the discipline as it is able to 1) accurately provide estimates of model parameters, 2) quantify parametric uncertainty of the models, 3) provide a means to evaluate relative model fit between different deterministic equations, 4) provide predictive uncertainty of sediment transport, 5) propagate uncertainty from the root causes into secondary and tertiary dependent functions, and 6) provide a means by which testing of established theory can be performed. |
