Combining Predictions and Assessing Uncertainty from Sediment Transport Equations Using Multivariate Bayesian Model Averaging

Abstract

A key assumption in the use of numerical sediment transport models is the selection and application of an equation to describe sediment transport capacity. This assumption introduces uncertainty in the model predictions because all sediment transport equations are simplifications of the physical processes. Bayesian model averaging (BMA) is a statistical method that characterizes the uncertainty due to the mathematical structure of a model and allows predictions from multiple models to be combined. In this paper, BMA is applied to quantify how the uncertainty originating from the transport equation affects the predictions from a sediment transport model. To apply BMA in this context, the likelihood function is modified to allow consideration of multiple model output variables. In addition, BMA’s assumption that the uncertainty associated with each model remains constant between the calibration and forecast periods is relaxed. The proposed multivariate BMA model is applied to transport equations included in the sedimentation and river hydraulics—one dimension (SRH-1D) model. For two flume experiments, the multivariate BMA model provides improved predictions over the individual transport equations and univariate BMA models, and it provides more realistic descriptions of the predictive uncertainty.