A methodology to systematically and quantitatively assess model predictive uncertainty was applied to saturated zone uranium transport at the 300 Area of the US Department of Energy Hanford Site in Washington State, USA. The methodology extends Maximum Likelihood Bayesian Model Averaging (MLBMA) to account jointly for uncertainties due to the conceptual-mathematical basis of models, model parameters, and the scenarios to which the models are applied. Conceptual uncertainty was represented by postulating four alternative models of hydrogeology and uranium adsorption. Parameter uncertainties were represented by estimation covariances resulting from the joint calibration of each model to observed heads and uranium concentration. Posterior model probability was dominated by one model. Results demonstrated the role of model complexity and fidelity to observed system behaviour in determining model probabilities, as well as the impact of prior information. Two scenarios representing alternative future behaviour of the Columbia River adjacent to the site were considered. Predictive simulations carried out with the calibrated models illustrated the computation of model- and scenario-averaged predictions and how results can be displayed to clearly indicate the individual contributions to predictive uncertainty of the model, parameter, and scenario uncertainties. The application demonstrated the practicability of applying a comprehensive uncertainty assessment to large-scale, detailed groundwater flow and transport modelling.