Monte Carlo simulations of a two-dimensional depth-averaged distributed bed-roughness flow model, TELEMAC-2D, are used to model a detailed tracer dispersion test in a complex reach of the River Severn in the Generalized Likelihood Uncertainty Estimation (GLUE) framework. A time efficient, zero equation, spatially distributed eddy viscosity model is derived from physical reasoning and used to close the flow equations. It is shown to have the property of low numerical diffusion, avoiding recourse to a globally large value of the eddy viscosity. For models of complex river flows, there are typically so many degrees of freedom in the specification of distributed parameters owing to the limitations of field data collection, that the identification of a unique model structure is unlikely. The data used here to constrain the model structure come from a continuous tracer injection experiment, comprising six spatially distributed time series of concentration measurements. Several hundred Monte-Carlo simulations of different model structures were investigated and it was found that multiple model structures produced feasible simulations of the tracer mixing, giving rise to the phenomenon of equifinality. Rather than optimizing the model structure on the basis of the constraining data, we derive relative possibility measures that express our relative degree of belief in each model structure. These measures can then be used as weights for assessing predictive uncertainty when using a range of model structures, to estimate the flow distribution under varying stages, or for providing maps indicating fully distributed confidence limits in the risk assessments process. Such an approach is used here, and helps to identify the circumstances under which two-dimensional modelling can be useful. The framework is not limited to the model structures that are developed herein, and more advanced process representation techniques can be included as computational efficiency increases.