[1] Fluvial sediment transport studies have long underscored the difficulty in reliably estimating transport model parameters, collecting accurate observations, and making predictions because of measurement error, natural variability, and conceptual model uncertainty. Thus, there is a need to identify modeling frameworks that accommodate these realities while incorporating functional relationships, providing probability-based predictions, and accommodating for conceptual model discrimination. Bayesian statistical approaches have been widely used in a number of disciplines to accomplish just this, yet applications in sediment transport are few. In this paper we propose and demonstrate a Bayesian statistical approach to a simple sediment transport problem as a means to overcome some of these challenges. This approach provides a means to rigorously estimate model parameter distributions, such as critical shear, given observations of sediment transport; provides probabilistically based predictions that are robust and easily interpretable; facilitates conceptual model discrimination; and incorporates expert judgment into model inference and predictions. We demonstrate a simple unisize sediment transport model and test it against simulated observations for which the ''true'' model parameters are known. Experimental flume observations were also used to assess the proposed model's robustness. Results indicate that such a modeling approach is valid and presents an opportunity for more complex models to be built in the Bayesian framework.

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A Bayesian approach to sediment transport modeling can provide a strong basis for evaluating and propagating model uncertainty, which can be useful in transport applications. Previous work in developing and applying Bayesian sediment transport models used a single grain size fraction or characterized the transport of mixed-size sediment with a single characteristic grain size. Although this approach is common in sediment transport modeling, it precludes the possibility of capturing processes that cause mixed-size sediments to sort and, thereby, alter the grain size available for transport and the transport rates themselves. This paper extends development of a Bayesian transport model from one to k fractional dimensions. The model uses an existing transport function as its deterministic core and is applied to the dataset used to originally develop the function. The Bayesian multi-fraction model is able to infer the posterior distributions for essential model parameters and replicates predictive distributions of both bulk and fractional transport. Further, the inferred posterior distributions are used to evaluate parametric and other sources of variability in relations representing mixed-size interactions in the original model. Successful OPEN ACCESSJ. Mar. Sci. Eng. 2015, 3 1067 development of the model demonstrates that Bayesian methods can be used to provide a robust and rigorous basis for quantifying uncertainty in mixed-size sediment transport. Such a method has heretofore been unavailable and allows for the propagation of uncertainty in sediment transport applications.

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