Estimating and propagating uncertainty in sediment transport using Bayesian statistics

It is generally accepted that observations of sediment transport are widely variable, with order-of-magnitude variation in some cases for a given flow condition. When modeled, however, predictions of sediment transport are generally represented by nonlinear rating curves in log-log space. Estimation of uncertainty in these relationships, and subsequent calculations such as cumulative sediment transport, is something that is not easily done. Nevertheless, characterizing and propagating uncertainty is an important problem. Recent literature has demonstrated the applicability of Bayesian statistics to this end and we highlight the benefits of this approach by way of expanding on several examples from the literature. This approach provides a robust way to estimate parameters, such as critical and reference shear; make predictive distributions; and propagate uncertainty starting at parameter distributions through cumulative sediment transport. Unlike purely statistical methods, deterministic models (i.e., established sediment transport equations) are readily used in this framework thereby allowing both deterministic and random elements. The high-level workflow of a Bayesian model is quite similar to that of a forward stochastic model—with the exception that the Bayesian approach provides a formal way of estimating parameters prior to making a predictive distribution—and so is likely familiar to those already experienced with Monte Carlo methods. Viewing sediment transport and cumulative sediment transport in this framework makes it possible to both estimate and propagate uncertainty and provides an intuitive way to view model predictions in terms of probability. Predictive distributions effectively provide a means to answer the question of "how close is close enough?" when making predictions for a nonlinear process that varies across orders-of-magnitude. While the theory behind Bayesian models is admittedly complex, current research is directed at distributing developed codes for wider use, thus there is value in providing a general understanding of what Bayesian methods are and how they can address the challenges of estimating and propagating uncertainty in sediment transport.