Accounting for uncertainty in cumulative sediment transport using Bayesian statistics

That sediment transport estimates have large uncertainty is widely acknowledged. When these estimates are used as the basis for a subsequent analysis, such as cumulative sediment loads or budgets, treatment of uncertainty requires careful consideration. The propagation of uncertainty is a problem that has been studied in many other scientific disciplines. In recent years, Bayesian statistical methods have been successfully used to this end in hydrology, ecology, climate science, and other disciplines where uncertainty plays a major role their applications in sediment transport, however, have been few. Previous work demonstrated how deterministic sediment transport equations can be brought into a probabilistic framework using Bayesian methods. In this paper, we extend this basic model and apply it to sediment transport observations collected on the Snake River in Wyoming, USA. These data were used previously to develop a 50-year sediment budget below Jackson Lake dam. We revisit this example to demonstrate how viewing sediment transport probabilistically can help better characterize the propagation of uncertainty in the calculation of cumulative sediment transport. We present the development of probabilistic sediment rating curves that rely on deterministic sediment transport equations and then show how these can be used to compute the distribution of sediment input and output for each year from 1958 to 2007. The Bayesian approach described provides a robust way to quantify uncertainty and then propagate it through to subsequent analyses. Results show that transport uncertainty is quantified naturally in the Bayesian approach, making it unnecessary for modelers to assume some specified error rate (e.g., +/- 5%) when developing estimates of cumulative transport. Further, we demonstrate that a Bayesian approach better constrains uncertainty and allows sediment deficit and surplus to be examined in terms of quantified risk. (C) 2012 Elsevier B.V. All rights reserved.