Bayesian sediment transport model for unisize bed load

Abstract

[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.

Multi-Fraction Bayesian Sediment Transport Model

“…The first model evaluates the bulk sediment transport, that is, it does not partition transport into different size fractions and therefore infers a reference stress that is representative of the mixture as a whole (bulk transport). This model is identical to that proposed in Schmelter et al [4,12] with the exception of the specification of the prior distribution for the variance parameter and the deterministic function for the likelihood mean. The bulk transport model is described as: …”

“…Equation (1) is the basis of a similarity collapse using τrj as the single adjustable parameter [3,15]. Equation (1) is similar in form to the equations proposed by Parker [16,17] and used in a previous Bayesian analysis by Schmelter et al [4]. The relation can be applied to bulk transport by dropping the j subscript.…”

“…The initial Bayesian models described in Schmelter et al [4,5,12] indicated that the inverse gamma, while conjugate, was not ideal for an uninformative prior. The multi-fraction model deviates from the original specification for variance distributions.…”

“…The scope of this study includes three general objectives: (1) improve the previous Bayesian models published by Schmelter and others [4,5,12,13] extending the model from one to many fractions and by including a more suitable prior and a dimensionally scalable MCMC (Markov Chain/Monte Carlo) algorithm; (2) test the novel model using laboratory flume data and validate the Bayesian model results against previous work and other statistical methods; and (3) evaluate the model by examining differences between the Bayesian model output and the validation data analysis, by exploring what is gained by adopting a Bayesian approach over previous approaches, and developing conclusions regarding the suitability of the Bayesian multi-fraction transport model.…”

An introduction to learning algorithms and potential applications in geomorphometry and Earth surface dynamics

“…In a similar application, Mondini et al (2013) map and classify landslides in southern Taiwan using a Bayesian framework. Examples from other areas of geomorphology include Gutierrez et al (2011), who 456 A. P. Valentine and L. M. Kalnins: An introduction to learning algorithms use a Bayesian network to predict shoreline evolution in response to sea-level change, and Schmelter et al (2011), who use Bayesian techniques for sediment transport modelling.…”