A Bayesian estimation of parameter-induced uncertainty in a nearshore alongshore current model

In many process-based models, parameters have to be estimated from data. It is important to obtain not only the optimum value of the parameters, but also to assess the uncertainty in the parameters and, hence, in the models' output. In this paper, the Bayesian Monte Carlo technique known as Generalised Likelihood Uncertainty Estimation (GLUE) is used to evaluate the parameter-induced predictive uncertainty of a three-parameter model that predicts alongshore currents over a nearshore barred profile. GLUE performs a fully random sampling of feasible-parameters space, assigning non-zero likelihoods to those model simulations that outperform a user-defined threshold. Based on data gathered at six cross-shore position across an inner bar at Egmond aan Zee, The Netherlands, non-zero likelihoods were found for a rather wide range of parameter values, largely induced by an interdependence between two parameters that affect the width of current jets across the bar. The width of the 95% uncertainty interval was found empirically to increase linearly with the predicted magnitude of the alongshore current, from about 0.02–0.06 m/s when the current magnitude is near zero to about 0.2 m/s when it is near its maximum of about 1.1 m/s. These widths are approximately equal to a rough estimate of the errors in the data. In many cases the 95% uncertainty interval brackets the observations, although there are also various instances where this is not the case and apparently model structural errors dominate over parameter-induced errors. Model non-linearity and parameter interdependence cause the marginal parameter posterior distributions to differ remarkably from those obtained from traditional first-order approximations.