Optimization of Bathymetry Estimates for Nearshore Hydrodynamic Models Using Bayesian Methods

Abstract

A Bayesian inverse framework is developed to optimize the skill of a predictive numerical model via interpolation of bathymetric measurements to provide the most probable bathymetric surface. The numerical model is a coupled wave flow model and predicts wave and hydrodynamic information (e.g., significant wave height and longshore velocity). The Bayesian method, coupled with Markov chain Monte Carlo (MCMC) optimization, is used to find the bathymetric field, which serves to minimize the residual errors between measured data and the corresponding numerical model results. By using a Bayesian approach, the range of probable model parameters is inferred from the observed data. Monte Carlo simulation is also applied to this numerical model to perform the uncertainty analysis of the model output fields (wave height and flow velocity). This analysis is performed by taking random samples from the probability distribution function (PDF) of inputs and running the model as required until the desired precision (±.5 m for significant wave height) in output fields is achieved. The case study used in this analysis is the DUCK94 experiment, which was conducted at the US Army Field Research Facility at Duck, North Carolina, in the fall of 1994. The unknown model parameters for the hydrodynamic model involve those controlling bathymetric resolution. Furthermore, the ability of the statistical model to estimate the observed data is tested by running the forward model for two sets of input parameters: the estimated input parameters updated by the previously mentioned statistical model and the prior (noninformative) parameters. Using the model parameters estimated from the Bayesian analysis leads to improved comparisons to data. Using the presented method, the relative errors between the model outputs and the observed data for significant wave height at nearshore gauges is reduced by 3%.