A Comparison of Bayesian Methods for Uncertainty Analysis in Hydraulic and Hydrodynamic Modeling

Abstract

We evaluate and compare the performance of Bayesian Monte Carlo (BMC), Markov chain Monte Carlo (MCMC), and the Generalized Likelihood Uncertainty Estimation (GLUE) for uncertainty analysis in hydraulic and hydrodynamic modeling (HHM) studies. The methods are evaluated in a synthetic 1D wave routing exercise based on the diffusion wave model, and in a multidimensional hydrodynamic study based on the Environmental Fluid Dynamics Code to simulate estuarine circulation processes in Weeks Bay, Alabama. Results show that BMC and MCMC provide similar estimates of uncertainty. The posterior parameter densities computed by both methods are highly consistent, as well as the calibrated parameter estimates and uncertainty bounds. Although some studies suggest that MCMC is more efficient than BMC, our results did not show a clear difference between the performance of the two methods. This seems to be due to the low number of model parameters typically involved in HHM studies, and the use of the same likelihood function. In fact, for these studies, the implementation of BMC results simpler and provides similar results to MCMC. The results of GLUE are, on the other hand, less consistent to the results of BMC and MCMC in both applications. The posterior probability densities tend to be flat and similar to the uniform priors, which can result in calibrated parameter estimates centered in the parametric space.

A Modified Particle Filter‐Based Data Assimilation Method for a High‐Precision 2‐D Hydrodynamic Model Considering Spatial‐temporal Variability of Roughness: Simulation of Dam‐Break Flood Inundation

“…Hydrodynamic models are effective tools to simulate water flows in natural and artificial water systems and have been widely used in real‐time flood forecasting (Xu et al, ), dam‐break flow simulation (Ye & Zhao, ), and sediment transport and water quality prediction (Camacho et al, ; Coraci et al, ). Water stages and discharges of dam‐break flood often experience drastic changes within a short period (Aureli et al, ), so the hydrodynamic model with a high performance is required for accurately simulating dam‐break flood inundation.…”

Uncertainty estimation in hydrodynamic modeling using Bayesian techniques

“…After 10 years of this compilation, there is a relevant amount of studies in this field concentrated on rainfall-runoff transformation (STEDINGER et al, 2008;VRUGT et al, 2008aVRUGT et al, , 2008b, supplied by numerous examples developed in previous years (see, for example, the compilation of BEVEN; BINLEY, 2014). Hydraulic modeling, in steady or unsteady regimes, on the contrary, has presented a modest number of examples (CAMACHO et al, 2015). In this case, the methods based on the theory of probability for uncertainty representation prevail (HALL, 2003), as well as those of approximate nature.…”

“…These two aspects are characteristic of situations in which it is not possible to obtain analytical solutions to quantify either the uncertainty associated with each one of the components of an environmental system model (such as input and output, parameters and model structure), which is generally non-linear in nature, or the predictive uncertainty. Among the techniques with such attributes, those having wide applicability in hydrologic and hydraulic modeling are the ones based on Monte Carlo experiments (CAMACHO et al, 2015) and on updating the prior knowledge on the uncertainties of each component of an environmental system model through Bayes's theorem (AYYUB;KLIR, 2006;HUTTON et al, 2011).…”

Monte Carlo simulation for uncertainty estimation on structural data in implicit 3-D geological modeling, a guide for disturbance distribution selection and parameterization

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