Markov Chain Monte Carlo (MCMC) uncertainty analysis for watershed water quality modeling and management

Watershed-scale water quality (WWQ) models are now widely used to support management decision-making. However, significant uncertainty in the model outputs remains a largely unaddressed issue. In recent years, Markov Chain Monte Carlo (MCMC), a category of formal Bayesian approaches for uncertainty analysis (UA), has become popular in the field of hydrological modeling, but its applications to WWQ modeling have been rare. This study systematically evaluated the applicability of MCMC in assessing the uncertainty of WWQ modeling, using Differential Evolution Adaptive Metropolis (DREAM(ZS)) and SWAT as the representative MCMC algorithm and WWQ model, respectively. The nitrate pollution in Newport Bay watershed was the case study for numerical experiments. It has been concluded that the efficiency and effectiveness of a MCMC algorithm would depend on some critical designs of the UA, including: (i) how many and which model parameters to be considered as random in the MCMC analysis; (ii) where to fix the non-random model parameters; and (iii) which criteria to stop the Markov Chain. The study results also indicate that the MCMC UA has to be management-oriented, that is, management objectives should be factored into the designs of the UA, rather than be considered after the UA.