Utilization of Markov chain Monte Carlo approach for calibration and uncertainty analysis of environmental models

Abstract

Markov chain Monte Carlo (MCMC) methods are widely used in various areas of study to appraise the posterior inference in a Bayesian framework and to analyze the properties of complex systems. Prevailing theory and investigations demonstrate convergence of well-constructed MCMC schemes to the appropriate limiting distribution under a variety of different conditions. Diversification in the use of MCMC schemes urges the modelers to exploit it for the calibration of environmental models. Especially, calibration of hydrological models has always remained a key challenge for the hydrologic as well as hydraulic engineers because the designing of hydraulic structures primarily depends on the truthfulness of these models. In this study, an MCMC sampler scheme is utilized for the calibration and uncertainty analysis of a hydrological model. This sampler scheme, named Differential Evolution Adaptive Metropolis or DREAM, runs multiple chains simultaneously for global exploration, and automatically tunes the scale and orientation of the proposal distribution in randomized subspaces during the search. Application of DREAM does not only improve the authenticity of the model parameters, it also provides information about the uncertainty limits of the predictions which helps in deciding the factor of safety in design procedures. A conceptual model is used and the model parameters are acquired through MCMC sampling procedure. The calibration and validation is done using different time slots and efficacy of DREAM method is expressed in both temporal scenarios using Nash Sutcliffe efficiency measure.