Bayesian Monte Carlo and maximum likelihood approach for uncertainty estimation and risk management: Application to lake oxygen recovery model

• Published in: Water research (Oxford) Vol. 108; pp. 301 - 311
• Main Authors: Chaudhary, Abhishek, Hantush, Mohamed M.
• Format: Journal Article
• Language: English
• Published: England Elsevier Ltd 01.01.2017
• Subjects: Bayes Theorem; Bayesian; Bayesian analysis; Calibration; Computer simulation; Data recovery; Dissolved oxygen; Environmental modeling; Freshwater; Lakes; Likelihood Functions; Mathematical models; Monte Carlo Method; Monte Carlo methods; Oxygen; Risk Management; Uncertainty; Uncertainty estimation; Water quality; ANW, USA, New York; Uncertainty estimation; Environmental modeling; Risk management; Dissolved oxygen; Water quality; Bayesian
• ISSN: 0043-1354; 1879-2448
• DOI: 10.1016/j.watres.2016.11.012

Model uncertainty estimation and risk assessment is essential to environmental management and informed decision making on pollution mitigation strategies. In this study, we apply a probabilistic methodology, which combines Bayesian Monte Carlo simulation and Maximum Likelihood estimation (BMCML) to calibrate a lake oxygen recovery model. We first derive an analytical solution of the differential equation governing lake-averaged oxygen dynamics as a function of time-variable wind speed. Statistical inferences on model parameters and predictive uncertainty are then drawn by Bayesian conditioning of the analytical solution on observed daily wind speed and oxygen concentration data obtained from an earlier study during two recovery periods on a eutrophic lake in upper state New York. The model is calibrated using oxygen recovery data for one year and statistical inferences were validated using recovery data for another year. Compared with essentially two-step, regression and optimization approach, the BMCML results are more comprehensive and performed relatively better in predicting the observed temporal dissolved oxygen levels (DO) in the lake. BMCML also produced comparable calibration and validation results with those obtained using popular Markov Chain Monte Carlo technique (MCMC) and is computationally simpler and easier to implement than the MCMC. Next, using the calibrated model, we derive an optimal relationship between liquid film-transfer coefficient for oxygen and wind speed and associated 95% confidence band, which are shown to be consistent with reported measured values at five different lakes. Finally, we illustrate the robustness of the BMCML to solve risk-based water quality management problems, showing that neglecting cross-correlations between parameters could lead to improper required BOD load reduction to achieve the compliance criteria of 5 mg/L. [Display omitted] •We present a modified Bayesian Monte Carlo maximum likelihood method - BMCML.•New approach combines model calibration, uncertainty estimation & risk management.•We derive analytical solution for lake DO concentration as a function of wind speed.•Model parameter covariations influences risk management solutions.•BMCML and MCMC performed equally well in simulating lake-oxygen recovery.