A Formal, Bayesian Approach for Uncertainty Analysis of a Watershed Model

Uncertainty analysis (UA) has received substantial attention in water resources during the last decade. Bayesian approaches are often preferred for UA. This study describes a formal Bayesian approach for the assessment of parameter uncertainty and predictive uncertainty using a spatially distributed hydrologic model and will demonstrate its application using data from a well monitored experimental watershed. A Markov-Chain Monte Carlo (MCMC) scheme has been used to sample posterior parameter distributions. A formal, flexible likelihood function that explicitly accounts for heteroscedasticity, temporal correlation and non-normality of simulation residuals has been used to describe closeness of the simulated and observed streamflow. Performance of the formal likelihood function will be compared to that of simple least squares with regard to generating accurate predictive uncertainty estimates at multiple streamflow gaging stations available in the experimental watershed. Limitation of the SLS assumptions with regard to the structure of model residuals will be illustrated and capability of the formal likelihood function to address these assumptions will be scrutinized. Finally, the maximum likelihood solutions identified by the uncertainty analysis method will be compared to the optimal solutions determined using a single objective optimization exercise to test effectiveness of the uncertainty analysis method to also identify the optimal solutions sought during model calibration.