Bayesian Approach for Uncertainty Analysis of an Urban Storm Water Model and Its Application to a Heavily Urbanized Watershed

Abstract

The significance of uncertainty analysis (UA) to quantify reliability of model simulations is being recognized. Consequently, literature on parameter and predictive uncertainty assessment of water resources models has been rising. Applications dealing with urban drainage systems are, however, very limited. This study applies formal Bayesian approach for uncertainty analysis of a widely used storm water management model and illustrates the methodology using a highly urbanized watershed in the Los Angeles Basin, California. A flexible likelihood function that accommodates heteroscedasticity, non-normality, and temporal correlation of model residuals has been used for the study along with a Markov-chain Monte Carlo-based sampling scheme. The solution of the UA model has been compared with the solution of the conventional calibration methodology widely practiced in water resources modeling. Results indicate that the maximum likelihood solution determined using the UA model produced runoff simulations that are of comparable accuracy with the solution of the traditional calibration method while also accurately characterizing structure of the model residuals. The UA model also successfully determined both parameter uncertainty and total predictive uncertainty for the watershed. Contribution of parameter uncertainty to total predictive uncertainty was found insignificant for the study watershed, underlying the importance of other sources of uncertainty, including data and model structure. Overall, the UA methodology proved promising for sensitivity analysis, calibration, parameter uncertainty, and total predictive uncertainty analysis of urban storm water management models.