Uncertainty analysis of streamflow simulations using multiple objective functions and Bayesian Model Averaging

Abstract

In this paper, multiple objective functions were used to conduct uncertainty analysis on calibrated streamflow simulations of SWAT-hillslope model (SWAT-HS), which is a semi-distributed model suited for humid, mountainous regions. SWAT-HS was set up for six watersheds of NYC water supply system and streamflow was simulated at a daily time step. Each SWAT-HS model setup was then passed through a calibration process for parameter optimization. This process involved constraining the model using several alternative objective functions which produce statistically acceptable streamflow simulations, which served as an ensemble of predictions for uncertainty analysis. We hypothesize that the uncertainty introduced by selecting a single objective function can be large with each objective function being sensitive to a specific hydrologic signature. Using multiple objective functions result in a wider range in optimum parameter values and an ensemble of simulations based on different objective functions can capture the overall prediction uncertainty through differences in parameter estimates. The Bayesian Model Averaging (BMA) method was then applied to ensemble predictions to quantify overall prediction uncertainty. The uncertainty analysis showed the similarity of uncertainty interval characteristics for all BMA based predictions across all watersheds. More than 94–97% of the observations were covered by uncertainty intervals estimated using multiple objective functions when compared to 73–79% of the observations when using a single objective function. No significant differences were observed among the six watersheds, and the results of their uncertainty analysis were similar. We propose the use of multiple objective functions as an option in ensemble modeling of streamflow and uncertainty analysis.