Propagation of uncertainty in a watershed model

Abstract

The Hydrological Simulation Program FORTRAN (HSPF) model was calibrated for the South Nation watershed located in Eastern Ontario. Three nonlinear automatic optimization techniques were applied and compared: Gauss-Marquardt-Levenberg (GML) method, Random Multiple Search Method (RSM), and Shuffled Complex Evolution method developed at the University of Arizona (SCE-UA). The best GML, RSM, and SCE-UA variable values beyond which objective function improvement is insignificant were suggested. It was found that more than one parameter set is able to maintain the model in a calibrated state which reflects correlation among model parameters and equations. The lowest value of the objective function (OF) does not necessarily correspond to the optimum solution. Comparison of scatter plots, graphs of residuals, and plots of cumulative differences are required to determine the best model parameter set. Combination of Nash and Sutcliffe (NS) model fit, coefficient of efficiency, and index of agreement proved to be the best statistics for model comparison. Proper definition of the OF is crucial to successful model calibration. Over 60 single and compound OFs were compared. The OF expressed as a log of observed and simulated flows was found to be the most appropriate single OF. A compound OF expressed as a sum of squared residuals of equally weighed log-transformed maximum (top 1% of flows), minimum (bottom 20% of flows), and middle flows was found to be best for most general model applications. Uncertainty of HSPF parameters was explored by the method of moments (MM), Monte Carlo (MC) with Latin hypercube and induced correlation, and response surface (RS) methods. Typically, the MM results in the most conservative uncertainty. The 95% confidence intervals of parameter uncertainty correspond to up to 10% variations in spring maximum flows. The predictive confidence interval and predictive noise for spring maximum and autumn minimum flows using single and compound OFs were computed. The predictive intervals were computed from the 95% confidence limits of the OF. It was found that HSPF can be an efficient tool to predict flows in ungaged watersheds with parameter transfer from calibrated neighbouring watersheds. The impact of DEM resolution on HSPF topographical parameters was studied.