Hydrologic Calibration Strategies for the HSPF Watershed Model: Identifying Effective Objective Functions for Use with the Parameter Estimation (PEST) Program

Hydrologic Simulation Program FORTRAN (HSPF) is a lumped-parameter watershed model implemented in EPA's Better Assessment Science Integrating Point and Nonpoint Sources (BASINS) system. In order to perform water quality simulations in specific study areas, HSPF’s hydrology must first be calibrated to observed streamflow data. PEST is a model-independent parameter optimization program which minimizes an “objective function” quantifying the misfit between model outputs and corresponding field measurements. PEST also performs nonlinear predictive confidence interval estimation in which PEST determines maximum and minimum limits on key model predictions. A PEST/HSPF Windows interface is being developed for incorporation in the BASINS GIS-based watershed and water quality modeling system. This study seeks to identify successful PEST/HSPF calibration protocols that successfully minimize key model predictions for incorporation in the interface design. We present specific details of PEST implementation for HSPF, including model setup, identification of sensitive parameters, and parameter transformations required to facilitate the parameter estimation process. Calibration parameter set nonuniqueness is demonstrated. PEST utilizes this non-uniqueness to define nonlinear predictive confidence interval estimates. PEST varies parameters, while maintaining the objective function at or below a user-defined threshold, to define the range of predictions that satisfy calibration constraints of the objective function. There is considerable flexibility in the choice of the criteria used in formulating the objective function, and in the comparative weights assigned to these criteria. In this case we are interested in predicting the impact of nonpoint source pollutant runoff on instream pollutant concentrations. As such, the ratio of overland flow runoff to instream flow is of particular interest to us as a model calibration outcome. Alternative methods of defining hydrologic calibration objective functions are evaluated. Contributions to the objective function can include flows (appropriately weighted according to magnitude), cumulative, monthly, or event-based volumes, and flow-based statistics. We also test the utility of including separate contributions, from baseflow and surface runoff, where modeled and observed flow separation is performed with a digital filter. In all cases, the effectiveness of different calibration objective functions is judged on the basis of the width of the predictive confidence interval, as calculated by PEST’s nonlinear predictive analyzer. Of those tested, we identify the calibration strategies found to most effectively minimize uncertainty in predicting the surface runoff flux: total streamflow ratio. We apply the strategies in a few distinct hydrologic regimes and consider issues associated with generalization of the approach.