Watershed model calibration using multi-objective optimization and multi-site averaging

Recent advances in optimizing watershed model calibration have focused mainly on incorporating multiple objective measures of model performance and improving optimization algorithms. However, some parameters vary widely among different calibration locations. We present a watershed model calibration method that combines multi-objective optimization with averaging across multiple calibration sites. Model parameters were first estimated by multi-objective optimization at each calibration site, and then finalized by weighted averaging the parameter values across sites. The weight for each site was calculated from the prediction error at that site. The calibration framework was applied to estimate 16 hydrological and nutrient parameters of the General Watershed Loading Function (GWLF) watershed model at the Rhode River basin, in Maryland, United States of America. When calibrated to a single watershed, GWLF gave reasonable predictions for monthly streamflow (r2 = 0.71–0.78), monthly total nitrogen (TN) loads (r2 = 0.55–0.65), annual streamflow (r2 = 0.80–0.91), and annual TN loads (r2 = 0.67–0.86); but success for total phosphorus (TP) loads varied among watersheds (r2 = 0.41–0.68 for monthly TP loads and r2 = 0.47–0.79 for annual TP loads). In comparison to the single-site calibrations, the multi-site weighted average approach combined with multi-objective optimization reduced the relative cumulative error of predictions in validation watersheds by 3.5–7.4% for monthly streamflow, 3.2–6.3% for monthly TN loads, and 4.3–5.9% for monthly TP loads, respectively.