Evaluating multiple performance criteria to calibrate the distributed hydrological model of the upper Neckar catchment

Performance criteria are used in the automated calibration of hydrological models to determine and minimise the misfit between observations and model simulations. In this study, a multiobjective model calibration framework is used to analyse the trade-offs between Nash–Sutcliffe efficiency of flows (NSE), the NSE of log-transformed flows (NSE_logQ), and the sum-squared error of monthly discharge sums (SSE_MQ). These criteria are known to put different emphasis on average and high flows, low flows, and average volume-balance components. Twenty-two upper Neckar subbasins whose catchment area ranges from 56 to 3,976 km² were modelled with the distributed mesoscale hydrological model (mHM) to investigate these trade-offs. The 53 global parameters required for each instance of the mHM model were estimated with the global search algorithm AMALGAM. Equally weighted compromise solutions based on the selected criteria and extreme ends of all bi-criterion Pareto fronts were used after each calibration run to analyse the trade-off between different performance criteria. Calibration results were further analysed with ten additional criteria commonly used for evaluating hydrological model performance. Results showed that the trade-off patterns were similar for all subbasins irrespective of catchment size and that the largest trade-offs were consistently observed between the NSE and NSE_logQ criteria. Simulations with the compromise solution provided a well-balanced fit to individual characteristics of the streamflow hydrographs and exhibited improved volume balance. Other performance criteria such as bias, the Pearson correlation coefficient, and the relative variability remained largely unchanged between compromise solutions and Pareto extremes. Parameter sets of the best NSE fit and the compromise solution of the largest basin (gauge at Plochingen) were used to simulate streamflow at the other 21 internal subbasins for a 10-year evaluation period without re-calibration. Both parameter sets performed well in the individual basins with median NSE values of 0.74 and 0.72, respectively. The compromise solution resulted in similar NSE_logQ-ranges and a 14.6 % lower median volume-balance error which indicates an overall better model performance. The results demonstrate that the performance criteria for hydrological model calibration should be selected in accordance with the anticipated model predictions. The compromise solution provides an advance to the use of single criteria in model calibration.