Development of objective function-based ensemble model for streamflow forecasts

The objective function plays an important role in hydrological model calibrations/training, since it largely determines the values of the model parameters and consequently influences the model performance. In this study, we establish two application-orientated objective functions, namely high flow balance error (HFBE) and mean squared percentage error (MSPE), for the forecasts of high flows and low flows, respectively. We examine the strengths and weaknesses of these streamflow forecast models trained with HFBE, MSPE and mean square error (MSE). Furthermore, we develop an objective function-based ensemble model (OEM) framework that can integrate the models trained with different objective functions. Our results in 273 catchments over USA show that the models trained on MSE have obvious underestimation in high-flow prediction. The models trained on HFBE can alleviate this underestimation and thus perform remarkably better for high-flow forecast. In addition, the models trained on MSPE outperform the other two models in low-flow forecast, but with an expense of the deterioration in the forecasting performance for high-flow. By incorporating the models trained on HFBE, MSPE and MSE, our proposed OEM performs well under all streamflow levels, with a median KGE of 0.96 and a median logNSE of 0.95. OEM realistically captures the mean and the variability of the observational streamflow under different scenarios with a variety of hydrometeorological conditions. This study highlights the necessity of applying objective functions that are appropriate for the modeling goal and the potential of ensemble learning methods for multi-objective optimization in hydrological modeling.