The role of ensemble learning in multi-optimization for streamflow prediction

The objective function plays an important role in the training process for deep learning models, since it largely determines the trained values of the model parameters and influences the model performance. In this study, we establish two application-orientated objective functions, namely high flow balance error (HFBE) and transformed mean absolute percentage error (MAPE*), for the forecasts of high flows and low flows, respectively, in the LSTM model. We examine the strength and weakness of these streamflow forecast models trained on HFBE, MAPE* and mean square error (MSE) based on multiple performance metrics. Furthermore, we propose the objective function-based ensemble model (OEM) framework that integrates the models trained on different objective functions, so as to take advantages of the trained models focusing on different aspects of streamflow and thus achieve a better overall performance. Our results in 273 catchments over USA show that the models trained on HFBE can alleviate underestimation in high flows existing in the models trained on MSE, and perform remarkably better for high flows. It is also found that the models trained on MAPE* outperform the other two models in low flow forecast, no matter what algorithm is used for the model establishment. By incorporating the three models trained on HFBE, MAPE* and MSE, respectively, our proposed OEM performs well in the forecasts of both high flows and low flows, and realistically capture the mean and the variability of the observational streamflow under different scenarios under a variety of hydrometeorological conditions. This study highlights the necessity of applying application-orientated objective functions for given projects and the great potential of the ensemble learning methods for multi-optimization in hydrological modeling.