Multi-objective optimization for construction of prediction interval of hydrological models based on ensemble simulations

•A novel methodology for constructing prediction interval is developed.•Multi-objective optimization is used to generate hydrological model ensemble.•A set of ensembles (Pareto-optimal front) is generated in one calibration.•The ensemble mean of the hydrological models can be used as point forecast.

SummaryPractice experience reveals that prediction interval is more reliable and informative compared to single simulation, as it indicates the precision of the forecast. However, traditional ways to implement the construction of prediction interval is very difficult. This paper proposed a novel method for constructing prediction interval based on a hydrological model ensemble. The excellent multi-objective shuffled complex differential evolution algorithm was introduced to calibrate the parameters of hydrological models so as to construct an ensemble of hydrological models, which ensures a maximum of the observed data to fall within the estimated prediction interval, and whose width is also minimized simultaneously. Meanwhile, the mean of the hydrological model ensemble can be used as single simulation. The proposed method was applied to a real world case study in order to identify the effectiveness of the construction of prediction interval for the Leaf River Watershed. The results showed that the proposed method is able to construct prediction interval appropriately and efficiently. Meanwhile, the ensemble mean can be used as single simulation because it maintains comparative forecasting accuracy as the traditional single hydrological model.