Abstract: Accurate and reliable hydrological forecasting plays an important role in water resources development and utilization. Ensemble forecasting could characterize forecast uncertainty in the form of probability distributions or intervals, which is a key issue in hydrological forecasting. In this paper, we describe a new hydrological ensemble forecasting method, namely a stochastic combination of multiple models (SCMM) that integrates several hydrological models together with linear weights and then optimizes the upper and lower limits of the weights using a multi-objective evolutionary algorithm. Finally, it creates ensemble forecasting samples through stochastically generating the weights within the optimized interval. In a case study of the medium-long-term runoff forecasting of the Huangjinxia reservoir located on the Han River, we construct six statistical forecast models considering two lead times of a month and ten days, and optimize the limits of the weights using the improved nondominated sorting genetic algorithm (NSGA-II) algorithm, yielding the ensemble forecast samples. Results show our method can better reflect the forecast uncertainty and improve significantly the average forecasts over those of the Bayesian model averaging method or a deterministic forecast model, thus providing a promising hydrological forecasting technique.

Key words: uncertainty, hydrological ensemble forecast, combination of multiple models, multi-objective optimization, Bayesian model averaging