Short-term runoff prediction using deep learning multi-dimensional ensemble method

Recently, deep learning models have been widely used in water conservancy engineering forecasting problems, due to their excellent ability to deal with the complex interactions between various hydrological factors. However, the existing research mainly focus on model structure adjustment and input feature selection, ignoring the influence of model ensemble on prediction. In this paper, a novel multi-model ensemble method, namely deep learning multi-dimensional ensemble method, is proposed to deal with multi-step runoff prediction problem. The method, which can significantly improve the runoff prediction performance, couples two ensemble techniques with different functional dimensions, namely snapshot ensemble and attention ensemble. Snapshot ensemble technique is used to enhance model generalization capabilities from single-model dimension. While, attention ensemble technique is employed to increase model prediction accuracy from multi-model dimension. Furthermore, a novel data-driven model, called deep learning multi-dimensional ensemble model, is proposed by combining three different deep learning neural networks with deep learning multi-dimensional ensemble method. The proposed model is applied in a real-world case study in the upstream of Yangtze River basin. Three evaluation indicators and ten comparative models are used to test the model performance. The test results not only show the superiority of proposed model over other comparison models, but also prove the effectiveness of the deep learning multi-dimensional ensemble method. The study highlights the power of the ensemble of deep learning model and the promising prospect of our deep learning multi-dimensional ensemble method in hydrological predictions.