Directed graph deep neural network for multi-step daily streamflow forecasting

Reliable and accurate multi-step streamflow forecasting is of vital importance for the utilization of water resources and hydropower energy system. In this paper, a spatial deep learning model, directed graph deep neural network, is proposed for multi-step streamflow forecasting. The proposed model uses spatial information capture process and feature aggregation process to exploit multi-site hydrological and meteorological information. The spatial information capture process consists of multiple convolutional layers to extract the precipitation information of meteorological stations. And the feature aggregation process uses the multi-layer perceptron to aggregate the precipitation information and the streamflow information. The proposed model is applied in a real-world case study in the upstream of Yangtze River basin. Experimental results demonstrate that the proposed model significantly outperforms artificial neural network, Long Short-Term Memory Network, Gated recurrent unit and Convolutional Neural Network in terms of forecasting accuracy. In addition to the forecast accuracy, the hidden Markov regression is employed to quantify the forecasting uncertainty given by the directed graph deep neural network. The uncertainty estimation result demonstrates that the hidden Markov regression is able to handle the heteroscedastic and non-normal forecasting uncertainty given by directed graph deep neural network.