A spatiotemporal graph convolution-based model for daily runoff prediction in a river network with non-Euclidean topological structure

Deep learning has gained its prevalence in conducting spatiotemporal runoff simulations. For spatial pattern recognition, a majority of previous spatiotemporal models preferred to receive image-like inputs and to learn their hidden features by convolutional neural networks (CNN) in Euclidean space. However, dealing with geospatially non-Euclidean topology-like structures has not been received sufficient attention in hydrological deep learning modeling and needs a further exploration. The purpose of this paper is to propose an innovative spatiotemporal graph convolution-based model for daily runoff prediction in a river network with non-Euclidean topological structure, named hierarchical static-dynamic spatiotemporal prediction model (HSDSTM). The river network is regarded as a graph, and its runoff stations and topological relationships are represented as nodes and edges of the graph. Both static and dynamic graphs are generated to model the spatial confluence process and to capture fixed attributes and varied correlations of topological connectivity, respectively. Instead of focusing on a single station, the proposed model is applied to simultaneously predict the multi-step ahead daily runoff of the multiple stations of a river network in the Mississippi River Basin (MRB). The results show that the HSDSTM significantly outperforms the baseline models with a higher accuracy at a significance level of 1%, which is examined by Diebold-Mariano test. The separate effectiveness of the static and dynamic graphs is compared and it indicates that the dynamic correlations provide more valuable information to enhance the precision than the static one. Not only does the proposed model achieve a lower error, but also it strengthens the physical meaning, since the static graphs reproduce the static confluence properties and the dynamic graph quantitatively describes the varied contributions of the upstream inflow. In conclusion, the research proves the potential of the proposed spatiotemporal model to accuracy improvements in a topological river network with the physical background.