Spatio-temporal connections in streamflow: a complex networks-based approach

This study introduces a new complex networks-based method to examine the spatio-temporal connections in streamflow. The method involves reconstruction of two (or more) time series jointly in a multi-dimensional phase space using a nonlinear phase space embedding procedure and construction of the spatio-temporal streamflow network of nodes and links based on the reconstructed vectors. After this spatio-temporal network construction, the clustering property of the network is measured using the clustering coefficient, which quantifies the tendency of a network to cluster. The approach is applied to monthly streamflow time series observed at each of 639 streamflow stations in the United States. Different distance threshold values are used to identify the presence/absence of links in the streamflow network and, hence, to calculate the clustering coefficient. The clustering coefficient results help to identify the critical distance threshold and optimal embedding dimension of each streamflow time series using different distance threshold values. The optimal embedding dimensions and the clustering coefficient values of the 639 streamflow time series are also discussed in terms of the role of catchment and flow properties (drainage area, elevation, flow mean, and flow coefficient of variation). The dimensions for the 639 streamflow time series are generally found to range from 2 to 18 (but even up to 30 for a few stations), indicating a wide range of complexity in the spatio-temporal connections in streamflow across the United States. The clustering coefficient values for the 639 stations are found to be in the range of 0.53-0.99, which suggest generally strong connections. The outcomes of this study clearly indicate the usefulness of the networks-based approach for examining the spatio-temporal connections in streamflow.