Temporal Dynamics of Groundwater Levels: A Complex Networks-Based Approach

This study explores the application of complex network theory to examine the temporal dynamics of groundwater levels in a region. It presents the first ever application of a coupled chaos theory-complex network framework to investigate the temporal dynamics and connectivity in groundwater levels in a region. For implementation, daily groundwater-level data observed over the period 2010-2014 from each of 71 wells across the United States are considered. Each well is considered as a network. In order to construct the temporal network from groundwater time series, basic concepts of chaos theory are coupled with those of complex network theory. First, the phase-space reconstruction technique is used to reconstruct the single-variable groundwater time series in a multi-dimensional phase space. Next, the optimum dimension required for the phase-space reconstruction is determined using the false nearest neighbour (FNN) algorithm. Each reconstructed vector in the phase space is considered as a node in the network, and the connections between the nodes (i.e., links) are identified based on the distance threshold between the reconstructed vectors. Four complex networks-based measures-degree centrality, betweenness centrality, closeness centrality, and clustering coefficient-are used to examine the properties of the groundwater-level network. The optimal embedding dimensions from the FNN method for the 71 groundwater level time series are found to range from 4 to 18, suggesting a wide range of complexity in the 71 groundwater level time series. However, a large majority (i.e., 62) of the time series have dimensions in the range of 4-10, suggesting low-to-medium-level complexity of the groundwater level dynamics. The results for the four network measures are degree centrality in the range 0.12-0.55, betweenness centrality in the range 604-4750, closeness centrality in the range 0.00009-0.00034, and clustering coefficient in the range 0.709-0.863. No region-specific patterns are observed in the four network measures, although, depending upon the measure, networks of wells in some states have higher/lower values and networks in some other states have a good mix of high and low values. Further, Spearman rank correlation analysis shows that the four network measures do not have significant relationships with key statistical characteristics (mean, standard deviation, and coefficient of variation) of the groundwater levels. This indicates that the differences in the network measures cannot be explained only by the basic statistical properties of the groundwater level records.