Collective dynamics analysis based on the multiplex network method to unravel the backbone of fluctuations in groundwater level data

Collective behavior of groundwater level (GWL) in the Tabriz plain, northwest Iran, was modeled in the framework of complex networks. The GWL is considerably influenced by the lack of recharge due to drought in recent years and the increasing water demand of the industrial city of Tabriz. In this order, convergent cross-mapping (CCM) method was utilized to infer the causal relations by adopting a robust statistical approach based on hypothesis testing. Reconstructing structure is a challenge in network-based approaches to capture the dynamical variability of the measurements. This study aims to construct functional connectivity for a better understanding of informational flows among the wells. Multiplex network (MUX) was used as a set of coupled networks through interconnected layers to structure the information obtained from collective dynamics and time-reversal. The proposed procedure was evaluated by performing a systematic analysis of random network (RN) as a well-known model to consider the topological characteristics. The influence of connectivity reconstruction on network topology was also investigated by the generated experiments for different numbers of the dynamical units and lengths of the simulations at each unit. The MUX was constructed from the GWL for monthly observations over 15 years (2001–2017). Afterwards, the time-series was divided into three categories to infer the network connections in different time periods for various sets of the monitoring wells. The analysis indicates that unphysical connections are reduced by increasing the number of the coupling units as a desirable feature for detecting the underlying connectivity. The MUX is employed with the proposed statistical approach to quantitatively unravel the backbone of fluctuations in the GWL whose indirect causal relations form the skeleton. The MUX dynamics efficiently determines the underlying processes and identifies spatio-temporal patterns of the GWL fluctuations in two layers of the constructed networks.