Multiplex Networks: A Framework for Studying Multiprocess Multiscale Connectivity Via Coupled‐Network Theory With an Application to River Deltas

Transport of water, nutrients, or energy fluxes in many natural or coupled human natural systems occurs along different pathways that often have a wide range of transport timescales and might exchange fluxes with each other dynamically. Although network approaches have been proposed for studying connectivity and transport properties on single-layer networks, theories considering interacting networks are lacking. We present a general framework for transport on multiscale coupled-connectivity systems, via multilayer networks which conceptualize the system as a set of interacting networks, each arranged in a separate layer, and with interactions across layers acknowledged by interlayer links. We illustrate this framework by examining transport in river deltas as a dynamic interaction of flow within river channels and overland flow on the islands, when controlled by the flooding level. We show the potential of the framework to answer quantitative questions related to the characteristic timescale of response in the system. Plain Language Summary The physical processes that shape landscapes leave behind patterns of connectivity along which fluxes occur via a multitude of processes, for example, flow through channels, subsurface or overland flow. The connectivity imposed by those processes (e.g., channel networks) exerts a significant control on the evolution and form of the underlying systems. We introduce a framework based on coupled networks, Multiplex, that allows to quantify the connectivity properties emerging from the simultaneous action of different processes, enabling thus to assess the overall system properties and dynamics. We illustrate this framework by examining the case of river deltas, where intermittent flooding and exchange of water, sediment, and nutrients between the channels and the islands maintains the delta top by trapping sediment, stabilizing banks, and enriching rivers with carbon and nutrients. By describing the delta system as a Multiplex—integrating the connectivity imposed by confined (in the channel network) and overland (on the islands) flows as well as the interactions (flux exchange) between them—we show the emergence of system transport properties and dynamics not foreseen by analyzing each process separately, and therefore revealing key information essential to predict the system response under changing forcing.