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Description: 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 (e.g., surface-subsurface). Understanding this type of transport is key to predicting how landscapes will change under changing forcing. Here, we present a general framework for studying transport on a multi-scale coupled-connectivity system, via a multilayer network, which conceptualizes 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 in the islands, when it is controlled by the flooding level. We show the potential of the framework to answer quantitatively questions related to the characteristic timescale of response in the system.