We present the first fully coupled 3D full-Stokes model of a tidewater glacier, incorporating ice flow, subglacial hydrology, plume-induced frontal melting and calving. We apply the model to Store Glacier (Sermeq Kujalleq) in west Greenland to simulate a year of high melt (2012) and one of low melt (2017). In terms of modelled hydrology, we find perennial channels extending 5 km inland from the terminus and up to 41 and 29 km inland in summer 2012 and 2017, respectively. We also report a hydrodynamic feedback that suppresses channel growth under thicker ice inland and allows water to be stored in the distributed system. At the terminus, we find hydrodynamic feedbacks exert a major control on calving through their impact on velocity. We show that 2012 marked a year in which Store Glacier developed a fully channelised drainage system, unlike 2017, where it remained only partially developed. This contrast in modelled behaviour indicates that tidewater glaciers can experience a strong hydrological, as well as oceanic, control, which is consistent with observations showing glaciers switching between types of behaviour. The fully coupled nature of the model allows us to demonstrate the likely lack of any hydrological or ice-dynamic memory at Store Glacier.