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The long-term evolution of channel longitudinal profiles within drainage basins is partly determined by the relative balance of hillslope sediment supply to channels and the evacuation of channel sediment. However, the lack of theoretical understanding of the physical processes of hillslope-channel coupling makes it challenging to determine whether hillslope sediment supply or channel sediment evacuation dominates over different timescales and how this balance affects bed elevation locally along the longitudinal profile. In this paper, we develop a framework for inferring the relative dominance of hillslope sediment supply to the channel versus channel sediment evacuation, over a range of temporal and spatial scales. The framework combines distinct local flow distributions on hillslopes and in the channel with surface grain-size distributions. We use these to compute local hydraulic stresses at various hillslope-channel coupling locations within the Walnut Gulch Experimental Watershed (WGEW) in southeast Arizona, USA. These stresses are then assessed as a local net balance of geomorphic work between hillslopes and channel for a range of flow conditions generalizing decadal historical records. Our analysis reveals that, although the magnitude of hydraulic stress in the channel is consistently higher than that on hillslopes, the product of stress magnitude and frequency results in a close balance between hillslope supply and channel evacuation for the most frequent flows. Only at less frequent, high-magnitude flows do channel hydraulic stresses exceed those on hillslopes, and channel evacuation dominates the net balance. This result suggests that WGEW exists mostly (similar to 50% of the time) in an equilibrium condition of sediment balance between hillslopes and channels, which helps to explain the observed straight longitudinal profile. We illustrate how this balance can be upset by climate changes that differentially affect relative flow regimes on slopes and in channels. Such changes can push the long profile into a convex or concave condition. (c) 2018 The Authors. Earth Surface Processes and Landforms published by John Wiley & Sons Ltd.