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Abstract Stream networks in Arctic and high-elevation regions underlain by frozen ground (i.e., permafrost) are expanding and developing in response to accelerating global warming, and intensifying summertime climate variability. The underlying processes governing landscape dissection in these environments are varied, complex and challenging to unravel due to air-temperature-regulated feedbacks and shifts to new erosional regimes as climate change progresses. Here we use multiple sources of environmental information and physical models to reconstruct and understand a 60-year history of landscape-scale channelization and evolution of the Muskox Valley, Axel Heiberg Island. A time series of air photographs indicates that freeze-thaw-related polygon fields can form rapidly, over decadal time scales. Supporting numerical simulations show that the presence of polygons can control how surface runoff is routed through the landscape, exerting a basic control on channelization, which is sensitive to the timing, duration and magnitude of hydrograph events, as well as seasonal air temperature trends. These results collectively highlight that the occurrence and dynamics of polygon fields modulate channel network establishment in permafrost-rich settings undergoing changes related to a warming climate.