Permafrost underlies about one fifth of the global land area and affects ground stability, freshwater runoff, soil chemistry, and surface-atmosphere gas exchange. The depth of thawed ground overlying permafrost (active layer thickness) has broadly increased across the Arctic in recent decades, coincident with a period of increased streamflow, especially the lowest flows (baseflow). Mechanistic links between active layer thickness and baseflow have recently been explored using linear reservoir theory, but most watersheds behave as nonlinear reservoirs. We derive theoretical nonlinear relationships between long-term average saturated soil thickness  (proxy for active layer thickness) and long-term average baseflow. When applied to 38 years of daily streamflow data for the Kuparuk River basin on the North Slope of Alaska, the theory predicts  increased  cm a⁻¹ between 1983 and 2020 ( cm total). The rate of increase nearly doubled to  cm a⁻¹ between 1990 and 2020, during which time local field measurements from Circumpolar Active Layer Monitoring sites indicate the active layer increased  cm a⁻¹. The predicted rate of increase more than doubled again between 2002 and 2020, outpacing a near doubling of observed active layer thickening, consistent with trends in terrestrial water storage inferred from Gravity Recovery and Climate Experiment satellite gravimetry and Modern-Era Retrospective Analysis for Research and Applications climate reanalysis. Overall, hydrologic change is accelerating in the Kuparuk River basin, and we provide a theoretical framework for estimating basin-scale changes in active layer water storage from streamflow measurements.