Permafrost underlies approximately 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, ALT) has broadly increased across the Arctic in recent decades, coincident with a period of increased streamflow, especially the lowest flows (baseflow). Mechanistic links between ALT 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 η (proxy for ALT) and long-term average baseflow. The theory is applied to 38 years of daily streamflow data for the Kuparuk River basin on the North Slope of Alaska. Between 1983–2020, the theory predicts that η increased 0.11±0.17 [2σ] cm a^-1, or 4.4±6.6 cm total. The rate of change nearly doubled to 0.20±0.24 cm a^-1 between 1990–2020, during which time field measurements from CALM (Circumpolar Active Layer Monitoring) sites in the Kuparuk indicate η increased 0.31±0.22 cm a^-1. The predicted rate of change more than doubled again between 2002–2020, mirroring a near doubling of observed ALT rate of change. The inferred increase in η is corroborated by GRACE (Gravity Recovery and Climate Experiment) satellite gravimetry, which indicates that terrestrial water storage increased ~0.80±3.40 cm a^-1, ~56% higher than the predicted increase in η. Overall, hydrologic change is accelerating in the Kuparuk River basin, and we provide a theoretical framework for estimating changes in active layer water storage from streamflow measurements alone.