Permafrost active layer thickness (ALT) is a sensitive indicator of permafrost response to climate change. In recent decades, ALT has increased at sites across the Arctic, concurrent with observed increases in annual minimum streamflow (baseflow). The trends in ALT and baseflow are thought to be linked via: 1) increased soil water storage capacity due to an increased active layer, and 2) enhanced soil water mobility within a more continuous active layer, both of which support higher baseflow in Arctic rivers. One approach to analyzing these changes in ALT and baseflow is to use baseflow recession analysis, which is a classical method in hydrology that relates groundwater storage S to baseflow Q with a power law-like relationship Q = aS^b. For the special case of a linear reservoir (b=1.0), the baseflow recession method has been extended to quantify changes in ALT from streamflow measurements alone. We test this approach at sites across the North American Arctic and find that catchments underlain by permafrost behave as nonlinear reservoirs, with scaling exponents b~1.5–3.0, undermining the key assumption of linearity that is commonly applied in this method. Despite this limitation, trends in a provide insight into the relationship between changing ALT and changing Arctic baseflow. Although care should be taken to ensure the theoretical assumptions are met, baseflow recession analysis shows promise as an empirical approach to constrain modeled permafrost change at the river basin scale.