A Model for Thaw and Erosion of Permafrost Riverbanks

How will bank erosion rates in Arctic rivers respond to a warming climate? Existing physical models predict that bank erosion rates should increase with water temperature as permafrost thaws more rapidly. However, the same theory predicts much faster erosion than is typically observed. We propose that these models are missing a key component: a layer of thawed sediment on the bank that buffers heat transfer and slows erosion. We developed a 1D model for this thawed layer, which reveals three regimes for permafrost riverbank erosion. Thaw-limited erosion occurs in the absence of a thawed layer, such that rapid pore-ice melting sets the pace of erosion, consistent with existing models. Entrainment-limited erosion occurs when pore-ice melting outpaces bank erosion, resulting in a thawed layer, and the relatively slow entrainment of sediment sets the pace of erosion similar to non-permafrost rivers. Third, the intermediate regime occurs when the thawed layer goes through cycles of thickening and failure, leading to a transient thermal buffer that slows thaw rates. Distinguishing between these regimes is important because thaw-limited erosion is highly sensitive to water temperature, whereas entrainment-limited erosion is not. Interestingly, the buffered regime produces a thawed layer and relatively slow erosion rates like the entrainment-limited regime, but erosion rates are temperature sensitive like the thaw-limited regime. The results suggest the potential for accelerating erosion in a warming Arctic where bank erosion is presently thaw-limited or buffered. Moreover, rivers can experience all regimes annually and transition between regimes with warming, altering their sensitivity to climate change.