Finite-element modeling of subglacial cavities and related friction law

Sliding velocity and basal drag are strongly influenced by changes in subglacial water pressure or subglacial water storage associated with opening and closing of water cavities in the lee of bedrock obstacles. To better understand this influence, finite-element simulations of ice flowing past bedrock obstacles with cavity formation are carried out for different synthetic periodic bedrock shapes. In the numerical model, the cavity roof is treated as an unknown free surface and is part of the solution. As an improvement over earlier studies, the cases of nonlinear ice rheology and infinite bedrock slopes are treated. Our results show that the relationship between basal drag and sliding velocity, the friction law, can be easily extended from linear to nonlinear ice rheology and is bounded even for bedrocks with locally infinite slopes. Combining our results with earlier works by others, a phenomenological friction law is proposed that includes three independent parameters that depend only on the bedrock geometry. This formulation yields an upper bound of the basal drag for finite sliding velocity and a decrease in the basal drag at low effective pressure or high velocity. This law should dramatically alter results of models of temperate glaciers and should also have important repercussions on models of glacier surges and fast glacier flows.