Effect of the Flow‐Law Exponent on Ice‐Stream Sensitivity to Melt

Abstract The flow‐law exponent, n , defines the relationship between stress and strain rate in ice. Growing evidence suggests that n ranges from 1 to 4 rather than taking the single, commonly used value of 3. Larger n implies that ice‐flow speeds are more sensitive to changes in stress. However, volume change is not necessarily proportional to ice‐flow speed, so the sensitivity of ice loss to n may vary. Flow laws also include a prefactor calibrated for each n , further complicating how n affects glacier behavior. We use idealized experiments to show how the model response to an increase in melt varies depending on n , the method used to initialize the flow‐law prefactor, and the sliding law, another key control on glacier velocity. We find that when models that differ in n alone are subjected to increasing melt, an idealized land‐terminating glacier on a prograde bed loses less mass with larger n , whereas an idealized marine‐terminating glacier on a retrograde bed loses less mass with smaller n . This suggests two categories of glaciers: mass‐balance‐controlled, for which larger n causes less volume loss, and dynamically controlled, for which larger n causes more volume loss. For both categories, reasonable values of n can cause the mass loss of a glacier in response to changes in melt to vary by ±100% depending on whether the prefactor depends on temperature or whether it varies spatially so simulations initially match. Further calibration of the prefactor for n ≠ 3 is thus key to understanding how n affects projections of ice‐sheet behavior.