Marine outlet glacier dynamics, steady states and steady-state stability

Laterally confined marine outlet glaciers exhibit a diverse range of behaviours. This study investigates time-evolving and steady configurations of such glaciers. Using simplified analytic models, it determines conditions for steady states, their stability and expressions for the rate of the calving-front migration for three widely used calving rules. It also investigates the effects of ice mélange when it is present. The results show that ice flux at the terminus is an implicit function of ice thickness that depends on the glacier geometric and dynamic parameters. As a consequence, stability of steady-state configurations is determined by a complex combination of these parameters, specifics of the calving rule and the details of mélange stress conditions. The derived expressions of the rate of terminus migration suggest a non-linear feedback between the migration rate and the calving-front position. A close agreement between the obtained analytic expressions and numerical simulations suggests that these expressions can be used to gain insights into the observed behaviour of the glaciers and also to use observations to improve understanding of calving conditions.