Ice sheet modelling using the level set method and data assimilation

Estimating future sea-level rise requires ice sheet models that are able to accurately simulate the evolution of ice sheets and glaciers. Ice flow behaviour is sensitive to terminus position and grounding line and fixed-grid methods are inadequate in capturing grounding line and terminus migration. A level set method is developed to handle topological changes to the ice geometry and to track the evolution of the ice-air and ice-water interface. This method is evaluated by comparing simulations of grounded and marine terminating ice sheet flow to various analytical and benchmark solutions. The level set method is shown to be a reliable approach for tracking the ice surface interface and terminus positions for advancing and retreating ice sheets. Predictions of short-term ice dynamic behaviour could be further improved by the seamless integration of time-ordered observations into the dynamical ice sheet model. We use a data assimilation method named Ensemble Transform Kalman Filter (ETKF) to assimilate observations of ice surface elevation and lateral ice extent by updating the level set function that describes the ice interface. Numerical experiments on an idealized marine-terminating glacier demonstrate the effectiveness of our data assimilation approach for tracking seasonal and multi-year glacier advance and retreat cycles. The model is also applied to simulate Helheim Glacier, a major tidewater-terminating glacier of the Greenland Ice Sheet that has experienced a recent history of rapid retreat. By assimilating observations from remotely-sensed surface elevation profiles we are able to more accurately track the migrating glacier terminus and glacier surface changes. These results support the use of data assimilation methodologies for obtaining more accurate predictions of short-term ice sheet dynamics.