  We implement a data assimilation framework for integrating ice surface and
terminus position observations into a numerical ice-flow model. The model uses
the well-known shallow shelf approximation (SSA) coupled to a level set method
to capture ice motion and changes in the glacier geometry. The level set method
explicitly tracks the evolving ice-atmosphere and ice-ocean boundaries for a
marine outlet glacier. We use an Ensemble Transform Kalman Filter 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.
