Although numerical models provide accurate solutions for ice sheet dynamics based on physics laws, they accompany intensified computational demands to solve partial differential equations. In recent years, convolutional neural networks (CNNs) have been widely used as statistical emulators for those numerical models. However, since CNNs operate on regular grids, they cannot represent the refined meshes and computational efficiency of finite-element numerical models. Therefore, instead of CNNs, this study adopts an equivariant graph convolutional network (EGCN) as an emulator for the ice sheet dynamics modeling. EGCN reproduces ice thickness and velocity changes in the Helheim Glacier, Greenland, and Pine Island Glacier, Antarctica, with 260 times and 44 times faster computation time, respectively. Compared to the traditional CNN and graph convolutional network, EGCN shows outstanding accuracy in thickness prediction near fast ice streams by preserving the equivariance to the translation and rotation of graphs.

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.