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Abstract

This work presents an ice-sheet modelling framework that combines a level-set approach with an ensemble data assimilation scheme. The zero-contour line of a level set function is used to depict the glacier surface. The transport equation of the level set function incorporates an ice velocity field, in our case derived from the shallow shelf approximation. In solving this level set equation, we are successfully able to simulate the evolving glacier surface. However, as with other nonlinear systems, uncertainties in the initial conditions can hamper forecast accuracy. For example, marine outlet glaciers are known to be sensitive to conditions at the terminus and the grounding line position. We propose a data assimilation method whereby noisy and partial observations of glacier surface height and glacier terminus position can be utilized to update the forecast level set through use of an ensemble transform Kalman filter. Using idealized numerical twin experiments, we demonstrate the potential of this topological data assimilation method for seasonal and multi-year predictions of glacier extent.