Simulating surface height and terminus position for marine outlet glaciers using a level set method with data assimilation

Abstract

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.

Figures (16)

• Figure 1: A grounded, marine-terminated ice sheet profile, illustrating how the level set function $\varphi(\bm{\mathrm{x}},t)$ separates the domain into three regions: the ice region ($\Omega_i$ with $\varphi<0$), the air/ocean region lying outside the ice ($\Omega_c$ with $\varphi>0$), and the interface between them ($z=h=H+b$ along $\varphi=0$).
• Figure 2: The ice--air interface or zero level set of $\varphi$ is represented by a solid line, lying in the neighbourhood of a discrete point at location $(i,j)$. The interface speed $S$ is known at all points inside the ice, denoted by '$\circ$' and the speed is extended outside the ice region to obtain $S^{\mathrm{ext}}$ at points '☆'.
• Figure 3: Illustration of the Ensemble Kalman Filter (EnKF) sequence. The goal of EnKF is to use available observation (purple triangle) to correct the model prediction and get closer to the unknown truth. Blue and red ellipses represent the uncertainty in forecast and assimilated states, respectively. Thin blue lines depict the evolution of ensembles, while the thick blue line traces the average or mean state.
• Figure 4: Initial profile of the idealized marine outlet glacier in Experiment 1.
• Figure 5: (a) Prescribed melt rate used as input for Experiment 1. (b) Computed variations in terminus position, with the one-year period $t \in [4.74, 5.74]$ highlighted by a dashed box.