Calibrating calving parameterizations using graph neural network emulators: Application to Helheim Glacier, East Greenland

Abstract. Calving is responsible for the retreat, acceleration, and thinning of numerous tidewater glaciers in Greenland. An accurate representation of this process in ice sheet numerical models is critical in order to better predict the future response of the ice sheet to climate change. While traditional numerical models have succeeded in simulating ice dynamics and calving under specific parameterized conditions, the computational demand of these models makes it difficult to efficiently fine-tune these parameterizations, adding to the overall uncertainty in future sea level rise. Here, we develop various standard Graph Neural Network (GNN) architectures, including graph convolutional network (GCN), graph attention network (GAT), and equivariant graph convolutional network (EGCN), to construct surrogate models of finite-element simulations from the Ice-sheet and Sea-level System Model. GNNs are particularly well suited for this problem as they naturally capture the representation of unstructured meshes used by finite-element models. When these GNNs are trained with the simulation results of Helheim Glacier, Greenland, for different calving stress thresholds, they successfully reproduce the evolution of ice velocity, ice thickness, and ice front migration between 2007 and 2020. GNNs show better fidelity than convolutional neural networks (CNN) particularly near the boundaries of fast ice streams, and EGCN outperforms the others by preserving the equivariance of graph structures. By using the GPU-based GNN emulators, which are 260–560 times faster than the numerical simulations, we determine the optimal range of the calving threshold that minimizes the misfit between the modeled and observed ice fronts.