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 to better predict the future response of the ice sheet to climate change. While traditional numerical models have been used to simulate 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. In this study, we adopt three standard graph neural network (GNN) architectures, including graph convolutional network, graph attention network, and equivariant graph convolutional network (EGCN), to develop surrogate models for 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 numerical simulations of Helheim Glacier, Greenland, for different calving stress thresholds, they successfully reproduce the observed evolution of ice velocity, ice thickness, and ice front migration between 2007 and 2020. Moreover, these emulators exhibit uncertainties of less than 10 %–20 % when extrapolating to out-of-sample calving parameterization cases. Among the three GNN architectures, EGCN outperforms the others by preserving the equivariance of graph structures. By leveraging the GPU-based GNN emulators, which are 30–34 times faster than traditional numerical simulations, we determine the temporal variations of the optimal calving threshold that minimizes the misfit between modeled and observed ice fronts. This fine-tuned calving parameterization, enabled by GNN emulators, can enhance the reliability of numerical models in capturing glacier mass loss driven by calving.