Discovery of ice shelf rheology via physics-informed neural network

Ice shelves are floating extension of grounded ice and play a crucial role in slowing ice discharge from ice sheet into the ocean. Due to its slender-body shape and large effective viscosity, 3-D ice shelf can be considered as a 2-D flow governed by the shallow-shelf approximation (SSA) equations. Accurate description of ice’s non-Newtonian rheologyis is critical for the prediction of ice discharge into the ocean. Lab experiment showed that ice exhibits a power lawrelationship between the stress and strain rate, known as Glen’s law, which has been applied to various ice models for decades. Yet, it was unclear if this laboratory-derived flow law capture the complex behaviors of glacier ice at the continental scale. Here, we leverage the availability of satellite data and deep learning to reveal the underlying rheology of glacial ice. We use physics-informed neural network, combining the shallow-shelf approximation equations with the ice velocity and thickness data measured from satellite, to infer the effective viscosity of ice shelves, which is otherwise difficult to directly measure. We found that the stress-strain rate relation of ice shelves varies between the compression and extension zone. In the compression zone, the rheology of ice exhibits transitions between different power-laws, consistent with lab experiments in Goldsby and Kohlstedt (2001). In the extensional zone, the ice shelf behaves as a perfect plastic. Our result yields new flow laws of ice shelves that are different from those commonly assumed in ice-sheet models, suggesting a need to reassess processes sensitive to ice rheology.