Inversion of a Stokes glacier flow model emulated by deep learning

Data assimilation in high-order ice flow modeling is a challenging and computationally costly task, yet crucial to find ice thickness and ice flow parameter distributions that are consistent with ice flow mechanics and mass balance while best matching observations. Failing to find these distributions that are required as initial conditions leads to a disequilibrium between mass balance and ice flow, resulting in nonphysical transient effects in the prognostic model. Here we tackle this problem by inverting an emulator of the Stokes ice flow model based on deep learning. By substituting the ice flow equations using a convolutional neural network emulator, we simplify, make more robust and dramatically speed up the solving of the underlying optimization problem thanks to automatic differentiation, stochastic gradient methods and implementation of graphics processing unit (GPU). We demonstrate this process by simultaneously inferring the ice thickness distribution, ice flow parametrization and ice surface of ten of the largest glaciers in Switzerland. As a result, we obtain a high degree of assimilation while guaranteeing an equilibrium between mass-balance and ice flow mechanics. The code runs very efficiently (optimizing one large-size glacier at 100 m takes < 1 min on a laptop) while it is open-source and publicly available.