Glacier ice thickness estimation using deep-learning-driven emulation of Stokes

Mountain glaciers are a major source of sea-level rise and also represent an important freshwater resource in many mountainous regions. Thus, accurate estimations of their thickness and, therefore, the total ice volume are important both in predicting and mitigating the global and local effects of climate change. However, to date, only 2% of the world’s glaciers outside the ice sheets have any thickness data, due to the logistical difficulties of obtaining such measurements, creating a large and policy-relevant scientific gap.

The recent development of a global-scale ice-velocity dataset, however, provides an ideal opportunity to fill this gap and determine ice thickness across the 98% of glaciers for which no thickness data is available. This can be done by inverting an ice-dynamics model to solve for the ice thickness. For accurate thickness results, this needs to be a full-Stokes model, but such a model is far too computationally cumbersome to apply on a global scale, and simpler, quicker methods usually based on the shallow ice approximation (SIA) are too inaccurate, particularly where sliding dominates glacier motion. The only attempt that has been made to leverage the global velocity dataset to retrieve ice thickness has, though, used the SIA, simply because higher-order approaches are not computationally realistic at this scale. Consequently, most of the widely-used global glacier models have made no concerted attempt to invert for global ice thickness, owing to these limitations.

As an additional related problem, failing to fully assimilate ice-velocity data into an ice-flow model necessarily introduces a shock when initialising prognostic glacier simulations, resulting in model glaciers and predictions that may diverge substantially from their real-world counterparts.

As a solution to these problems, we present results from a deep-learning-driven inversion model that emulates the performance of state-of-the-art full-Stokes models at a thousandth of the computational cost. This model, by solving an optimisation problem, can fully use and assimilate all available input datasets (surface velocity and topography, ice thickness, etc.) as components of its cost function to simultaneously invert for and optimise multiple control parameters (here, we focus on ice thickness). This approach also gives us the possibility of using the same ice-velocity field for inversion and forward modelling, reducing the magnitude of the shock inherent in traditional modelling approaches. With a view to a large-scale application to all the world’s 200,000 glaciers, we present initial thickness-inversion results for the relatively well-documented European Alps to help constrain model parameters and provide a test bed for extension to other glaciated regions, with initial extension to the Caucasus and the Southern Alps.