Global ice-thickness inversion using a deep-learning-aided 3D ice-flow model with data assimilation

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 worlds glaciers outside the ice sheets have any thickness observations, 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 ice thickness. For accurate thickness results, this needs to be a higher-order 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 unsuitable, 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 systematic attempt to invert global ice thickness, owing to these limitations. Allied to this is that, once an inversion is done, subsequent forward modelling is rarely physically consistent with the physics used in the inversion, leading to model inconsistencies that affect the accuracy of simulations. As a solution to these problems, we extend our recent work on the European Alps using a deep-learning-driven inversion model, the Instructed Glacier Model (IGM), that emulates the performance of state-of-the-art higher-order models at a thousandth of the computational cost. This model, by solving a multi-variable 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 invert ice thickness. This approach also gives us the possibility of using consistent ice-flow physics for inversion and forward modelling, reducing the magnitude of the shock inherent in traditional modelling approaches. We present here the first results of glacier-ice-thickness inference at a global scale obtained by the inversion of a higher-order three-dimensional ice-flow model.