Inversion of a Stokes glacier flow model emulated by deep learning

Abstract

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.

Committed Ice Loss in the European Alps Until 2050 Using a Deep‐Learning‐Aided 3D Ice‐Flow Model With Data Assimilation

“…To invert ice thickness across the Alps, we use the IGM Stokes-flow emulator, detailed in Jouvet (2022), at a resolution of 100 m. This is a deep-learning-driven emulator (based on a convolutional neural network) trained on full-Stokes simulations of 10 Alpine glaciers, which has shown 90% accuracy in matching physical solutions while running a thousand times faster (see Text S1 in Supporting Information S1 for details). For inversion purposes, we split the Alps into 12 glacier clusters (Figure 1).…”

“…Here, we use the Instructed Glacier Model (IGM; Jouvet, 2022), a deep-learning-based 3D ice-flow model, that can assimilate all available data, optimize the model glacier and make projections with a consistent inverse and forward model without post-initialization parameter calibration, thereby resolving traditional initialization problems due to inconsistencies between actual ice flow regime, reconstructed glacier geometry, and ice flow assumptions between forward and inverse modeling. We therefore simulate the evolution of all Alpine glaciers under today's climate to the middle of the 21st century, forced with the mean climatic-surface-elevation-change (CSEC, see methods below) distribution for 2000-2019.…”

What is the global glacier ice volume outside the ice sheets?

“…Furthermore, ice thickness inversion models are sensitive to the assumptions on model parameters, in particular those related to ice flow, but ice thickness observations are currently too scarce and unevenly distributed between regions to constrain these parameters. The inversion models (Huss and Farinotti, 2012; Farinotti and others, 2019; Werder and others, 2020; Jouvet and others, 2022; Van Wyk de Vries and others, 2022; Millan and others, 2022 a ) are constrained by surface data as information on basal conditions is widely lacking. However, despite significant methodological advances, such as by Millan and others (2022 a ), thickness inversions remain ill-posed problems (Bahr and others, 2015), and the ill-posed inversion can exponentially increase any errors due to poorly constrained parameters.…”

Coupled 3-D full-Stokes modelling of tidewater glaciers

“…We find it difficult to envisage an alternative modelling framework for the detailed simulation of individual tidewater glaciers discussed in this paper, as a full-Stokes approach will always be required at the grounding line at the very least. Discrete-element models (Åström and others, 2013;Benn and others, 2017b;Vallot and others, 2018) are too computationally expensive to be used for large areas or simulations of over a few weeks, and recent machine-learning emulator approaches (Jouvet and others, 2021;Jouvet, 2022) would have to be trained on full-Stokes simulations in the first place (and, given the heterogeneity of tidewater glaciers, might have to be retrained for each individual glacier). We therefore believe that the goal of a fully coupled 3-D full-Stokes model of a tidewater glacier remains a desirable one.…”