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High-dimensional flow law parameter calibration and uncertainty quantification over Antarctic ice shelves: a variational Bayesian approach using deep learning
  • Bryan Riel,
  • Brent Minchew
Bryan Riel
Massachusetts Institute of Technology

Corresponding Author:briel@mit.edu

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Brent Minchew
Massachusetts Institute of Technology, Department of Earth, Atmospheric and Planetary Sciences
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The flow and deformation of glacier ice in response to stress is often described using Glen’s Flow Law, a power-law relation that compactly represents ice rheology with a prefactor, A, and stress exponent, n. For natural ice, these parameters (and the parameters subsumed within them) come with large uncertainties that have not been robustly quantified with observations. Modern remote sensing technologies that collect data with finer resolutions and broader coverage provide us with an opportunity to robustly calibrate these rheological parameters for certain environments. Here, we utilize publicly available observations of ice sheet surface velocity and elevation acquired with remote sensing platforms to calibrate the flow law parameters over select Antarctic ice shelves. We build upon recent work that used remote sensing observations to quantify the relationship between ice stress and strain rate in extensional flow to infer an exponent of n = 4.1 +/- 0.4 for Antarctica. Here, we model two-dimensional flow and perform parameter calibration by constructing and training physics-informed neural networks (PINNs) to learn spatially-varying A and uniform n for each ice shelf. We cast the parameter estimation problem as a neural network optimization problem through minimization of a cost function that includes both data reconstruction errors and momentum balance residuals derived from the 2D shallow-shelf approximation. Additionally, we formulate the networks to predict spatially-varying uncertainties for A by using variational inference techniques, which approximate Bayesian inference (traditionally a computationally-intensive procedure) as an additional optimization objective. Finally, we demonstrate the use of time-dependent surface velocities, which are becoming increasingly more available over the ice sheets, to independently constrain the stress exponent n, confirming the appropriateness of n = 4 derived from previous work. Overall, calibration of these parameters with robust uncertainties are critical for placing observational constraints on prognostic ice flow model parameters and to improve our understanding of flow and fracture processes on ice shelves in Antarctica.