High-dimensional flow law parameter calibration and uncertainty
quantification over Antarctic ice shelves: a variational Bayesian
approach using deep learning
Abstract
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.