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.

The Greenland Ice Sheet discharges ice to the ocean through hundreds of outlet glaciers. Recent acceleration of Greenland outlet glaciers has been linked to both oceanic and atmospheric drivers. Here, we leverage temporally dense observations, regional climate model output, and newly developed time series analysis tools to assess the most important forcings causing ice flow variability at one of the largest Greenland outlet glaciers, Helheim Glacier, from 2009 to 2017. We find that ice speed correlates most strongly with catchment-integrated runoff at seasonal to interannual scales, while multi-annual flow variability correlates most strongly with multi-annual terminus variability. The multiple relevant time scales and the influence of subglacial topography on Helheim Glacier’s dynamics highlight different regimes that can inform modeling and forecasting of its future. Notably, our results suggest that the recent terminus history observed at Helheim is a response to, rather than the cause of, upstream changes.

Regional-scale, continuously-operating Global Navigation Satellite System (GNSS) networks are a powerful tool to monitor plate motion and surface deformation. Since their inception, their size, density, and length of observation record have steadily increased throughout the world. Simultaneously, researchers have had to write accompanying software to enable the analysis (especially the decomposition) of the ever-increasing amount of available timeseries in an efficient way. These codes and respective studies have individually set standards for different subsets of the following desirable qualities: portability (between locations), speed (code runtime), automation (avoiding or simplifying manual inspection of each station), use of spatial correlation (exploiting the fact that stations experience common signals), availability (open source), and documentation (of the usage and underlying methods). In this study, we present the DISSTANS Python package, which aims to combine the aforementioned achievements in a single software by offering generic (therefore portable), parallelizable (fast) methods that can exploit the spatial structure of the observation records in a user-assisted, semi-automated framework, including uncertainty propagation. The code is open source, includes an application interface documentation as well as usage tutorials, is easily extendable, and is based on the previously published and validated method of Riel et al. (2014). We also present two case studies to validate our code, one using a synthetic dataset and one using real GNSS network timeseries.