A new approach to inferring basal drag and ice rheology in ice streams, with applications to West Antarctic Ice Streams

Abstract

Drag at the bed and along the lateral margins are the primary forces resisting flow in outlet glaciers. Simultaneously inferring these parameters is challenging since basal drag and ice viscosity are coupled in the momentum balance, which governs ice flow. We test the ability of adjoint-based inverse methods to infer the slipperiness coefficient in a power-law sliding law and the flow-rate parameter in the constitutive relation for ice using a regularization scheme that includes coefficients weighted by surface strain rates. Using synthetic data with spatial variations in basal drag and ice rheology comparable to those in West Antarctic Ice Streams, we show that this approach allows for more accurate inferences. We apply this method to Bindschadler and MacAyeal Ice Streams in West Antarctica. Our results show relatively soft ice in the shear margins and spatially varying basal drag, with an increase in drag with distance upstream of the grounding line punctuated by localized areas of relatively high drag. We interpret soft ice to reflect a combination of heating through viscous dissipation and changes in the crystalline structure. These results suggest that adjoint-based inverse methods can provide inferences of basal drag and ice rheology when regularization is informed by strain rates.

Data‐Driven Inference of the Mechanics of Slip Along Glacier Beds Using Physics‐Informed Neural Networks: Case Study on Rutford Ice Stream, Antarctica

“…As an example, we may encourage softer ice in high strain-rate areas (such as lateral shear margins) and anisotropic smoothing of the rheology and drag to enforce lower spatial gradients in the along-flow direction where strain-rates are orders of magnitude lower. As demonstrated by Ranganathan et al (2020), such constraints can effectively reduce the inherent trade-offs between rheology and drag variations.…”

Inferred basal friction and mass flux affected by crystal-orientation fabrics

“…We invert for f ( x ) using the canonical method by MacAyeal (1993) and Joughin and others (2004) of reducing the surface-velocity misfit by minimising an appropriate cost functional. Following ice-flow models such as Úa (Gudmundsson and others, 2012; Ranganathan and others, 2020), we adopt the cost functional which penalises both the surface-velocity misfit and large gradients in f 2 , the former depending on the surface velocity uncertainties as prescribed by diagonal matrix β , the latter depending on the magnitude of the regularisation parameter γ f . Note that the ‘true’ velocity field is well-defined only for our synthetic experiments (taken to be the Johnson states), whereas for real inversions it is to be replaced by the observed velocity field.…”

“…Recognising this, some state-of-the-art parameter inversion in glaciology is concerned with jointly inferring both f 2 (or the equivalent thereof) and the flow-rate factor A (see e.g. Arthern, 2015; Isaac and others, 2015; Ranganathan and others, 2020). Without doing so, errors in the prescribed rate-factor field will manifest themselves in the inferred friction coefficient field (e.g.…”

“…Using inverse methods that rely on surface-velocity and ice-thickness observations to infer the basal friction coefficient, large spatio-temporal variations in the friction coefficient, or corresponding basal drag, have previously been inferred over ice streams in Greenland and Antarctica (e.g. Joughin and others, 2004; Sergienko and others, 2014; Ranganathan and others, 2020; Maier and others, 2021).…”

Data-Driven Inference of the Mechanics of Slip Along Glacier Beds Using Physics-Informed Neural Networks

“…softer ice in high strain-rate areas (such as lateral shear margins) and anisotropic smoothing to enforce lower spatial gradients in the along-flow direction. As demonstrated by [60], such constraints can effectively reduce the inherent trade-offs between rheology and drag variations.…”