Abstract

Abstract. The subglacial bed topography is critical for modelling the evolution of Thwaites Glacier in the Amundsen Sea Embayment (ASE), where rapid ice loss threatens the stability of the West Antarctic Ice Sheet. However, mapping of subglacial topography is subject to uncertainties of up to hundreds of metres, primarily due to large gaps of up to tens of kilometres in airborne ice-penetrating radar flight lines. Deterministic interpolation approaches do not reflect such spatial uncertainty. While traditional geostatistical simulations can model such uncertainty, they become difficult to apply because of the significant non-stationary spatial variation of topography over such large surface area. In this study, we develop a non-stationary multiple-point geostatistical (MPS) approach to interpolate large areas with irregular geophysical data and apply it to model the spatial uncertainty of entire ASE basal topography. We collect 166 high-quality topographic training images (TIs) of resolution 500 m to train the gap-filling of radar data gaps, thereby simulating realistic topography maps. The TIs are extensively sampled from deglaciated regions in the Arctic as well as Antarctica. To address the non-stationarity in topographic modelling, we introduce a Bayesian framework that models the posterior distribution of non-stationary TIs assigned to the local line data. Sampling from this distribution then provides candidate training images for local topographic modelling with uncertainty, constrained to radar flight line data. Compared to traditional MPS approaches that do not consider uncertain TI sampling, our approach results in a significant improvement in the topographic modelling quality and efficiency of the simulation algorithm. Finally, we simulate multiple realizations of high-resolution ASE topographic maps. We use the multiple realizations to investigate the impact of basal topography uncertainty on subglacial hydrological flow patterns.

Highlights

  • The characterization of subglacial topography is important for Thwaites Glacier in the Amundsen Sea Embayment, which is experiencing accelerating ice loss (Rignot et al, 2019) that could destabilize the West Antarctic Ice Sheet (Joughin et al, 2014)

  • We show that the training image sampling process accommodates a range of data configurations

  • Multiple-point geostatistics (Journel and Zhang, 2006; Mariethoz and Caers, 2014; Srivastava, 2018; Strebelle, 2002) is the field of study that focuses on the digital representation of physical reality by reproducing high-order statistics inferred from training images

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Summary

Introduction

The topography beneath the Greenland and Antarctic ice sheets is essential for nearly every ice sheet investigation, including modelling subglacial hydrology (e.g. De Fleurian et al, 2018; MacKie et al, 2021a; Siegert et al, 2016; Sommers et al, 2018), interpreting geologic conditions (Bingham and Siegert, 2009; King et al, 2009; Rippin et al, 2014; Holschuh et al, 2020; Alley et al, 2021), estimating ice volume and sea level rise contributions (e.g. Fretwell et al, 2013; Morlighem et al, 2020) and ice sheet modelling for sea level rise projections (e.g. Le clec’h et al, 2019; Schlegel et al, 2018; Seroussi et al, 2017). Yin et al.: Mapping topography of West Antarctica with non-stationary MPS gaps in data remain, which are generally interpolated deterministically using methods such as kriging (Herzfeld et al, 1993), the ArcGIS Topogrid algorithm (Fretwell et al, 2013), spline interpolation (Lytheand Vaughan, 2001; Holt et al, 2006) or ice sheet model inversions (Farinotti et al, 2017; Huss and Farinotti, 2012; Morlighem et al, 2017, 2020) These approaches produce topography that is unrealistically smooth and provide limited morphological information. We use the topographic simulations to model subglacial hydrologic flow in order to investigate the impact of topographic uncertainty on hydrologic uncertainty

Radar data set and training images
Overview
Direct sampling
A metric space for training images
Illustration case and overview of the mapping strategy
Formulation of the problem through probability aggregation
Most probable set of training images
Aggregation by weighting log ratios
Direct sampling with uncertain TI sampling
Training image sampling and DS simulation
Uncertainty in subglacial hydrological flow
Conclusions
Full Text
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