Stochastic modeling of subglacial topography exposes uncertainty in water routing at Jakobshavn Glacier

Abstract

Subglacial topography is an important feature in numerous ice-sheet analyses and can drive the routing of water at the bed. Bed topography is primarily measured with ice-penetrating radar. Significant gaps, however, remain in data coverage that require interpolation. Topographic interpolations are typically made with kriging, as well as with mass conservation, where ice flow dynamics are used to constrain bed geometry. However, these techniques generate bed topography that is unrealistically smooth at small scales, which biases subglacial water flowpath models and makes it difficult to rigorously quantify uncertainty in subglacial drainage patterns. To address this challenge, we adapt a geostatistical simulation method with probabilistic modeling to stochastically simulate bed topography such that the interpolated topography retains the spatial statistics of the ice-penetrating radar data. We use this method to simulate subglacial topography using mass conservation topography as a secondary constraint. We apply a water routing model to each of these realizations. Our results show that many of the flowpaths significantly change with each topographic realization, demonstrating that geostatistical simulation can be useful for assessing confidence in subglacial flowpaths.

Proper orthogonal decomposition of ice velocity identifies drivers of flow variability at Sermeq Kujalleq (Jakobshavn Isbræ)

“…type 1b above), and where base-level water flow, generated from frictional melting, will flow throughout the year. Uncertainties in basal topography create uncertainties in the exact locations of PDAs (Mackie et al, 2021): hence in areas where multiple PDAs are confluent, we have higher confidence that these are areas of high hydrological activity. The dynamic response to hydrological forcing will vary through time as the drainage system evolves.…”

Mapping high-resolution basal topography of West Antarctica from radar data using non-stationary multiple-point geostatistics (MPS-BedMappingV1)

“…The topography beneath the Greenland and Antarctic ice sheets is essential for nearly every ice sheet investigation, including modeling subglacial hydrology (MacKie et al, 2021), interpreting geologic conditions (Holschuh et al, 2020), estimating ice volume and sea level rise contributions (Fretwell et al, 2013), and ice sheet modeling for sea level rise projections (Le clec'h https://doi.org/10.5194/gmd-2021-297 Preprint. Discussion started: 14 September 2021 c Author(s) 2021.…”

“…Furthermore, deterministically interpolated topography does not sample the uncertainty space, making it difficult to quantify uncertainty in ice sheet models with respect to topographic uncertainty. These issues have previously been addressed with two-point geostatistical simulation, such as sequential Gaussian simulation (SGSIM) (MacKie et al, 2021). The objective of geostatistical simulation is to generate multiple realizations of phenomena that reproduce the spatial variability of observations, as modeled by variogram or spatial covariance and can be used to quantify uncertainty (e.g.…”

“…Thwaites Glacier has previously been simulated by Goff et al (2014), though only one realization was generated. Geostatistical simulation has also been applied in Antarctica and Greenland to quantify uncertainty in subglacial hydrology (MacKie et al, 2020(MacKie et al, , 2021Zuo et al, 2020).…”

“…Pyrcz and White, 2015) or using covariates (e.g. Almeida and Journel, 1994;MacKie et al, 2021). However, such approaches typically model the variation in the mean (trend) or some degree of correlation (co-simulation).…”