A Markov chain Monte Carlo approach for geostatistically simulating mass-conserving subglacial topography

Niya Shao , Emma MacKie, Michael Field, Felicity McCormack

Subglacial topography is critically important for simulating ice sheet evolution and projecting sea-level contributions. However, the subglacial topography of the Antarctic Ice Sheet is sparsely measured. Obtaining a gridded topography map used in ice sheet simulations requires interpolating the sparse measurements or inverting topography from observations of ice velocity and surface elevation. Traditional inverse methods based on the mass conservation law often produce a single topography that is overly smooth and does not capture the non-uniqueness of the solutions to mass conservation. Instead of solving for a single topography deterministically, stochastic methods can be developed to simulate equiprobable realizations of mass-conserving topography with realistic roughness. In this study, we develop a new algorithm that combines geostatistical simulations with Markov chain Monte Carlo (MCMC) to stochastically generate subglacial topography realizations for Denman Glacier. The final topography ensemble shows significant elevation differences to BedMachine and large topographic uncertainty. This topography ensemble can be incorporated in ensemble modeling, allowing the propagation of topographic uncertainty to the uncertainty in sea level contribution predictions.