Stochastic Simulation of Mass-Conserving Subglacial Topography with Monte Carlo Markov Chain

Abstract

While subglacial topography serves a crucial role in ice sheet models, it remains generally sparsely sampled across Antarctica. Subglacial topography is primarily measured by airborne ice-penetrating radar with data gaps exceeding 100s of kilometers. Traditional kriging methods used to interpolate the sparse radar data cause spurious effects on ice flow divergence. Numerically solving for mass conservation equations addresses this issue but may smooth out the roughness of topography observed in the covariance structure of radar data. In this study, we propose a novel approach to generate an ensemble of realistically rough and mass-conserving subglacial topography. We utilize the Monte Carlo Markov Chain algorithm, where in each iteration of the Markov Chain, the topography is perturbed by Sequential Gaussian Simulation to reproduce the covariance structure in the radar data. The perturbed topography is then accepted with a probability constrained by both prior probability based on the radar measurement uncertainty and likelihood indicated by the topography’s deviation from mass conservation law. After the Markov Chain converges to a stable state, an ensemble of topography is sampled from the chain. We tested the method on Denman Glacier and produced posterior distribution of topography constrained by radar measurements and mass conservation. Moreover, the covariance structure of radar data is preserved in every generated topography realization. The method we developed provides a possibility to incorporate realistically rough topography into ice sheet models while avoiding artifacts caused by the violation of mass conservation. Furthermore, multiple subglacial topography realizations allow the propagation of inherent uncertainties in the sparsity of radar measurement to the result of downstream models.