Ice-sheet thickness reconstruction with uncertainty quantification

forthcoming

The Antarctic and Greenland ice sheets are fundamental to the Earth's climate system and the main contributors to sea-level rise. The overall ice-thickness distribution of an ice sheet is computed from sparse ice-thickness measurements using reconstruction methods. This data sparsity results in a marked uncertainty of the ice-thickness reconstructions, which is never taken into account in a mathematically rigorous manner. This implies large deviations between different ice-thickness reconstructions, delivering inconsistent estimates of sea-level rise rates. To remedy this, we propose formulating the ice-thickness reconstruction as a Bayesian inverse problem that combines data and mathematical models for ice-sheet dynamics. The solution of this inverse problem is a probability distribution for the ice-thickness, resulting in a rigorous quantification of uncertainty. However, conventional numerical methods either break down or become impractically slow when solving this problem. To circumvent this, we propose the design of a Monte-Carlo Markov-Chain (MCMC) method that combines ideas from multi-fidelity and the stochastic Newton MCMC methods. These are two sophisticated mathematical techniques that have achieved extraordinary reductions in computational time, allowing for previously unfeasible computations. We will apply our method to reconstruct the ice-thickness of the Antarctic Peninsula Ice sheet (APIS). This important Antarctic region has a complex geometry that has defied existing ice-thickness reconstruction methods. Our Bayesian inversion approach has the potential of reconciling dissimilar estimates of ice-discharge by quantifying confidence intervals via uncertainty. This highly interdisciplinary project will develop the applicant's mathematical and glaciological knowledge in an internationally-recognized research team. Research will be complemented with enriching activities such as Antarctic fieldwork (as training) and supervision of PhD students.