Using observations of surface fracture to address ill-posed ice softness estimation over Pine Island Glacier

Abstract. Numerical models used to simulate the evolution of the Antarctic Ice Sheet require the specification of basal boundary conditions on stress and local deviations in the assumed material properties of the ice. In general, scalar fields representing these unknown components of the system are found by solving an inverse problem given observations of model state variables – typically ice flow speed. However, these optimisation problems are ill posed, resulting in degenerate solutions and poor conditioning. In this study, we propose the use of fracture and strain rate data to provide prior information to the inverse problem, in an effort to better constrain the inferred ice softness compared to more heuristic regularisation techniques. We use Pine Island Glacier as a case study and consider both a 'snapshot' inverse problem in which ice softness and basal slip parameters are sought simultaneously over the glacier as a whole, and a 'time-dependent' problem in which ice softness alone is sought over the floating ice shelf at regular intervals. In the first case, we construct a prior encoding the assumption that the ice softness will be close to our initial guess except from where we see fractures or high shear strain rates in satellite data. We investigate the solutions and conditioning of this data-informed inverse problem versus alternatives. The second proposed method makes the assumption that changes to ice softness occurring on monthly-to-annual timescales will be dominated by the fracturing of ice. We show that these methods can result in softness fields on floating ice that visually mimic fracture patterns without significantly affecting the quality of the solution misfit, perhaps leading to greater confidence in the softness fields as a representation of the true material properties of the ice shelf.