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

Many numerical models used to simulate ice streams require the specification of control fields representing the slipperiness of the ice/bed interface and local deviations in the assumed rheological properties of the ice. These poorly constrained components of the system are often found by solving an inverse problem given observations of model state variables - typically ice flow speed. However, these inverse problems are generally ill-posed, resulting in degenerate or error-dominated solutions. The clearest way to improve this is to take advantage of additional prior information regarding the control fields. 

In this study, we investigate two ways of using maps of surface fracture, derived from Sentinel-1 satellite imagery, to provide prior information to the inverse problem. We first consider a prior that assumes values of effective viscosity significantly different from Glen's flow law are, for the most part, due to observable fractures. Using Pine Island Glacier as a case study, we investigate the solutions and conditioning of this data-informed inverse problem and compare with a typical heuristic regularisation technique. We find that the inclusion of fracture data results in softness fields that resemble fracture features on floating ice. On grounded ice, despite the prevalence of surface crevassing, the softness fields look no more plausible when fracture data is included - suggesting that the presence of surface fracture is not the largest contribution to our uncertainty in the ice rheology. We go on to investigate the use of timeseries of fracture maps to constrain the evolution of the softness field on ice shelves through time, making the assumption that changes to ice rheology occurring on annual timescales are dominated by the fracturing of ice. We show that this method can result in softness fields that visually mimic fracture patterns on floating ice without significantly affecting the quality of the misfit. Such softness fields could be used to constrain evolution equations in isotropic damage models.