Grounding-zone ice thickness from InSAR: inverse modelling of tidal elastic bending

Ice-thickness measurements in Antarctic ice-shelf grounding zones are necessary for calculating the mass balance of individual catchments, but remain poorly constrained for most of the continent. We describe a new inverse modelling optimization approach to estimate ice thickness in the grounding zone of Antarctic outlet glaciers and ice shelves using spatial patterns of tide-induced flexure derived from differential interferometric synthetic aperture radar (InSAR). We demonstrate that the ill-posedness of the inverse formulation of the elastic-plate equations for bending can be controlled by regularization. In one dimension, the model recreates smooth, synthesized profiles of ice thickness from flexure information to within 1-2%. We test the method in two dimensions and validate it in the grounding zone of Beardmore Glacier, a major outlet glacier in the Transantarctic Mountains, using interferograms created from TerraSAR-X satellite imagery acquired in 2012. We compare our results with historic and modern ice-thickness data (radio-echo sounding from 1967 and ground-penetrating radar from 2010). We match both longitudinal and transverse thickness transects to within 50 m root-mean-square error using an effective Young's modulus of 1.4 GPa. The highest accuracy is achieved close to the grounded ice boundary, where current estimates of thickness based on surface elevation measurements contain a systematic bias towards thicker ice.