Treatment of the ice-shelf backpressure and buttressing in two horizontal dimensions

The ice discharge from the grounded parts of marine ice sheets into the ocean is modulated by their floating extensions-ice shelves. The ice-shelf impact on the grounded ice is typically described as 'backpressure' or 'buttressing'. Theoretical analyses of their effects have been restricted to one horizontal dimension. This study revisits the concepts of 'backpressure' introduced by Thomas (1977) and 'buttressing' numbers and ratios introduced by Gudmundsson (2013) and extends their theoretical analysis to two horizontal dimensions. Using the integral form of the momentum-balance formulation suitable for fast-flowing ice streams and ice shelves, our analysis provides a natural definition for the total backpressure force exerted by an ice shelf to the grounded ice upstream of its grounding line. The results of numerical analyses suggest that ice shelves whose second principal stress component is compressional over larger areas may provide more buttressing compared to ice shelves with smaller areas of compressional stresses or to ice shelves with both principal stresses being tensile.