Lagrangian analysis of ICESat altimetry reveals patterns of ice shelf basal melting

Iceberg calving and ice shelf basal melting are normal mass-loss processes that over time roughly balance the outflow of ice from the Antarctic Ice Sheet. Most basal melting is thus compensated by ice advection and is not detected by the traditional methods of analyzing surface elevation changes in a fixed geographic coordinate system (Eulerian). Here we present a new method that derive elevation changes in a "Lagrangian" sense from repeat-track ICESat laser altimetry, where specific locations are followed on the advancing ice shelf surface. We use a published ice shelf velocity field to correct for ice advection between consecutive repeats, and then convert the Lagrangian dh/dt estimates into ice thickness changes based on a model of the firn layer. In some locations, the derived ice thickness changes are much larger the Eulerian approach. The Lagrangian approach reduces the noise level of the derived ice thickness changes and reveals clear spatial patterns that we interpret as variations in basal melting. For the largest Antarctic ice shelves (Ross and Filchner-Ronne), we find that the Lagrangian thinning rates increase progressively towards the fronts, which is consistent with oceanographic models that suggest higher basal melt rates in the frontal zone. There are few examples of localized Lagrangian thickening, suggesting that basal melting is likely dominating over basal freezing in the interior of most ice shelves. Combined with data on surface mass balance and firn compaction, our Lagrangian approach can provide new insights into the magnitude and extent of basal melting, as well as being an important validation for models of ice-ocean interaction.