Diagnosing the sensitivity of grounding line flux to changes in sub-ice shelf melting

We look for an improved physical understanding for how ice dynamics link ice thickness perturbations, via changes in sub-ice shelf melting, to changes in ice shelf buttressing and grounding line flux. More specifically, we seek a connection among grounding line flux, ice shelf buttressing and basal melting. By studying the ice dynamics for both idealized (MISMIP+) and realistic (Larsen C) ice shelves, we find a strongly direction-dependent buttressing number that links local changes in ice shelf thickness and dynamics with changes in the integrated grounding line flux. From these two examples, this buttressing metric, defined using the first principal stress, is better overall for quantifying changes in grounding line flux than a similar metric defined using the second principal stress or stress along the flow direction. This correlation is possibly controlled by the relative relationship of geometric/dynamic features between the perturbation point and the grounding line, indicating a dynamic (time evolving) sensitivity field of integrated grounding line flux to basal melt. We find this buttressing metric only shows a robust relationship with the integrated grounding line flux for regions near the center of an ice shelf; for points too near the grounding line or the calving front, no clear relationship exists. This motivates our exploration of an adjoint-based method for defining integrated grounding line flux sensitivity to local changes in ice shelf geometry.