Hypsometry and sensitivity of the mass balance to changes in equilibrium-line altitude: the case of the Southern Patagonia Icefield

We study the relation between glacier hypsometry and sensitivity of mass-balance rate to changes in equilibrium-line altitude (ELA) to assess whether hypsometry can reliably be used to estimate the sensitivity of unmeasured glaciers to changes in ELA. We express the sensitivity of mass-balance rate to ELA, d(B) over dot/dELA, as a function of accumulation area ratio (AAR), its derivative against altitude, dAAR/dELA, and mass-balance functions of ELA. We then apply the concept to 139 glaciers in the Southern Patagonia Icefield for which we derive hypsometry and AAR, and analyze the influence of hypsometry on their mass-balance rate sensitivity. We confirm that glaciers where the bulk of area is located above (below) the ELA are the least (most) sensitive. Glaciers with unimodal hypsometric curves where the peak of area fraction is around the present ELA, and glaciers with bi- or multimodal area distributions, with the ELA located approximately between the bulges, have intermediate sensitivities. We conclude that hypsometry can be used as a first-order estimator of mass-balance rate sensitivity to ELA change.