Equipping an ice-flow model with calving and ice-front migration

Global sea-level rise is significantly influenced by glacier melting and retreat palpable all around the world. Of particular interest are marine- and lake-terminating (MALT) glaciers, which, despite their small number, store a substantial portion of the global glacier ice volume. One key component of the glacier mass budget in MALT glaciers is frontal ablation, which involves mass loss at calving fronts through calving, subaerial melting and sublimation, and subaqueous melting. In order to estimate the impact of frontal ablation on the evolution of MALT glaciers, ice-flow models need to exhibit a calving criterion as well as a tracking algorithm for frontal migration. Most of the regionally or globally applicable glacier evolution models (GEM) either lack explicit tracking of ice fronts or, if at all, rely on simple empiric calving parametrization. Here we equip a regionally applicable GEM with a state-of-the-art calving module with the aim to lift the confidence of projecting MALT glacier evolution under climate changes.

In this calving module, an implicit level-set tracking scheme is implemented. The level set function (LSF) evolves based on the frontal ice velocity, melting and calving rate. While subaerial melting is ignored, the ice velocity is determined from the Instructed Glacier Model (IGM). The model is applied to an idealized synthetic glacier geometry featuring undulating bed topography in a 2-D space is used. These synthetic experiments enabled to test the sanity of the implementation, mass and shape conservations as well as numerical stability. Furthermore, the implementation allows for appropriate ice front advance and retreat.

The second part of calving algorithm involves estimation of the calving rate using Eigen calving. It assumes calving rates to be proportional to along and transversal strain rates. The calving algorithm is integrated with the Instructed Glacier Model and applied to selected glaciers of the Kongsfjorden region, Svalbard. Abundant calibration data is available from remote sensing in form of multi-temporal ice-front positions. This approach provides a robust framework for incorporating calving dynamics into regional glacier evolution models. It addresses key gaps in existing methodologies and enhances the ability to better predict glacier front propagation.