Till calving do us apart: Systematising data assimilation of frontal ice retreat for glacier evolution modelling of marine- and lake-terminating glaciers

Iceberg calving is a major component of the mass budget of marine- and lake-terminating glaciers. Despite increased attention to calving processes over the past few decades, large uncertainties persist in regional and global calving estimates. Although numerous empirical calving relations have been developed and implemented in glacier evolution models, iceberg calving remains a dominant source of uncertainty in future projections of marine- and lake-terminating glaciers. One of the major challenges in calving estimates is accurately tracking the ice front position at the subgrid scale. Subgrid-scale level-set methods have recently emerged as an effective approach to overcome this limitation by representing the calving front as a dynamically evolving interface.

​In this study, we present the application of a calving algorithm based on the level-set method coupled with the eigen-calving law. The method allows for a natural and robust treatment of complex topological changes at calving fronts, including retreat, advance, merging, and fragmentation. For regional application, the heterogeneity of observed retreat and glacier-specific characteristics hinders a direct spatial transfer of calving parameters. Moreover, the temporal stability of this parameter is not assured. Calibration during a single period does not guarantee good performance later. This calls for glacier-specific and transient calibration strategies to constrain calving behaviour. For this purpose, the calving algorithm is incorporated into an existing data assimilation framework that uses an Ensemble Kalman Filter. The coupled system is implemented within the Instructed Glacier Model (IGM).

We apply the model on the Kronebreen-Kongsbreen complex in Kongsfjorden, Svalbard, for the period 2000-2025. Observed calving front positions are assimilated to constrain modelled front evolution, thereby reducing uncertainty in calving front migration. By directly incorporating observational information, data assimilation avoids the need for manual, time-consuming parameter tuning. The model performs well in regions characterized by retrograde bed slopes and higher ice velocities, as in the Kronebreen complex. In contrast, the presence of bedrock ridges and narrow lateral valleys introduces additional noise into strain-based calving estimates, as observed at Kongsbreen. Despite these challenges, the results demonstrate that incorporating observational constraints via data assimilation provides an effective and scalable simulation of calving-front evolution for water-terminating glaciers.