A statistically inferred calving parameterization for spatial and temporal decomposition of tidewater glaciers in Greenland

Calving is responsible for the retreat and mass loss of many major tidewater glaciers in Greenland, enhancing its contribution to sea level rise. However, our understanding of calving remains limited, and its representation in ice sheet numerical models is overly simplified, limiting our ability to project the future mass balance of the ice sheet. Most existing physical-based calving laws are generally restricted to particular types of glaciers, regions, and oceanic conditions. The main obstacle in developing a physically-based calving law is its high spatial and temporal variability, as well as the large uncertainties associated with the model and observations since the field sites of the ice front are generally difficult to access. In this study, we develop a statistically inferred calving parameterization that decomposes the spatial and temporal dependency of the calving rate for 4 major glaciers around Greenland. By analyzing the observed retreat and velocity change of Helheim, Jakobshavn, Kangerlussuaq, and Upernavik glaciers on Greenland from 2007 to 2020, we find that the water depth at the calving front is the primary control of the spatial variability of the calving rate and that the temporal variability is governed by a single scalar time series of the maximal frontal ablation rate for each glacier. We calibrate and apply this calving parameterization, and simulate the four glaciers using the Ice Sheet and Sea-level System Model (ISSM) from 2007 to 2022. We are able to reproduce both the long-term trend, the seasonal variability of the calving front positions, as well as the ice velocities with excellent accuracy. We conclude that the spatial dependency of calving comes from the water depth and this finding can be used as a guide for future development of calving laws.