Horizontal Force Balance Calving Laws: Ice Shelves, Marine- and Land-Terminating Glaciers

Predicting calving in glacier models is challenging, as observations of diverse calving styles appear to contradict a universal calving law. Here, we generalize and apply the analytical Horizontal Force Balance (HFB) fracture model from ice shelves to land- and marine-terminating glaciers. We consider different combinations of "crack configurations" including dry or meltwater surface crevasses above saltwater- or meltwater-filled basal crevasses. Our generalized model analytically reveals that, in the absence of meltwater, calving criteria depends on two dimensionless variables: buttressing B and dimensionless water level λ. Using a calving regime diagram, we quantitatively demonstrate that glaciers are generally more prone to calving with reduced buttressing B and lower water level λ. For a specified set of B, λ and crack configuration, an analytical calving law can be derived. For example, the calving law for an ice shelf, land-, or marine-terminating glacier with a dry surface crevasse above a saltwater basal crevasse reduces to a state with no buttressing (B = 0). With climate warming, glaciers are expected to become more vulnerable to calving due to meltwater-driven surface and basal crevassing. Our findings provide a framework to understand diverse calving styles.