The Statistical Physics of Iceberg Calving and the Emergence of Universal Calving Laws

Determining a calving law valid for all glaciological regimes has proven to be a difficult problem in glaciology. For this reason, most models of the calving process are semi-empirical, with little connection to the underlying fracture processes. In this study, I introduce methods rooted in statistical physics to show how calving laws, valid for any glaciological domain, can emerge naturally as a large spatial-scale/long temporal-scale limit of an underlying continuous or discrete fracture process. An important element of the method developed here is that iceberg calving is treated as a stochastic process and that the probability that an iceberg will detach in a given interval of time can be described by a probability distribution function. Using limiting assumptions about the underlying probability distribution, the theory is shown to be able to simulate a range of calving styles including the sporadic detachment of large, tabular icebergs from ice tongues and ice shelves and the more steady detachment of smaller sized bergs from tidewater/outlet glaciers. The method developed has the potential to provide a physical basis to include iceberg calving into numerical ice sheet models that can be used to produce more realistic estimates of the glaciological contribution to sea level rise.