Comprehensive Assessment of Stress Calculations for Crevasse Depths and Testing with Crevasse Penetration as Damage

Abstract. Crevasse depth calculations with the Nye formulation or linear elastic fracture mechanics are used in many applications, including calving laws, determination of stable cliff heights, shelf vulnerability to collapse via hydrofracture, and damage evolution in ice. The importance of improving the representation of these processes for reducing sea-level rise uncertainty makes careful calculation of stresses for crevasse depths critical. The resistive stress calculations used as input for these crevasse predictions have varied across studies, including differences such as the use of flow direction stress versus maximum principal stress, the inclusion of crevasse-parallel deviatoric stress, and calculation of effective strain rate. Some studies even use deviatoric stress in the place of resistive stress for crevasse depth calculations. Many studies do not provide an adequate description of how stress was calculated. We provide a systematic review of how resistive stress calculations found in literature result in differing crevasse depth predictions and where these differences are pronounced. First, we study differences in crevasse size calculated from idealized representative strain rate states and then from velocity observations of several Antarctic ice shelves. To test whether the patterns of crevasse depths predicted from these stresses have a strong connection to bulk rheology, we use crevasse penetration as damage and compare predicted velocities from an ice sheet model against observed velocity. We find that the selection of stress calculation can change crevasse size predictions by a factor of two and that differences are pronounced in shear margins and regions of unconfined, spreading flow. The most physically; consistent calculation uses the maximum principal stress direction, includes vertical strain rate from continuity in the effective strain rate calculation, and uses three-dimensional resistive stress (𝑅_𝑥𝑥 = 2𝜏_𝑥𝑥 + 𝜏_𝑦𝑦). However, this calculation has rarely been used to date in studies requiring crevasse depth predictions. We find that this most physically consistent stress calculation produces a damage pattern that qualitatively matches surface features and quantitatively reproduces observed velocities better than other stress calculations; we therefore recommend the use of this stress calculation. This result also suggests that other stress calculations likely overpredict shear margin vulnerability to hydrofracture and would overpredict calving in shear margins and spreading fronts when implemented in the crevasse depth calving law.