Ice shelf evolution combining flow, flexure, and fracture

Abstract

Ice shelves regulate ice sheet dynamics, with their stability influenced by horizontal flow and vertical flexure. MacAyeal and others (2021) developed the theoretical foundation for a coupled flow-flexure model (the “M21 model”), combining the Shallow Shelf Approximation with thin-beam flexure, providing a computationally efficient tool for studying phenomena like ice shelf rumpling and lake drainage. However, the M21 model relies on proprietary software, is unstable under compressive flow conditions, and does not incorporate fracture processes critical for capturing ice-shelf damage evolution. We present an open-source version of the M21 model addressing these limitations. Using the free Python libraries Firedrake and icepack, we introduce a plastic failure mechanism, effectively limiting bending stresses and thereby stabilizing the model. This enhancement expands the viscous M21 model into a viscoplastic flow-flexure-fracture (3F) framework. We validate the 3F model through test cases replicating key ice shelf phenomena, including marginal rumpling and periodic surface meltwater drainage. By offering this tool as open-source software, we aim to enable broader adoption, with the ultimate aim of representing surface meltwater induced flow-flexure-fracture processes in large-scale ice sheet models.