A Micro-Mechanical Model for the Transformation of Dry Polar Firn Into Ice Using the Level-Set Method

Abstract

Interpretation of greenhouse gas records in polar ice cores requires a good understanding of the mechanisms controlling gas trapping in polar ice, and therefore of the processes of densification and pore closure in firn (compacted snow). Current firn densification models are based on a macroscopic description of the firn and rely on empirical laws and/or idealized geometries to obtain the equations governing the densification and pore closure. Here, we propose a physically-based methodology explicitly representing the porous structure and its evolution over time. In order to handle the complex geometry and topological changes that occur during firn densification, we rely on a Level-Set representation of the interface between the ice and the pores. Two mechanisms are considered for the displacement of the interface: (i) mass surface diffusion driven by local pore curvature and (ii) ice dislocation creep. For the latter, ice is modeled as a viscous material and the flow velocities are solutions of the Stokes equations. First applications show that the model is able to densify firn and split pores. Using the model in cold and arid conditions of the Antarctic plateau, we show that gas trapping models do not have to consider the reduced compressibility of closed pores compared to open pores in the deepest part of firns. Our results also suggest that the mechanism of curvature-driven surface diffusion does not result in pore splitting, and that ice creep has to be taken into account for pores to close. Future applications of this type of model could help quantify the evolution and closure of firn porous networks for various accumulation and temperature conditions.