A continuum mechanics perspective on the rheology of firn in the context of firn densification

While the complex nonlinear rheology of ice is well known and often discussed, for example in the context of large-scale ice sheet modeling, calving, and isotropy occurring at shear margins, the rheology of firn is often considered to be rather simple. According to Truesdell’s first metaphysical principle, which states that ”all properties of a mixture must be mathematical consequences of properties of the constituents” (Truesdell, C. (1984), Rational Thermodynamics, Springer-Verlag, p. 221), the material behavior of firn should be related to that of ice, since firn is primarily a mixture of ice and air. What distinguishes firn from ice is its microstructure. The field of continuum mechanics provides methods to relate the microstructural properties of a material to its macroscopic material behavior.

Here we review a homogenization method developed for the densification of nonlinear creeping metallic powders and first applied to the simulation of firn densification by Gagliardini and Meyssonnier (1997, Annals of Glaciology, 24, pp. 242–248). The method links the rheology of ice to that of firn by describing firn as a porous medium with an ice matrix. The advantage of this approach is that it is formulated in all three spatial dimensions, allowing the inclusion of horizontal divergence due to ice flow without additional parameterization. A large database of dated firn cores allows the determination of the governing model parameters using an optimization approach. We discuss the results, advantages, and limitations of this approach, as well as validation strategies.