Growth rate dependence of the permeability and percolation threshold of young sea ice

The permeability of sea ice is difficult to observe, and physically based permeability models are lacking so far. Here a model for the permeability of sea ice is presented that combines extensive microstructure observations and modelling with directed percolation theory. The model predicts the dependence of sea ice permeability on brine porosity and growth rate, as well as a percolation transition to impermeable sea ice due to necking of the pores. It is validated by numerical simulations of sea ice permeability on 3D images from X-ray microtomographic imaging and by other existing permeability data. A fundamental model result is that the percolation threshold of sea ice scales as ϕ_c ∝ a₀^-1 where a₀ is the plate or brine layer spacing. As the plate spacing decreases with growth velocity V, this implies that the percolation threshold increases as ϕ_c ∝ V^1/3, with the cubic root of the growth rate. For growth rates of natural sea ice the percolation threshold is expected to be in the range of 1 to 4 percent volume fraction of brine. While developed for columnar sea ice, a simple modification for granular surface ice also agrees with observations. The model is valid for sea ice during the growth phase, prior to warming and melting. Permeability modelling of spring and summer sea ice, with wider secondary brine channels present, requires 3D pore space observations in warming sea ice that currently are sparse.