Polar firn forms a porous and permeable medium. We take 3D micro structural properties obtained by X-ray micro Computer- Tomography to model the measured permeability. The empirical relationship fairly well simulates low permeable layers and the stratigraphic induced variability of the measured profile, but fails for high permeable layers. By applying a sequence of morphological opening the connectivity function is obtained. High permeable layers are characterized by large well connected pores. The occurrence of these specific layers can be linked to the time, the firn was exposed to near-surface temperature gradient metamorphism, convection and coarsening.