A model for ice sheets and glaciers in fractal dimensions

Several studies have confirmed the fractal geometry of various glacial fields on Earth and the presence of self-organizing glacial environments. These have been confirmed using satellite geodesy such as Landsat data and SPOT Panchromatic satellite data. In this manuscript, we study ice sheet dynamics and glacier in fractal dimensions based on the notion of “product-like fractal measure” recently introduced in Literature. This approach is practical to model continuum processes characterized by anisotropies. We discuss two main problems based on the shallow-ice approximation: the ice-sheet profile and the parallel-sided slab problems in fractal dimensions. In the first problem, a deformation in the Vialov profile has been observed. In particular, for fractal dimensions much less than unity, the surface profile is peakish at the end of the horizontal extent. This observation holds for various Glen’s flow parameter. When cap is expanding sideways, we have revealed the emergence of accumulation and ablation mainly for low fractal dimensions. In the second problem, both the temperature profile and the horizontal velocity are affected by fractal dimensions. The surface temperature decreases to a temperature higher than the one obtained in the basic approach, i.e. integer dimensions. This may have some impacts on climate change.