Spiky ice and penitente tilting

Under certain conditions, at high altitude, the surface of snow develops spike-like structures known as penitentes. This is a rather counterintuitive phenomenon, which is a consequence of surface sublimation at a given point as a result of the incidence of light scattered by the surrounding region. Following the existing literature, we model the time evolution of the phenomenon described above as a 1D diffusion equation with a non-local source term, as it represents the light coming from all the line of sight defined for a point of the curve. For small initial perturbations in the surface, the system undergoes a thermodynamic instability which triggers the formation of spikes. For sunlight coming in at a given angle, numerical simulations account for a feature observed in the real system: penitentes get tilted in the direction of the sunlight.