Formation of spiky structures in high-altitude snow patches: penitente tilting

TL;DR

This paper models the formation of penitentes, spiky snow structures at high altitudes, as a radiation-driven instability using a 1D diffusion equation, explaining their tilt towards sunlight.

Contribution

It introduces a novel 1D nonlocal radiation model to simulate penitente formation and tilt, advancing understanding of their thermodynamic instability mechanisms.

Findings

Penitentes form from small surface perturbations due to radiation-induced instability.

Simulations reproduce the tilt of penitentes in the direction of sunlight.

The model aligns with observed features of high-altitude snow spikes.

Abstract

Penitentes are spikes formed on the surface of the snow, which are present typically at high altitude in the Andes and Himalayas. They are a consequence of a thermodynamic instability, as a result of the surface sublimation at a given point due to the incidence of light scattered by surrounding features. Here, based on existing literature, we model the time evolution of penitente formation as a purely radiation-driven phenomenon. The physical system is governed by a 1D diffusion equation with a nonlocal source term, which represents the light coming in from all the line of sight accessible from that point of the curve. For small perturbations on the initial profile, the surface undergoes an instability which triggers the formation of spiky structures. For solar radiation coming in the surface at a given angle, our numerical simulations account for a feature observed in the real system: penitentes get tilted in the direction of the sunlight.