Some insights from the second principle for snow modelling

As snowpacks are largely governed by thermodynamics, special care is usually given as to ensure the first principle, i.e. energy conservation, in their mathematical and numerical descriptions. On the other hand, the second principle, i.e. entropy production, has received less attention. However, the second principle, and its numerical translation, has proven to be a powerful tool in applied mathematics to ensure the stability of mathematical and numerical models. The goal of this work is thus to present the derivation of thermodynamically consistent numerical snowpack models. This rigorous approach restricts the number of acceptable numerical schemes that unconditionally comply with the second principle, and which are thus free of spurious oscillations, overshoots, or divergence. As examples, we consider some regularly encountered cases of numerical instabilities in snowpack models, and re-visit them based on the second principle point of view.