The specific surface area (SSA) of snow is a critical structural quantity that controls snow properties and constantly evolves over time. An accurate understanding and modeling of the dynamical evolution of the SSA is thus of primary importance for snowpack models. For this, we simulate the evolution of randomly generated bi-continuous microstructures that resemble real snow microstructures and investigate the control of the ambient conditions (temperature and temperature gradient) and of the physical processes at play on the rate of change of the SSA. Based on this, we propose a new physicallyinformed governing law for the coarsening of microstructures. This law could also benefit other materials than snow, for instance metal alloys. It involves three new material properties, corresponding to the sensitivity to isothermal and temperature gradient conditions and a length scale controlling the transition from kinetics-limited to diffusion-limited regimes. This law accurately predicts the simulation outputs under various conditions. We also propose a potential parametrization of the three newly introduced material properties and evaluate it against snow coarsening data. This work opens the path to a closed system of physics-based equations governing snow microstructural evolution, with direct applicability in snowpack models.