Gauge theory approach to describe ice crystals habit evolution for ice clouds radiative transfer modeling

Abstract

Ice clouds, particularly cirrus, play a crucial role in Earth’s radiative balance, yet remain poorly represented in current climate models. A major source of uncertainty stems from the variability of their microphysical properties, especially the shape of ice crystals. In this paper, we propose a heuristic framework to describe the evolution of four main crystal habits — droxtals, plates, columns, and rosettes — commonly identified in situ observations and widely adopted in radiative transfer simulations. Rather than predicting the exact final morphology of individual crystals, our approach aims to assess the likelihood that, at a given time and under specified thermodynamic conditions, a crystal will most closely correspond to one of these canonical shapes used in cirrus modeling. In this study, we establish the theoretical foundations of this new approach by employing a non-Abelian gauge theory within a field-theoretical framework. Specifically, we impose an SU(2)$\otimes$U(1) symmetry on the fields associated with the probability of habit growth. This symmetry leads to a modified system of coupled Fokker–Planck equations, which capture the stochastic dynamics of ice crystal growth while incorporating phenomenological interactions among different habits. Our framework thus outlines a novel theoretical direction for integrating symmetry principles and field-theoretical tools into the modeling of habit dynamics in ice clouds. At this stage, numerical solutions of the proposed equations have not yet been implemented; developing and validating these with experimental data represents the next step of this research.