Gauge theory approach to describe ice crystals habit evolution in ice clouds

Abstract

Ice clouds, particularly cirrus clouds, significantly influence Earth's radiative balance but remain poorly characterized in current climate models. A major uncertainty arises from the variability of their microphysical properties, especially the evolution of ice crystal habits under depositional growth. We propose a heuristic method to describe habit evolution based on four fundamental shapes identified in the literature and from in situ observations: droxtals, plates, columns, and rosettes. These represent the primary forms that are relevant under depositional growth, excluding aggregation. In this study, we employ a non-Abelian gauge theory within a field-theoretical framework, imposing an SU(2) $\otimes$ U(1) symmetry on the fields associated with each habit probability growth. This symmetry enables the derivation of a modified system of coupled Fokker-Planck equations, capturing the stochastic growth dynamics of ice crystals while incorporating phenomenological mutual influences among habits. This framework outlines a novel theoretical direction for integrating symmetry principles and field-theoretical tools into the modelling of habit dynamics in ice clouds.