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

Year: 2026

Authors: Di Natale G., De Cosmo F.P., Cieri L.

Autors Affiliation: CNR, Natl Inst Opt, Via Madonna Piano 10, I-19100 Sesto Fiorentino, Firenze, Italy; CNR, Inst Applicat Calculous, Via Madonna Piano 10, I-19100 Sesto Fiorentino, Firenze, Italy; Univ Valencia, Inst Fis Corpuscular IFIC, CSIC, Parc Cient, E-46980 Paterna, Valencia, Spain.

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)circle times 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.

Journal/Review: PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS

Volume: 685      Pages from: 131312-1  to: 131312-16

More Information: We would like to thank German Rodrigo and German Sborlini for their careful reading of the manuscript and for their valuable comments. This work is supported by the Spanish Government (Agencia Estatal de Investigacion MCIN/AEI/10.13039/50110001 1033) Grants No. PID2020-114473GB-I00, No. PID2022-141910NB-I00, No. PID2023-146220 NB-I00 and No. CEX2023-001292-S. LC is supported by Generalitat Valenciana GenT Excellence Programme (CIDEGENT/2020/011) . Part of the research activities described in this paper were carried out with contribution of the Next Generation EU funds within the National Recovery and Resilience Plan (PNRR) , Mission 4-Education and Research, Component 2-From Research to Business (M4C2) , Investment Line 3.1-Strengthening and creation of Research Infrastructures, Project IR0000038-Earth Moon Mars (EMM) . EMM is led by INAF in partnership with ASI and CNR. The work was supported also by the FIT-FORUM project CUP: F33C23000240005 and CASIA project CUP: F93C23000430001 of the ASI.
KeyWords: Ice crystals habit; Gauge theory; Field theory; Ice clouds; Climate models; Fokker-Planck equation
DOI: 10.1016/j.physa.2026.131312