Comment on jecats-2026-12

Abstract

Abstract. Condensation trails (contrails) evolve from formation and rapid growth to dissipation or transition into cirrus clouds (i.e., the long-term diffusion regime), where the latter phase largely determines their radiative forcing. This research develops a high-speed Eulerian contrail plume solver for large-scale analyses while approximating the multi-physical processes governing plume evolution. We propose a unified Eulerian framework for the long-term regime of contrails that integrates the population balance equation with ice-particle growth dynamics. Under suitable assumptions, the governing nonlinear field equations admit dimensional separability, allowing the horizontal and vertical evolution to be nearly decoupled. Consequently, the plume microphysics is described by a highly nonlinear system of ((z,t)) partial differential equations (PDEs), while the horizontal evolution governs plume spreading. Since this work considers single-plume analysis, we focus mainly on the coupled vertical PDE system, extending existing large-scale contrail models from tracking bulk quantities to resolving the plume's spatiotemporal evolution. The PDEs incorporate several underexplored factors, including multiphase behavior of the bulk settling velocity of ice particles in turbulent flows, a parameterization of ice-crystal habit dynamics that modifies growth, sublimation, and settling, as well as stochastic diffusion and vertical wind. The model also introduces adjustable parameters that can be calibrated using ground-truth data to optimize the nonlinear PDEs. Owing to its computational speed (roughly below 1 second to simulate 10 hours of plume evolution), the solver is well suited for large-scale simulations of contrail evolution and radiative forcing. Notably, although the mathematical framework is general capable of resolving/approximating polydispersity, the current solver assumes a monodisperse distribution.