On the long-term propagation of contrails using a novel high-fidelity advection-diffusion model

There is growing evidence suggesting that condensation trails (contrails) contribute to aviation-induced atmospheric warming at least as significantly as carbon dioxide emissions. Mitigating the warming effects of contrails requires the development of effective avoidance strategies, which in turn depend on accurate and computationally efficient contrail models. Contrails undergo multiple formation and evolutionary stages, beginning with their initial formation, progressing through a rapid growth phase, and culminating in their eventual dissipation or conversion into cirrus clouds. The long-term evolution of contrails—particularly their transformation into cirrus clouds—plays a critical role in defining their radiative forcing and climate impact. This stage of evolution is predominantly governed by advection-diffusion processes, coupled with particle-growth dynamics. We propose a novel contrail evolution model based on a coupled system of nonlinear advection-diffusion equations (ADE). This model integrates underexplored or previously neglected influences, including spatiotemporal wind variability, spatiotemporal and nonlinear diffusion coefficients accounting for diffusion limitation behavior, as well as significant ice-particle slip mechanisms. The proposed model is solved using an analytic discretization method, which outperforms classical numerical methods in terms of computational speed and accuracy. The model's performance is further compared against ground-based camera observations of contrails, providing an empirical basis for assessing its predictive capability. In addition, the model introduces several theoretical adjustable parameters, which can be calibrated using ground truth data to optimize its representation of advection-diffusion processes. This adaptability ensures that the model remains robust under varying atmospheric conditions and operational scenarios. By advancing our understanding of contrail dynamics and providing a computationally efficient solution framework, this work lays the foundation for more effective contrail avoidance strategies.