| 22 Sep 2025
A multi-physics Eulerian framework for long-term contrail evolution
Abstract. Condensation trails (contrails) are increasingly recognized as a major contributor to aviation-induced atmospheric warming, rivaling the impact of carbon dioxide. Mitigating their climate effects requires accurate and computationally efficient models to inform avoidance strategies. Contrails evolve through distinct stages, from formation and rapid growth to dissipation or transition into cirrus clouds, where the latter phase critically determines their radiative forcing. This long-term evolution is primarily driven by advection-diffusion processes coupled with ice-particle growth dynamics. We propose a new multi-physics Eulerian framework for long-term contrail simulations, integrating underexplored or previously neglected factors, including spatiotemporal wind variability; nonlinear diffusion coefficients accounting for potential diffusion-blocking mechanisms; a novel multiphase theoretical model for the bulk settling velocity of ice particles; and ice-crystal habit dynamics. The Eulerian model is solved using a recently proposed discretization approach to enhance both accuracy and computational efficiency. Additionally, the Eulerian model introduces several theoretical, adjustable parameters that can be calibrated using ground-truth data to optimize the built-in nonlinear advection–diffusion equations (ADEs). We further demonstrate that the governing nonlinear ADEs admit dimensional separability under suitable assumptions, making the multi-physics Eulerian model particularly promising for large-scale simulations of contrail plumes and, ultimately, their associated radiative forcing.
This work presents a novel contrail evolution model for the long-term phase of the contrail lifecycle after the breakdown of the vortex wake. The novelty of the model sits in its explicit coupling of macroscopic and microscopic physical processes in an Eulerian framework, addressing previously underexplored effects that arise out of this coupling. As such, the horizontal and vertical evolution of the contrail plume, as well as the distributions of ice particle habits within the plume, display interesting behaviors that will bring meaningful impact to the field of contrail modelling.
While I believe this manuscript has the potential to be publishable in this journal, there are several significant changes that I feel should be made before doing so. The challenges I have are related to one another, and I believe the authors can readily address them. I’ll outline them here and provide further details below, including recommendations for changes that I believe would both improve the manuscript and address these issues.
Before detailing major and minor recommended changes, I would like to address some of things I enjoyed about the work:
Major Points
I recommend that the paper should undergo restructuring, deciding what its main narrative is, what is essential to that, and what is consequently peripheral. If the work’s intent is to present a new contrail model, then it should spend time evaluating that new model (see more below). If the work’s intent is to showcase the physical behaviors derived from application of the new model, then less time should be spent on outlining and detailing aspects of the internal workings of the model. To do all of this in a single publication would make the work exceedingly long, which is why I understand the authors having written the work as presented. However, by trying to do all of it, several problems arise, including the 1/2/3 outlined above. Once the choice of intent is decided, the gaps that this choice leaves behind should be addressed directly by the authors in the work, clearly outlining the scope of the present work and what they intend to do in future publications or encourage others to examine.
A restructuring and refocusing should also help with the balance between model setup and model exploration. Currently, there are too many (albeit excellently written) pages of model derivation for the reader to get through (see Minor Points for recommendations), with a then quite short results section. The reader feels rushed towards the end of the work and takes less meaning away than the work deserves. After a reduced outline of the model, I would thus recommend including an examination/evaluation of the choices that were presented throughout the setup, demonstrating that the model produces contrail shapes and lifetimes that are in keeping with expectation, before moving on to exploring the impactful results related to the novel physics. A section where such model outputs are briefly compared to existing models as reviewed in the introduction (e.g., CoCiP, APCEMM, LES from Simon Unterstrasser and collaborators), or even to the limited observations that we have, is essential to demonstrate these points to the reader. Highlighting where the model outputs are similar to or differ from these other models, and why, helps set the context for interpreting the physical behaviors on show. I have a feeling that the authors have already pursued such comparisons and intended to perhaps place them in an additional manuscript, so hopefully these additions shouldn’t be a large volume of work, but they are necessary here to demonstrate the capabilities of the model.
In terms of the results as presented, Sections 6.1 & 6.2 feel appropriate as they focus on specific physics introduced as novel and offer interpretation/discussion. The start of Section 6.3 offers some exploration of the columnar crystal settling phenomenon, but then figures are presented in rapid fire, with insufficient explanation to the reader as to their intended meaning, why they’re significant, or whether their content is what we might expect given the model parameterizations and initial conditions. All of these results are interesting and potentially impactful, but without the accompanying discussion, they don’t add the value that they should.
I realize that by asking for this additional analysis and discussion, the length of the work is starting to creep upwards. However, I strongly believe that, as discussed above, there are critical elements which are missing, and several sections which could be reasonably moved to an appendix.
Minor Points