| 08 Apr 2026
Contrail formation for aircraft with hydrogen combustion – Part 3: A neural-network-based parameterization of ice crystal number
Abstract. Contrail cirrus clouds are a major contributor to the climate impact of aviation. Large-scale models, such as general circulation models (GCMs) with an integrated contrail module, are used to estimate the radiative forcing of these clouds. However, small-scale processes cannot be explicitly resolved in these models and must therefore be parameterized. In this study, we develop a novel parameterization for the number of contrail ice crystals formed on ambient aerosols entrained into the exhaust plume behind aircraft burning hydrogen. The continuous entrainment of ambient aerosols, combined with higher supersaturation in hydrogen exhaust plumes, results in longer-lasting ice crystal formation than in conventional kerosene combustion, where ice crystals predominantly form on emitted soot. We construct the parameterization from a comprehensive database of time-resolved contrail formation simulations conducted with the Lagrangian Cloud Module in a box model approach. Shallow neural networks are used to reproduce the simulation outcome, complemented by analytical scaling relations to extend the applicability of the parameterization. The parameterization incorporates dependencies on ambient conditions, ambient aerosol properties and aircraft-related parameters. We compare the new parameterization with an existing one originally developed for conventional kerosene combustion that treats ice crystal formation as a single nucleation pulse. The comparison reveals that the assumption of a nucleation pulse is not reasonable for hydrogen combustion scenarios. We find it essential to base the parameterization on time-resolved simulations, as this realistically captures ice crystal formation on continuously entrained ambient aerosols.
This is an important and relevant study that explores how contrails form and evolve in the absence of engine-emitted particles/nuclei. The focus and motivation is the case of H2 fuel, which does not have the potential for carbonaceous particle emissions. The study specifically addresses how the lack of engine-emitted particles changes the nature of the contrail particle formation process and that it is significantly different when contrails are forming only on ambient particles. Existing tools that have been developed for carbon-based fuel use make some assumptions, which may be valid for the carbon-fuel case, but which are totally inappropriate for the case where only ambient nuclei are involved. This is an important distinction and calls into question previous modeling studies that used tools developed for carbon-based fuel. This is an important advance in understanding and needs to be recognized by the community.
There are several points that I feel should be further clarified and also some minor fixes that should be addressed.
Further clarification:
The paper focused on the distinction between modeling the entrained ambient particles with their continual entrainment from the "single nucleation pulse" that has been published previously. These are important distinctions and are the main point of the paper. But to put this comparison/distinction in context, a sentence or two should also make the comparison to carbon-based fuels (where pulse nucleation may be more appropriate). In particular, when discussing figure 9 c and d, those results beg the question of how those figures compare to a conventional fuel's N_act in m-1. For K15-H2 vs box model w/ mic. the factors range from ~4 to ~12 or so. What is the range when comparing to carbon-based fuels?
On lines 427-428, there is discussion about " . . . slower dilution yields fewer ice crystals in the box model because early-activated aerosols have more time to consume the available water vapor and therefore suppress later activation more efficiently." This is an important additional distinction connected with the continual entrainment vs pulse nucleation. I think this needs to be discussed in more detail. The differences between the curves "with mic" and "no mic" in Figures 9 a and b vs c and d are, perhaps, somewhat related to this, since the supersaturation continues even after the pulse step and as some water is being continually removed by entrained ambient particles. Is the competition between newly entrained particles and the already growing "early-activated" aerosols clearly described and properly captured by the kinetics? The "early-activated" particles have more surface area, which may already be ice, so the water uptake is presumably significantly favored on those particles relative to newly entrained particles. This should be discussed and explained in more detail.
In addition, wouldn't these argument suggest that the behavior of the two modeling approaches should also differ prior to the pulse nucleation in Figure 9? The subsequent paragraph explains why the K15-H2 droplets are larger, but shouldn't similar arguments suggest that there should be differences between K15-H2 and the box model prior to the step change?
Line 440: "This continuous process is especially critical for hydrogen combustion," This seems very true and is the motivation and focus of the paper. But this study, and this particular phrase, also raises the question of what would happen if all particles/nuclei could be removed from carbon-based fuel exhaust? Recent studies have highlighted that stage lean-burn combustors using JetA have essentially no soot emissions. If oil emissions were also eliminated (thought experiment), the same situation of needing ambient aerosol to nucleate contrail particles would exist. It seems the authors should mention that this modeling approach would apply to that situation, also. Of course, the water EIs and CO2 Eis would be different, but the modeling approach of continual entrainment of the primary nuclei would still be needed.
Minor comments:
1) Line 18, in the introduction, the authors appropriately quote references on the importance of contrails to aviation's radiative forcing. But they should also mention Petzold et al., 2025 Nature Communications, which raise questions that those earlier papers may be over estimates. Clearly more work in needed, but that study should be acknowledged.
Line 30 "Since thermodynamics and microphysics are substantially different for . . . " There should be no comma after "Since"
Line 434 " . . . it does not check, whether an aerosol particle . . ." There should be no comma after "check".