A Contrail Life Cycle Model with Interaction of Overlapping Contrails

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

• Line 5, The authors mentioned that contrails represent one of the most unpredictable or quantifiable environmental impacts of air traffic in. The word “quantifiable” seems to be in contradiction with the description as “unpredictable”. Please check it.
• Line 113, Although the authors stated that Gaussian plume model has been already validated, the author should provide a more detailed method and/or results for validation, given the significance of the simulation in this paper.
• Line 139, The author introduced the 2D Gaussian distribution functions; the abstract also stated that the method was the 3-D Gaussian plume model. The author requests to check if there is any contradiction.
• Equation 17 seems to be missing the density of ice. Please have the author check it.
• Line 256/259/266，The coefficient "1.1" is used in all the equations. Please explain the origin of this coefficient. 
• Line 259/26 “d_0,1<1.1σ_h1 +1.1σ_h0” may expressed as “1.1σ_h1 -1.1σ_h0 < d_0,1 <1σ_h1 +1.1σ_h0”，, which seems to be more precise.
• 6.1. S0: There is a relatively small difference in the lifetimes of C0 and C1 without intersection. Is it due to the model accuracy or error? Or is it because 45◦ angle deviation and the environmental conditions are different? An explanation is needed. The authors may provide some clarification on this.
• The authors seem to have used two criteria to determine the end of the lifetime: IWC < 10−8 kg m−3 or rH_ice < 100%. We would like to discuss that: IWC is a judgment from a visual perspective, and rH_ice < 100% seems to mark the beginning of the decrease in particle radius and IWC. Does the contrail lifetime end immediately if rH_ice is less than 100%?

Overall, extending the analysis from the lifecycle of a single contrail to the evolution of crossed double contrails is a very interesting and novel perspective. The author also provided certain case studies. Considering the difficulty and importance of model validation, it is hoped that the author can conduct more extensive research while ensuring the accuracy of the model.  Further researches may include the overlapping of multiple contrails, or the quantification of the influence of the environment parameters.

Author Response

Please find attached my reoly to the Review Report. 

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

The manuscript addresses an important question, how overlapping contrails interact and alter microphysics and lifetime, and the model approach is promising. However, some essential points need to be addressed before publication:

1. Validation and robustness: Results rely on a single, fixed meteorological snapshot and constant turbulence. Please run a small ensemble or at least one time-varying meteorology case, if possible.
2. Physical basis: Provide stronger physical justification for the rules for mass/ice exchange in the intersection volume.
3. Sensitivity analyses: Key parameters (Nice, EIwater, turbulence ε, diffusivities) strongly influence lifetime. Include sensitivity runs or state uncertainty ranges and how they affect the reported overlap effect.
4. Figures: Improve figure resolution and captions, include units on axes when missing, and clarify legends.
5. Language: Perform a careful English edit for grammar and clarity.

Addressing these points will substantially strengthen the manuscript and support the main conclusions.

Author Response

Dear Reviewer No 2,

please find attached my response to your valuable comments. 

Best wishes

Judith Rosenow

Author Response File: Author Response.pdf

Reviewer 3 Report

Comments and Suggestions for Authors

This is a great paper, methodologically rigorous, well-motivated, and making a clear incremental contribution to contrail lifecycle modelling by addressing interaction effects that are commonly neglected.

1. Introduction, Background, and Literature

The introduction and state-of-the-art sections demonstrate good engagement with the contrail literature and correctly situate the work within ongoing challenges of contrail lifecycle modelling and environmental impact assessment. This is the one aspect of the paper to be improved. Please add the following reference:

1. How Well Can Persistent Contrails Be Predicted?
2. Beyond Contrail Avoidance: Efficacy of Flight Altitude Changes to Minimise Contrail Climate Forcing
3. Contrails and Their Dependence on Meteorological Situations
4. Meteorological Conditions That Promote Persistent Contrails
5. Design of a Hydrogen Aircraft for Zero Persistent Contrails
6. Influence of Sustainable Aviation Fuels on the Formation of Contrails and Their Properties
7. Innovative Box-Wing Aircraft: Emissions and Climate Change
8. Impact of Hybrid-Electric Aircraft on Contrail Coverage
9. Characterizing the Full Climate Impact of Individual Real-World Flights Using a Linear Temperature Response Model
10. Linear Contrails Detection, Tracking and Matching with Aircraft Using Geostationary Satellite and Air Traffic Data

One and two are fundamental aspects for the introduction, three and four concern the influence of meteorology, five to eight should be added to the discussion adding technology implications, and finally nine and ten as other relevant articles to the content generally.

2. Research Design

The research design is appropriate and well matched to the stated objectives. The study is a mono-method, physics-based modelling investigation, extending an existing validated contrail lifecycle model to incorporate interaction effects between multiple contrails.

3. Methods and Data Analysis

The methods are described in extensive and rigorous detail. The mathematical formulation of the Gaussian plume model, diffusion tensor, microphysical growth, sedimentation, and humidity interaction is explicit, internally consistent, and grounded in established theory.

4. Results Presentation

Results are clearly structured, logically sequenced, and consistently linked back to the defined scenarios. Figures are used effectively to illustrate temporal evolution of microphysical variables, contrail geometry, altitude, and lifetime.

5. Conclusions and Claims

The conclusions are well supported by the results and remain within the evidential scope of the study. Claims regarding lifetime reduction, the dominant role of atmospheric conditions, and the relative importance of overlap geometry are proportional and carefully framed.

6. Figures and Tables

Figures and tables are clear, well-labelled, and directly support the narrative. Axes, units, and captions are sufficient for standalone interpretation, and schematic figures are particularly effective in explaining complex intersection geometries.

Author Response

Dear Reviewer No 3,

please find attached our response to your positive feedback. 

Thank your for time and effort you invested in the manuscript. 

Best wishes

Judith Rosenow

Author Response File: Author Response.pdf