Dear Dr Añel,

thank you very much for your message and for pointing out these issues with our manuscript and its compliance with the *Code and Data Policy*. We apologise for the inconvenience caused.

Regarding the model code, we have now archived ICON-ART in Zenodo. Due to specific restrictions associated with the ICON-ART licence, which is not fully public, the code is currently deposited in a private Zenodo record. The corresponding DOI is: https://doi.org/10.5281/zenodo.16615114

Concerning the model output, the full raw data volume is approximately 72 TB, which makes it impractical to store entirely in a public repository. However, all data needed to reproduce the figures and analysis in the paper have been prepared and deposited as follows:

- Monthly model output used in the analysis: https://doi.org/10.5281/zenodo.16740291

- Model output interpolated to measurement sites: https://doi.org/10.5281/zenodo.16795424

In addition, the input data sets used in the simulations are now also archived:

- POPE emission input data interpolated to the ICON-ART PRIEST grid: https://doi.org/10.5281/zenodo.16539566

- CAM-chem background concentrations interpolated to the ICON-ART PRIEST grid: https://doi.org/10.5281/zenodo.16510044

We will update the *Code and Data Availability* section in the revised manuscript to include all these DOIs and a clear description of the contents of each repository, in accordance with the journal’s policy.

Thank you again for your comment in order to improve the quality and reproducibility of our current research.

With best regards,

Hiram Meza

on behalf of all co-authors

Dear Referee 1,

Thank you very much for your thorough and constructive review, and for recognizing the novelty and relevance of our work and the suitability of the manuscript for GMD. We have carefully considered all your comments and have revised the manuscript accordingly. Below we respond point by point.

Major comment 1: Model setup, conservation laws, and RO₂ treatment.

You raised two closely related concerns: (i) the combination of CAM-chem chemical fields with ICON meteorology and the alleged violation of conservation laws, and (ii) the physically inconsistent treatment of RO₂.

(a) Use of CAM-chem fields and conservation of momentum/mass

We apologize that the original text did not clearly convey how the CAM-chem output is used in PRIEST. In the present version of ICON-ART PRIEST:

NOx, OH, HO₂, H₂O, RO₂ and VOCs from CAM-chem are not transported prognostic tracers in ICON.

They enter the PFAS chemistry only as prescribed background fields to compute reaction rates. The only substances that are actually transported and deposited by ICON-ART PRIEST are the PFCA tracers (PFOA, PFNA, etc.). The CAM-chem-derived species have no associated continuity or momentum equation in ICON, so there is no second “dynamical core” transporting them.

Because of (1), there is no overlapping of dynamical cores.

ICON’s dynamical core transport only the meteorological state and the transported PFAS tracers. The CAM-chem fields are used diagnostically as space–time snapshots (monthly means), and do not evolve dynamically within ICON. Therefore, the conservation equations solved by ICON are not altered or duplicated, and momentum conservation is not violated.

The CAM-chem fields enter as monthly means, which already filter out sub-monthly dynamical variability.

The original CAM-chem fields are 6-hourly and fully consistent with their own dynamics, but by the time they are monthly averaged, much of the dynamical information associated with advective transport and transient perturbations is removed. The ICON model thus treat them as slowly varying background fields rather than as dynamically active tracers. In this sense, they behave like climatological or reanalysis-based oxidant fields often used in offline chemistry calculations.

This type of semi-offline coupling is standard practice in atmospheric modeling.

Regional and global chemistry models (e.g. limited-area models driven by global CTMs) routinely use oxidants or other species from external models as time-varying boundary/initial or background fields without being considered as overlapping dynamical cores. We have now made this point more explicit in the revised text to avoid the impression that two independent dynamical systems are transporting the same tracers.

To make all this transparent, we have explicitly mentioned it in the description of the chemical setup in Sect. 2.2.1. We now explicitly state that:

NOx, OH, HO₂, H₂O, RO₂, and VOCs from CAM-chem are used as prescribed monthly fields.

Only PFAS species are transported by ICON-ART PRIEST.

The CAM-chem fields have no momentum or transport equations in ICON and thus do not affect momentum conservation.

We hope this clarifies that no fundamental physical conservation law is violated by our current setup.

(b) RO₂ calculation and mass balance

Regarding the second part of your first major comment (RO₂ calculation), we agree that OH, NOx, HO₂, RO₂ and VOCs are chemically coupled in reality. In the current PRIEST version:

CH₄, C₂H₆, and C₃H₈, as well as OH, HO₂ and NOx, from CAM-chem are used as background concentrations to diagnose RO₂.

These background species are not transported or chemically updated within ICON. Hence, as background fields, they do not directly affect the internal mass conservation of transported PFAS tracers in ICON-ART PRIEST.

Our initial reasoning was that, since the VOCs and oxidants are not prognostic in ICON and only the PFAS species are transported and deposited, the global mass balance of PFAS would not be compromised by the approximate RO₂ calculation. However, we agree with you that from a chemical-mechanism point of view, using a simplified RO₂ diagnostic based on a subset of VOCs and prescribed OH/HO₂/NOx is not ideal and breaks, at least conceptually, the strict chemical linkage among these species.

To address this concern, we have:

Clarified in the revised manuscript that RO₂, OH, HO₂ and NOx are treated as prescribed background fields in the current PRIEST version, and we openly discuss the associated limitation for chemical consistency (Sect. 2.2.1 and Sect. 4).

Reduced the risk of internal inconsistencies in the PFAS chemistry.

We have revisited the implementation of the reaction mechanism to ensure that the conversion rates involving OH, HO₂ and NOx in the PFAS pathway are fully consistent with the prescribed CAM-chem fields used in the reactions, to avoid any hidden mass imbalance affecting PFAS yields.

Outlined a concrete plan for improving RO₂ in a future PRIEST release.

We now explicitly state that RO₂ will be calculated interactively within an extended chemical mechanism in a future version of ICON-ART PRIEST, so that RO₂ production and loss are treated consistently with the VOC and oxidant fields. This will remove the current diagnostic approximation and ensure a fully self-consistent photochemical system.

We also note, as pointed out by the additional reviewer (published by our editor, Dr. Hoffmann), that while the semi-offline treatment of non-PFAS reactants introduces errors due to the mismatch between CAM-chem chemistry and ICON dynamics, these errors are expected to be significantly smaller than the PFAS-specific uncertainties at this stage. We agree with this assessment and have strengthened the uncertainty and sensitivity analysis accordingly.

Major comment 2: Further analysis of model performance, sensitivity, and uncertainties.

We fully agree that a more systematic assessment of uncertainties and sensitivities is important at this early stage of PFAS modeling. Following your suggestion, we conducted a new suite of eleven additional simulations (each 2 years long, with the first year used as spin-up) designed to separate the influence of emissions, oxidant fields, and internal variability:

Group 1 (Control + oxidant sensitivity):

1 Control experiment using the POPE “Best Guess” emission scenario.

4 oxidant sensitivity experiments, where OH and RO₂ concentrations are scaled (0× and 10×) to explore the sensitivity of PFCA formation to these reactants.

Group 2 (emission uncertainty and initialization):

6 emission-uncertainty experiments, using the Upper Bound (UB) and Lower Bound (LB) POPE emission scenarios, each initialized at three different times (one month before, at, and one month after 2006-01-01) to sample internal variability associated with different initial conditions.

From these experiments we performed the following analyses (now summarized in a new Appendix E):

Relative mean differences of annual mean PFOA and PFNA columns and deposition for both groups relative to the Control, and between the different initialization dates (Appendix Tables E1–E3 and Figs. E1–E4).

This analysis shows that POPE emission uncertainties (UB vs. LB) lead to substantially larger changes in PFOA/PFNA than the differences caused by varying the initialization date, indicating that emission uncertainty is a primary driver of PFAS spread in our system.

ANOVA and paired permutation tests:

An ANOVA was conducted to test differences in the means between Group 2 experiments (UB/LB) and the Control.

Additionally, because the experiments share a common emission origin within each scenario, we applied a paired permutation test to assess the significance of differences in spatial patterns.

The tables with these statistical results are now included as Tables E1–E3 in the revised manuscript.

Linearity analysis for oxidant sensitivity (Group 1):

We examined whether PFOA/PFNA production scales linearly with available OH and RO₂, or whether competing loss pathways saturate the PFAS yield.

The analysis shows that PFOA production is strongly and approximately linearly sensitive to OH, while PFNA exhibits a much weaker response to OH changes.

PFNA also shows only a very small sensitivity to RO₂ variations, suggesting that for increased RO₂ concentrations, other chemical pathways (e.g. RO₂/OH + NO, RO₂/OH + RO₂) consume RO₂ without producing PFCA, leading to a saturation effect.

The corresponding diagnostics are now presented in Fig. E5.

Signal-to-Noise ratio (SNR) analysis:

To quantify the relative importance of emissions (“signal”) versus internal variability from different initialization times (“noise”), we computed the Signal-to-Noise ratio for Group 2.

The resulting maps (Fig. E6) show a strong signal, i.e. emissions clearly dominate over internal variability in determining the simulated PFCA fields. This supports the interpretation that uncertainties in emissions are a key limitation of current PFAS modeling, consistent with your comment and Dr. Hoffmann’s assessment.

These new analyses directly respond to your request to better identify the main sources of uncertainty and to clarify whether discrepancies in surface concentrations and deposition patterns are dominated by model physics, oxidant fields, or emissions. We have added a new subsection in the Discussion summarizing these findings and explicitly stating that, at this stage, uncertainties in emissions and in oxidant fields are larger than those introduced by the semi-offline coupling.

### Major comment 2 – Further analysis of model performance, sensitivity, and uncertainties

We fully agree that a more systematic assessment of uncertainties and sensitivities is important at this early stage of PFAS modeling. Following your suggestion, we conducted a new suite of **eleven additional simulations** (each 2 years long, with the first year used as spin-up) designed to separate the influence of emissions, oxidant fields, and internal variability:

- **Group 1 (Control + oxidant sensitivity):**

    - 1 **Control experiment** using the POPE “Best Guess” emission scenario.

    - 4 **oxidant sensitivity experiments**, where OH and RO₂ concentrations are scaled (0× and 10×) to explore the sensitivity of PFCA formation to these reactants.

- **Group 2 (emission uncertainty and initialization):**

    - 6 **emission-uncertainty experiments**, using the Upper Bound (UB) and Lower Bound (LB) POPE emission scenarios, each initialized at three different times (one month before, at, and one month after 2006-01-01) to sample internal variability associated with different initial conditions.

From these experiments we performed the following analyses (now summarized in a new Appendix E):

1. **Relative mean differences** of annual mean PFOA and PFNA columns and deposition for both groups relative to the Control, and between the different initialization dates (Appendix Tables E1–E3 and Figs. E1–E4).

    - This analysis shows that POPE emission uncertainties (UB vs. LB) lead to substantially larger changes in PFOA/PFNA than the differences caused by varying the initialization date, indicating that **emission uncertainty is a primary driver** of PFAS spread in our system.

2. **ANOVA and paired permutation tests**:

    - An **ANOVA** was conducted to test differences in the means between Group 2 experiments (UB/LB) and the Control.

    - Additionally, because the experiments share a common emission origin within each scenario, we applied a **paired permutation test** to assess the significance of differences in spatial patterns.

    - The tables with these statistical results are now included as **Tables E1–E3** in the revised manuscript.

3. **Linearity analysis for oxidant sensitivity (Group 1):**

    - We examined whether PFOA/PFNA production scales linearly with available OH and RO₂, or whether competing loss pathways saturate the PFAS yield.

    - The analysis shows that **PFOA production is strongly and approximately linearly sensitive to OH**, while PFNA exhibits a much weaker response to OH changes.

    - PFNA also shows only a very small sensitivity to RO₂ variations, suggesting that for increased RO₂ concentrations, other chemical pathways (e.g. RO₂/OH + NO, RO₂/OH + RO₂) consume RO₂ without producing PFCA, leading to a **saturation effect**.

    - The corresponding diagnostics are now presented in **Fig. E5**.

4. **Signal-to-Noise ratio (SNR) analysis:**

    - To quantify the relative importance of emissions (“signal”) versus internal variability from different initialization times (“noise”), we computed the **Signal-to-Noise ratio** for Group 2.

    - The resulting maps (Fig. E6) show a **strong signal**, i.e. emissions clearly dominate over internal variability in determining the simulated PFCA fields. This supports the interpretation that uncertainties in emissions are a key limitation of current PFAS modeling, consistent with your comment and Dr. Hoffmann’s assessment.

These new analyses directly respond to your request to better identify the main sources of uncertainty and to clarify whether discrepancies in surface concentrations and deposition patterns are dominated by model physics, oxidant fields, or emissions. We have added a new subsection in the Discussion summarizing these findings and explicitly stating that, at this stage, uncertainties in emissions and in oxidant fields are larger than those introduced by the semi-offline coupling.





The specific comments were addressed into the updated manuscript.



Once again, we thank you sincerely for your insightful comments. They have helped us to clarify the physical consistency of our setup, to better articulate the limitations of the current semi-offline approach, and to substantially strengthen the uncertainty and sensitivity analysis in the revised manuscript.



Kind regards,

Hiram Meza

Dear Referee 2,

Thank you very much for your thoughtful and honest assessment of our work, and for recognizing both the importance of the PFAS problem and the challenge of evaluating a model-development paper at this early stage.

Regarding the mismatch between simulated and observed spatial variability of PFOA and PFNA, we now make much clearer that several factors contribute: (i) large uncertainties in global PFAS emissions, (ii) the simplified PFAS mechanism, (iii) the semi-offline use of CAM-chem oxidant fields, and (iv) limited observations. To address this, we have added a new set of short ensemble simulations in which we vary POPE emissions (Upper/Lower Bound and Best Guess), oxidant fields (scaling OH and RO₂), and initialization dates. From these, we compute relative differences, ANOVA and permutation tests, and a Signal-to-Noise ratio. The results (now summarized in a new appendix) show that uncertainties in emissions and oxidants clearly dominate over internal model variability, which directly answers your concern about what drives the mismatches and where improvements should focus.

In line with Reviewer 1’s comment, we also clarify the treatment of CAM-chem oxidants: NOx, OH, HO₂, RO₂, H₂O and VOCs from CAM-chem are used as prescribed monthly-mean background fields only; they are not transported by ICON, and only PFAS species are prognostic tracers. This avoids overlapping dynamical cores and ensures that conservation in ICON applies to the transported PFAS tracers. At the same time, we explicitly discuss the limitations of this semi-offline setup and outline a planned future version with a more interactive treatment of RO₂ and oxidant chemistry.

Concerning your specific comments:

We have addressed each of your specific comments in the updated manuscript.



We are grateful for your careful reading and suggestions, which have helped us sharpen the discussion of uncertainties and make the model’s limitations and next steps much more transparent.



Warm regards,

Hiram Meza

on behalf of all co-authors

Dear Dr. Hoffmann and Additional Reviewer,

Thank you very much for your careful evaluation and for recognizing the importance of explicit aqueous/aerosol chemistry and multi-mode aerosol treatment for PFAS modeling. Your comments align very well with those of Referees 1 and 2 and have helped us sharpen both the discussion and the analysis.

Semi-offline treatment of non-PFAS reactants We agree with your assessment that using semi-offline non-PFAS reactants (from CAM-chem) introduces inconsistencies between dynamics and chemistry, but that these are likely smaller than the PFAS-specific uncertainties at this stage. In the revised manuscript we clarify that:

NOx, OH, HO₂, RO₂, H₂O and VOCs from CAM-chem are used as prescribed monthly background fields only.

Only PFAS species are prognostic tracers transported by ICON-ART PRIEST; CAM-chem fields are not transported and have no momentum equation in ICON.

We also explicitly discuss this semi-offline choice as a current limitation and outline that a more interactive oxidant/RO₂ treatment is planned for future versions.

Uncertainties, sensitivities and variability In response to your and the other reviewers’ requests, we have added a dedicated uncertainty and sensitivity analysis based on eleven additional simulations (short 2-year runs, first year as spin-up):

Varying POPE emissions (Best Guess, Upper Bound, Lower Bound) and initialization dates.

Scaling OH and RO₂ to assess the sensitivity of PFOA/PFNA production to oxidant fields.

From these experiments we analyze relative differences, apply ANOVA and permutation tests, and compute a Signal-to-Noise ratio. The results (now summarized in a new appendix) show that:

Emission and oxidant uncertainties clearly dominate over internal variability,

PFOA is strongly sensitive to OH, while PFNA is comparatively less sensitive and shows signs of saturation with respect to RO₂ (other RO₂ loss pathways becoming more important).

Regarding the reduced variability at a given site (Table 1), we now explicitly discuss that this is consistent with:

1. the use of monthly oxidant fields,
2. the model resolution, and
3. unresolved sub-grid variability in emissions. We have added text to make this interpretation clear and to emphasize that resolving finer time/space variability in emissions and oxidants is an important avenue for future work.

Phase state of PFCA in model–observation comparisons You are correct in your inference: the PFCA concentrations used for comparison with observations are total (gas + particle) phase. We now state this explicitly in the manuscript where the comparison is introduced.

We are grateful for your positive assessment and for the focused suggestions on uncertainties and variability, which have led to substantial improvements in the revised version.

Kind regards,

Hiram Meza

on behalf of all co-authors