the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 20 Jul 2026
Simulation of Atmospheric Ozone Layer Formation and Study on the Influence of Equatorial Atmospheric Vertical Motion on the Ozone Layer
Abstract. Stratospheric ozone is crucial for protecting terrestrial ecosystems and maintaining climate stability by absorbing solar ultraviolet radiation. Its distribution is jointly determined by photochemical reactions and atmospheric dynamic processes. Equatorial vertical motion, as a key component of global circulation, profoundly influences ozone production and depletion by regulating precursor transport, photolysis rates, and temperature fields. Based on the Chapman mechanism and catalytic reaction theory, this study establishes a photochemical-dynamic coupled numerical model covering the surface to 500 km, simulating the formation process of the equatorial ozone layer. Through multiple controlled experiments, the effects of vertical motions with different intensities are systematically quantified. Results demonstrate that vertical motion significantly reshapes the steady state and structure of the ozone layer: stronger motion leads to reduced ozone layer thickness, elevated concentration peak altitude, and a transition from multi-peak to nearly single-peak vertical distribution. Notably, the simulations reveal for the first time that in the absence of external dynamic forcing apart from Earth’s revolution around the Sun and its rotation, the ozone system itself exhibits an intrinsic oscillation period of approximately 31 months. Based on this finding, we propose a novel scientific hypothesis: this intrinsic period may serve as a "baseline frequency anchor" that facilitates research on the periods of the stratospheric Quasi-Biennial Oscillation (QBO) and the Tropospheric Biennial Oscillation (TBO). This suggests that the ozone layer may not be merely a passive responder within the climate system, but rather an active component with autonomous oscillation capability capable of modulating atmospheric circulation through radiative feedbacks. This study provides new numerical evidence and theoretical perspectives for understanding the spatiotemporal evolution of the ozone layer and stratosphere-troposphere interactions.
Status: final response (author comments only)
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RC1: 'Comment on egusphere-2026-3004', Anonymous Referee #1, 20 Jul 2026
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AC1: 'Reply on RC1', Xiangping xiao, 30 Jul 2026
Dear Reviewer,
We sincerely appreciate your thorough and professional comments, which have been extremely helpful in improving our work. Before preparing this response, we conducted additional simulations over several days to examine the ozone evolution under conditions with zero residual vertical velocity and only perturbative motions. Our detailed responses to each point are provided below.
- Experimental design lacks sufficient detail for reproducibility.
We fully agree that the experimental setup must be described with adequate precision. In the revised manuscript, we will specify that the stiff ODE system is solved using the Radau method (via scipy.integrate.solve_ivp), with the relative tolerance set to 1e-6 and absolute tolerance to 1e-11. The solution is saved at halfhourly intervals.
The simulation starts at the vernal equinox of 2025 (i.e., 17:01:00 UTC on March 20). The atmosphere is divided into 47 vertical levels, with layer heights as follows: [500000, 460000, 420000, 380000, 340000, 300000, 260000, 220000, 190000, 170000, 150000, 130000, 110000, 94000, 82000, 70000, 62000, 57000, 53000, 50000, 45000, 41000, 37000, 35000, 33000, 32000, 31000, 30000, 29000, 28000, 27000, 25000, 23000, 21000, 19000, 18000, 17000, 16000, 15000, 13000, 11000, 9000, 7000, 5000, 2000, 1000, 0]. The simulation data for the quiescent (no vertical motion) case are provided in the attachment.
- Results section formatting and figure quality; reference error (I.P. Gibel).
Figures: We acknowledge that the figures in the submitted version suffered from reduced resolution during document compilation. We will provide all original highresolution figures to ACP when demanded.
References: We regret the citation error regarding I.P. Gibel. This error occurred because we directly copied the citation from another paper without verifying the original author's name after downloading and reading the source article. We have now carefully checked all other references one by one and confirmed that no similar issues exist. The incorrect entry has been corrected.
- Model top at 500 km vs. ozone peak at ~40 km; justification for extending beyond 100 km.
We appreciate this comment. Our rationale for including altitudes above 100 km is that, although the atmosphere is extremely tenuous at these levels, it still absorbs a portion of solar radiation—particularly in the extreme ultraviolet (EUV) bands. While the conventional "edge of space" is often defined at ~100 km, we believe that including the upper layers improves the physical completeness of the radiative transfer calculation and yields results that more closely resemble real atmospheric conditions.
- Discrepancies in vertical velocity magnitudes and unrealistically high total column ozone (TCO) under no vertical motion (~2500 DU vs. observed ~300 DU).
We thank the reviewer for raising these critical issues. We offer the following clarifications and describe the additional work we have undertaken in response:
The velocities we referred to are not the residual BrewerDobson circulation velocities, but rather a combined vertical velocity that includes both advective and perturbative components. We realise that our previous wording was ambiguous and may have caused confusion. This will be improved in the revised manuscript.
In direct response to the reviewer's concern, we performed additional simulations over the past few days. These experiments show that even when the residual vertical circulation is set to zero, the inclusion of perturbative vertical velocities(ranges from 1 to 7 mm/s[1]) alone leads to a substantial reduction in TCO. Moreover, when tropopauselevel exchange (where vertical speeds can reach up to 15 m/s [2]) is considered, the TCO decreases even more significantly. These new results will be incorporated into the revised manuscript to provide a more comprehensive sensitivity analysis.
Nomotion baseline (2550 DU): We fully agree that this value is far higher than the observed global mean (~300 DU). However, the static atmosphere is a purely hypothetical baseline, not a realistic scenario. The key contribution of our work is to quantify the relationship between vertical motion and TCO reduction. Our simulations reveal a nearperfect logarithmic negative correlation (correlation coefficient close to −1) between vertical velocity and TCO, which we consider a novel and robust finding. In the updated version, we will present this scaling relationship more clearly and emphasise that the baseline itself is not intended to represent a physical state.
Observational support from ENSO: The negative correlation we identified is also strongly supported by observational evidence during El Niño events. During the 1997–1998 El Niño, equatorial TCO dropped to 200–225 DU, with a distinct "seesaw" pattern: ozone negative anomalies coincided with uppertropospheric (200 hPa) divergence zones (e.g., eastern Pacific, eastern Africa), while positive anomalies aligned with convergence zones (e.g., western Pacific, eastern Indian Ocean)[3]. More recently, Jingyu Li et al. [4] confirmed that ENSO induces an eastwest dipole response in tropical tropospheric column ozone: during El Niño, TCO significantly decreases over the centraleastern Pacific and increases over the western Pacific. These observed patterns are fully consistent with our modelled negative correlation between vertical motion and ozone abundance, and we will expand this discussion in the revised paper to better contextualise our findings.
We are genuinely grateful for the reviewer's insightful and constructive comments. Your feedback has already significantly strengthened our work, and we hope that the clarifications and additional simulation results provided above adequately address your concerns. We look forward to the opportunity to receive further valuable suggestions that will help us improve the manuscript to the standard expected by ACP.
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AC2: 'The references in the previous reply(Reply on AC1)', Xiangping xiao, 30 Jul 2026
References:
[1] Sakazaki, T., T. Sasaki, M. Shiotani, Y. Tomikawa, and D. Kinnison (2015), Zonally uniform tidal oscillations in the tropical stratosphere, Geophys. Res. Lett., 42, 9553–9560, doi:10.1002/ 2015GL066054.
[2] Kumar, K. K. (2006), VHF radar observations of convectively generated gravity waves: Some new insights, Geophys. Res. Lett., 33, L01815, doi:10.1029/2005GL024109.
[3] Chernikov, A. A., Borisov, Y. A., & Zvyagintsev, A. M. The Impact of the 1997–1998 El Niño Event on the Earth's Ozone Layer. Meteorologiya i Gidrologiya, (in Russian). (translatedinto Chinese in Meteorological Science and Technology, 1998, No. 3, pp. 46-49)
[4] Jingyu Li, Haolin Wang, Qi Fan, and Xiao Lu, Tropospheric ozone responses to the El Niño–Southern Oscillation (ENSO): quantification of individual processes and future projections from multiple chemical models. Chem. Phys., 25, 12983–13006. 10.5194/acp-25-12983-2025(2025).
Citation: https://doi.org/10.5194/egusphere-2026-3004-AC2
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AC1: 'Reply on RC1', Xiangping xiao, 30 Jul 2026
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RC2: 'Comment on egusphere-2026-3004', Anonymous Referee #2, 14 Aug 2026
The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2026/egusphere-2026-3004/egusphere-2026-3004-RC2-supplement.pdf
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AC3: 'Reply on RC2', Xiangping xiao, 24 Aug 2026
Dear Reviewer,
We sincerely thank you for your thorough and constructive comments on our manuscript. Your critical evaluation has helped us identify several areas where our presentation was insufficient or unclear, and we have taken your suggestions seriously in preparing this revised version. Below we provide point-by-point responses to your concerns, along with detailed explanations and supplementary materials that address the issues you raised.
Reviewer Comment:
How is radiative transfer calculated? Is it with simple optical depth functions or a more sophisticated treatment that includes scattering? Is an established model used?
Our Response:
The radiative transfer calculation in our model includes both direct and diffuse (scattering) radiation. Specifically, the atmospheric radiation treatment accounts for extinction due to both absorption and scattering in the direct beam, as well as multiple scattering contributions. This is not a simple optical-depth-only scheme; rather, it incorporates a comprehensive radiative transfer approach that considers scattering effects.
Reviewer Comment:
What is the range of wavelengths for the photolysis calculation?
Our Response:
The wavelength ranges used for photolysis of each species are provided in Table S1 (see attachment). We have included this table as supplementary material for clarity.
Reviewer Comment:
Are all chemical species advected or just ozone? What numerical treatment is used for advection?
Our Response:
All chemical species included in the model are subject to vertical advection. The vertical velocity field is prescribed directly, rather than derived from a dynamical model. The values we adopted are based on a synthesis of observational data on equatorial atmospheric vertical motions from multiple sources. Furthermore, the objective of this paper is to investigate how varying vertical velocities influence ozone layer formation. Adopting a full dynamical model would not readily allow us to impose the diverse range of vertical motions considered here, as some of these prescribed values are not physically realised in the actual atmosphere. We acknowledge that prescribing vertical velocity in this manner does not guarantee strict mass conservation when considered in isolation. However, in the real atmosphere, vertical motion is accompanied by horizontal transport. In view of the relatively weak horizontal gradients of ozone and other species over the region of interest, we consider it reasonable that the residual mass imbalance is largely compensated by horizontal mixing, and that the resulting influence on our conclusions is likely to be minor.
Reviewer Comment:
What photochemical regime is intended to be represented by the model: the stratospheric photochemical regime of catalytic ozone destruction? The mesospheric regime? The tropospheric regime? All of the above? The paper claims to use approximately 100 gas-phase reactions (line 141) but I could only see 34 reactions in Table 4-1. Table 4-1 appears to have serious issues. There is a duplicate reaction (O + O₂ + M), and there is a reaction that I am not familiar with and that I could not immediately locate in the NASA JPL manual from which it ostensibly originated (2 O₃ → 3 O₂), and at least one crucial reaction for NOx photochemistry in the troposphere appears to be missing (HO₂ + NO → NO₂ + OH) calling into question the applicability to the troposphere. The treatment of third bodies is confusing (sometimes listed as M and sometimes listed as a specific constituent on the left-hand-side and right-hand-side of the reaction), and it would not surprise me if there are other anomalies in Table 4-1.
Our Response:
We thank the reviewer for this careful and detailed examination. We address each point in turn:
- Photochemical regime: Our model simulates atmospheric chemical processes from 0 to 500 km altitude. Reactions such as O + O₂ + M → O₃ + M are not restricted to any specific atmospheric layer; they occur wherever the necessary conditions are met. Thus, our model does not predefine a fixed regime (stratospheric, mesospheric, or tropospheric) but rather allows chemistry to evolve across the entire vertical domain.
- Number of reactions: We apologise for the confusion. Due to space limitations in the printed manuscript, we did not list all ~100 reactions in Table 4-1. The complete set of reactions used in the model is now provided in Table S2 (attached as supplementary material). This table includes the full reaction set and should resolve the apparent discrepancy.
- Duplicate reaction (O + O₂ + M): We sincerely apologise for this error. During the preparation of Table 4-1, this reaction was inadvertently pasted twice. We had noticed and corrected this issue during final proofreading, but unfortunately the uncorrected version was uploaded.
- Reaction 2O₃ → 3O₂: This reaction can be found in the NIST chemical kinetics database (see Fig. s1included in the attachment). In our revised manuscript, we will clearly cite both JPL and NIST as sources for the reaction set(In the paper, we only stated that the data are primarily derived from JPL). The temperature conditions required for this reaction are met in the middle thermosphere. However, our simulations show that ozone concentrations in the middle thermosphere are effectively zero (or near-zero) — see Table 5-3, Table 5-4, and Table S3 in the attachment. We also note that the rate constant for this reaction is very small (5.84×10⁻²⁸ m³/s at 400 K), making the reaction extremely slow. We included it originally to assess its potential impact, but our results confirm that it is negligible.
Furthermore, as shown in Table S3, a midnight ozone maximum is present at 82 km after 1400 days of integration, which compares favourably with the nighttime ozone number densities observed by the OAO-2 satellite over the 70–100 km altitude range [1,2]. It should be noted that the units in Tables 5-3, 5-4, and S3 are in molecules per cubic metre, while those in references [1,2] are in molecules per cubic centimetre.
- Missing HO₂ + NO → NO₂ + OH: This reaction is not missing; it is included in our full reaction list (see Table S2). We apologise for the oversight in the abbreviated table.
- Treatment of third bodies: We agree that the notation was confusing. The reactions O + O₂ + M → O₃ + M and O + O₂ + O → O₃ + O have different rate coefficients: 6.0×10⁻⁴⁶ × (T/300.0)-2.4m⁶/s for the former, and 2.15×10⁻⁴⁶ × exp(345.0/T) m⁶/s for the latter. We included both versions to test whether treating O as a separate third body, rather than including it in M, would significantly affect the results. Our tests showed that the differences are negligible. In the results presented in the paper, O is included in M (i.e., the separate O + O₂ + O reaction is not used in the final calculations). We will clarify this in the revised text.
Reviewer Comment:
There are initial profiles of precursor chemicals relevant for ozone photochemistry (CH₄, CO, N2O, and H2O). Under vertical advection are these constituents gradually lifted out of the atmosphere? Is there a compositional lower boundary condition?
Our Response:
Yes, these precursor species are advected vertically along with the flow. At the surface (lower boundary), we prescribe mixing ratios of N2O = 330 ppbv, CH₄ = 1780ppbv, CO = 150 ppbv, and H2O = 1.6%. We also include a wet deposition process for soluble species. These boundary conditions are held fixed throughout the simulations.
Reviewer Comment:
The vertical velocity profiles used are questionable. The value chosen for the stratosphere is 1-2 orders of magnitude larger than what is inferred from reanalyses, which is order 0.3 mm s⁻¹ (e.g., Abalos et al., 2015), whereas the paper uses 0.3 - 2 cm/s (Line 124).
Our Response:
We refer the reviewer to our previous response (AC1) on this matter.
As a further note, we are aware that some of the vertical velocity values adopted in this study exceed those derived from reanalysis products. Nevertheless, a central objective of this work is to investigate the sensitivity of the ozone layer to a wide spectrum of vertical advection rates. In addition, our results show that atmospheric motion substantially affects both the ozone column abundance and its vertical structure. This suggests that, conversely, future observations of the ozone column and its vertical distribution could potentially serve as a useful proxy for inferring atmospheric dynamical states.
Reviewer Comment:
The zero motion limit predicts ozone that is an order of magnitude larger than what is observed. I appreciate that in observations, the effects of vertical velocity are already relevant, but previous studies of photochemical equilibrium have found much more realistic estimates for the total column ozone. Extraordinary care in describing the model and why it leads to these large values is required to substantiate this dubious finding.
Our Response:
We thank the reviewer for raising this important point. Our response is provided in AC1.
Reviewer Comment:
The idea that photochemical equilibrium can involve very slow accumulation of ozone is one that I find plausible, so I do believe that weak vertical motion could lead to large reductions of ozone compared to zero motion, but owing to issues noted above, I cannot meaningfully evaluate the specific numbers reported in the submitted paper.
Our Response:
We appreciate the reviewer's willingness to consider our conceptual framework. We hope that the clarifications and supplementary materials provided above (especially the full reaction list and detailed model descriptions) will now allow a more meaningful evaluation of our quantitative results.
Reviewer Comment:
It is claimed that ozone exhibits internal oscillatory behavior (Line 275). In the face of such a counterintuitive claim, a compelling explanation of how such behavior emerges in the model under analysis is required. No such physical explanation is offered. The prospect that such an oscillation is a numerical artifact was not ruled out. I quite doubt that such an oscillation is a meaningful behavior of the actual photochemical system or any credible model thereof. The Chapman Cycle does not exhibit oscillatory behavior at a given altitude. In trying to imagine how oscillatory behavior could emerge, it might be that it emerges as a dynamic of the column as a whole, yet this would seem to require, at a minimum, that there is some process that is moving information upward and not just downward (as results from photolysis). In the absence of vertical motion, there is no such process moving information upward. The paper does not offer any physical explanation or justification for the internal oscillation, thereby falling far short of the evidentiary standards of ACP.
Our Response:
We thank the reviewer for this critical observation. Our subsequent sensitivity tests have revealed that the oscillatory behaviour is driven by the diurnal and annual variations in solar radiation at the top of the atmosphere, which arise from Earth's rotation and revolution around the Sun. When we fix the incoming solar radiation at a constant value (e.g., the value at noon on a specific day), the internal oscillations disappear entirely. This strongly suggests that the oscillations are not numerical artefacts but are instead a response to the time-varying solar forcing. We acknowledge that our original manuscript did not provide a sufficient physical explanation for this behaviour, and we will revise the text to include this important finding and a clear mechanistic interpretation.
Reviewer Comment:
To conclude: this paper poses an interesting question that merits theoretical attention from the community, but its extraordinary claims are not explained by physical argumentation and are only supported by an incompletely documented model that is driven by implausible parameters and, when relevant, disagrees by an order of magnitude with prior modeling efforts.
Our Response:
We are grateful for the reviewer's recognition of the scientific interest of our research question. We acknowledge that our initial submission had shortcomings in model documentation and physical interpretation. We have taken all the reviewer's comments seriously and have made substantial efforts to address them: we now provide a complete reaction list, clarify the radiative transfer and advection treatments, explain the rationale for the vertical velocity values, and offer a physical explanation for the oscillatory behaviour. We believe that our study offers a valuable complementary perspective on the sensitivity of the ozone layer to vertical transport, and we hope that the revised manuscript meets the high standards of ACP. We are confident that the additional explanations and supplementary materials will allow readers to evaluate our work more meaningfully.
We thank the reviewer once again for the time and effort invested in improving our manuscript. We look forward to your further feedback.
Yours sincerely,
Xiangping Xiao, Wei Jiang, Chanjuan Liu
References
- G. ROBLE and P. B. HAYS, 1973: The Nighttime Distribution of Ozone in the Low-Latitude Mesosphere. Pure and Applied Geophysics (PAGEOPH). Vol. 106-108
- G. ROBLE and P. B. HAYS, 1974: Ondetermining the ozone number density distribution from OAO-2 stellar occultation measurements. Planet. Space Sci. 22, 1337 to 1340.
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AC3: 'Reply on RC2', Xiangping xiao, 24 Aug 2026
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This paper attempts to study the ozone layer formation and the influence of vertical model on ozone. This paper does not meet the standards I would expect of a credible scientific work submitted to ACP as a preprint.
Main criticisms:
- The experimental design section does not include enough detail for this study to be reproducible.
- The results section consists of a series of poorly formatted bullet points and low resolution figures. The references have not been checked. I.P. Gibel is not the correct author for the paper listed.
- The model top is at 500 km with 47 vertical levels. Ozone concentrations peak at about 40 km. There is little justification for studying beyond ~100 km (conventional definition of the edge of space).
- Many values seem to be off by an order of magnitude. For example, the authors claim that " Vertical velocities in the stratosphere typically range from 0.3–2 cm/s". Typical upwelling values are in the range 0.2 to 0.5 mm/s [1]. With no vertical motion, the total column ozone in their model is ~2500 DU. Observed global mean total column ozone is around 300 DU [2]. The model appears to need unrealisticaly high stratospheric upwelling to produce realistic ozone values of ~270 DU.
References:
[1] Butchart, N. (2014), The Brewer-Dobson circulation, Rev. Geophys., 52, doi:10.1002/2013RG000448.
[2] Chipperfield, M. P. and Bekki, S.: Opinion: Stratospheric ozone – depletion, recovery and new challenges, Atmos. Chem. Phys., 24, 2783–2802, https://doi.org/10.5194/acp-24-2783-2024, 2024.