Review for Dube et al., entitled "N2O as a Regression Proxy for Dynamical Variability in Stratospheric Trace Gas Trends," submitted to ACPD

Dube et al. present an analysis of measurements from two satellite instruments, the Atmospheric Chemistry Experiment Fourier Transform Spectrometer (ACE-FTS) and the Optical Spectrograph and InfraRed Imager System (OSIRIS), as well as output from the WACCM Chemistry Climate Model (CCM) simulations. The study aims to estimate changes in important stratospheric trace gases (HCl, N2O, O3, and NOy) and examine inter-hemispheric asymmetry in their trends. The authors propose N2O (long-lived greenhouse gas in the stratosphere) as a dynamical proxy for stratospheric circulation in a mutivariabte linear regression (MLR) model used to calculate trace gas trends. The analysis suggests that changes in the stratospheric circulation, indicated by N2O, are able to explain increases in Northern Hemisphere HCl and negative O3 trends. However, the exact cause of lower stratospheric ozone trends remains unknown.

Overall, this manuscript is well-written and contributes to our understanding of inter-hemispheric asymmetry in stratospheric trace gases during the ACE-FTS measurement period. It reinforces previous findings regarding the utility of N2O as a dynamic proxy in the MLR model. Furthermore, the divergence between WACCM and ACE-FTS HCl trends emphasizes the impact of chlorine-containing very short-lived substances (VSLS) on ozone recovery, suggesting a slower recovery due to the absence of these VSLS species in the WACCM simulations.

While the manuscript is strong, I have a few suggestions that the authors may consider addressing:

1. Including the goodness of fit (R2) distribution for both regression models, specifically for ACE-FTS and WACCM-SD, would provide valuable insights into the reliability of trend estimates and the quality of each regression model. This would enhance the assessment of the trend estimates obtained using the LOTUS setup.
2. Recently, Li et al. (2023, ACPD) employed a multivariate regression model with the eddy heat flux as a dynamical proxy to demonstrate inter-hemispheric asymmetry in stratospheric ozone trends. It would be interesting if the authors could compare N2O as a dynamical proxy to the eddy heat flux to determine if N2O proxy performs better.
3. To improve the clarity of the presentation, it would be beneficial to compare the evolution of trace gases at selected latitude/altitude bins (e.g., 30S, 30N, 30 hPa, 5 hPa) as well as the regression fits. This approach would facilitate the visualization of differences between ACE-FTS and WACCM simulated HCl, N2O, O3, and NOy, making it easier to compare the model/observations as well as performance of the regression models.
4. The authors argue that the discrepancy in HCl trend between WACCM and ACE-FTS results from the absence of Cl-containing VSLS species in the WACCM simulations. It would strengthen their claim if they could provide additional evidence, such as comparing the vertical distribution of HCl between WACCM and ACE for the initial and last five years of the time series.

Minor comment:

• In line 145, the phrase "In the middle row" is unnecessary as the figure caption already provides this information.
• In line 146, the word "emission" should be replaced with "emissions of chlorine-containing source gases" or something similar.

References:

Li, Y., Dhomse, S. S., Chipperfield, M. P., Feng, W., Bian, J., Xia, Y., and Guo, D.: Stratospheric ozone trends and attribution over 1984–2020 using ordinary and regularized multivariate regression models, EGUsphere [preprint], https://doi.org/10.5194/egusphere-2023-591, 2023.

General comment:

This paper investigates trends in stratospheric trace gases, like N2O, HCl, NOy and O3, which all show a hemispheric asymmetry over the last about two decades. By including N2O (detrended by accounting for its tropospheric trend) in the multi-linear regression model it is aimed at separating the effect of stratospheric circulation changes on the trends. This method is applied to satellite and model data and it is argued that the hemispherically asymmetric HCl trends (increases in NH) are due to changes in the stratospheric circulation. Also the negative O3 trends above 30hPa in the NH are related to circulation changes, but not the trends at lower levels.

The paper addresses an important topic in atmospheric research, and adds new insights to our understanding of the causes of stratospheric trace gas trends. It is well written and the results are clearly presented. I recommend publication after addressing the comments below. 

Minor comments:

1. I'm somewhat confused about the motivation of the study to "isolate trends due to circulation changes from trends due to ozone depleting substances", as stated e.g. in the abstract (P1, L4). How can the total effect of ODS be separated, as it includes also an effect via ozone-induced circulation changes. Isn't the N2O just a proxy for stratospheric circulation changes, regardless of their causes (e.g. ODS). Also, I don't see this as a problem for the paper, just the reasoning should be clarified, here and throughout the paper.

2. I understand that the standard MLR model assumes an instantaneous response, as it includes no time lags (P5, L27). Especially for ENSO this could be problematic, as the stratospheric response to SST changes is likely delayed in the stratosphere. Including lag time in the ENSO regressor could improve the MLR model for stratospheric circulation, as shown e.g. by Diallo et al. (2019, ACP, 10.5194/acp-19-425-2019) and could be mentioned.

3. I'm somewhat unsure about the conclusion that "the N2O proxy cannot explain the negative ozone trends that are observed in the tropics below 20hPa" (e.g. P14, L296, or similarly in the abstract). First, I don't see negative O3 trends in the tropics below 20hPa in this study (at least not significant, Fig. 4). Second, including the N2O proxy in the MLR causes the O3 trends in this region to be more negative. So just based on the data shown here, I'd conclude that there is a slow-down in tropical upwelling during 2004-2018 which causes positive tropical O3 trends. This is not what other studies showed, although for different periods (e.g. Ball et al., 2018 for 1998-2016). It is also counter-intuitive to the O3-response to an expected increase in tropical upwelling over time, what climate models predict on the long term. I'd find it interesting to see the trend in tropical upwelling w* (e.g. as contours in Fig. 4), to see how this changes in the WACCM simulation over the considered period.

I guess the differences to previous studies are explainable by the different periods considered. Anyway, I suggest to be more careful with the discussion and relation to past studies. 

Specific comments:

P2, L26: A clear relation of the hemispherically asymmetric trace gas trends to circulation changes was shown by Stiller et al. (2017, ACP, https://doi.org/10.5194/acp-17-11177-2017), involving a latitudinal circulation shift. This could be mentioned here as well.

P5, L142: I'd add "... N2O, below about 10hPa", as above the signs of the trends could be opposite (Fig. 1).

P6, L162: Better say "small" instead of "minimal"? It's a max 1%/dec trend due to photolysis changes compared to ~5%/dec net trend values.

P8, L209: I'd delete "positive".

P11, L251: The result here that negative O3 trends below about 30hPa are not explained by circulation and transport is different from what other recent papers proposed (e.g., Wargan et al., 2018; Orbe et al., 2020). I think this would be worth a more thorough discussion. 

P13, L288: more precisely "...result in air moving slower and deeper through the stratosphere in the NH ..."

Technical corrections:

P2, L27: year missing for Abalos et al.

P4, L101: time series 

P8, L206: delete "the"

P12, L67: agree

P15, L313: standard