General Comment:

Gravity waves (GW) are a major source of the internal variability of the middle atmosphere. Motivated by lidar observations there is a claim that the gravity wave potential energy density (GWPED) during daylight can be enhanced compared to nighttime measurements at the upper stratosphere and mesosphere. This study seeks to present a theoretical approach to explain this enhancement by gravity wave-ozone interaction, due to changed heating/cooling rates caused by the vertical transport of air parcels by GW assuming idealized inertia gravity waves and an upward level-to-level propagation.  The derived theoretical model of GW- ozone interaction was implemented in the well-established HAMMONIA model and all results are based on such model runs.

However, there are major (almost fatally flawed) concerns to some parts of the submitted paper, which certainly require a more controversial and critical scientific analysis to support the results.

Specific comments:

While reading the manuscript, the reviewer usually browses the web is to collect background information. During this search, I noticed that the Institute of the Author listed a similar paper with the same title as accepted publication in ACP. If the paper is already accepted this review might already be obsolete (see attached screenshot from 31.01.2022).

Lidar observations have become a standard technique to measure temperature fluctuations in the middle atmosphere. Already a few decades ago such observations were used to derive GWPED. This study was motivated by lidar observations conducted during a campaign at the Davis station (69°S) in Antarctica (Kaifler et al., 2015) and mid-latitude observations at Kühlungsborn (54°N)  (Baumgarten et al., 2017,2018). The reviewer did look at all three publications and tried to understand what is mentioned on page 3 lines 53-62. The Antarctic observations (Kaifler et al., 2015) are seasonal summer and winter differences and do not allow to distinguish a day-night comparison and, thus, it is hard to attribute the seasonal GWPED difference between the stratosphere and mesosphere to be caused by GW-ozone interaction. The seasonal differences of the tropospheric GW sources and mean circulation at the middle atmosphere should be considered and are likely contributing a lot to these differences. Secondly, the wind profile is dramatically different between a polar summer and winter condition, which directly affects the critical level filtering due to the strong zonal wind reversal at the summer MLT.

At the mid-latitudes, Baumgarten et al., 2017 showed different climatologies of GWPED for different filtering methods. This points to another major concern when using the numbers. The GWPED seems to depend on the analysis method, which does not provide confidence that the ratios between the stratosphere and mesosphere can be derived reliable enough to support the hypothesis of the proposed GW-ozone effect. In particular, this is also mentioned in Kaifler et al., 2015 as well. Due to the decreased iron layer thickness during the summer at the MLT, the estimated GWPED values are more uncertain and sometimes not derivable applying the same filtering methodology. Erhard et al., 2015 also performed a detailed study to investigate the sensitivity of the different methods to estimate GWPED.  These aspects deserve some more clarification in the introduction.

Another crucial concern when dealing with lidar and model data to investigate day-and-night differences are atmospheric tides. The ozone volume mixing ratio shows a very fast response to the terminator (sunlight) (e.g., https://doi.org/10.5194/acp-18-4113-2018). This time scale is much shorter than the investigated intrinsic gravity wave periods. Thus, it appears to be unlikely that an air parcel that is in the updraft part of an inertia gravity wave could sustain the volume mixing ratio over hours without getting back to the chemical equilibrium to the ambient atmosphere. Radiative processes seem to happen on much shorter time scales. Thus, the theoretical description of the paper might be correct, but the total effect could be much smaller as one needs a convolution with the time scales.

Atmospheric tides are also important to estimate reliable GWPED. Baumgarten et al., 2019 (https://doi.org/10.5194/angeo-37-581-2019) demonstrated that there is also some interday tidal variability. Most of the above mention filtering techniques do not account for tides, which have almost similar or larger amplitudes compared to gravity waves at the stratosphere and mesosphere. Thus, the GWPED needs to be corrected for such tidal contaminations. This is also an issue for the HAMMONIA data, which is also affected by tidal modes. It remains unclear how day-night differences could be distinguished from the diurnal excitation due to the ozone absorption and associated heating rates. The advantage of tides is that the migrating tidal modes DW1, SW2, TW3 are sun-synchronous and fulfill the requirements assumed for the theoretical framework presented in the submitted manuscript. GW have random phases concerning their temporal behavior due to the various excitation mechanisms therefore it is unlikely that the updraft phase remains sun-synchronous, which is the key assumption in the manuscript. More likely is a random superposition of GW and a potential cancelation of the updraft and downdraft phases, which may result in a total zero effect.

The results indicate that the effect of gravity-wave-ozone coupling is most pronounced above the stratopause. Recently, a concept called multi-step vertical coupling (MSVC) was introduced Becker and Vadas, 2018 and later publications. Primary GW launched in the troposphere such as mountain waves, frontal waves, jet instabilities, etc. propagate vertically and dissipate generating a body force, which again causes secondary waves, which propagate further upward and so forth up to the thermosphere.  

Considering the above-mentioned physical processes it appears to be unlikely that the ratios between the stratospheric and mesospheric GWPED can be solely explained by the proposed GW-ozone interaction. MSVC, the horizontal propagation of GW, or atmospheric tides play also important roles and deserve a detailed and critical assessment in this regard to understand the vertical profile of GWPED.

However, the theoretical model of dynamical coupling of the ozone heating rate with wave dynamics is certainly of interest but should be contextualized with atmospheric tides and tidal excitations. The claim in the abstract that “ozone-gravity wave interaction is largely responsible for this effect” is certainly not so straightforward justified given the other dynamical aspects and the idealized model simulations.

The paper presents a possible mechanism of amplitude amplification of gravity waves by the interaction between ozone and gravity waves in the upper stratosphere/lower mesosphere. The paper is divided into three parts: an introduction, a section on the interaction between ozone and gravity waves, and a section titled "Summary and Conclusions." There are 6 Figures that present the results. I had difficulty following the content of the paper for several reasons.

First, the paper is written very compactly. The derivation of the main equations proving the positive feedback of the ozone-gravity wave coupling uses components from different sources, and I would have liked a clearer separation to make it easier for the reader. Also a clear distinction between methodology and results would be most welcome! Therefore, I propose to revise the layout of the manuscript and make it clearer. 

The second aspect may be a misunderstanding on my part: I cannot accept the dynamical concept of assumed gravity wave-ozone coupling (heating rate). My understanding is that propagating internal gravity waves cause positive and negative vertical displacements of the background airflow. Therefore, air transported through a gravity wave experiences both adiabatic cooling and heating. It seems to me (I found no other reference in the text) that only positive vertical velocities (i.e., displacements) are considered here to establish the "successive" or "cumulative amplitude amplification". Averaged over a horizontal wavelength or one period, the net effect of gravity wave-induced cooling and warming should be zero. In conclusion, I don't see any point in publishing the results as they have been written up now. A better presentation of the underlying concept is urgently needed. Again, I could be wrong: reading the text, I would assume that gravity wave-ozone coupling leads to an increase in background temperature when gravity waves are present and ozone photochemistry is working. Is this correct? I hope, I'm right in this aspect. If not, any clarification of the dynamical concept in the paper is highly appreciated.

There is a third point that should be considered in a new version of the manuscript. The whole gravity wave concept relies on linear wave theory. However, the authors use a density scale height H that is strictly only applicable for an isothermal atmosphere as it is constant with altitude. Already in the textbooks by Gill (1982, page 50 top) and by Dutton (1976, pages 67-68) altitude-dependent scale heights are mentioned or proposed. Recently, Reichert et al. (2021) used a height-dependent H for investigating conservative growth rates from ground-based lidar measurements. So, it would be worthwhile to estimate the amplitude growth in an atmosphere with temperature varying with altitude. Especially, in the summer mesosphere where the temperatures can drop drastically from the stratopause to the cold mesopause, this effect might account for some of the observed exponential increase.

Last but not least, I see an essential difference in the gravity wave regimes of the upper stratosphere and lower mesosphere between summer and winter. This picture results from Figure 6 of Reichert et al (2021): it shows almost no seasonal variability of Ep in the layer 65 to 80 km altitude in contrast to the layers below. Thus, the mesosphere seems to be a region where gravity waves always exist almost independent from the local excitation at the place of the observations. Where these waves come from, if they are from primary or secondary or other sources, I don't know but they seem to be present all the time. In conclusion, the strong summer increase can probably also be explained by the reduced local excitation conditions, i.e. the strongly reduced Ep values at lower layers. Sure, this is for one location in the lee of the Andes but it is a convincing example. By the way, there is a further aspect not discussed in the paper: the superposition of gravity waves from different sources entering the observational volume horizontally and leading to enhanced Ep values as indicated by Reichert et al. (2021) as well.

I would have liked to see the authors pay more attention to these possible dynamical aspects and their potential impact on growth rates. A discussion of both the dynamical and ozone temperature aspects would improve the paper and relate its new results to known published knowledge.

Minor Comments:

line 48: "over-exponential" is probably not well-selected as term: what does it mean? I guess, you refer to exponential growth with a enhanced rate, correct?

line 79-80: here, the concept of w'>0 is introduced for the first time. I thought, well, why do the author not consider w'<0 as well as vertical displacements related to these vertical oscillations vary in time and space regularly in a gravity wave.

line 114: introduce minus sign in density equation

line 115: why is v_0 d/dy missing in the total derivative?

line 238: Figure 8 of Reichert et al. (2021) shows that the majority of vertical wavelengths is about and large than 15 km. So, the choice of the selected parameters (especially with reference to the Andes) is not clear to me.

line 266: Why do you use "but" not "and"?

References:

Dutton, J. A., 1976: The Ceaseless Wind. 1st ed., McGraw-Hill, New York and London, 579 pp.

Gill, A. E., 1982: Atmosphere-Ocean Dynamics, Academic Press, 1st edn.,662 pp.

Reichert, R. et al. 2021: High-cadence lidar observations of middle atmospheric temperature and gravity waves at the Southern Andes hot spot. Journal of Geophysical Research: Atmospheres, 126, e2021JD034683. https://doi.org/10.1029/2021JD034683