the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 03 Feb 2026
Observation of the Lunar Tide in the Middle Atmosphere by the Aura Microwave Limb Sounder
Abstract. Because of the near-polar, sun-synchronous orbit of the Aura satellite, the Microwave Limb Sounder (Aura/MLS) observes the lunar tide as a lunar semimonthly variation of geopotential height and temperature in the middle atmosphere. The FFT spectrum of the mesospheric geopotential height time series from 2004 to 2021 shows a significant spectral peak at a period of 14.7653 days which is a half lunar month. The lunar tidal signal is clearer in geopotential height than in temperature. For the first time, the characteristics of the lunar tide in geopotential height (or pressure) are observed for the middle atmosphere. The latitudinal dependence of the observed mesospheric lunar tidal amplitude is in a good agreement with the numerical simulation of Geller. The climatology of the lunar tide shows larger amplitudes in January than in July at low latitudes, in agreement with the simulation. Generally, the observed lunar tide in geopotential height is smaller by a factor 2–3 than the simulated lunar tide. The vertical phase gradient of the observed lunar tide agrees well with the simulated vertical phase gradient.
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Notice on discussion status
The requested preprint has a corresponding peer-reviewed final revised paper. You are encouraged to refer to the final revised version.
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Preprint
(10598 KB)
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The requested preprint has a corresponding peer-reviewed final revised paper. You are encouraged to refer to the final revised version.
- Preprint
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- Final revised paper
Journal article(s) based on this preprint
Interactive discussion
Status: closed
-
RC1: 'Comment on egusphere-2026-368', Anonymous Referee #1, 16 Mar 2026
- AC1: 'Comment on egusphere-2026-368', Klemens Hocke, 18 Mar 2026
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RC2: 'Comment on egusphere-2026-368', Anonymous Referee #2, 28 Apr 2026
Review of Observation of the Lunar Tide in the Middle Atmosphere by the Aura Microwave Limb Sounder
Summary of the paper
This paper presents the first identification of the lunar tide in the geopotential height observations of the middle atmosphere from Aura/MLS. The lunar tide is identified as a clear semi-monthly variation in Aura/MLS observations between 2004 and 2021. A comparison with model results from Geller (1970) as well as temperature observations from TIMED/SABER have been discussed. The paper further examines the vertical, seasonal and latitudinal structure of the lunar tide. The results show that lunar tide signal is stronger in January than in July and peaks near the equator.
Summary of the review and major comments
The main question addressed in this paper is whether the semidiurnal lunar M2 tide can be reliably identified in Aura/MLS through its semi-monthly signature, and whether the vertical, seasonal and latitudinal structure of the retrieved lunar tide signal is consistent with previous modeling and observational work. The paper contains a significant new result, i.e. the lunar tide can be identified clearly in satellite geopotential height observations. The comparison with model results and TIMED/SABER observations aids in interpreting the Aura/MLS results. However, some issues require clarification before the manuscript can be recommended for publication.
• Line 43–48 – The manuscript refers to the (2,2) and (2,4) modes of the lunar tide, but these are not really defined for the reader. Since the later interpretation of the phase profiles also relies on this terminology, a brief explanation of what these mode labels mean and why they are relevant here would help the reader follow the later discussion.
• Line 90 – The most important issue in the paper is the explanation of how the semidiurnal lunar M2 tide appears as a semi-monthly signature in Aura/MLS because of the sun-synchronous sampling. This is central to the interpretation of the entire analysis but is currently explained mostly qualitatively. Since the analysis relies on the 14.7653-day signal as the observational signature of M2, it would improve the paper if the authors could include a clearer explanation, or a short mathematical derivation, of this sampling/aliasing framework.
• Line 104-105 - The text states “the arithmetic mean of all observed atmospheric profiles is computed” each day, but Aura samples each latitude twice per orbit at two fixed local solar times (~01:45 and ~13:45 LST at the equator). This daily mean combines sampled from both Aura local-time branches. Since the two overpasses are separated by about 12 hours, this works for the semidiurnal tide because the two samples are nearly in phase for a ~12.42-hour oscillation. Could the authors state this explicitly in the methodology, since this seems important for justifying the daily averaging procedure used to construct the time series?
• Line 137 – 148 - Line 137 - 148 The manuscript does show January-versus-July variability for Aura/MLS at ~82 km in Figure 7. However, the vertical-profile comparison with Geller (1970) in Figures 4 and 5 seems to be compared with the full-record Aura/MLS amplitudes, whereas the values from Geller are for January and July. Since the Aura/MLS data also show a pronounced January-July difference in Figure 7, it would help if the authors could clarify how the full-record Aura/MLS amplitudes in Figures 4 and 5 should be compared with the January and July values from Geller (1970).
• Line 172–179 and 206–215 – Figures 8 and 9 show enhanced amplitudes at high latitudes in winter, and the discussion relates this to radar observations and possible SSW-related amplification. At the same time, the manuscript also states that contamination by planetary wave-like oscillations cannot be excluded. Could the authors comment on how much contamination from other variability is expected at high latitudes in winter, and whether the signal seen at high latitudes in Figure 9 can still be confidently interpreted as a lunar tide signature?
Minor comments
• Line 74 - The authors mention the vertical range of the atmospheric profiles between 15 to 95 km and then note on line 86 that ‘The temperature and geopotential height values beyond 90 km altitude are less reliable’. However, it is not explicitly whether the analysis will be limited below 90 km. The vertical profiles in Figures 4 and 6 appear to slightly extend over 90 km, and the text describes the upper limit for these figures at 90.4 km. A simple line stating the altitude or pressure range used in the analysis will improve the clarity for the reader.
• Line 77 - Could the authors briefly explain how the interpolation errors would affect the analysis or results? i.e. would the method used here affect the retrieved amplitudes and phases?
Typographical and stylistic comments/suggestions
• Line 93 – ‘The bulge toward to the moon’ > ‘the bulge toward the moon’
• Line 150 – ‘obsevations’ > ‘observations’
• Line 177 – Please provide citations for the ‘numerous reports’
• Line 187 – ‘geopotent’ > ‘geopotential’
• Line 189 – ‘geopotantial’ > ‘geopotential’
• Line 204 – ‘geopotantial’ > ‘geopotential’- AC2: 'Reply on RC2', Klemens Hocke, 29 Apr 2026
Interactive discussion
Status: closed
-
RC1: 'Comment on egusphere-2026-368', Anonymous Referee #1, 16 Mar 2026
This paper presents the first study of the lunar tide in geopotential heights since the study by Geller (1970). The author investigates the lunar tide as observed by Aura/MLS between 2004 and 2021 and discusses the results with respect to the simulations by Geller (1970). The paper is well written, and the results are presented in a generally clear manner.
The findings are of interest to the scientific community. However, I believe ACP may not be the most suitable journal for this type of paper, and I would suggest considering submission to Annales Geophysicae (or similar) instead. Regardless of the journal choice, I strongly recommend that the author address the following concerns.
Line 11. Please consider using “thermal tides” instead of “solar tides”. Technically speaking, solar tides can still be gravitational, so using the word “thermal” makes the distinction clear.
Lines 20-21. This sentence needs to be revised. The amplification of the lunar tide at MLT altitudes is typically observed during major sudden stratospheric warmings (SSWs) that are accompanied by a strong polar night jet oscillation (PJO). In contrast, the lunar tide observed during winters with major SSWs but without strong PJOs appears very similar to that of winters with no major warmings. For example, see:
https://doi.org/10.1029/2019JD030828
Lines 41-42. The phrasing here is a bit confusing to me. Why would a “more standing” wave have a smaller amplitude compared to a “more propagating” wave? Besides, what does “more propagating” really mean in this context? Did you mean “less dissipated”? Please clarify this.
Lines 59-60. Could it be that the reason of a not so clear M2 signature in the temperature measurements is partly due to previously reported issues with Aura/MLS temperature measurements? The studies by Wing et al. (2018) and Marlon et al. (2021) show, e.g., that MLS has a seasonal and altitude dependant bias in temperature compared to SABER and lidar.
https://amt.copernicus.org/articles/11/6703/2018/
https://acp.copernicus.org/articles/21/6079/2021/
Line 78. Please consider removing the “I like”. You can simply write, “Firstly, to avoid errors due to the interpolation.”
Line 90. How does Aura/MLS actually measure the lunar tide? How often does the satellite observe the same geographic location again? My understanding is that the ground track repeats about 15-16 days.
Has the author attempted to use the longitudinal structure of the observations to extract the zonal wavenumber of the signal? This could be a useful diagnostic. The dominant semidiurnal lunar tide should appear primarily as a zonal wavenumber 2, which would help to confirm that the observed ~14-day modulation is indeed related to the lunar tide.
At the same time, could aliasing associated with the fixed local-time sampling of the satellite lead to mixing with other apparent zonal components (e.g., wavenumbers 1 or 3)? A discussion of this issue would be helpful.
Line 106. Please be careful with the wording. Zero padding does not enhance frequency resolution, but rather increases FFT sample density, which results in a better definition of the peaks, but not a higher resolution.
And, are there any gaps in the data? If so, how were they handled?
Line 107. Instead of “at the left and at the right”, I would rather write “before and after”.
Lines 113-121. I found this paragraph somewhat difficult to follow and had to read it more than once to fully understand the data processing procedure. I get the main workflow: apply FFT to the entire time series to identify the lunar peak. Then, apply a band pass filter around the M2 peak and reconstruct the amplitude envelope to track the seasonal variability of the lunar tide. However, this part could benefit from a slightly more detailed description of the steps involved. Expanding it a bit would likely make the procedure easier to follow, particularly for readers with less experience in signal processing, and would help them implement the approach more easily.
Line 123. Was the FFT applied to the geopotential heights or to the geopotential height perturbations? In line 107, the author mentions that a mean was subtracted from the dataset, so I am a bit confused. Please make this clear.
Lines 150-151. How close a value of 0.02 K is to the precision limit of the temperature measurements? In line 84, it is mentioned that the precision in the stratosphere is 1 K. I guess the number of samples considerably reduces the 1 K sigma, so there’s no need to worry about the precision. But, is this 1 K precision really only measurement noise, or does it also include geophysical variability? This distinction could affect how confidently such a small signal (0.02 K) can be detected.
Line 155. The author mentions that the vertical wavelength of the lunar tide is roughly 500 km in the mesosphere. Is that correct? 500 km? Could the author please describe how this number was determined? From Figure 6, I can estimate a value close to 290 km at the steepest parts of the profile, but it’s not clear how a value of 500 km would be obtained.
Line 159. Could you please make Figure 7 wider? And also add more ticks in the x-axis? This will make the differences between January and July easier to identify.
Line 169. Would it be possible to add a sketch depicting Geller’s Figure 10? Having access to a paper from 1970 is not that straightforward, and the Doi provided in the references does not work.
Line 172. Did the author do a similar analysis separating years with strong PJOs (or at least major SSWs) from those without? That would certainly help to determine if the enhancement of the lunar tide is due to SSWs.
Line 173. Could the author please provide more details on how the climatology was determined? Additionally, as suggested in the previous point, comparing a climatology of years with major SSWs to one of years without could help assess the impact of these events on the lunar tide.
Line 187. Please change “geopotent” by “geopotential”.
Line 197. Please change “showed that the lunar tide in is more amplified” by “showed that the lunar tide is more amplified”.
Line 204. Please change “geopotantial” by “geopotential”.
Line 212. Several studies have investigated the lunar tide during the northern hemisphere’s winter. However, citing only one, which is 20 years old, presents a limited perspective. For example, more recent works such as Chau et al. (2015), Siddiqui et al. (2015), Conte et al. (2017), Conte et al. (2019) offer additional insights.
Line 215. The fact that the lunar tide is stronger in January than in July is one of the main points raised in several parts of the article, but it is discussed very briefly. It would be helpful if a few more sentences were devoted to discussing this point.
Line 220. “The observed mean lunar tide is up to 55m (geopotential height amplitude) in the mesosphere while the simulation shows amplitudes between 99m in July and 220m in January at 90km height”. How should this be interpreted? Most of the results in this paper are presented at 82 km of height. Figure 4 shows a vertical profile of the lunar tide in geopotential height but over the entire time series, without discriminating between January and July. And Figure 7 displays the lunar tide as a function of time, but at 82 km altitude.
Citation: https://doi.org/10.5194/egusphere-2026-368-RC1 - AC1: 'Comment on egusphere-2026-368', Klemens Hocke, 18 Mar 2026
-
RC2: 'Comment on egusphere-2026-368', Anonymous Referee #2, 28 Apr 2026
Review of Observation of the Lunar Tide in the Middle Atmosphere by the Aura Microwave Limb Sounder
Summary of the paper
This paper presents the first identification of the lunar tide in the geopotential height observations of the middle atmosphere from Aura/MLS. The lunar tide is identified as a clear semi-monthly variation in Aura/MLS observations between 2004 and 2021. A comparison with model results from Geller (1970) as well as temperature observations from TIMED/SABER have been discussed. The paper further examines the vertical, seasonal and latitudinal structure of the lunar tide. The results show that lunar tide signal is stronger in January than in July and peaks near the equator.
Summary of the review and major comments
The main question addressed in this paper is whether the semidiurnal lunar M2 tide can be reliably identified in Aura/MLS through its semi-monthly signature, and whether the vertical, seasonal and latitudinal structure of the retrieved lunar tide signal is consistent with previous modeling and observational work. The paper contains a significant new result, i.e. the lunar tide can be identified clearly in satellite geopotential height observations. The comparison with model results and TIMED/SABER observations aids in interpreting the Aura/MLS results. However, some issues require clarification before the manuscript can be recommended for publication.
• Line 43–48 – The manuscript refers to the (2,2) and (2,4) modes of the lunar tide, but these are not really defined for the reader. Since the later interpretation of the phase profiles also relies on this terminology, a brief explanation of what these mode labels mean and why they are relevant here would help the reader follow the later discussion.
• Line 90 – The most important issue in the paper is the explanation of how the semidiurnal lunar M2 tide appears as a semi-monthly signature in Aura/MLS because of the sun-synchronous sampling. This is central to the interpretation of the entire analysis but is currently explained mostly qualitatively. Since the analysis relies on the 14.7653-day signal as the observational signature of M2, it would improve the paper if the authors could include a clearer explanation, or a short mathematical derivation, of this sampling/aliasing framework.
• Line 104-105 - The text states “the arithmetic mean of all observed atmospheric profiles is computed” each day, but Aura samples each latitude twice per orbit at two fixed local solar times (~01:45 and ~13:45 LST at the equator). This daily mean combines sampled from both Aura local-time branches. Since the two overpasses are separated by about 12 hours, this works for the semidiurnal tide because the two samples are nearly in phase for a ~12.42-hour oscillation. Could the authors state this explicitly in the methodology, since this seems important for justifying the daily averaging procedure used to construct the time series?
• Line 137 – 148 - Line 137 - 148 The manuscript does show January-versus-July variability for Aura/MLS at ~82 km in Figure 7. However, the vertical-profile comparison with Geller (1970) in Figures 4 and 5 seems to be compared with the full-record Aura/MLS amplitudes, whereas the values from Geller are for January and July. Since the Aura/MLS data also show a pronounced January-July difference in Figure 7, it would help if the authors could clarify how the full-record Aura/MLS amplitudes in Figures 4 and 5 should be compared with the January and July values from Geller (1970).
• Line 172–179 and 206–215 – Figures 8 and 9 show enhanced amplitudes at high latitudes in winter, and the discussion relates this to radar observations and possible SSW-related amplification. At the same time, the manuscript also states that contamination by planetary wave-like oscillations cannot be excluded. Could the authors comment on how much contamination from other variability is expected at high latitudes in winter, and whether the signal seen at high latitudes in Figure 9 can still be confidently interpreted as a lunar tide signature?
Minor comments
• Line 74 - The authors mention the vertical range of the atmospheric profiles between 15 to 95 km and then note on line 86 that ‘The temperature and geopotential height values beyond 90 km altitude are less reliable’. However, it is not explicitly whether the analysis will be limited below 90 km. The vertical profiles in Figures 4 and 6 appear to slightly extend over 90 km, and the text describes the upper limit for these figures at 90.4 km. A simple line stating the altitude or pressure range used in the analysis will improve the clarity for the reader.
• Line 77 - Could the authors briefly explain how the interpolation errors would affect the analysis or results? i.e. would the method used here affect the retrieved amplitudes and phases?
Typographical and stylistic comments/suggestions
• Line 93 – ‘The bulge toward to the moon’ > ‘the bulge toward the moon’
• Line 150 – ‘obsevations’ > ‘observations’
• Line 177 – Please provide citations for the ‘numerous reports’
• Line 187 – ‘geopotent’ > ‘geopotential’
• Line 189 – ‘geopotantial’ > ‘geopotential’
• Line 204 – ‘geopotantial’ > ‘geopotential’- AC2: 'Reply on RC2', Klemens Hocke, 29 Apr 2026
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Klemens Hocke
The requested preprint has a corresponding peer-reviewed final revised paper. You are encouraged to refer to the final revised version.
- Preprint
(10598 KB) - Metadata XML
This paper presents the first study of the lunar tide in geopotential heights since the study by Geller (1970). The author investigates the lunar tide as observed by Aura/MLS between 2004 and 2021 and discusses the results with respect to the simulations by Geller (1970). The paper is well written, and the results are presented in a generally clear manner.
The findings are of interest to the scientific community. However, I believe ACP may not be the most suitable journal for this type of paper, and I would suggest considering submission to Annales Geophysicae (or similar) instead. Regardless of the journal choice, I strongly recommend that the author address the following concerns.
Line 11. Please consider using “thermal tides” instead of “solar tides”. Technically speaking, solar tides can still be gravitational, so using the word “thermal” makes the distinction clear.
Lines 20-21. This sentence needs to be revised. The amplification of the lunar tide at MLT altitudes is typically observed during major sudden stratospheric warmings (SSWs) that are accompanied by a strong polar night jet oscillation (PJO). In contrast, the lunar tide observed during winters with major SSWs but without strong PJOs appears very similar to that of winters with no major warmings. For example, see:
https://doi.org/10.1029/2019JD030828
Lines 41-42. The phrasing here is a bit confusing to me. Why would a “more standing” wave have a smaller amplitude compared to a “more propagating” wave? Besides, what does “more propagating” really mean in this context? Did you mean “less dissipated”? Please clarify this.
Lines 59-60. Could it be that the reason of a not so clear M2 signature in the temperature measurements is partly due to previously reported issues with Aura/MLS temperature measurements? The studies by Wing et al. (2018) and Marlon et al. (2021) show, e.g., that MLS has a seasonal and altitude dependant bias in temperature compared to SABER and lidar.
https://amt.copernicus.org/articles/11/6703/2018/
https://acp.copernicus.org/articles/21/6079/2021/
Line 78. Please consider removing the “I like”. You can simply write, “Firstly, to avoid errors due to the interpolation.”
Line 90. How does Aura/MLS actually measure the lunar tide? How often does the satellite observe the same geographic location again? My understanding is that the ground track repeats about 15-16 days.
Has the author attempted to use the longitudinal structure of the observations to extract the zonal wavenumber of the signal? This could be a useful diagnostic. The dominant semidiurnal lunar tide should appear primarily as a zonal wavenumber 2, which would help to confirm that the observed ~14-day modulation is indeed related to the lunar tide.
At the same time, could aliasing associated with the fixed local-time sampling of the satellite lead to mixing with other apparent zonal components (e.g., wavenumbers 1 or 3)? A discussion of this issue would be helpful.
Line 106. Please be careful with the wording. Zero padding does not enhance frequency resolution, but rather increases FFT sample density, which results in a better definition of the peaks, but not a higher resolution.
And, are there any gaps in the data? If so, how were they handled?
Line 107. Instead of “at the left and at the right”, I would rather write “before and after”.
Lines 113-121. I found this paragraph somewhat difficult to follow and had to read it more than once to fully understand the data processing procedure. I get the main workflow: apply FFT to the entire time series to identify the lunar peak. Then, apply a band pass filter around the M2 peak and reconstruct the amplitude envelope to track the seasonal variability of the lunar tide. However, this part could benefit from a slightly more detailed description of the steps involved. Expanding it a bit would likely make the procedure easier to follow, particularly for readers with less experience in signal processing, and would help them implement the approach more easily.
Line 123. Was the FFT applied to the geopotential heights or to the geopotential height perturbations? In line 107, the author mentions that a mean was subtracted from the dataset, so I am a bit confused. Please make this clear.
Lines 150-151. How close a value of 0.02 K is to the precision limit of the temperature measurements? In line 84, it is mentioned that the precision in the stratosphere is 1 K. I guess the number of samples considerably reduces the 1 K sigma, so there’s no need to worry about the precision. But, is this 1 K precision really only measurement noise, or does it also include geophysical variability? This distinction could affect how confidently such a small signal (0.02 K) can be detected.
Line 155. The author mentions that the vertical wavelength of the lunar tide is roughly 500 km in the mesosphere. Is that correct? 500 km? Could the author please describe how this number was determined? From Figure 6, I can estimate a value close to 290 km at the steepest parts of the profile, but it’s not clear how a value of 500 km would be obtained.
Line 159. Could you please make Figure 7 wider? And also add more ticks in the x-axis? This will make the differences between January and July easier to identify.
Line 169. Would it be possible to add a sketch depicting Geller’s Figure 10? Having access to a paper from 1970 is not that straightforward, and the Doi provided in the references does not work.
Line 172. Did the author do a similar analysis separating years with strong PJOs (or at least major SSWs) from those without? That would certainly help to determine if the enhancement of the lunar tide is due to SSWs.
Line 173. Could the author please provide more details on how the climatology was determined? Additionally, as suggested in the previous point, comparing a climatology of years with major SSWs to one of years without could help assess the impact of these events on the lunar tide.
Line 187. Please change “geopotent” by “geopotential”.
Line 197. Please change “showed that the lunar tide in is more amplified” by “showed that the lunar tide is more amplified”.
Line 204. Please change “geopotantial” by “geopotential”.
Line 212. Several studies have investigated the lunar tide during the northern hemisphere’s winter. However, citing only one, which is 20 years old, presents a limited perspective. For example, more recent works such as Chau et al. (2015), Siddiqui et al. (2015), Conte et al. (2017), Conte et al. (2019) offer additional insights.
Line 215. The fact that the lunar tide is stronger in January than in July is one of the main points raised in several parts of the article, but it is discussed very briefly. It would be helpful if a few more sentences were devoted to discussing this point.
Line 220. “The observed mean lunar tide is up to 55m (geopotential height amplitude) in the mesosphere while the simulation shows amplitudes between 99m in July and 220m in January at 90km height”. How should this be interpreted? Most of the results in this paper are presented at 82 km of height. Figure 4 shows a vertical profile of the lunar tide in geopotential height but over the entire time series, without discriminating between January and July. And Figure 7 displays the lunar tide as a function of time, but at 82 km altitude.