the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 21 Jan 2022
Estimating the uncertainty of middle-atmospheric temperatures retrieved from airborne Rayleigh lidar measurements
Abstract. Possible uncertainties of lidar measurements of middle-atmospheric temperatures, measured with the novel airborne Rayleigh lidar system ALIMA, are investigated on the basis of data from the SouthTRAC-GW campaign in September 2019 and corresponding simulations of photon counts of the ALIMA system. We evaluate uncertainties due to the attenuation by Rayleigh extinction and ozone absorption, (signal-induced) photon noise, the photon background, and the nonlinearity of photon counting detectors. Ozone absorption induces an altitude-dependent cold bias in the retrieved temperatures of 2 K between 25 km to 55 km. Rayleigh extinction introduces a similar uncertainty of 2 K below 25 km that can be decreased by a suitable correction. Photon noise can introduce uncertainties of ±25 K at high altitudes (above 70 km) for high temporal resolutions (1 min), but on average the photon noise influences the temperature by only 1 K to 2 K at 70 km and decreases downwards. Uncertainties related to the photon background and the nonlinearity of the detectors, with a dead time correction applied, play a minor role in the temperature uncertainty. The analysis of the photon background in the ALIMA measurements of six research flights of the SouthTRAC-GW campaign proves the assumption of a constant photon background with altitude as well as the Poisson distribution of the photon counts. The airborne operation of ALIMA is advantageous as the high flight altitudes reduce the Rayleigh extinction by up to 17 % and thus result in higher signal levels compared to a ground-based operation. Overall, our analysis reveals that temperatures can be retrieved from ALIMA measurements with a remaining uncertainty of ≤ 1 K if all known biases are corrected.
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Interactive discussion
Status: closed
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RC1: 'Comment on amt-2021-310', Anonymous Referee #1, 18 Feb 2022
This paper focuses on the retrieval of middle atmospheric temperatures from the backscatter signals of an airborne Rayleigh lidar system. The technique was introduced forty years ago by Hauchecorne and Chanin (1980). It has been in operational use for more than 30 years at a number of stations, e.g. within the Network for the Detection of Atmospheric Composition Change (http://www.ndacc.org). Essentially, the paper re-iterates data analysis considerations that have become standard for many years. So nearly all results presented in the paper have been well known in the scientific community: Ozone absorption needs to be accounted for, or will introduce a bias (Leblanc et al. 1998; Sica et al. 2001). Uncertainties introduced by photon noise, background light, counter non-linearity, Rayleigh extinction are all well known and extensively discussed, e.g., by Leblanc et al. (2016). Lidar return signals have been simulated, and retrieval algorithms have been tested by Leblanc et al. (1998, 2004). Modern optimal estimation algorithms for temperature retrieval from Rayleigh lidar signals are given by Sica and Haefele (2015), and Jalali et al. (2018).
I did not understand the attempt to quantify signal-induce-noise (SIN) in section 4.4. I am not sure if SIN can be detected in this way. A more standard way would be to look at the decay of the background for varied maximum light exposures of the photo-detector.
Unfortunately, overall, I see very little new scientific findings in this paper, and feel that very major revisions are needed, before this is acceptable for publication in AMT.
What is new:
The comparison of observed, simulated, and ERA-5 analysed temperature waves in Fig. 4 is new and interesting. It shows the capabilites of the airborne lidar to observe large gravity waves over one of the worlds hot-spots. This is worth presenting, maybe expanding.
The claim that the skewed Poisson statistics of photon counting introduce a high bias in retrieved density and a low bias in retrieved temperature is new to me, but not explained very clearly. I would expect that this bias would be within the estimated uncertainty, and would only be significant at very low total photon counts. However, it would be interesting to have a more detailed look at this.
In summary, I suggest major revisions for this paper. All the parts that re-iterate well known facts, already described in, e.g., Leblanc et al. (2016) should be dropped, or should be shortened to a few paragraphs. The focus of the paper should be on the new findings, e.g. those I mentioned above. Most AMT readers have little time, so new papers need to be concise and need to present important new findings only.
References:
Jalali, A., Sica, R. J., and Haefele, A., (2018), Improvements to a long-term Rayleigh-scatter lidar temperature climatology by using an optimal estimation method, Atmos. Meas. Tech., 11, 6043–6058, https://doi.org/10.5194/amt-11-6043-2018
Leblanc, T., McDermid, I. S., Hauchecorne, A., and Keckhut, P. (1998), Evaluation of optimization of lidar temperature analysis algorithms using simulated data, J. Geophys. Res., 103( D6), 6177–6187, https://doi.org/10.1029/97JD03494
Leblanc, T., et al. (2004), The NDSC ozone and temperature lidar Algorithm Intercomparison Initiative (A2I): Project overview, European Space Agency, Special Publication, 2(561), pp. 881-884, ISSN 03796566.
Leblanc, T., et al. (2016), Proposed standardized definitions for vertical resolution and uncertainty in the NDACC lidar ozone and temperature algorithms – Part 3: Temperature uncertainty budget, Atmos. Meas. Tech., 9, 4079–4101, https://doi.org/10.5194/amt-9-4079-2016
Sica, R.J., Zylawy, Z.A., and Argall, P.S., (2001), Ozone corrections for Rayleigh-scatter temperature determinations in the middle atmosphere
Journal of Atmospheric and Oceanic Technology, 18(7), pp. 1223–1228.Sica R., and Haefele, A. (2015), Retrieval of temperature from a multiple-channel Rayleigh-scatter lidar using an optimal estimation method, Appl. Opt. 54, 1872-1889, https://doi.org/10.1364/AO.54.001872
Citation: https://doi.org/10.5194/amt-2021-310-RC1 -
AC2: 'Reply on RC1', Stefanie Knobloch, 10 May 2022
The comment was uploaded in the form of a supplement: https://amt.copernicus.org/preprints/amt-2021-310/amt-2021-310-AC2-supplement.pdf
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AC2: 'Reply on RC1', Stefanie Knobloch, 10 May 2022
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RC2: 'Comment on amt-2021-310', Anonymous Referee #2, 06 Mar 2022
This manuscript aims at characterizing measurement uncertainty for an airborne Rayleigh lidar (ALIMA), looking upward towards the stratosphere and mesosphere. One of the science objectives is to observe density and/or temperature disturbances associated with the propagation and dissipation of gravity wave in the middle atmosphere. The authors use lidar signal simulation to estimate certain components of this uncertainty.
Most of the manuscript repeats what has been already published, and so my main recommendation is to re-submit after major revisions, including a re-organization of the manuscript to re-balance the weight given to each section, based on what has been already published and what has not. I recommend to refer to Leblanc et al. (2016) (citation below) who provide, for example, quantitative estimates of the uncertainty associated with molecular extinction and ozone absorption (this part should be straightforward and not exceed a paragraph or two in the revised manuscript).
Unfortunately, the manuscript suffers from a major mistake in the quantification of the temperature correction associated with ozone absorption. If I am not mistaken, their ozone optical depth and ozone absorption correction were computed using O3 mixing ratio rather than O3 number density, which explains why they found a maximum impact at 35 km rather than 22-24 km. Fig 7 (left) of Leblanc et al. (2016) and Figs. 4 and 5 of Sica et al. (2001) both show a maximum impact in the lower stratosphere associated with O3 ND peaking at 23-26 km.
I also strongly recommend that the authors make a clear distinction between what is uncertainty, error, and bias, which eventually, will greatly help them re-shape the manuscript towards a well-defined objective. I believe the current objective of the authors is to assess the quality of the ALIMA measurements, and eventually provide a full uncertainty budget. Lidar simulation is not needed for most of this estimation work. Some of the figures shown in past publications can serve as guidance to present their results in the revised manuscript.
Here are suggested definitions that might help re-focusing the next manuscript:
Bias = a value, negative or positive, describing an observed, systematic (i.e., repeatable) difference between 2 observations
Error = A value, negative or positive, describing the actual (unknown) difference between the true value and the measured value
Uncertainty = A value, always positive, describing statistically the best estimate (or magnitude) of the (unknown) error arising from a specific physical effect or retrieval approach that drives the final, reported value away from its true value.
For example, “temperature uncertainty due to ozone absorption” is an estimate of the error due to the fact that the ozone absorption is not perfectly accounted for in the temperature measurement/retrieval. Unlike error and bias, uncertainty is a controlled quantity.
Minor comments:
Page 4, line 102 : sigmaray depends on wavelength. Specify the wavelength.
Page 4, lin2 109, “well mixed”: Not sure what “well mixed” means here.
Page 5, line 153, “the here”: missing word
Page 6, line 162, “geographic validity”: this term is unclear. Did the author mean “spatial coincidence”?
Page 9, lines 118-119 “(0.25° x 0.25° x 137 levels)”: Provide the model’s approximate horizontal and vertical resolutions in kilometers for the geographic and vertical range considered (this is what matters in this paragraph).
Page 11, lines 268-270: I don’t understand the sentence “the on average cold bias of ≤ 1 K in the stratosphere is related to the performance of the hydrostatic integration since other uncertainties are either excluded or do not act in this altitude range”. Uncertainty is a quantity provided together with a measurement and which role is to provide a statistical estimate of the measurement error.
Page 14, lines 314-321 and fig 8a: This paragraph, used together with Fig 8a, is misleading as, at a given altitude (e.g., 35 km) it is the ratio of the extinction at z and z+dz that matters (the total optical depth is not the impacting variable). To really illustrate how extinction impacts the temperature measurement, the ratio of extinction at z and z+dz should be plotted in fig 8a. The total optical depth only influences the magnitude of the signal (attenuated 10x between a flight at the tropopause and a flight near the ground).
Page 16, line 360, “uncertainty”: Once again, this is ambiguous. I think the authors refer to the error caused by neglecting ozone absorption, which is not the same thing as uncertainty.
Leblanc et al., 2016 citation:
Leblanc, T., R. J. Sica, J. A. E. van Gijsel, A. Haefele, G. Payen, and G. Liberti (2016), Proposed standardized definitions for vertical resolution and uncertainty in the NDACC lidar ozone and temperature algorithms – Part 3: Temperature uncertainty budget, Atmos. Meas. Tech., 9(8), 4079-4101.
Citation: https://doi.org/10.5194/amt-2021-310-RC2 -
AC3: 'Reply on RC2', Stefanie Knobloch, 10 May 2022
The comment was uploaded in the form of a supplement: https://amt.copernicus.org/preprints/amt-2021-310/amt-2021-310-AC3-supplement.pdf
-
AC3: 'Reply on RC2', Stefanie Knobloch, 10 May 2022
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EC1: 'Comment on amt-2021-310', Robert Sica, 09 Mar 2022
Unfortunately the revisions required for this manuscript are sufficient enough to warrant it being rejected. The Referees and I have left significant comments we believe are necessary to address in a revised manuscript, as well as correction of what appears to be a significant error in the calculation of the ozone correction (see Referee ’s report). Upon addressing these concerns I encourage you to resubmit the manuscript.
My comments on the initial submission follow.
I don't think the level of scholarship in this version of the manuscript is sufficient, as some similar and significant previous Rayleigh lidar work with significant overlap to this manuscript is not discussed. In my References below are two very important papers for you to discuss and compare your results. The Leblanc et al work is a detailed assessment of the traditional analysis and has detailed uncertainty calculations you should refer to in your work. The Sica and Haefele work describes an optimal estimation based method for retrieving temperature. One advantage of this method is issues like SNR cutoffs are defined quantitatively by the retrieval and don't requiring guessing about SNR like in the traditional method.
The other reference papers are a few selected works my group has done on gravity waves using the Purple Crow Lidar which should be cited and discussed. There have been other significant studies with higher power Rayleigh and sodium lidar systems you should discuss as well; I leave it to you to track these down.
Minor comments on the submission.
Line 83: you should write background as B(z); if you require a simplifying assumption it could be then assumed constant, but it is not constant in general on many systems.line 86: typo, "E.g." starts a sentence instead of continues the sentence.
bottom of page 5: if I read what you are doing correctly you are using a temperature consistent as opposed to a density consistent seed; in other words in the former case you take a seed temperature and in the later you normalize the density to be consistent with the assumed temperature (because pressure is what is relevant). Perhaps you could make this point clearer to the reader and explain why you picked it?
line 422: you don't mention your result is only true for non-paralyzable system, why are paralyzable systems not discussed? Please include both, and if you want to only discuss one say why.
References
1. Important Rayleigh T work
Leblanc, T. et al. (2016), Proposed standardized definitions for vertical resolution and uncertainty in the NDACC lidar ozone and temperature algorithms -- Part 3: Temperature uncertainty budget, Atmospheric Measurement Techniques, 9(8), 4079-4101, doi:10.5194/amt-9-4079-2016.Sica, R. J., and Haefele, A. (2015), Retrieval of temperature from a multiple-channel Rayleigh-scatter lidar using an optimal estimation method, Applied Optics, 54(8), 1872-1889, doi:10.1364/AO.54.001872.
2. A few Gravity Wave papers
Sica, R. J. (1999), Measurements of the effects of gravity waves is the middle atmosphere using parametric models of density fluctuations. Part II: Energy dissipation and eddy diffusion, Journal of the Atmospheric Sciences, 56(10), 1330-1343.
Sica, R. J., and Russell, A. T. (1999), How many waves are in the gravity wave spectrum?, Geophysical Research Letters, 26(24), 3617-3620.
Sica, R. J., and Russell, A. T. (1999), Measurements of the effects of gravity waves in the middle atmosphere using parametric models of density fluctuations. Part I: Vertical wavenumber and temporal spectra, Journal of the Atmospheric Sciences, 56(10), 1308-1329.
Sica, R. J., and Thorsley, M. D. (1996), Measurements of superadiabatic lapse rates in the middle atmosphere, Geophysical Research Letters, 23(20), 2797-2800.
The Purple Crow Lidar (system description)
Sica, R. J. et al. (1995), Lidar Measurements Taken with a Large-Aperture Liquid Mirror.1. Rayleigh-Scatter System, Applied Optics, 34(30), 6925-6936.Citation: https://doi.org/10.5194/amt-2021-310-EC1 -
AC1: 'Final response: letter to the editor', Stefanie Knobloch, 10 May 2022
The comment was uploaded in the form of a supplement: https://amt.copernicus.org/preprints/amt-2021-310/amt-2021-310-AC1-supplement.pdf
-
AC1: 'Final response: letter to the editor', Stefanie Knobloch, 10 May 2022
Interactive discussion
Status: closed
-
RC1: 'Comment on amt-2021-310', Anonymous Referee #1, 18 Feb 2022
This paper focuses on the retrieval of middle atmospheric temperatures from the backscatter signals of an airborne Rayleigh lidar system. The technique was introduced forty years ago by Hauchecorne and Chanin (1980). It has been in operational use for more than 30 years at a number of stations, e.g. within the Network for the Detection of Atmospheric Composition Change (http://www.ndacc.org). Essentially, the paper re-iterates data analysis considerations that have become standard for many years. So nearly all results presented in the paper have been well known in the scientific community: Ozone absorption needs to be accounted for, or will introduce a bias (Leblanc et al. 1998; Sica et al. 2001). Uncertainties introduced by photon noise, background light, counter non-linearity, Rayleigh extinction are all well known and extensively discussed, e.g., by Leblanc et al. (2016). Lidar return signals have been simulated, and retrieval algorithms have been tested by Leblanc et al. (1998, 2004). Modern optimal estimation algorithms for temperature retrieval from Rayleigh lidar signals are given by Sica and Haefele (2015), and Jalali et al. (2018).
I did not understand the attempt to quantify signal-induce-noise (SIN) in section 4.4. I am not sure if SIN can be detected in this way. A more standard way would be to look at the decay of the background for varied maximum light exposures of the photo-detector.
Unfortunately, overall, I see very little new scientific findings in this paper, and feel that very major revisions are needed, before this is acceptable for publication in AMT.
What is new:
The comparison of observed, simulated, and ERA-5 analysed temperature waves in Fig. 4 is new and interesting. It shows the capabilites of the airborne lidar to observe large gravity waves over one of the worlds hot-spots. This is worth presenting, maybe expanding.
The claim that the skewed Poisson statistics of photon counting introduce a high bias in retrieved density and a low bias in retrieved temperature is new to me, but not explained very clearly. I would expect that this bias would be within the estimated uncertainty, and would only be significant at very low total photon counts. However, it would be interesting to have a more detailed look at this.
In summary, I suggest major revisions for this paper. All the parts that re-iterate well known facts, already described in, e.g., Leblanc et al. (2016) should be dropped, or should be shortened to a few paragraphs. The focus of the paper should be on the new findings, e.g. those I mentioned above. Most AMT readers have little time, so new papers need to be concise and need to present important new findings only.
References:
Jalali, A., Sica, R. J., and Haefele, A., (2018), Improvements to a long-term Rayleigh-scatter lidar temperature climatology by using an optimal estimation method, Atmos. Meas. Tech., 11, 6043–6058, https://doi.org/10.5194/amt-11-6043-2018
Leblanc, T., McDermid, I. S., Hauchecorne, A., and Keckhut, P. (1998), Evaluation of optimization of lidar temperature analysis algorithms using simulated data, J. Geophys. Res., 103( D6), 6177–6187, https://doi.org/10.1029/97JD03494
Leblanc, T., et al. (2004), The NDSC ozone and temperature lidar Algorithm Intercomparison Initiative (A2I): Project overview, European Space Agency, Special Publication, 2(561), pp. 881-884, ISSN 03796566.
Leblanc, T., et al. (2016), Proposed standardized definitions for vertical resolution and uncertainty in the NDACC lidar ozone and temperature algorithms – Part 3: Temperature uncertainty budget, Atmos. Meas. Tech., 9, 4079–4101, https://doi.org/10.5194/amt-9-4079-2016
Sica, R.J., Zylawy, Z.A., and Argall, P.S., (2001), Ozone corrections for Rayleigh-scatter temperature determinations in the middle atmosphere
Journal of Atmospheric and Oceanic Technology, 18(7), pp. 1223–1228.Sica R., and Haefele, A. (2015), Retrieval of temperature from a multiple-channel Rayleigh-scatter lidar using an optimal estimation method, Appl. Opt. 54, 1872-1889, https://doi.org/10.1364/AO.54.001872
Citation: https://doi.org/10.5194/amt-2021-310-RC1 -
AC2: 'Reply on RC1', Stefanie Knobloch, 10 May 2022
The comment was uploaded in the form of a supplement: https://amt.copernicus.org/preprints/amt-2021-310/amt-2021-310-AC2-supplement.pdf
-
AC2: 'Reply on RC1', Stefanie Knobloch, 10 May 2022
-
RC2: 'Comment on amt-2021-310', Anonymous Referee #2, 06 Mar 2022
This manuscript aims at characterizing measurement uncertainty for an airborne Rayleigh lidar (ALIMA), looking upward towards the stratosphere and mesosphere. One of the science objectives is to observe density and/or temperature disturbances associated with the propagation and dissipation of gravity wave in the middle atmosphere. The authors use lidar signal simulation to estimate certain components of this uncertainty.
Most of the manuscript repeats what has been already published, and so my main recommendation is to re-submit after major revisions, including a re-organization of the manuscript to re-balance the weight given to each section, based on what has been already published and what has not. I recommend to refer to Leblanc et al. (2016) (citation below) who provide, for example, quantitative estimates of the uncertainty associated with molecular extinction and ozone absorption (this part should be straightforward and not exceed a paragraph or two in the revised manuscript).
Unfortunately, the manuscript suffers from a major mistake in the quantification of the temperature correction associated with ozone absorption. If I am not mistaken, their ozone optical depth and ozone absorption correction were computed using O3 mixing ratio rather than O3 number density, which explains why they found a maximum impact at 35 km rather than 22-24 km. Fig 7 (left) of Leblanc et al. (2016) and Figs. 4 and 5 of Sica et al. (2001) both show a maximum impact in the lower stratosphere associated with O3 ND peaking at 23-26 km.
I also strongly recommend that the authors make a clear distinction between what is uncertainty, error, and bias, which eventually, will greatly help them re-shape the manuscript towards a well-defined objective. I believe the current objective of the authors is to assess the quality of the ALIMA measurements, and eventually provide a full uncertainty budget. Lidar simulation is not needed for most of this estimation work. Some of the figures shown in past publications can serve as guidance to present their results in the revised manuscript.
Here are suggested definitions that might help re-focusing the next manuscript:
Bias = a value, negative or positive, describing an observed, systematic (i.e., repeatable) difference between 2 observations
Error = A value, negative or positive, describing the actual (unknown) difference between the true value and the measured value
Uncertainty = A value, always positive, describing statistically the best estimate (or magnitude) of the (unknown) error arising from a specific physical effect or retrieval approach that drives the final, reported value away from its true value.
For example, “temperature uncertainty due to ozone absorption” is an estimate of the error due to the fact that the ozone absorption is not perfectly accounted for in the temperature measurement/retrieval. Unlike error and bias, uncertainty is a controlled quantity.
Minor comments:
Page 4, line 102 : sigmaray depends on wavelength. Specify the wavelength.
Page 4, lin2 109, “well mixed”: Not sure what “well mixed” means here.
Page 5, line 153, “the here”: missing word
Page 6, line 162, “geographic validity”: this term is unclear. Did the author mean “spatial coincidence”?
Page 9, lines 118-119 “(0.25° x 0.25° x 137 levels)”: Provide the model’s approximate horizontal and vertical resolutions in kilometers for the geographic and vertical range considered (this is what matters in this paragraph).
Page 11, lines 268-270: I don’t understand the sentence “the on average cold bias of ≤ 1 K in the stratosphere is related to the performance of the hydrostatic integration since other uncertainties are either excluded or do not act in this altitude range”. Uncertainty is a quantity provided together with a measurement and which role is to provide a statistical estimate of the measurement error.
Page 14, lines 314-321 and fig 8a: This paragraph, used together with Fig 8a, is misleading as, at a given altitude (e.g., 35 km) it is the ratio of the extinction at z and z+dz that matters (the total optical depth is not the impacting variable). To really illustrate how extinction impacts the temperature measurement, the ratio of extinction at z and z+dz should be plotted in fig 8a. The total optical depth only influences the magnitude of the signal (attenuated 10x between a flight at the tropopause and a flight near the ground).
Page 16, line 360, “uncertainty”: Once again, this is ambiguous. I think the authors refer to the error caused by neglecting ozone absorption, which is not the same thing as uncertainty.
Leblanc et al., 2016 citation:
Leblanc, T., R. J. Sica, J. A. E. van Gijsel, A. Haefele, G. Payen, and G. Liberti (2016), Proposed standardized definitions for vertical resolution and uncertainty in the NDACC lidar ozone and temperature algorithms – Part 3: Temperature uncertainty budget, Atmos. Meas. Tech., 9(8), 4079-4101.
Citation: https://doi.org/10.5194/amt-2021-310-RC2 -
AC3: 'Reply on RC2', Stefanie Knobloch, 10 May 2022
The comment was uploaded in the form of a supplement: https://amt.copernicus.org/preprints/amt-2021-310/amt-2021-310-AC3-supplement.pdf
-
AC3: 'Reply on RC2', Stefanie Knobloch, 10 May 2022
-
EC1: 'Comment on amt-2021-310', Robert Sica, 09 Mar 2022
Unfortunately the revisions required for this manuscript are sufficient enough to warrant it being rejected. The Referees and I have left significant comments we believe are necessary to address in a revised manuscript, as well as correction of what appears to be a significant error in the calculation of the ozone correction (see Referee ’s report). Upon addressing these concerns I encourage you to resubmit the manuscript.
My comments on the initial submission follow.
I don't think the level of scholarship in this version of the manuscript is sufficient, as some similar and significant previous Rayleigh lidar work with significant overlap to this manuscript is not discussed. In my References below are two very important papers for you to discuss and compare your results. The Leblanc et al work is a detailed assessment of the traditional analysis and has detailed uncertainty calculations you should refer to in your work. The Sica and Haefele work describes an optimal estimation based method for retrieving temperature. One advantage of this method is issues like SNR cutoffs are defined quantitatively by the retrieval and don't requiring guessing about SNR like in the traditional method.
The other reference papers are a few selected works my group has done on gravity waves using the Purple Crow Lidar which should be cited and discussed. There have been other significant studies with higher power Rayleigh and sodium lidar systems you should discuss as well; I leave it to you to track these down.
Minor comments on the submission.
Line 83: you should write background as B(z); if you require a simplifying assumption it could be then assumed constant, but it is not constant in general on many systems.line 86: typo, "E.g." starts a sentence instead of continues the sentence.
bottom of page 5: if I read what you are doing correctly you are using a temperature consistent as opposed to a density consistent seed; in other words in the former case you take a seed temperature and in the later you normalize the density to be consistent with the assumed temperature (because pressure is what is relevant). Perhaps you could make this point clearer to the reader and explain why you picked it?
line 422: you don't mention your result is only true for non-paralyzable system, why are paralyzable systems not discussed? Please include both, and if you want to only discuss one say why.
References
1. Important Rayleigh T work
Leblanc, T. et al. (2016), Proposed standardized definitions for vertical resolution and uncertainty in the NDACC lidar ozone and temperature algorithms -- Part 3: Temperature uncertainty budget, Atmospheric Measurement Techniques, 9(8), 4079-4101, doi:10.5194/amt-9-4079-2016.Sica, R. J., and Haefele, A. (2015), Retrieval of temperature from a multiple-channel Rayleigh-scatter lidar using an optimal estimation method, Applied Optics, 54(8), 1872-1889, doi:10.1364/AO.54.001872.
2. A few Gravity Wave papers
Sica, R. J. (1999), Measurements of the effects of gravity waves is the middle atmosphere using parametric models of density fluctuations. Part II: Energy dissipation and eddy diffusion, Journal of the Atmospheric Sciences, 56(10), 1330-1343.
Sica, R. J., and Russell, A. T. (1999), How many waves are in the gravity wave spectrum?, Geophysical Research Letters, 26(24), 3617-3620.
Sica, R. J., and Russell, A. T. (1999), Measurements of the effects of gravity waves in the middle atmosphere using parametric models of density fluctuations. Part I: Vertical wavenumber and temporal spectra, Journal of the Atmospheric Sciences, 56(10), 1308-1329.
Sica, R. J., and Thorsley, M. D. (1996), Measurements of superadiabatic lapse rates in the middle atmosphere, Geophysical Research Letters, 23(20), 2797-2800.
The Purple Crow Lidar (system description)
Sica, R. J. et al. (1995), Lidar Measurements Taken with a Large-Aperture Liquid Mirror.1. Rayleigh-Scatter System, Applied Optics, 34(30), 6925-6936.Citation: https://doi.org/10.5194/amt-2021-310-EC1 -
AC1: 'Final response: letter to the editor', Stefanie Knobloch, 10 May 2022
The comment was uploaded in the form of a supplement: https://amt.copernicus.org/preprints/amt-2021-310/amt-2021-310-AC1-supplement.pdf
-
AC1: 'Final response: letter to the editor', Stefanie Knobloch, 10 May 2022
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