Solitary wave characteristics on the fine structure of mesospheric sporadic sodium layer

Qiu, Shican; Shi, Mengxi; Soon, Willie; Jia, Mingjiao; Xue, Xianghui; Li, Tao; Ju, Peng; Dou, Xiankang

doi:https://doi.org/10.5194/acp-2021-1085

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https://doi.org/10.5194/acp-2021-1085

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21 Mar 2022

| 21 Mar 2022

Status: this preprint was under review for the journal ACP but the revision was not accepted.

Solitary wave characteristics on the fine structure of mesospheric sporadic sodium layer

Shican Qiu, Mengxi Shi, Willie Soon, Mingjiao Jia, Xianghui Xue, Tao Li, Peng Ju, and Xiankang Dou

Abstract. The most fantastic phenomenon of the mesospheric sodium layer is the so-called sporadic sodium layer (SSL or Na_S), which are proposed to be closely related to wave fluctuations. Solitary wave is a particular solution of partial differential equation whose energy travels as a localized wave packet, and a soliton is a special solitary wave which has a particle-like behavior with strong stable form. In this research, the solitary wave theory is applied for the first time to study the fine structure of Na_S. We perform soliton fitting processes on the observed data from the Andes Lidar Observatory, and find out that 24/27 Na_S events exhibit similar features/characteristics to a soliton. Time series of the net anomaly of the Na_S reveal the same variation process to the solution of a generalized five-order KdV equation. Our results therefore suggest the Na_S phenomenon would be an appropriate tracer for nonlinear wave studies in the atmosphere.

Received: 24 Dec 2021 – Discussion started: 21 Mar 2022

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Shican Qiu, Mengxi Shi, Willie Soon, Mingjiao Jia, Xianghui Xue, Tao Li, Peng Ju, and Xiankang Dou

Status: closed

RC1:
'Comment on acp-2021-1085', Anonymous Referee #3, 31 Mar 2022
Sporadic sodium layer events are frequently observed by the Na lidars around the world. This study provides another potential underline mechanism that could be helpful for the understanding of this dramatic event in the upper atmosphere. Here, the author utilizes the solitary wave theory to explain several sporadic sodium layer events in the upper mesosphere observed by a Na Doppler lidar at ALO. The waveform of the solidary wave is derived by fitting the residual of the observed Na layer anomalies to the solution of the KdV equation that describes the solitary wave. The author suggests that the observed “solidary wave” is “consistent with the shallow water model”, and presents an example of Nas coexisting with a strong wind shear in the lidar data. I know ALO has several nightglow instruments operating as well, so is it possible to check and see if these nightglow instrument captured any of these reported “solidary wave” events in Table 1? This would strengthen the author’s argument with further experimental evidence. In addition, why does not the author fit the 5^th order KdV solution for all of these event, since it appears the 5^th order solution generates better fitting? On the other hand, my major concern is the author seems to suggest the Nas is the product of Na+ layer in solidary wave form through Na ion-molecular chemistry, if I understand it correctly. A sharp Na+ layer with high peak ion density near and below 90 km, where neutral-molecular chemistry dominates, is highly unlikely in my opinion. There is not argument of the chemical reaction time, and how it compares with time of the wave event. In addition, the author completely ignores the possibility that it can also be a dynamic feature.

Technical comments:

The title of the paper does not reflect the key point of the manuscript. Since the whole paper is focusing on solidary wave mechanism for Nas, it would be beneficial to somehow include “solidary wave” in the title.

Page 2, Line 2: The author states the Na layer shape is “normally with a Gaussian distribution”. But This is really depending on the temporal resolution of how the lidar data are processed. For short time scale, the layer does not appear to be Gaussian at all. If the “solidary wave” lasted less than one hour in the Na lidar observations, this assumption will not apply. The author should be very careful about this statement. So more clarification would be required.

Page 2, Line 10: The author states “the ion-molecular theory is the most possible mechanism for Nas”. This statement is still debatable. Although there is high correlation between Nas and Es (or Na+) in the MLT, the dynamic effected cannot be ruled out, since the ion-neutral collision rate is still high, especially near and below ~100 km. In fact, some recent simulations indicate the dynamic effect can play important role in the Na layer structure in the lower thermosphere up to ~120 km or even higher.

Page 2, Line 24-25: Most of these references were published more than a decade ago, so I would not say they are “recently”.

Page 3, line 14: should be “in the mesopause region”.

Page 3, after equation 2, the author states the variable ‘n’ could be regarded as Na+ produced Na. I understand this statement follows the previous one (#3). But, again, I think the author should also consider/include the possibility of dynamic transport of Na atoms in the argument.

Page 5, line 4: It reads somewhat awkward that u2 is defined before the definition of u1. In addition, what is "the limiting wave amplitude"? Please clarify.

Page 9, line 25-26: This statement need further clarification. The vertical scale of Nas is less than 10 km because of the limitation set up the Na lidar range, but it does not mean the vertical propagation of the “solidary wave” is limited to the same scale. It would be highly possible that the wave propagates beyond the mesospheric Na layer (the Na lidar range) with larger vertical scale.

Page 13 on the author contribution. I do not see any data from the Chinese Meridian Project in this study, but the author Xiankang Dou “provided data from the Chinese Meridian Project”?

Page 20 figure 3: The author might need to adjust the color level of the contour plots of horizontal winds, since there are some large chunks of blank area in the two plots, where the lidar data should be still good.

Table 1, Would it be possible to generate a few figures to make some of the important parameters more visible, in addition to this table? It is difficult to digest the information from this busy table.
Citation: https://doi.org/10.5194/acp-2021-1085-RC1
- AC1: 'Reply on RC1', Shican Qiu, 13 Jun 2022
  
  The comment was uploaded in the form of a supplement: https://acp.copernicus.org/preprints/acp-2021-1085/acp-2021-1085-AC1-supplement.pdf
  
  Citation: https://doi.org/10.5194/acp-2021-1085-AC1
RC2:
'Comment on acp-2021-1085', Anonymous Referee #1, 04 Apr 2022

The comment was uploaded in the form of a supplement: https://acp.copernicus.org/preprints/acp-2021-1085/acp-2021-1085-RC2-supplement.pdf

Citation: https://doi.org/10.5194/acp-2021-1085-RC2
- AC2: 'Reply on RC2', Shican Qiu, 13 Jun 2022
  
  The comment was uploaded in the form of a supplement: https://acp.copernicus.org/preprints/acp-2021-1085/acp-2021-1085-AC2-supplement.pdf
  
  Citation: https://doi.org/10.5194/acp-2021-1085-AC2
RC3:
'Comment on acp-2021-1085', Anonymous Referee #2, 11 Apr 2022

Review "Solitary wave characteristics on the fine structure of mesospheric

sporadic sodium layer" by Qiu et al.

In the current version of the manuscript,

Qiu et al. have reported their work on studies of the sporadic sodium layer (Nas), one of the most active research areas in the upper atmosphere subject.

They have introduced this subject concisely in the abstract section, for example, the definition of Nas and the possible mechansim

(e.g., ion-molecule chemistry mechanism and recombination with electrons) as well as Nas relationship with waves.

Then the authors have introduced the solitary wave theory and has applied it to try to explain the fine structure of mesospheric Nas observed

by a narrow band lidar at Andes Lidar Observatory.

In section 2, the authors have described the solitary wave theory but they have assumed that the particle density changes with time is constant,

which is probably wrong in particular for the sporadic Na layer for this study.

Acturally I am quite struggled to understand the sections 2 and 3 but it looks that using the the solitary wave fitting

method clearly matches the observation data better than after they have selected Nas cases.

Based on this and their Figure 4, the authors then conclude that "this solitary wave theory could possibly explain some characteristcs of Nas".

The authors have also warned that

"it is worth noting that the numerical simulation of the higher-order KdV equation is probably only suitable

for explaining the events similar to the selected case" and

"In contrast, the other events with shorter

durations and cloud-like shapes are less consistent with the higher-order simulation results. This discrepancy also implies

30 that the NaS with different characteristics may have different fine structures."

This is quite confusing and there is not clear conclusions and convincing results from the current work.

It also depends on the method the authors have applied to do the data analysis (for example, they have applied the gaussian fit

first for the lidar measurements dataset then subtract it then use the anomlay to do the analysis, see their method in Page 5).

It looks the guassian fit used in the Equation 12 is not suitable for the Nas layer (Shown in the Figure 2c). Is that the reason to apply the solitary fitting for the density aomaly?

If so, the caption (measureed data) in the Figure 2d is misleading because it is the Na density difference from Lidar and guassian fit.

If you choose to different Guassian fit (for example, super gaussian fit function), will the result be different?

Somehow, I am lost in understanding how to obtain the equation (21).

The parameters used in the fitting expression are different for different cases (which shown in Table 4).

So my feeling is that these parameter will give better fit for the data rather than an explaination of Nas layer.

There are also many assumptions and it is very hard to judge and is unclear if they are reasonable or not.

For example, For the equation (2), why Na "could possible be regarded as the input of sodium sources from Na+ through chemical reactions"?

Please keep in mind the source of Na is from the the ablation of incoming meteors.

Again, why the authors assume the same airmasses (conservation of particle number) in Equation (2) to let dn/dt equals zero?

This mean the production and loss term of Na is always the same. Is this applicable for Nas layer?

Why the authors only consider "the dispersion term of a surface wave in incompressible shallow fluid" In equation (8)

and how this equation 8) is derived?

Does this mean that only one single Nas layer can be done in the current method? However, from the Lidar observations, it looks that the peak

Nas layer occurrs at different altitude (here just shows one case 2015-02-02 used in the Table 1, see the figure at

http://lidar.erau.edu/data/nalidar/plots/2015/20150202_Dmerge_15min_0.5km_90s_20_p.jpg)

What is the value of "the fluid depth h" used for different cases because this is required to calculate the depth of wave d?

My other major concern is the lack of the explaination for sporadic Na Layer formation in the current version of the manuscript, which

seems to me it still unclear why solitary wave causes the sporadic Na layer.

If we look at one case used in the current manuscript, for example their Figure 3, there is strong correlation

of Nas layer (Figure 3a) with zonal mean wind shear in Figure3f where Richardson number is calculated from the Eqauation 36, which has the zonal mean wind changes with altitude from the lidar data.

Of course, this suggests that atmospheric waves are related to

the Nas formation, but how the authors can attribute it to solitary waves, instead of gravity waves or tidal waves etc..

This may be not true because the authors have not applied a similar analysis for the the neutral Na data without Nas layer.

To be specified, what the results will look like if the authors apply the same method to the neutral Na data excluding Nas layer?

I understand that may be tough since there are some creteria to be met (for example, set the Na concentration and layer depth).

My other major concern is the lack of the explaination for sporadic Na Layer formation in the current version of the manuscript, which

seems to me it still unclear why solitary wave causes the sporadic Na layer.

If we look at one case used in the current manuscript, for example their Figure 3, there is strong correlation

of Nas layer (Figure 3a) with zonal mean wind shear in Figure3f where Richardson number is calculated from the Eqauation 36, which has the zonal mean wind changes with altitude from the lidar data.

Of course, this suggests that atmospheric waves are related to

the Nas formation, but how the authors can attribute it to solitary waves, instead of gravity waves or tidal waves etc..

This may be not true because the authors have not applied a similar analysis for the the neutral Na data without Nas layer.

To be specified, what the results will look like if the authors apply the same method to the neutral Na data excluding Nas layer?

I understand that may be tough since there are some creteria to be met (for example, set the Na concentration and layer depth).

If the result using the neutral Na data by ignoring Nas is similar as presented in the current manuscript, then that would indicate

the current conclusion is wrong.

It has been also widely accepted ion–molecule chemistry in plasma layers is the major mechanism for producing Nas layers at different latitudes,

which based on the work from Cox and Plane (1998) (i.e., downward motion of sporadic plasma layer Es as a source of Nas formation by

neutralized Na+ via an ion–molecule mechanism). This has been tested and supported from the observations including Na lidar measurements from different locations.

Can you do a similar to see if this mechanism won't explain the Nas layer occurrs over Ande station?

Citation: https://doi.org/10.5194/acp-2021-1085-RC3
- AC3: 'Reply on RC3', Shican Qiu, 13 Jun 2022
  
  The comment was uploaded in the form of a supplement: https://acp.copernicus.org/preprints/acp-2021-1085/acp-2021-1085-AC3-supplement.pdf
  
  Citation: https://doi.org/10.5194/acp-2021-1085-AC3

Status: closed

RC1:
'Comment on acp-2021-1085', Anonymous Referee #3, 31 Mar 2022
Sporadic sodium layer events are frequently observed by the Na lidars around the world. This study provides another potential underline mechanism that could be helpful for the understanding of this dramatic event in the upper atmosphere. Here, the author utilizes the solitary wave theory to explain several sporadic sodium layer events in the upper mesosphere observed by a Na Doppler lidar at ALO. The waveform of the solidary wave is derived by fitting the residual of the observed Na layer anomalies to the solution of the KdV equation that describes the solitary wave. The author suggests that the observed “solidary wave” is “consistent with the shallow water model”, and presents an example of Nas coexisting with a strong wind shear in the lidar data. I know ALO has several nightglow instruments operating as well, so is it possible to check and see if these nightglow instrument captured any of these reported “solidary wave” events in Table 1? This would strengthen the author’s argument with further experimental evidence. In addition, why does not the author fit the 5^th order KdV solution for all of these event, since it appears the 5^th order solution generates better fitting? On the other hand, my major concern is the author seems to suggest the Nas is the product of Na+ layer in solidary wave form through Na ion-molecular chemistry, if I understand it correctly. A sharp Na+ layer with high peak ion density near and below 90 km, where neutral-molecular chemistry dominates, is highly unlikely in my opinion. There is not argument of the chemical reaction time, and how it compares with time of the wave event. In addition, the author completely ignores the possibility that it can also be a dynamic feature.

Technical comments:

The title of the paper does not reflect the key point of the manuscript. Since the whole paper is focusing on solidary wave mechanism for Nas, it would be beneficial to somehow include “solidary wave” in the title.

Page 2, Line 2: The author states the Na layer shape is “normally with a Gaussian distribution”. But This is really depending on the temporal resolution of how the lidar data are processed. For short time scale, the layer does not appear to be Gaussian at all. If the “solidary wave” lasted less than one hour in the Na lidar observations, this assumption will not apply. The author should be very careful about this statement. So more clarification would be required.

Page 2, Line 10: The author states “the ion-molecular theory is the most possible mechanism for Nas”. This statement is still debatable. Although there is high correlation between Nas and Es (or Na+) in the MLT, the dynamic effected cannot be ruled out, since the ion-neutral collision rate is still high, especially near and below ~100 km. In fact, some recent simulations indicate the dynamic effect can play important role in the Na layer structure in the lower thermosphere up to ~120 km or even higher.

Page 2, Line 24-25: Most of these references were published more than a decade ago, so I would not say they are “recently”.

Page 3, line 14: should be “in the mesopause region”.

Page 3, after equation 2, the author states the variable ‘n’ could be regarded as Na+ produced Na. I understand this statement follows the previous one (#3). But, again, I think the author should also consider/include the possibility of dynamic transport of Na atoms in the argument.

Page 5, line 4: It reads somewhat awkward that u2 is defined before the definition of u1. In addition, what is "the limiting wave amplitude"? Please clarify.

Page 9, line 25-26: This statement need further clarification. The vertical scale of Nas is less than 10 km because of the limitation set up the Na lidar range, but it does not mean the vertical propagation of the “solidary wave” is limited to the same scale. It would be highly possible that the wave propagates beyond the mesospheric Na layer (the Na lidar range) with larger vertical scale.

Page 13 on the author contribution. I do not see any data from the Chinese Meridian Project in this study, but the author Xiankang Dou “provided data from the Chinese Meridian Project”?

Page 20 figure 3: The author might need to adjust the color level of the contour plots of horizontal winds, since there are some large chunks of blank area in the two plots, where the lidar data should be still good.

Table 1, Would it be possible to generate a few figures to make some of the important parameters more visible, in addition to this table? It is difficult to digest the information from this busy table.
Citation: https://doi.org/10.5194/acp-2021-1085-RC1
- AC1: 'Reply on RC1', Shican Qiu, 13 Jun 2022
  
  The comment was uploaded in the form of a supplement: https://acp.copernicus.org/preprints/acp-2021-1085/acp-2021-1085-AC1-supplement.pdf
  
  Citation: https://doi.org/10.5194/acp-2021-1085-AC1
RC2:
'Comment on acp-2021-1085', Anonymous Referee #1, 04 Apr 2022

The comment was uploaded in the form of a supplement: https://acp.copernicus.org/preprints/acp-2021-1085/acp-2021-1085-RC2-supplement.pdf

Citation: https://doi.org/10.5194/acp-2021-1085-RC2
- AC2: 'Reply on RC2', Shican Qiu, 13 Jun 2022
  
  The comment was uploaded in the form of a supplement: https://acp.copernicus.org/preprints/acp-2021-1085/acp-2021-1085-AC2-supplement.pdf
  
  Citation: https://doi.org/10.5194/acp-2021-1085-AC2
RC3:
'Comment on acp-2021-1085', Anonymous Referee #2, 11 Apr 2022

Review "Solitary wave characteristics on the fine structure of mesospheric

sporadic sodium layer" by Qiu et al.

In the current version of the manuscript,

Qiu et al. have reported their work on studies of the sporadic sodium layer (Nas), one of the most active research areas in the upper atmosphere subject.

They have introduced this subject concisely in the abstract section, for example, the definition of Nas and the possible mechansim

(e.g., ion-molecule chemistry mechanism and recombination with electrons) as well as Nas relationship with waves.

Then the authors have introduced the solitary wave theory and has applied it to try to explain the fine structure of mesospheric Nas observed

by a narrow band lidar at Andes Lidar Observatory.

In section 2, the authors have described the solitary wave theory but they have assumed that the particle density changes with time is constant,

which is probably wrong in particular for the sporadic Na layer for this study.

Acturally I am quite struggled to understand the sections 2 and 3 but it looks that using the the solitary wave fitting

method clearly matches the observation data better than after they have selected Nas cases.

Based on this and their Figure 4, the authors then conclude that "this solitary wave theory could possibly explain some characteristcs of Nas".

The authors have also warned that

"it is worth noting that the numerical simulation of the higher-order KdV equation is probably only suitable

for explaining the events similar to the selected case" and

"In contrast, the other events with shorter

durations and cloud-like shapes are less consistent with the higher-order simulation results. This discrepancy also implies

30 that the NaS with different characteristics may have different fine structures."

This is quite confusing and there is not clear conclusions and convincing results from the current work.

It also depends on the method the authors have applied to do the data analysis (for example, they have applied the gaussian fit

first for the lidar measurements dataset then subtract it then use the anomlay to do the analysis, see their method in Page 5).

It looks the guassian fit used in the Equation 12 is not suitable for the Nas layer (Shown in the Figure 2c). Is that the reason to apply the solitary fitting for the density aomaly?

If so, the caption (measureed data) in the Figure 2d is misleading because it is the Na density difference from Lidar and guassian fit.

If you choose to different Guassian fit (for example, super gaussian fit function), will the result be different?

Somehow, I am lost in understanding how to obtain the equation (21).

The parameters used in the fitting expression are different for different cases (which shown in Table 4).

So my feeling is that these parameter will give better fit for the data rather than an explaination of Nas layer.

There are also many assumptions and it is very hard to judge and is unclear if they are reasonable or not.

For example, For the equation (2), why Na "could possible be regarded as the input of sodium sources from Na+ through chemical reactions"?

Please keep in mind the source of Na is from the the ablation of incoming meteors.

Again, why the authors assume the same airmasses (conservation of particle number) in Equation (2) to let dn/dt equals zero?

This mean the production and loss term of Na is always the same. Is this applicable for Nas layer?

Why the authors only consider "the dispersion term of a surface wave in incompressible shallow fluid" In equation (8)

and how this equation 8) is derived?

Does this mean that only one single Nas layer can be done in the current method? However, from the Lidar observations, it looks that the peak

Nas layer occurrs at different altitude (here just shows one case 2015-02-02 used in the Table 1, see the figure at

http://lidar.erau.edu/data/nalidar/plots/2015/20150202_Dmerge_15min_0.5km_90s_20_p.jpg)

What is the value of "the fluid depth h" used for different cases because this is required to calculate the depth of wave d?

My other major concern is the lack of the explaination for sporadic Na Layer formation in the current version of the manuscript, which

seems to me it still unclear why solitary wave causes the sporadic Na layer.

If we look at one case used in the current manuscript, for example their Figure 3, there is strong correlation

of Nas layer (Figure 3a) with zonal mean wind shear in Figure3f where Richardson number is calculated from the Eqauation 36, which has the zonal mean wind changes with altitude from the lidar data.

Of course, this suggests that atmospheric waves are related to

the Nas formation, but how the authors can attribute it to solitary waves, instead of gravity waves or tidal waves etc..

This may be not true because the authors have not applied a similar analysis for the the neutral Na data without Nas layer.

To be specified, what the results will look like if the authors apply the same method to the neutral Na data excluding Nas layer?

I understand that may be tough since there are some creteria to be met (for example, set the Na concentration and layer depth).

My other major concern is the lack of the explaination for sporadic Na Layer formation in the current version of the manuscript, which

seems to me it still unclear why solitary wave causes the sporadic Na layer.

If we look at one case used in the current manuscript, for example their Figure 3, there is strong correlation

of Nas layer (Figure 3a) with zonal mean wind shear in Figure3f where Richardson number is calculated from the Eqauation 36, which has the zonal mean wind changes with altitude from the lidar data.

Of course, this suggests that atmospheric waves are related to

the Nas formation, but how the authors can attribute it to solitary waves, instead of gravity waves or tidal waves etc..

This may be not true because the authors have not applied a similar analysis for the the neutral Na data without Nas layer.

To be specified, what the results will look like if the authors apply the same method to the neutral Na data excluding Nas layer?

I understand that may be tough since there are some creteria to be met (for example, set the Na concentration and layer depth).

If the result using the neutral Na data by ignoring Nas is similar as presented in the current manuscript, then that would indicate

the current conclusion is wrong.

It has been also widely accepted ion–molecule chemistry in plasma layers is the major mechanism for producing Nas layers at different latitudes,

which based on the work from Cox and Plane (1998) (i.e., downward motion of sporadic plasma layer Es as a source of Nas formation by

neutralized Na+ via an ion–molecule mechanism). This has been tested and supported from the observations including Na lidar measurements from different locations.

Can you do a similar to see if this mechanism won't explain the Nas layer occurrs over Ande station?

Citation: https://doi.org/10.5194/acp-2021-1085-RC3
- AC3: 'Reply on RC3', Shican Qiu, 13 Jun 2022
  
  The comment was uploaded in the form of a supplement: https://acp.copernicus.org/preprints/acp-2021-1085/acp-2021-1085-AC3-supplement.pdf
  
  Citation: https://doi.org/10.5194/acp-2021-1085-AC3

Shican Qiu, Mengxi Shi, Willie Soon, Mingjiao Jia, Xianghui Xue, Tao Li, Peng Ju, and Xiankang Dou

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Short summary

The solitary wave theory is applied for the first time to study the sporadic sodium layers (Na_S). We perform soliton fitting processes on the observed data from the Andes Lidar Observatory, and find out that 24/27 Na_S events exhibit similar features to a soliton. Time series of the net anomaly reveal the same variation process to the solution of a five-order KdV equation. Our results suggest the Na_S phenomenon would be an appropriate tracer for nonlinear wave studies in the atmosphere.


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