The Response of Stratospheric Gravity Waves to the 11-Year Solar Cycle
Round 1
Reviewer 1 Report
Comments and Suggestions for AuthorsThe manuscript presents an interesting study on the influence of the 11-year solar cycle on stratospheric gravity waves, but it requires significant improvements in methodological clarity and statistical analysis. Enhancing the detail and coherence in the results section, along with better contextualization within existing literature, will strengthen the overall impact and validity of the findings.
Title and Abstract (Lines 1-18):
The title specifies "stratospheric gravity waves," but the abstract and introduction often refer to "gravity waves" in general without always specifying the stratosphere. This could lead to confusion about the scope of the study.
Introduction (Lines 19-65):
The introduction lacks a clear research question or hypothesis. While it provides a broad overview of gravity waves and their sources, it does not specify the novel contribution or the specific gaps in existing research that this study aims to fill.
Data Selection and Method:
The section lacks detail on the criteria for data selection and quality control measures applied to the FY-3C satellite data.
The methodology for gravity wave extraction is described briefly, but there is no justification for the chosen bandpass filter ranges (2-20 km, 2-10 km, 12-20 km). It is unclear why these specific ranges were selected and how they compare to previous studies.
Statistical Methods (Lines 129-138):
The significance test using the P-value is mentioned, but there is no discussion of how multiple comparisons are handled, which could inflate Type I error rates.
The methodology section does not clearly define the criteria for determining "significant" correlations, which could lead to ambiguous interpretations of the results.
Results (Lines 139-172):
While Pearson correlation coefficients are presented, the results section lacks a deeper statistical analysis. For instance, there is no discussion of the confidence intervals or potential confounding factors that might influence the observed correlations.
There is no mention of the strength and direction of correlations (e.g., weak, moderate, strong). This information is crucial for interpreting the significance of the results.
Some statements in the results section are ambiguous and lack clarity. For example, phrases like "the overall correlation is significant" (line 159) need to be supported with specific values and statistical tests.
The section mentions variability in gravity wave parameters but does not provide a detailed analysis of this variability. A discussion on the sources and implications of this variability would strengthen the results.
The process of deriving the results from the data is not clearly explained. For instance, how the seasonal and latitudinal variations were calculated and what specific statistical methods were used for these calculations should be detailed.
The results section makes broad statements about the influence of the 11-year solar cycle on gravity waves without sufficient evidence to support such generalizations. More nuanced conclusions, acknowledging the limitations and scope of the study, would be more appropriate.
There is no mention of negative results or non-significant findings. Including these is important for a balanced and transparent presentation of the research outcomes.
Comments on the Quality of English LanguageThere are several grammatical errors and typos throughout the manuscript which can affect readability and the overall quality of the paper.
The manuscript lacks a clear structure in some parts, particularly in the transition between sections, which can make it difficult for readers to follow the flow of information.
Author Response
The manuscript presents an interesting study on the influence of the 11-year solar cycle on stratospheric gravity waves, but it requires significant improvements in methodological clarity and statistical analysis. Enhancing the detail and coherence in the results section, along with better contextualization within existing literature, will strengthen the overall impact and validity of the findings.
Response:
We gratefully appreciate for your valuable comment, which has significantly helped us improve the manuscript.
Title and Abstract (Lines 1-18):
The title specifies "stratospheric gravity waves," but the abstract and introduction often refer to "gravity waves" in general without always specifying the stratosphere. This could lead to confusion about the scope of the study.
Response:
Revised as suggested.
Revisions in the manuscript:
(Line 6)
to invert global stratospheric gravity wave disturbances
(Line 7)
It provides the global stratospheric gravity wave distribution
(Line 10-12)
Through analyzing the intensity of stratospheric gravity wave disturbances across different latitude bands, we found that in high-latitude regions, stratospheric gravity wave disturbances are most sensitive and respond most quickly to variations in solar activity.
Introduction (Lines 19-65):
The introduction lacks a clear research question or hypothesis. While it provides a broad overview of gravity waves and their sources, it does not specify the novel contribution or the specific gaps in existing research that this study aims to fill.
Response:
We made corresponding supplementary discussions based on the reviewer's comments.
Revisions in the manuscript:
(Lines 68-79)
Previous studies analyzing the response of GWs to solar activity have only considered immediate responses, without accounting for the potential delayed response of gravity waves due to atmospheric background parameters, which is a key focus of this paper. Additionally, many studies in the past obtained the gravity waves using high passfilter with cut-off vertical wavelength of 10 km [29]. Consequently, their results completely suppressed the gravity waves with vertical wavelengths >10 km, which are dominant over the middle and high latitude regions[30]. So, in order to cover as many gravity waves information，we investigate gravity waves, respectively, in two separate vertical wavelengths, one is 2 - 10 km(short-wavelength GWs), and the other is 12–20 km (long-wavelength GWs). GWs at different latitudes are influenced by excitation sources, background winds, etc., and their correlation with solar activity may differ, which lacks comparative analysis in previous studies.
Data Selection and Method:
The section lacks detail on the criteria for data selection and quality control measures applied to the FY-3C satellite data.
Response:
Revised as suggested.
Revisions in the manuscript:
(Line 121-125)
Before extracting atmospheric gravity wave disturbances, quality control was performed on the atmospheric temperature data detected by the FY-3C satellite. In the aforementioned grid, all data were statistically analyzed by month regardless of year, and temperature data with deviations beyond three times the standard deviation were excluded.
The methodology for gravity wave extraction is described briefly, but there is no justification for the chosen bandpass filter ranges (2-20 km, 2-10 km, 12-20 km). It is unclear why these specific ranges were selected and how they compare to previous studies.
Response:
Revised as suggested.
Revisions in the manuscript:
(Line 71-76)
Additionally, many studies in the past obtained the gravity waves using high passfilter with cut-off vertical wavelength of 10 km. Consequently, their results completely suppressed the gravity waves with vertical wavelengths >10 km, which are dominant over the middle and high latitude regions. So, in order to cover as many gravity waves information，we investigate gravity waves, respectively, in two separate vertical wavelengths, one is 2 - 10 km(short-wavelength GWs), and the other is 12–20 km (long-wavelength GWs).
Statistical Methods (Lines 129-138):
The significance test using the P-value is mentioned, but there is no discussion of how multiple comparisons are handled, which could inflate Type I error rates.
Response:
This paper only conducted a correlation analysis between gravity wave disturbance intensity and sunspot numbers. The correlation analyses at different latitude bands and altitude layers are independent and do not interfere with each other. Therefore, we think that the significance analysis in this paper does not involve multiple comparisons.
The methodology section does not clearly define the criteria for determining "significant" correlations, which could lead to ambiguous interpretations of the results.
Response:
We made corresponding supplementary discussions based on the reviewer's comments.
Revisions in the manuscript:
(Line 161-164)
We consider the correlation analysis results with a p-value greater than 0.1 to be non-significant. Results with a p-value less than 0.1 but greater than 0.05 are considered weakly significant. Results with a p-value less than 0.05 are considered significant, and those with a p-value less than 0.01 are considered highly significant.
Results (Lines 139-172):
While Pearson correlation coefficients are presented, the results section lacks a deeper statistical analysis. For instance, there is no discussion of the confidence intervals or potential confounding factors that might influence the observed correlations.
Response:
We made corresponding supplementary discussions based on the reviewer's comments.
Revisions in the manuscript:
(Line 302-304)
Although only 9 years of observational data were used, not covering the entire solar activity cycle, it still reflects to some extent the response of gravity wave disturbance intensity to the 11-year solar activity cycle.
There is no mention of the strength and direction of correlations (e.g., weak, moderate, strong). This information is crucial for interpreting the significance of the results.
Response:
We made corresponding supplementary discussions based on the reviewer's comments.
Revisions in the manuscript:
(Line 154-157)
Based on the obtained Pearson correlation coefficients, we consider a correlation coefficient greater than 0.8 to be strongly correlated, a coefficient between 0.5 and 0.8 to be moderately correlated, and a coefficient less than 0.5 to be weakly correlated.
Some statements in the results section are ambiguous and lack clarity. For example, phrases like "the overall correlation is significant" (line 159) need to be supported with specific values and statistical tests.
Response:
We revised these statements.
Revisions in the manuscript:
(Line 185-186)
leading to more orographic gravity waves and influences from land-sea boundaries.
(Line 203-204)
gravity wave disturbances in the mid-latitude regions exhibit seasonal variations
The section mentions variability in gravity wave parameters but does not provide a detailed analysis of this variability. A discussion on the sources and implications of this variability would strengthen the results.
Response:
We made corresponding supplementary discussions based on the reviewer's comments.
Revisions in the manuscript:
(Line 205-208)
This phenomenon is mainly due to the different zonal wind directions in the Northern Hemisphere during winter and summer, which produce different filtering effects on orographic gravity waves, leading to seasonal variations in gravity wave intensity (Lindzen, R. S. 1981).
The process of deriving the results from the data is not clearly explained. For instance, how the seasonal and latitudinal variations were calculated and what specific statistical methods were used for these calculations should be detailed.
Response:
We made corresponding supplementary discussions based on the reviewer's comments.
Revisions in the manuscript:
(Line 139-141)
Finally, the extracted gravity wave intensities of different wavelengths were averaged according to latitude bands and seasons.
The results section makes broad statements about the influence of the 11-year solar cycle on gravity waves without sufficient evidence to support such generalizations. More nuanced conclusions, acknowledging the limitations and scope of the study, would be more appropriate.
Response:
We made corresponding supplementary discussions based on the reviewer's comments.
Revisions in the manuscript:
(Line 297-304)
We used methods such as zonal averaging and seasonal averaging to mitigate the variations in gravity wave intensity caused by short-term solar eruptive activities (e.g., flares, coronal mass ejections) leading to geomagnetic storms, and short-term intense atmospheric activities such as typhoons and severe convective weather. This allows the results to better reflect the trend of gravity wave responses to the 11-year solar activity cycle. Although only nine years of observation data were used, not covering the entire solar activity cycle, it still provides a reasonable reflection of the response of gravity wave disturbance intensity to the 11-year solar activity cycle.
There is no mention of negative results or non-significant findings. Including these is important for a balanced and transparent presentation of the research outcomes.
Response:
We made corresponding supplementary discussions based on the reviewer's comments.
Revisions in the manuscript:
(Lines 322-326)
As shown by the correlation coefficients in Tables 1-3 for the equatorial and mid-latitude regions, the majority of the non-lagged correlation coefficients of the zonally averaged gravity wave values are negative, which is consistent with previous studies. Additionally, the zonally averaged gravity wave values, compared to single-station gravity wave disturbance values, better reflect the overall conditions of the latitude band.
(Lines 328-331)
Furthermore, the significance analysis shows that the P-value for a 2-year lag is significantly lower than the P-value for no lag, indicating that the credibility of the gravity waves' response to solar activity in the equatorial and mid-latitude regions is higher when considering a 2-year lag.
Author Response File: 
Author Response.docx
Reviewer 2 Report
Comments and Suggestions for AuthorsThis paper employed the Fengyun 3C: an low earth orbiting satellite measured temperature between 20 and 50 km, to study the possible gravity wave solar cycle dependence. The authors also utilzied the statistical method to carry out correlation analyis of the zonal mean temperature perturbation and the sun spot variations. They also modulate the lag between temperature perturbation and sun sport variation to see whether there is strong correlation between 20-50 km gravity wave activity and solar activity. The paper's theme is interesting, however, some revisons are needed before it is suitable for publication
The author shall emphasize that their gravity wave activity results are the zonal mean. Unfortunately, I do not see this emphasis. As the zonal mean shall remove hugh amount of variabilities. Furthemore, when they expand their discussions, they shall not just present boring statements that the solar activity impact the whole atmosphere, and may need time to impact gravity wave. They shall also expand discussion on the zonal mean, especially when they provide the different conclusions from previous studies. Some of them focused on several single stations, while som of them also use satellites.
Additionally, the data description needs some improvements. The author shall clarify for each latitude bans, whether everyday has measurement results or not. For these Figure, do these line plots consist of points everyday from year 2015 to 2023??
Line 63 background wind, temperature and dissipation parameter
Line 66 remove ‘paremeters’
Line 124-125 remove ‘This is scientifically significant for developing high-precision numerical forecasts of the middle and upper atmosphere with gravity wave parameterization.’
Comments on the Quality of English Languagemoderate english revision needed
Author Response
This paper employed the Fengyun 3C: an low earth orbiting satellite measured temperature between 20 and 50 km, to study the possible gravity wave solar cycle dependence. The authors also utilzied the statistical method to carry out correlation analyis of the zonal mean temperature perturbation and the sun spot variations. They also modulate the lag between temperature perturbation and sun sport variation to see whether there is strong correlation between 20-50 km gravity wave activity and solar activity. The paper's theme is interesting, however, some revisons are needed before it is suitable for publication
Response:
We gratefully appreciate for your valuable comment, which has significantly helped us improve the manuscript.
The author shall emphasize that their gravity wave activity results are the zonal mean. Unfortunately, I do not see this emphasis. As the zonal mean shall remove hugh amount of variabilities. Furthemore, when they expand their discussions, they shall not just present boring statements that the solar activity impact the whole atmosphere, and may need time to impact gravity wave. They shall also expand discussion on the zonal mean, especially when they provide the different conclusions from previous studies. Some of them focused on several single stations, while som of them also use satellites.
Response:
We made corresponding supplementary discussions based on the reviewer's comments.
Revisions in the manuscript:
(Lines 138-139)
Then, by performing zonal averaging based on the five defined latitudes, the average disturbance of gravity waves in different latitude bands are derived.
(Lines 322-326)
As shown by the correlation coefficients in Tables 1-3 for the equatorial and mid-latitude regions, the majority of the no-lag correlation coefficients for zonal-averaged gravity waves are negative, which is consistent with previous studies. Additionally, the zonal-averaged gravity wave values better reflect the general conditions of the latitude band .
(Lines 328-331)
Furthermore, the significance analysis shows that the P-value for a 2-year lag is significantly lower than the P-value for no lag, indicating that the credibility of the gravity waves' response to solar activity in the equatorial and mid-latitude regions is higher when considering a 2-year lag.
.
Additionally, the data description needs some improvements. The author shall clarify for each latitude bans, whether everyday has measurement results or not. For these Figure, do these line plots consist of points everyday from year 2015 to 2023??
Response:
GNOS generates approximately 430 temperature profiles daily, distributed globally, covering almost all latitude bands. However, this study focuses on gravity wave disturbances in different latitude bands, so seasonal processing is more appropriate. Therefore, the curves in the figures are composed of data points for each quarter.
Revisions in the manuscript:
(Line 139-141)
Finally, the extracted gravity wave intensities for different bands are averaged according to latitude bands and seasons.
Line 63 background wind, temperature and dissipation parameter
Response:
Revised as suggested.
Revisions in the manuscript:
(Line 54-55)
background wind, temperature and dissipation parameter
Line 66 remove ‘paremeters’
Response:
Revised as suggested.
Revisions in the manuscript:
(Line 56)
Line 124-125 remove ‘This is scientifically significant for developing high-precision numerical forecasts of the middle and upper atmosphere with gravity wave parameterization.’
Response:
Revised as suggested.
Revisions in the manuscript:
(Line 145)
Author Response File: Author Response.docx
Reviewer 3 Report
Comments and Suggestions for AuthorsAttached file
Comments for author File: 
Comments.pdf
Attached file
Author Response
The paper focus on the correlation between the intensity of gravity wave disturbances across different latitude bands, altitudes and wavelengths with respect of the variation of the solar activity, represented by the sunspot number. The analysis is performed using the Pearson correlation coefficient and a standard significance test which gives the probability that the two variables are uncorrelated (null hypothesis).
In my opinion, the analysis presents evident shortcomings which diminishes the relevance of the analysis, even though the addressed topic is very interesting.
In addition, the results are poorly organized and presented, especially in terms of figures.
I believe that the manuscript may be reconsidered for publication on Remote Sensing after major deficiencies have been addressed.
Response:
We gratefully appreciate for your valuable comment. We will make detailed revisions according to your suggestions, which will significantly improve our manuscript.
General Comments:
- I believe that the 9 plots of the sunspot number are not necessary. In general, the 9 figures may be re-arrange in only 3 divided in short-wavelengths, long-wavelengths and full. In this way they are also representative of the three subsections in the Results section. The correlation coefficients in the legend are difficult to read and confusing, maybe they can be included in the legend.
Response:
We removed the sunspot number from Figures 2-9, but retained the data from Figure 1 for better presentation of the results. When we combined the 9 images into 3, the curves in the figures became numerous and cluttered; therefore, we have kept the structure of the 9 images. We adjusted the presentation of the correlation coefficients to facilitate reader comprehension.
Revisions in the manuscript:
(figure 1-9)
- The variability of GWs’ intensity is related to many atmospheric and lower magnetospheric processes, such as heating, variation in the global atmospheric circulation, geomagnetic storms, upper-atmosphere ionization levels and others. Certainly most of them have a direct connection (and sometimes correlation) with the solar activity. Do the authors think that their statistical analysis is capable of
distinguish which is the main process driving the GWs intensity variations? In addition, do the authors believe that this kind of analysis is suitable to capture the majority of the possible sources of GWs variation? Since these couplings act on different spatial and temporal scales, in my opinion, more sophisticated correlation and statistical tools and a more refined analysis of the temporal lags might better highlight some of these aspects.
Response:
Geomagnetic storms, ionospheric storms, and other space weather phenomena caused by short-term solar eruptions, as well as typhoons and strong convective weather, can affect the intensity of gravity waves, especially geomagnetic and ionospheric activities are closely related to solar activity. However, the gravity wave disturbances caused by these phenomena do not affect the conclusions of this paper. This study focuses on the long-term response of gravity wave disturbances within the 20-50 km altitude range to solar activity. In the data processing, we did not differentiate the driving sources of gravity waves. By using zonal and seasonal averaging methods, we further mitigated the impact of short-term or localized gravity wave variations. While local and short-term gravity wave variations may influence the analysis to some extent, they do not affect the overall trend of gravity wave responses to the 11-year solar activity cycle.
Revisions in the manuscript:
(Line 297-302)
We used methods such as zonal averaging and seasonal averaging to mitigate the variations in gravity wave intensity caused by short-term solar eruptive activities (e.g., flares, coronal mass ejections) leading to geomagnetic storms, and short-term intense atmospheric activities such as typhoons and severe convective weather. This allows the results to better reflect the trend of gravity wave responses to the 11-year solar activity cycle.
(Line 352-354)
However, this paper only analyzed the overall response of gravity waves without analyzing gravity waves from different excitation sources, which will be further investigated in future work.
- In my opinion, another major limitation of the analysis is the length of the time series. They cover less than one solar cycle and thus it results impossible to highlight long-term variations (contrary to what is often written in the manuscript) related for instance to the solar cycles’ variability as well as the cycle polarity. In addition, it is not very clear to me what is the cadence of the two time series (daily-based, monthly-based,…).
Response:
We greatly appreciate the reviewer pointing out the limitations of our study concerning the length of the data period. Although we only used 9 years of observational data, this period covers more than 80% of a solar activity cycle, which can reasonably reflect the response to solar activity. This approach is similar to studies by Li et al. 2010(10 years) and Ern et al. 2011(9 years). We have also addressed this limitation in the paper.
Revisions in the manuscript:
(Line 302-304)
Although only nine years of observation data were used, not covering the entire solar activity cycle, it still provides a reasonable reflection of the response of gravity wave disturbance intensity to the 11-year solar activity cycle.
- The major limitation of the Pearson correlation coefficient is that it can only highlight linear correlations; therefore I think that the high values obtained in some regions by the authors are mainly due to a global and large-scale trend, whose study is strongly limited by the shortness of the data set.
Response:
The Pearson correlation coefficient can only assess the linear relationship between two continuous variables, which has certain limitations. Therefore, it is appropriate to use the Pearson correlation coefficient only when one variable changes proportionally to another variable. The variation in gravity wave disturbance intensity is closely related to atmospheric phenomena such as orographic gravity waves and strong convective events, which are significantly influenced by solar activity. Hence, it is reasonable to assume a linear relationship between gravity waves and solar activity. As more observational data becomes available, we will gradually address the limitation of the small data sample. This limitation has also been acknowledged in our paper.
Revisions in the manuscript:
(Line 302-304)
Although only nine years of observation data were used, not covering the entire solar activity cycle, it still provides a reasonable reflection of the response of gravity wave disturbance intensity to the 11-year solar activity cycle.
- In general, I cannot notice any specific trends of the correlation coefficients, both in terms of sign and absolute value, with the different altitudes, latitudes and and wavelengths analyzed by the authors. In the result section, the authors often argue about differences in terms of GWs disturbance intensity at different latitudes, but I believe that this represents mainly a check of a correct GW extraction rather
than a consequence of the solar activity.
Response:
We made corresponding supplementary discussions based on the reviewer's comments.
Revisions in the manuscript:
(Lines 218-223)
For example, in the mid-latitude region of the Southern Hemisphere, the correlation coefficients at 25 km, 35 km, and 45 km altitudes are 0.554, 0.695, and 0.776, respectively. However, this phenomenon is not observed in the 2-year lag analysis. This might be because the correlation coefficients in the 2-year lag analysis have already reached a strong correlation, resulting in smaller distinctions across different altitude layers.
(Lines 266-269)
For example, in the mid-latitude region of the Northern Hemisphere, the correlation coefficients at 25 km, 35 km, and 45 km altitudes are 0.639, 0.742, and 0.77, respectively. This trend is consistent with the equatorial region and the mid-latitude region of the Southern Hemisphere.
- I find that, the result section presents only a description of the figures and in a poorly organized manner. The reader needs to reach the conclusions to understand more about the possible explanations of the different GWs response in different regions and for different temporal lags; thus, in general, the results section lacks scientific outcomes.
Response:
We made corresponding supplementary discussions based on the reviewer's comments.
Revisions in the manuscript:
(Lines 212-216)
This indicates that the impact of solar activity intensity changes on stratospheric gravity waves in mid- and low-latitude regions is delayed, reaching its peak after a 2-year lag. The cause of this phenomenon is likely due to the delayed response of fundamental atmospheric parameters and activities to solar activity[35,36].
(Lines 258-261)
Consistent with previous studies, the simultaneous response of mid- and low-latitude regions to solar activity shows a negative correlation[9,15]. However, since their results did not undergo significance analysis, the conclusions, although similar, are questionable.
(Lines 332-338)
The correlation between GW and solar activity may depend on GW sources (e.g., topography, convection) and gravity wave propagation conditions at different latitudes [10,13]. Parameters affecting gravity wave propagation, such as zonal wind speed and atmospheric temperature, respond differently to the solar activity cycle depending on latitude [39]. Additionally, Liu et al. 2017 pointed out that the response of gravity wave potential energy to solar activity depends on latitude and height, and exhibits hemispherical asymmetry.
Specific Comments:
- Maybe the use of the acronym GWs (gravity waves) from time to time would improve the readability.
Response:
Revised as suggested.
- line 1, line 20: What the authors mean with near space? I think the GWs are one of the main source for the Earth’s upper-atmosphere and lower-plasmasphere.
Response:
Revised as suggested.
Revisions in the manuscript:
(Lines 21)
Gravity wave is one of the main atmospheric fluctuations in the Earth’s upper-atmosphere and lower-plasmasphere.
- line 99: “2.2. the method of Gravity wave extraction” → “2.2. The method of Gravity wave extraction” (or “Gravity wave extraction technique”)
Response:
Revised as suggested.
- line 76: “2. data selection and method” → “2. Data selection and methods”
Response:
Revised as suggested.
- lines 104-106: “high latitudes...southern hemisphere.” →it is very long and difficult to follow, maybe as, “two at high latitudes and two at mid-latitudes, 60-90 degree and 30-60 degree respectively, in both the hemispheres and one equatorial band between 30 degree North and South”.
Response:
Revised as suggested.
Revisions in the manuscript:
(Lines 117-118)
two at high latitudes and two at mid-latitudes, 60-90 degree and 30-60 degree respectively, in both the hemispheres and one equatorial band between 30 degree North and South
- line 115: “equation 1” → please, check the format for equations’ references.
Response:
Revised as suggested.
- line 137: “The smaller the p value, the more significant the correlation between the sunspot number and gravity wave intensity” → I would rephrase it as “The smaller the p-value, the more significant is the correlation coefficient obtained from the analysis between sunspot number and GW intensity.
Response:
Revised as suggested.
Revisions in the manuscript:
(Lines 154-156)
- Fig. 1 (caption): “The blue curve represents...of the Southern hemisphere” → It is already expressed by the legend and it can be removed from the caption.
Response:
Revised as suggested.
Author Response File: Author Response.docx
Round 2
Reviewer 1 Report
Comments and Suggestions for AuthorsThe authors have considered my comment very well, and all my doubts have been cleared. A commendable work. No further comments.
Reviewer 2 Report
Comments and Suggestions for AuthorsThe author has answered my questions and concerns well. Now the paper is ok for publication
Comments on the Quality of English Languageminor english revision needed
