the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Stratospheric ozone trends and attribution over 1984–2020 using ordinary and regularised multivariate regression models
Yajuan Li
Martyn P. Chipperfield
Wuhu Feng
Jianchun Bian
Dong Guo
Abstract. Accurate quantification of longterm trends in stratospheric ozone can be challenging due to their sensitivity to natural variability, the quality of the observational datasets, nonlinear changes in forcing processes as well as the statistical methodologies. Multivariate linear regression (MLR) is the most commonly used tool for ozone trend analysis, however, the complex coupling in most atmospheric processes can make it prone to the overfitting or multicollinearityrelated issues when using the conventional Ordinary Least Squares (OLS) setting. To overcome this issue, we adopt a regularised (Ridge) regression method to estimate ozone trends and quantify the influence of individual processes. Here, we use the Stratospheric Water and OzOne Satellite Homogenized (SWOOSH) merged data set (v2.7) to derive stratospheric ozone profile trends for the period 1984–2020. Beside SWOOSH, we also analyse a machinelearningbased satellitecorrected gapfree global stratospheric ozone profile dataset from a chemical transport model (MLTOMCAT), and output from two chemical transport model (TOMCAT) simulations forced with ECMWF reanalyses ERAInterim and ERA5.
With Ridge regression, the stratospheric ozone profile trends from SWOOSH data show smaller declines during 1984–1997 compared to OLS with the largest differences in the lowermost stratosphere (> 4 % per decade at 100 hPa). Upper stratospheric ozone has increased since 1998 with maximum (~2 % per decade near 2 hPa) in local winter for midlatitudes. Negative trends with large uncertainties are observed in the lower stratosphere with the most pronounced in the tropics. The largest differences in post1998 trend estimates between OLS and Ridge regression methods appear in the tropical lower stratosphere (with ~7 % per decade difference at 100 hPa). Ozone variations associated with natural processes such as the quasibiennial oscillation (QBO), the solar variability, the El Niño–Southern Oscillation (ENSO), the Arctic oscillation (AO) and the Antarctic oscillation (AAO) also indicate that Ridge regression coefficients are somewhat smaller and less variable compared to the OLSbased estimates. Additionally, MLTOMCAT based trend estimates are consistent with SWOOSH data set. Finally, we argue that the large differences between the satellitebased data and model simulations confirm that there are still large uncertainties in ozone trend estimates especially in the lower stratosphere, and caution is needed when discussing results if explanatory variables used are correlated.

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Interactive discussion
Status: closed

RC1: 'my comments', Mark Weber, 07 Jun 2023
This paper reports on ozone trends derived from observations (SWOOSH
daatset) and three versions of the TOMCAT chemistrytransportmodel
(CTM). One of the CTMs (MLTOMCAT) has been adjusted to satellite
observations, while the other two used meteorological data from
different reanalyses, ERA5 and its predescessor ERA Interim (up to
2019). Two types of regression models are used for ozone trend
estimates before and after the peak of stratospheric halogens
occurring in the middle 1990. The first is the ordinaryleastsquares
regession (OLS), the second is the ridge regression. The main
idea behind the ridge regression is to introduce an additional
contraint in the cost function that minimises the fit coefficients.
Such a regression is generally recommended to avoid overfitting.In general the ridge regression reduces the (absolute) trends (and all
other fit coefficients) and on the other hand reduces the variances
(and correlation) between regression model and the underlying data.
The trends after 1998 in the upper stratosphere are positive and
significant in agreement with other studies (~2%/decade, e.g.
GodinBeekmann et al., 2022). The ridge regression roughly halves
these trends. Overall the paper is well written. Some issues still
need to be addressed before acceptance of the paper.discussion points:
l. 30, l. 34 and other places: Differences in ozone trends at 100 hPa
from OLS and ridge are laerger than 4%/decase (7%/decade in the
tropics), but the trend uncertainties are on the order of 24%. This
means that these differences are not significantly different from
zero. More relevant is the difference in the upper stratosphere
(~1%/decade vs ~2%/decade), both significant. This should be mentioned
here.l. 37: It is not surprising that MLTOMVCAT agrees better with SWOOSH
than the other models. Satelite corrections are derived from the same
data that are also part of SWOOSH (e.g. MLS). This should be
mentioned here and also in the main text.l. 102: A detailed comparison between ERAITOMCAT and ERA5TOMCAT has
been reported in Li et al. 2022. In this paper the model data have
been extended to 2020, however, ERAI ends in 2019 and trends are only
reported up to 2018 for the ERAIdriven model. As the differences
between both models are not discussed in detail here but well covered
in Li et al. 2022, it could be safeley omitted from this paper.l. 161: The MLS setup is very different from Li et al. 2022. For
instance, now twelve (monthly) trend terms are used instead of one
(annual) and more proxies are used (e.g. EP flux). Please motivate why
you added more terms into the regression.l. 165: Here you mention the use of the EP flux proxy, but its
contribution to ozone changes is not discussed in the paper. Its
contribution needs to be added in Fig. 10.l. 170: Only years 1991 and 1992 have been removed to avoid the use of
an aerosol proxy, but Pinatubo eruption affected more years, e.g. end
of 1990, 1993 and 1994. Please comment.l. 175: Detrending means that the longterm trends in the proxies are
moved to the linear trend terms. In Weber et al. 2022 we argued argued
that the longterm dynamic trends are largely removed by the trends
in the proxies, so that linear trends are then approximating the
ODS related trends. In your case, the linear trends are combining
dynamic and chemical trends. That should be mentioned here.l. 178: Collinearity means that both vectors (or timeseries) are 100%
correlated, which is not the case here. What you mean is that many
proxies are highly correlated with each other. It is suggested to
avoid the term collinear throughout the text.l. 187: "OLS will be not robust and will result in inaccurate model."
I think this is not correct. The OLS regression model will yield the
same (overall) results after orthogonalising all proxies, so OLS
remains robust (as also your results show). The ridge regression is
another representation with different constraints, but not necessarily
better than OLS. Ridge and OLS derived trends in nearly all cases
agree to within the uncertainties of the trends (Figs 2 and 3).
Suggest to omit this sentence.l. 202: What is the training dataset? Suggest omit "to the training data"
l. 203: Omit "when the MSE reaches the minimum"; reference to
Pedregosa et al. suffices.l. 207: "crossvaldiated MSE" needs to be explained in the text. One
may also want to state the drawback of ridge regression: the fit
residuals (correlation between model and regression) will be larger
(smaller) than that from OLS.l. 239: different period is used for ERAI. Does that have an effect on
the trends. Shouldn't ERAI be compared with other data using the same
period. see also comment earlierl. 241: readability of numbers in the tables will be improved if only
one digit is only shown, e.g. 3.4(2.5) instead of 339(2.47).l. 249: Within the uncertainties of both regressions the trend results
(ridge and OLS) are not different from each other! I think this should
be mentioned in the main text as well (see earlier comment). Is the
annual mean the average of the twelve monthly means?
Is the uncertainty of the annual trend the standard deviation from
taking the mean from the monthly values or are the uncertainties from
the individual months are errorpropagated into the annual mean? Please
explain.l. 265: mention here that the large differences in trends are within the
uncertainties of the individual trends (see above)l. 335: In the lower stratosphere ridge and OLS are not reliable and
fail to capture the large variability. In addition, the data quality
of satelites is lower in this region. So the "linear relationship" is
not the issue herel. 340: "These differences between OLS and ridge based ozone profile
trends imply that Ridge regression to some extent has improved the
reliability of the model in the presence of multicollinearity." This
is not generally true as discussed above. Again: Differences between OLS and
ridgebased trends are within the uncertainties of the individual
trends.l. 346: "Considering the nonlinear effect, the monthly terms of QBO
proxies are used for regression analyses" I do not understand what is
meant to be said here. Statement can be omitted.l. 355: "corresponds to the more positive ozone trends in both
simulations". To me it is not clear how longterm ozone trends can be
associated with QBO (contains only periodic changes after detrending)l. 358: "... may account for the more positive ozone trends", see
previous commentl. 363; How is the anomaly defined (amplitude, i.e. max minus minimum
response relative to the long term ozone mean ozone times the sign of
the fit coefficient?). Please specifiy.l. 388: ozone trends are only shown below 60degs, but solar response
up to 90degs. Ozone is not well sampled above 5060 degs in the early
period by SWOOSH. Is the solar response a result from a fit solely
limited to the late period after 1998? Why are ozone trends above 60
degs not shown?l. 395: use only single digits (see earlier comments). Is the table
needed as the numbers can be derived from Fig. 9?l. 409: see commnts to l. 388. please add the results of the EP flux
proxy (I guess it is the vertical component of the EP flux)l. 425: "The negative AO (AAO) indices in the extratropics ...". This
is evident in the models and MLTomcat above 60 degs but not in
SWOOSH. Can this be explained? Are the regressions above 60degs
problematic?l. 444: "it is inappropriate to use the same regression model for all
locations" Not clear what is meant here, you mean you cannot use a
ridge regression with a contant tuning parameter or you mean OLS. As
discussed earlier I do not think that the use of OLS is inaproppriate.l. 456: "The largest difference between OLS and Ridge regression
methods appears in the tropical lower stratosphere (with ~7 % per
decade difference at 100 hPa).", but do not forget the the trend
uncertainties for both reression are very high (~23%/decade)technical (selected):
l. 37: change to "the SWOOSH dataset"
l. 58: "controlled by transport and" (omit "the")
l. 150: add Snow et al. 2014 (doi:10.1051/swsc/2014001) as reference
for the MgII indexl. 183: I am not sure if "objective function" is the right term,
suggest "cost function" instead.l. 194: "as described in Hastie" (add "das described in")
l. 204: "the Python scikrit module" (add "the")
l. 220: better: "where MRE is minimum"
l. 226: "fit residuals", I guess you mean trends
l. 231: Reword: You probably mean less variability in the ridge model
and lower absolute fit coefficients in the ridge regression. Please reword.l. 233: "insignificant due to large uncertainties )up to
2424%/decade" (replace "with" with "due to" and remove "up to")l. 233: "These large uncertainties" (remove "decreases and")
l. 239: "We note" (remove "should")
l. 249: change "compared between" to "derived from"
l. 256: "across all three" (remove "the")
l. 257: change "relatively" to "slightly"
l. 262: change "in the NH" to "at NH"
l. 280: "and ERA5 shows". remove "and" and start a new sentence here
l. 281: remove "more overestimated"
l. 289: change "monthly mean variations" to "seasonal variations"
l. 302: change "... to some extent with smaller coefficients" to "absolute
ridgebased trends and fit coefficients are smaller"l. 310: "based on the ridge regression" (add "the")
l. 312: change "minimal" to "minimum"
l. 363: "QBO response on ozone" (add "response")
l. 373: change " there is a minimal solar cycle signal (negative
and statistically significant) at ~10 hPa" to "there is a negative
and statistically significant solar cycle response at ~10 hPa"l. 403: "being about twice larger" (add "being")
l. 468: change "The negative AO/AAO coefficients" to "The negative
phase of AO/AAO"Citation: https://doi.org/10.5194/egusphere2023591RC1 
AC1: 'Reply on RC1', Yajuan Li, 10 Aug 2023
The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2023/egusphere2023591/egusphere2023591AC1supplement.pdf

AC1: 'Reply on RC1', Yajuan Li, 10 Aug 2023

RC2: 'Autorgression (AR1) not accounted for', Mark Weber, 13 Jun 2023
There was one point I missed in my review. For trends from monthly mean ozone time series a correction is applied in the regression to account for autoregression (AR1). This correction does not change trends so much but increases the uncertainties due to the reduction of degreeoffreedom associated with AR. It can be applied to both OLS and ridge regression and should be done. If not, at least a good reason should be given why it is not needed here.
Citation: https://doi.org/10.5194/egusphere2023591RC2 
AC2: 'Reply on RC2', Yajuan Li, 10 Aug 2023
The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2023/egusphere2023591/egusphere2023591AC2supplement.pdf

AC2: 'Reply on RC2', Yajuan Li, 10 Aug 2023

RC3: 'Comment on egusphere2023591', JensUwe Grooß, 23 Jun 2023
Editor Review of the Manuscript "Stratospheric ozone trends and
attribution over 19842020 using ordinary and regularised multivariate
regression models" by Li et al.As one of the reviewers of this manuscript did not commit a review
and the other review was quite positive, I decided to base the decision
of this manuscript on only one regular review and this editor review.Although I am not an expert on regression methods, I find the paper
written clearly and understandable. Especially, the uncertainties of
the derived ozone trends depending on the regression methods seem
important to me. Also the depiction of the contribution of the natural
processes to ozone changes is described well.I would, however, suggest some more discussion of the results: To me
it is not clear, in how far the the shown differences in regression
methods are now explaining the discrepancy in the lower stratosphere
that was first pointed out by Ball et al. (2020). Besides the
variability induced by the regression method, is there a model
improvement with respect to the Multimodelmean shown by Ball et
al. ? Or is this only the difference between free running CCMs and
the CTM shown here.What can be learned from the machinelearning results (MLTOMCAT).
Does the similarity with SWOOSH suggest that the basic mechanisms are
well understood or would you expect this similarity as it is
constructed by machinelearning using the observations?Why are the trends in the tropics so different between the two
reanalyses? Is this due to the vertical velocities?Therefore I suggest minor revisions to include this discussion, that
would potentially bring the shown results better into the context of
the present literature.Citation: https://doi.org/10.5194/egusphere2023591RC3 
AC3: 'Reply on RC3', Yajuan Li, 10 Aug 2023
The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2023/egusphere2023591/egusphere2023591AC3supplement.pdf

AC3: 'Reply on RC3', Yajuan Li, 10 Aug 2023
Interactive discussion
Status: closed

RC1: 'my comments', Mark Weber, 07 Jun 2023
This paper reports on ozone trends derived from observations (SWOOSH
daatset) and three versions of the TOMCAT chemistrytransportmodel
(CTM). One of the CTMs (MLTOMCAT) has been adjusted to satellite
observations, while the other two used meteorological data from
different reanalyses, ERA5 and its predescessor ERA Interim (up to
2019). Two types of regression models are used for ozone trend
estimates before and after the peak of stratospheric halogens
occurring in the middle 1990. The first is the ordinaryleastsquares
regession (OLS), the second is the ridge regression. The main
idea behind the ridge regression is to introduce an additional
contraint in the cost function that minimises the fit coefficients.
Such a regression is generally recommended to avoid overfitting.In general the ridge regression reduces the (absolute) trends (and all
other fit coefficients) and on the other hand reduces the variances
(and correlation) between regression model and the underlying data.
The trends after 1998 in the upper stratosphere are positive and
significant in agreement with other studies (~2%/decade, e.g.
GodinBeekmann et al., 2022). The ridge regression roughly halves
these trends. Overall the paper is well written. Some issues still
need to be addressed before acceptance of the paper.discussion points:
l. 30, l. 34 and other places: Differences in ozone trends at 100 hPa
from OLS and ridge are laerger than 4%/decase (7%/decade in the
tropics), but the trend uncertainties are on the order of 24%. This
means that these differences are not significantly different from
zero. More relevant is the difference in the upper stratosphere
(~1%/decade vs ~2%/decade), both significant. This should be mentioned
here.l. 37: It is not surprising that MLTOMVCAT agrees better with SWOOSH
than the other models. Satelite corrections are derived from the same
data that are also part of SWOOSH (e.g. MLS). This should be
mentioned here and also in the main text.l. 102: A detailed comparison between ERAITOMCAT and ERA5TOMCAT has
been reported in Li et al. 2022. In this paper the model data have
been extended to 2020, however, ERAI ends in 2019 and trends are only
reported up to 2018 for the ERAIdriven model. As the differences
between both models are not discussed in detail here but well covered
in Li et al. 2022, it could be safeley omitted from this paper.l. 161: The MLS setup is very different from Li et al. 2022. For
instance, now twelve (monthly) trend terms are used instead of one
(annual) and more proxies are used (e.g. EP flux). Please motivate why
you added more terms into the regression.l. 165: Here you mention the use of the EP flux proxy, but its
contribution to ozone changes is not discussed in the paper. Its
contribution needs to be added in Fig. 10.l. 170: Only years 1991 and 1992 have been removed to avoid the use of
an aerosol proxy, but Pinatubo eruption affected more years, e.g. end
of 1990, 1993 and 1994. Please comment.l. 175: Detrending means that the longterm trends in the proxies are
moved to the linear trend terms. In Weber et al. 2022 we argued argued
that the longterm dynamic trends are largely removed by the trends
in the proxies, so that linear trends are then approximating the
ODS related trends. In your case, the linear trends are combining
dynamic and chemical trends. That should be mentioned here.l. 178: Collinearity means that both vectors (or timeseries) are 100%
correlated, which is not the case here. What you mean is that many
proxies are highly correlated with each other. It is suggested to
avoid the term collinear throughout the text.l. 187: "OLS will be not robust and will result in inaccurate model."
I think this is not correct. The OLS regression model will yield the
same (overall) results after orthogonalising all proxies, so OLS
remains robust (as also your results show). The ridge regression is
another representation with different constraints, but not necessarily
better than OLS. Ridge and OLS derived trends in nearly all cases
agree to within the uncertainties of the trends (Figs 2 and 3).
Suggest to omit this sentence.l. 202: What is the training dataset? Suggest omit "to the training data"
l. 203: Omit "when the MSE reaches the minimum"; reference to
Pedregosa et al. suffices.l. 207: "crossvaldiated MSE" needs to be explained in the text. One
may also want to state the drawback of ridge regression: the fit
residuals (correlation between model and regression) will be larger
(smaller) than that from OLS.l. 239: different period is used for ERAI. Does that have an effect on
the trends. Shouldn't ERAI be compared with other data using the same
period. see also comment earlierl. 241: readability of numbers in the tables will be improved if only
one digit is only shown, e.g. 3.4(2.5) instead of 339(2.47).l. 249: Within the uncertainties of both regressions the trend results
(ridge and OLS) are not different from each other! I think this should
be mentioned in the main text as well (see earlier comment). Is the
annual mean the average of the twelve monthly means?
Is the uncertainty of the annual trend the standard deviation from
taking the mean from the monthly values or are the uncertainties from
the individual months are errorpropagated into the annual mean? Please
explain.l. 265: mention here that the large differences in trends are within the
uncertainties of the individual trends (see above)l. 335: In the lower stratosphere ridge and OLS are not reliable and
fail to capture the large variability. In addition, the data quality
of satelites is lower in this region. So the "linear relationship" is
not the issue herel. 340: "These differences between OLS and ridge based ozone profile
trends imply that Ridge regression to some extent has improved the
reliability of the model in the presence of multicollinearity." This
is not generally true as discussed above. Again: Differences between OLS and
ridgebased trends are within the uncertainties of the individual
trends.l. 346: "Considering the nonlinear effect, the monthly terms of QBO
proxies are used for regression analyses" I do not understand what is
meant to be said here. Statement can be omitted.l. 355: "corresponds to the more positive ozone trends in both
simulations". To me it is not clear how longterm ozone trends can be
associated with QBO (contains only periodic changes after detrending)l. 358: "... may account for the more positive ozone trends", see
previous commentl. 363; How is the anomaly defined (amplitude, i.e. max minus minimum
response relative to the long term ozone mean ozone times the sign of
the fit coefficient?). Please specifiy.l. 388: ozone trends are only shown below 60degs, but solar response
up to 90degs. Ozone is not well sampled above 5060 degs in the early
period by SWOOSH. Is the solar response a result from a fit solely
limited to the late period after 1998? Why are ozone trends above 60
degs not shown?l. 395: use only single digits (see earlier comments). Is the table
needed as the numbers can be derived from Fig. 9?l. 409: see commnts to l. 388. please add the results of the EP flux
proxy (I guess it is the vertical component of the EP flux)l. 425: "The negative AO (AAO) indices in the extratropics ...". This
is evident in the models and MLTomcat above 60 degs but not in
SWOOSH. Can this be explained? Are the regressions above 60degs
problematic?l. 444: "it is inappropriate to use the same regression model for all
locations" Not clear what is meant here, you mean you cannot use a
ridge regression with a contant tuning parameter or you mean OLS. As
discussed earlier I do not think that the use of OLS is inaproppriate.l. 456: "The largest difference between OLS and Ridge regression
methods appears in the tropical lower stratosphere (with ~7 % per
decade difference at 100 hPa).", but do not forget the the trend
uncertainties for both reression are very high (~23%/decade)technical (selected):
l. 37: change to "the SWOOSH dataset"
l. 58: "controlled by transport and" (omit "the")
l. 150: add Snow et al. 2014 (doi:10.1051/swsc/2014001) as reference
for the MgII indexl. 183: I am not sure if "objective function" is the right term,
suggest "cost function" instead.l. 194: "as described in Hastie" (add "das described in")
l. 204: "the Python scikrit module" (add "the")
l. 220: better: "where MRE is minimum"
l. 226: "fit residuals", I guess you mean trends
l. 231: Reword: You probably mean less variability in the ridge model
and lower absolute fit coefficients in the ridge regression. Please reword.l. 233: "insignificant due to large uncertainties )up to
2424%/decade" (replace "with" with "due to" and remove "up to")l. 233: "These large uncertainties" (remove "decreases and")
l. 239: "We note" (remove "should")
l. 249: change "compared between" to "derived from"
l. 256: "across all three" (remove "the")
l. 257: change "relatively" to "slightly"
l. 262: change "in the NH" to "at NH"
l. 280: "and ERA5 shows". remove "and" and start a new sentence here
l. 281: remove "more overestimated"
l. 289: change "monthly mean variations" to "seasonal variations"
l. 302: change "... to some extent with smaller coefficients" to "absolute
ridgebased trends and fit coefficients are smaller"l. 310: "based on the ridge regression" (add "the")
l. 312: change "minimal" to "minimum"
l. 363: "QBO response on ozone" (add "response")
l. 373: change " there is a minimal solar cycle signal (negative
and statistically significant) at ~10 hPa" to "there is a negative
and statistically significant solar cycle response at ~10 hPa"l. 403: "being about twice larger" (add "being")
l. 468: change "The negative AO/AAO coefficients" to "The negative
phase of AO/AAO"Citation: https://doi.org/10.5194/egusphere2023591RC1 
AC1: 'Reply on RC1', Yajuan Li, 10 Aug 2023
The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2023/egusphere2023591/egusphere2023591AC1supplement.pdf

AC1: 'Reply on RC1', Yajuan Li, 10 Aug 2023

RC2: 'Autorgression (AR1) not accounted for', Mark Weber, 13 Jun 2023
There was one point I missed in my review. For trends from monthly mean ozone time series a correction is applied in the regression to account for autoregression (AR1). This correction does not change trends so much but increases the uncertainties due to the reduction of degreeoffreedom associated with AR. It can be applied to both OLS and ridge regression and should be done. If not, at least a good reason should be given why it is not needed here.
Citation: https://doi.org/10.5194/egusphere2023591RC2 
AC2: 'Reply on RC2', Yajuan Li, 10 Aug 2023
The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2023/egusphere2023591/egusphere2023591AC2supplement.pdf

AC2: 'Reply on RC2', Yajuan Li, 10 Aug 2023

RC3: 'Comment on egusphere2023591', JensUwe Grooß, 23 Jun 2023
Editor Review of the Manuscript "Stratospheric ozone trends and
attribution over 19842020 using ordinary and regularised multivariate
regression models" by Li et al.As one of the reviewers of this manuscript did not commit a review
and the other review was quite positive, I decided to base the decision
of this manuscript on only one regular review and this editor review.Although I am not an expert on regression methods, I find the paper
written clearly and understandable. Especially, the uncertainties of
the derived ozone trends depending on the regression methods seem
important to me. Also the depiction of the contribution of the natural
processes to ozone changes is described well.I would, however, suggest some more discussion of the results: To me
it is not clear, in how far the the shown differences in regression
methods are now explaining the discrepancy in the lower stratosphere
that was first pointed out by Ball et al. (2020). Besides the
variability induced by the regression method, is there a model
improvement with respect to the Multimodelmean shown by Ball et
al. ? Or is this only the difference between free running CCMs and
the CTM shown here.What can be learned from the machinelearning results (MLTOMCAT).
Does the similarity with SWOOSH suggest that the basic mechanisms are
well understood or would you expect this similarity as it is
constructed by machinelearning using the observations?Why are the trends in the tropics so different between the two
reanalyses? Is this due to the vertical velocities?Therefore I suggest minor revisions to include this discussion, that
would potentially bring the shown results better into the context of
the present literature.Citation: https://doi.org/10.5194/egusphere2023591RC3 
AC3: 'Reply on RC3', Yajuan Li, 10 Aug 2023
The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2023/egusphere2023591/egusphere2023591AC3supplement.pdf

AC3: 'Reply on RC3', Yajuan Li, 10 Aug 2023
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