the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 15 Aug 2022
Nonlinear resonant interactions of atmospheric tides with annual oscillation based on meteor radar observation and reanalysis data
Abstract. Nonlinear interactions among gravity waves and among tides and planetary waves (PWs) have extensively been studied, however, resonant interactions between tides and annual (AO) and semiannual (SAO) oscillations were not reported. By using meteor radar observations and reanalysis data for 9 years, we demonstrate that the sum and difference resonant interactions between the diurnal (DT)/semidiurnal (SDT) tides and the AO/SAO do occur in the mesosphere and lower thermosphere (MLT). Both the frequencies and wavenumbers of the secondary waves in the sum (difference) resonant interactions just equal the sum (difference) frequencies and wavenumbers between the DT/SDT and the AO/SAO. Spectral analysis shows that only the DT, SDT, AO, SAO and their secondary waves are the predominant components in both the zonal and meridional winds at 90 km with the spectral amplitudes of 3.5–17.7 ms-1, being much stronger than all the other spectral amplitudes, including the amplitudes (2.1–2.2 ms-1) of the relatively strong terdiurnal tide and 16-day PW. At some altitudes in the MLT, the secondary waves are more intense than the DT/SDT, thus in tidal studies, the magnitude of the secondary waves may be regarded as the tidal one if the observational period is not long enough or their spectral peaks are not distinguished carefully.
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CC1: 'Comment on acp-2022-407', Paul PUKITE, 16 Aug 2022
The paper states:
"Although nonlinear interactions between atmospheric waves have attracted wide attention, interactions of both global-scale tides and annual and semiannual oscillations were not reported yet."
Should add a citation to the research discovering the interaction of annual and semiannual cycles with the long-period tidal cycles generating the well-known ~2.33 year quasi-biennial oscillation (QBO) of the equatorial upper-atmosphere. As the QBO is a wavenumber=0 behavior, only the nodal 27.2/13.6 day cycle is involved and will produce an aliased floor(365.24 days/yr / 27.2 day/nodal) = 0.428/yr forced frequency response. The two match precisely and the harmonic satellite peaks are also observed in the QBO results.
1. Pukite, P., Coyne, D., & Challou, D. (2019). Mathematical Geoenergy: Discovery, Depletion, and Renewal (Vol. 241). John Wiley & Sons. Chap.11 https://agupubs.onlinelibrary.wiley.com/doi/10.1002/9781119434351.ch11
2. Pukite, Paul R. "Analytical Formulation of Equatorial Standing Wave Phenomena: Application to QBO and ENSO." AGU Fall Meeting Abstracts. 2016. https://ui.adsabs.harvard.edu/abs/2016AGUFMOS11B..04P/abstract
3. Pukite, Paul. "Nonlinear long-period tidal forcing with application to ENSO, QBO, and Chandler wobble." EGU General Assembly Conference Abstracts. 2021.
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This paper by Huang at al should be published as it will focus attention on the non-linear (and aliased) tidal aspects of atmospheric and oceanic behavior, which have been overlooked in favor of the linear, non-aliased cycles, leading to divergent interpretations behind the physical gravity-wave forcing mechanisms.
Citation: https://doi.org/10.5194/acp-2022-407-CC1 -
AC1: 'Reply on CC1', Kaiming Huang, 06 Nov 2022
The comment was uploaded in the form of a supplement: https://acp.copernicus.org/preprints/acp-2022-407/acp-2022-407-AC1-supplement.pdf
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AC1: 'Reply on CC1', Kaiming Huang, 06 Nov 2022
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RC1: 'Comment on acp-2022-407', Anonymous Referee #1, 10 Sep 2022
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CC2: 'Reply on RC1', Paul PUKITE, 12 Sep 2022
See my comment on how to do the aliasing correctly. A train of annual or semi-annual impulses creates a completely different set of spectral frequencies than the simple plus and minus interaction of two frequencies.
Citation: https://doi.org/10.5194/acp-2022-407-CC2 -
AC2: 'Reply on RC1', Kaiming Huang, 06 Nov 2022
The comment was uploaded in the form of a supplement: https://acp.copernicus.org/preprints/acp-2022-407/acp-2022-407-AC2-supplement.pdf
-
CC2: 'Reply on RC1', Paul PUKITE, 12 Sep 2022
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RC2: 'Comment on acp-2022-407', Anonymous Referee #2, 12 Sep 2022
General comments:
This study derived the spectra of the wind observations from a meteor radar and MERRA2 reanalysis data from 2012 to 2021 using the two-dimensional Fourier transform and Lomb-Scargle spectrum analysis. The manuscript showed mainly a spectral analysis of the nonlinear resonant interactions of the diurnal (DT)/semidiurnal (SDT) tides and the annual (AO) / semiannual (SAO) oscillations. The authors concluded that “.. there exist several significant peaks in the upper and lower sidebands of the DT. These spectral peaks are located right at the sum and difference frequencies between the DT and the AO and SAO, meaning that these waves are generated through the nonlinear resonant interactions between the DT and the AO/SAO. The amplitudes of the secondary waves excited through the difference (sum) resonant interactions between the DT and the AO and SAO …”
A contradiction existing in this manuscript is this study analyzing a nonlinear phenomenon with the Fourier-based methods. The summation of sine or cosine functions, which is linear and stationary, makes mathematical sense to fit the data but does not make physical sense of a nonlinear process.
Another problem of this manuscript is the missing investigation of the physical mechanism. The authors showed only the spectra of the wind data with discussion. Accordingly, the reviewer suggests a major revision.
Specific comments:
The realistic atmosphere is a nonlinear system. However, the nonlinearity can induce spurious harmonic components that cause energy spreading and result in the spectra making little physical sense (Huang et al. (1998), https://doi.org/10.1098/rspa.1998.0193). The summation of the Fourier components fitting the nonlinear and non-stationary nature of data generates artificial harmonics, which misleads the true energy distribution in the frequency or wavenumber domain. In my opinion, the authors mistook the artificial harmonics for the nature signal of the possible nonlinear wave-wave interaction.
The reviewer recommends that the authors should derive the Hilbert and marginal spectra of the wind data and prove the authenticity of the Fourier-based spectra as shown in the manuscript. The HHT is a method for studying the nonlinear wave-wave interaction and energy transfer. The authors should prove if the spectral peaks are natural or not before investigating the physical mechanism.
Note that this study shows only the spectra of the data. Investigation of the physical mechanism is missing. Does the interaction of the tidal modes and the atmospheric background circulation cause the nonlinear process? How’s the atmospheric gravity waves dump their momentum energy into the wind flow? Does the QBO driven by tropospheric activities also play a role in the mechanism of the nonlinear interaction? The QBO is highly nonlinear and nonstationary because it varies significantly during the study period from 2012 to 2021. Investigating the mechanism in detail is also required.
Citation: https://doi.org/10.5194/acp-2022-407-RC2 -
AC3: 'Reply on RC2', Kaiming Huang, 06 Nov 2022
The comment was uploaded in the form of a supplement: https://acp.copernicus.org/preprints/acp-2022-407/acp-2022-407-AC3-supplement.pdf
-
AC3: 'Reply on RC2', Kaiming Huang, 06 Nov 2022
Status: closed
-
CC1: 'Comment on acp-2022-407', Paul PUKITE, 16 Aug 2022
The paper states:
"Although nonlinear interactions between atmospheric waves have attracted wide attention, interactions of both global-scale tides and annual and semiannual oscillations were not reported yet."
Should add a citation to the research discovering the interaction of annual and semiannual cycles with the long-period tidal cycles generating the well-known ~2.33 year quasi-biennial oscillation (QBO) of the equatorial upper-atmosphere. As the QBO is a wavenumber=0 behavior, only the nodal 27.2/13.6 day cycle is involved and will produce an aliased floor(365.24 days/yr / 27.2 day/nodal) = 0.428/yr forced frequency response. The two match precisely and the harmonic satellite peaks are also observed in the QBO results.
1. Pukite, P., Coyne, D., & Challou, D. (2019). Mathematical Geoenergy: Discovery, Depletion, and Renewal (Vol. 241). John Wiley & Sons. Chap.11 https://agupubs.onlinelibrary.wiley.com/doi/10.1002/9781119434351.ch11
2. Pukite, Paul R. "Analytical Formulation of Equatorial Standing Wave Phenomena: Application to QBO and ENSO." AGU Fall Meeting Abstracts. 2016. https://ui.adsabs.harvard.edu/abs/2016AGUFMOS11B..04P/abstract
3. Pukite, Paul. "Nonlinear long-period tidal forcing with application to ENSO, QBO, and Chandler wobble." EGU General Assembly Conference Abstracts. 2021.
----------------------------------------------------
This paper by Huang at al should be published as it will focus attention on the non-linear (and aliased) tidal aspects of atmospheric and oceanic behavior, which have been overlooked in favor of the linear, non-aliased cycles, leading to divergent interpretations behind the physical gravity-wave forcing mechanisms.
Citation: https://doi.org/10.5194/acp-2022-407-CC1 -
AC1: 'Reply on CC1', Kaiming Huang, 06 Nov 2022
The comment was uploaded in the form of a supplement: https://acp.copernicus.org/preprints/acp-2022-407/acp-2022-407-AC1-supplement.pdf
-
AC1: 'Reply on CC1', Kaiming Huang, 06 Nov 2022
-
RC1: 'Comment on acp-2022-407', Anonymous Referee #1, 10 Sep 2022
-
CC2: 'Reply on RC1', Paul PUKITE, 12 Sep 2022
See my comment on how to do the aliasing correctly. A train of annual or semi-annual impulses creates a completely different set of spectral frequencies than the simple plus and minus interaction of two frequencies.
Citation: https://doi.org/10.5194/acp-2022-407-CC2 -
AC2: 'Reply on RC1', Kaiming Huang, 06 Nov 2022
The comment was uploaded in the form of a supplement: https://acp.copernicus.org/preprints/acp-2022-407/acp-2022-407-AC2-supplement.pdf
-
CC2: 'Reply on RC1', Paul PUKITE, 12 Sep 2022
-
RC2: 'Comment on acp-2022-407', Anonymous Referee #2, 12 Sep 2022
General comments:
This study derived the spectra of the wind observations from a meteor radar and MERRA2 reanalysis data from 2012 to 2021 using the two-dimensional Fourier transform and Lomb-Scargle spectrum analysis. The manuscript showed mainly a spectral analysis of the nonlinear resonant interactions of the diurnal (DT)/semidiurnal (SDT) tides and the annual (AO) / semiannual (SAO) oscillations. The authors concluded that “.. there exist several significant peaks in the upper and lower sidebands of the DT. These spectral peaks are located right at the sum and difference frequencies between the DT and the AO and SAO, meaning that these waves are generated through the nonlinear resonant interactions between the DT and the AO/SAO. The amplitudes of the secondary waves excited through the difference (sum) resonant interactions between the DT and the AO and SAO …”
A contradiction existing in this manuscript is this study analyzing a nonlinear phenomenon with the Fourier-based methods. The summation of sine or cosine functions, which is linear and stationary, makes mathematical sense to fit the data but does not make physical sense of a nonlinear process.
Another problem of this manuscript is the missing investigation of the physical mechanism. The authors showed only the spectra of the wind data with discussion. Accordingly, the reviewer suggests a major revision.
Specific comments:
The realistic atmosphere is a nonlinear system. However, the nonlinearity can induce spurious harmonic components that cause energy spreading and result in the spectra making little physical sense (Huang et al. (1998), https://doi.org/10.1098/rspa.1998.0193). The summation of the Fourier components fitting the nonlinear and non-stationary nature of data generates artificial harmonics, which misleads the true energy distribution in the frequency or wavenumber domain. In my opinion, the authors mistook the artificial harmonics for the nature signal of the possible nonlinear wave-wave interaction.
The reviewer recommends that the authors should derive the Hilbert and marginal spectra of the wind data and prove the authenticity of the Fourier-based spectra as shown in the manuscript. The HHT is a method for studying the nonlinear wave-wave interaction and energy transfer. The authors should prove if the spectral peaks are natural or not before investigating the physical mechanism.
Note that this study shows only the spectra of the data. Investigation of the physical mechanism is missing. Does the interaction of the tidal modes and the atmospheric background circulation cause the nonlinear process? How’s the atmospheric gravity waves dump their momentum energy into the wind flow? Does the QBO driven by tropospheric activities also play a role in the mechanism of the nonlinear interaction? The QBO is highly nonlinear and nonstationary because it varies significantly during the study period from 2012 to 2021. Investigating the mechanism in detail is also required.
Citation: https://doi.org/10.5194/acp-2022-407-RC2 -
AC3: 'Reply on RC2', Kaiming Huang, 06 Nov 2022
The comment was uploaded in the form of a supplement: https://acp.copernicus.org/preprints/acp-2022-407/acp-2022-407-AC3-supplement.pdf
-
AC3: 'Reply on RC2', Kaiming Huang, 06 Nov 2022
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