Introduction
Quasi-2-day wave (Q2DW) is a salient traveling planetary wave (PW) of the summer mesosphere, initially identified by Muller & Kingsley (1974)1 using meteor wind data. Since then, it has been extensively studied by several investigators from both hemispheres using ground-based, satellite-based observations and reanalysis datasets2, 3, 4, 5, 6–7. The Q2DW originates as a result of a Rossby-gravity normal mode sustained by barotropic/baroclinic instability of the summer mesospheric easterly jet, with peak activity typically in July–August in the northern hemisphere (NH) and January–February in the southern hemisphere (SH)8, 9–10. The Q2DW significantly influences the mesosphere and lower thermosphere (MLT) dynamics due to its fast phase speed and substantial amplification during ascent.
Moreover, the Q2DW influences upper atmospheric dynamics by interacting nonlinearly with tides, modulating neutral wind and dynamo electric fields11,12. Its dissipation also impacts polar mesospheric cloud occurrences by altering summer polar mesosphere temperatures5,13. Recently, Yue and Gan (2021)14 highlighted the Q2DW modulation of daytime CO2 mixing ratio in the MLT. Thus, comprehension of the underlying mechanisms governing the intermittency, propagation, and interaction of the Q2DW with other planetary-scale waves is crucial.
In contrast, a quasi-16-day wave (Q16DW) exhibits slower propagation and typically occurs during winter due to its inability to traverse the summer middle atmospheric easterlies15,16. However, past observations have detected Q16DW in the summer mid- and high-latitude mesosphere (see Sect. “Origin of modulation”). Initially identified by Kingsley et al. (1978)17 with periods of 12–20 days using meteor wind data, the Q16DW has since been extensively studied globally18, 19, 20, 21–22. However, the Q2DW and Q16DW relationship has not been exclusively explored yet.
The present study highlights an intriguing case of Q2DW amplitude modulation by quasi-16-day periods during 2019, shedding light on its potential role in carrying the signature of Q16DW from the southern hemisphere’s winter to the northern hemisphere’s summer. This aspect of interhemispheric coupling mediated by wave amplitude modulation remains least explored, and our work aims to provide new insights into this phenomenon. The paper is structured into four sections discussing the dataset (section “Observations”), Q2DW activity in specular meteor radar (SMR) winds (section “Meteor radar observation of Q2DW activity”), Quasi-16-day modulation in the summer MLT winds (section “Quasi-16-day modulation in the summer MLT winds”), dominant zonal wavenumber (ZWN) mode of the Q2DW and their coupling with Q16DW (section “Zonal wavenumber diagnosis”), modulation sources (section “Origin of modulation”), and excitation sources of primary Q2DW and Q16DW ZWN components (section “Plausible excitation source”), concluding with a summary of our findings (section “Summary and conclusions”).
Observations
Our observational data consist of wind measurements from the specular meteor radars (SMR) located at São João do Cariri (CA) (7.4°S, 36.5°W) and Wuhan (WU) (30.5°N, 114.6°E), and the multi-static SMR network MMARIA (Multistatic Multifrequency Agile Radar for Investigations of the Atmosphere) Germany. The observed area of the latter is centered around Juliusruh (JU) (54.6°N, 13.4°E). Technical details of these instruments are summarized in Lima et al. (2007)23, Zhao et al. (2005)24, and Poblet et al. (2023)25, respectively. Meteor radar utilizes radio wave pulses reflected by meteor trails, which drift with neutral winds. Wind profiles are derived by calculating the line-of-sight Doppler velocity, echo range, and arrival angle. The details of the methodology can be found in the paper by Hocking et al. (2001)26. The current study uses hourly zonal winds (U) and meridional winds (V) within the MLT region (~ 80 to 100 km altitude), derived at a vertical resolution of 2 km for WU and JU, and 3 km for CA.
Additionally, we utilize the Modern-Era Retrospective analysis for Research and Applications version 2 (MERRA-2), the latest global atmospheric reanalysis for the satellite era developed by NASA’s Global Modeling and Assimilation Office (GMAO) using the GEOS-5.12.4 model27. For this study, we have used 3 hourly U and V on a 2.5° × 2.5° latitude–longitude grid across 72 pressure levels (985 to 0.01 hPa, ~ 0 to 75 km). Importantly, MERRA-2 assimilates Aura MLS temperature and ozone profiles, providing improved representation of the middle atmosphere. Its suitability for studies involving tides and planetary waves has been highlighted in the SPARC Reanalysis Intercomparison Project Final Report28. MERRA-2 data set complements the SMR observations, providing a comprehensive picture of dynamic variability below 80 km. Furthermore, it offers the opportunity to investigate the interhemispheric coupling associated with the PWs.
The observational interval spans from 1 June to 3 October 2019. However, an extended observational interval from 1 May to 31 December 2019 is utilized for the spectral analysis to mitigate the edge effect in the result.
Results and discussions
Meteor radar observation of Q2DW activity
An evolutionary Lomb Scargle (ELS) Periodogram has been estimated using the Lomb Scargle technique applied to the hourly V using a 21-day window, progressively shifted by an hour over the entire observational interval29,30. This window size effectively resolves sidebands produced due to coupling with the PW periods (2–20 days). The Q2DW analysis has been exclusively limited to the V because of notably higher amplitude in V than in U31, 32–33. Figure 1a, b and c represent ELS amplitude spectra of V at 80 km (height) at CA, WU, and JU, respectively, in the period range 4–80 h (encompassing dominant tide and Q2DW periods). Notably, a transient enhancement around the 48-h period with prominent sidebands at 42 and 55-h is observed across all radar sites from June to August, persisting longer at lower latitudes (Fig. 1a) and diminishing towards higher latitudes (Fig. 1b, c).
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Fig. 1
Q2DW activity observed in meteor radar-derived winds. Evolutionary Lomb Scargle amplitude spectra (4–80 h period range) in m s−1 using SMR-derived V at (a) 81 km, CA (7.4° S, 36.5° W), (b) 80 km, WU (30.5° N, 114.6° E), and (c) 80 km, JU (54.6° N, 13.4° E) from 1 June to 3 October 2019. Altitude profile (80–100 km) of the Q2DW amplitude in m s−1 at (d) CA, (e) WU, and (f) JU. The letters JN, JL, A, and S in the x-axis denote June, July, August, and September; the subsequent number indicates the day of the given month. The white curve represents the 95% confidence level.
Closely-spaced sidebands near 48 h may result from possible modulation of the Q2DW with longer-period PWs. It is important to mention here that the appearance of such sidebands generally implies secondary wave generation due to nonlinear interactions among primary waves. Since the theme of the present paper is to investigate the modulation of a propagating wave component that carries the imprint of another wave, we have not looked into the details of wave-wave nonlinear interactions which is well-investigated in the available literatures. The wave-wave non-linear interaction process is described in Note S1 in the Supplementary Information. Furthermore, it can be mentioned that even the modulating periodicity (longer period) is found to be absent in the background winds during the temporal span of interest as will be shown later, which trivialize the context of nonlinear interaction in the present study.
Coupling between the Q2DW and longer period PWs using long-term MLT winds has been reported in previous studies34,35. Further, utilizing a sliding 6-day time window across the entire observational span, we assessed the ELS amplitude corresponding to the 48-h period (representative of Q2DW) to understand the short-term variability potentially induced by PW modulation. Figures 1d, e and f illustrate the temporal evolution of Q2DW activity at 80–98 km altitude at CA, WU, and JU, revealing distinct bursts of the Q2DW amplitude during July at all sites. The Q2DW peaks at higher altitudes at midlatitude (JU) than at low latitude (WU) in the NH (Fig. 1e, f), indicating latitudinally upward propagation. Unfortunately, due to finite data gaps at CA (indicated by white patches), further analysis is restricted to WU and JU observations.
Quasi-16-day modulation in the summer MLT winds
Figure 2a and e depict wavelet spectra of the hourly V at 80 km in the PW period range (4–20 days) at WU and JU, respectively. Bold white curves in each plot represent the 95% confidence level. No simultaneous longer-period PW activity, along with the Q2DW enhancement, can be found, although they can be noted elsewhere. The wavelet spectra of U at 80 km also exhibit similar features, as shown in Figure S1 in the Supplementary Information. This finding negates the presence of any independently propagating PWs therein. Next, we investigate whether the Q2DW carries any signatures of long-period modulation. For this purpose, the daily amplitudes of the Q2DW are estimated by employing the non-linear least square fit to the time series data using a 6-day window, progressively shifted by 1 day using the following equation.
1
where p = 1, 2, 3, 4 denotes Q2DW, diurnal, semidiurnal, and terdiurnal components, Ap is the amplitude, t is the universal time, and φp is the phase. Tp is the time period (T1 = 48 h; T2 = 24 h; T3 = 12 h; T4 = 8 h). Y(t) is the hourly V, and Yo is the mean wind over the fitting window. The resulting wavelet amplitude spectra estimated from the daily Q2DW amplitude at 80 km reveal a significant quasi-16-day (12–20 days) modulation at both WU (Fig. 2b) and JU (Fig. 2f). Therefore, even though the observed quasi-16-day period cannot be attributed to an independent propagating wave in the lower MLT summer winds, the Q2DW appears crucial in carrying the Q16DW signature from the lower altitudes. This resembles the mechanism by which intraseasonal oscillation (ISO)36 modulate faster waves such as gravity waves and tides, that carry the ISO signature to the higher altitudes. To understand the vertical structure (80–100 km) of the dominant wave within the Q2DW period range, Lomb Scargle amplitude spectra of V during July at WU (Fig. 2c) and JU (Fig. 2g) are examined. At WU, the upper sideband (USB ~ 42-h) of the Q2DW is active within the 80–85 km altitude. The Q2DW amplitude peaks around 85 km and decreases at higher altitudes, while the lower sideband (LSB ~ 55-h) shows activity in the 85–95 km altitude (Fig. 2c). Conversely, at JU above 85 km, both the Q2DW and its sidebands amplified (Fig. 2g), with the Q2DW peaking at approximately 92 km. The USB looks stronger as compared to the LSB.[See PDF for image]
Fig. 2
Quasi-16-day modulation of the Q2DW amplitude observed in meteor radar-derived winds. Wavelet amplitude spectra (PW period range) of (a) V, and (b) Q2DW amplitude at 80 km during the observational days, and the vertical evolution (80–98 km) of dominant waves (Lomb Scargle amplitude spectra) during July in the period range (c) 4–80 h, and (d) 4–20 days using SMR-derived V at WU (30.5° N, 114.6° E). (e, f, g, h) represents the same as (a, b, c, d) but at JU (54.6° N,13.4° E). The white curve in the wavelet spectra represents the 95% confidence level.
Figure 2d and h illustrate the same as Fig. 2c and g, but within PW period range at WU and JU, respectively. In July, the dominant PWs included Q6DW, Q10DW, and Q16DW. Notably, Q16DW is observed in the upper MLT (above 90 km) (Fig. 2d), coinciding with the Q2DW dissipation altitudes (Fig. 2c) at WU, suggesting a possible link between Q2DW dissipation and Q16DW enhancement. While Q6DW and Q10DW are present at JU, no significant Q16DW is detected (Fig. 2h), indicating that Q16DW probably appears at higher altitudes in concert with Q2DW dissipation altitudes at JU.
Figure 3 illustrates the Q16DW activity in the summer upper mesosphere and its temporal relationship with the Q2DW modulation. At WU (Fig. 3a), the Q16DW appears at altitudes above 90 km, coinciding with the region where the 16-day modulation of the Q2DW amplitude vanishes (Fig. 3b). In contrast, at JU, the 16-day modulation of Q2DW amplitude persists throughout the 80–98 km altitude (Fig. 3d), which may explain the lack of concurrent Q16DW activity (Fig. 3c). However, Q16DW may still emerge at higher altitudes, potentially aligning with the dissipation altitudes of Q2DW. The meteor radar observations imply that a Q16DW modulates the Q2DW. Initially, Q2DW serves as a carrier of Q16DW signature until dissipation, leading to Q16DW manifestation in the upper MLT summer winds. However, the absence of the Q16DW in the background winds at altitudes where modulation in the Q2DW is observed prompts further investigation into the potential origin of this modulation. Identifying primary zonal wavenumber modes of Q2DW is crucial for understanding the modulation onset, which is explored using the MERRA-2 dataset in the subsequent sections.
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Fig. 3
Q16DW activity in the summer upper mesosphere and its temporal variation in response to the Q2DW modulation. Temporal variability of the Q16DW amplitude in (a) V and (b) Q2DW amplitude, using SMR observations at WU (30.5° N, 114.6° E). (c, d) represent the same as (a, b) but at JU (54.6° N, 13.4° E). The white curve in the wavelet spectra represents the 95% confidence level.
Zonal wavenumber diagnosis
A combined Fourier Wavelet (CFW) technique37,38 is performed in the 2-dimensional space–time MERRA-2 V data to calculate the ZWN-period spectra. The CFW is a two-step method. First, a Fourier transform is applied along the longitudinal domain to obtain time series of spatial Fourier coefficients. In the second step, a wavelet transform is performed on these time series to derive wavelet coefficients, which are then used to calculate the CFW spectrum. The novelty of the method lies in identifying the temporal occurrence of wave activity. ZWN 0 signifies zonal symmetry, while positive/negative ZWN denotes westward (W)/eastward (E) propagation.
Since at 80 km, the Q2DW amplitude exhibits a maximum at CA, the ZWN-period spectra is calculated at CA latitude, i.e., 7.5° S, and the nearest pressure level to 80 km, i.e., 0.01 hPa, available from MERRA-2. The ZWN versus period spectra at 0.01 hPa (~ 75 km), 7.5° S calculated by averaging the CFW spectra in July 2019 are shown in Fig. 4a. The Q2DW is found to be westward (W) traveling corresponding to ZWN 3 (Fig. 4a), hereafter referred to as Q2DWW3. The time evolution of the dominant period of westward traveling ZWN 3 (W3) at 0.01 hPa, 7.5° S (Fig. 4d), reveals two distinct peaks of enhancement, centered at a period of 48 h. Hence, the representative period of Q2DWW3 can be reasonably considered as 48 h for further analysis, which aligns with previous studies2,31,39.
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Fig. 4
Global distribution of the dominant zonal wavenumber modes associated with Q2DW and Q16DW. (a) Period (4–70 h) versus zonal wavenumber (ZWN) amplitude spectra at 75 km (0.01 hPa), 7.5° S during July. Height-time section of the (b) Q2DWW3, and (c) Q16DWE2 amplitude at the equator. Temporal variability of (d) W3 in the 4–70 h period at 0.01 hPa, 7.5° S. Latitude-time section of (e) Q2DWW3, and (f) Q16DWE2 at 50 km. (g, h) represent the same as (e, f) but at 75 km. MERRA-2 V and U data are utilized for Q2DW and Q16DW analysis, respectively. Dashed black vertical lines mark the peak amplitude day of Q2DWW3. The white curve represents the 95% confidence level.
Figure 4b represents the height-time profile of the Q2DWW3 amplitude at the equator. The Q2DWW3 has two distinct peaks on 9 July and 25 July (marked by dashed vertical black lines), showcasing 16-day modulation persisting above 50 km. The latitude-time sections of the Q2DWW3 reveal equatorial symmetry at 50 km (Fig. 4e), and asymmetric extension to NH mid-latitudes at 75 km (Fig. 4g), mirroring the 16-day modulation.
Origin of modulation
From the aforementioned observations, the modulation appears to originate near the equator at around 50 km altitude, suggesting a likelihood of finding the Q16DW nearby. To investigate this further, the dominant period of all ZWN modes ranging from −6 to + 6 is examined using MERRA-2 U data (Figure S2 in Supplementary Information). The eastward traveling Q16DW corresponding to ZWN 2 (Q16DWE2) is found to be dominant among all the traveling PWs of different ZWN at 50 km, equator (Figure S2e in Supplementary Information). The prominence of the Q16DWE2 is also apparent in MERRA-2 V (Figure S3 in Supplementary Information), although its amplitude is smaller than that observed in MERRA-2 U. Generally, the Q16DW is more prominent in U than in V, so the analysis focuses on U only21,40,41.
Figure 4c, f and h represent the same as Fig. 4b, e and g, but for the Q16DWE2. The altitude profile of the Q16DWE2 amplitude shows an enhancement at 50 km from 1 June to early July (Fig. 4c). The latitude-time section of the Q16DWE2 at 50 km (Fig. 4f) and 74 km (Fig. 4h) indicates its activity only in the winter SH. McDonald et al. (2011)20 also observed a stronger amplitude of eastward propagating Q16DW in the winter SH compared to the westward propagating components. Interestingly, there is a decrease in amplitude and latitude spread of Q16DWE2 at higher altitudes (~ 74 km), suggesting a potential role of Q2DW in vertically carrying the signature of Q16DW to the summer hemisphere via modulation.
The limitation of Q16DWE2 activity within the lower atmosphere (~ 0 to 20 km) at 30.5° N (~ WU latitude) and 54.6° N (~ JU latitude) is evident from vertical profiles as shown in Fig. 5a and b, respectively, using MERRA-2 U. The Q16DW also seems confined within the lower atmosphere at WU (Fig. 5c) and JU (Fig. 5d), using MERRA-2 U. Figure 5e, f, g and h represent the same as Fig. 5a, b, c and d, but using MERRA-2 V. Similar features of Q16DWE2 and Q16DW are also observed in MERRA-2 V (Fig. 5e, f, g, h). This is likely due to strong summer mesospheric easterlies impeding direct Q16DW propagation. Consequently, the highest probability of occurrence is observed in winter15,16. Nonetheless, the presence of the Q16DW in the summer mid-latitude upper MLT (Figs. 2d and 3a) aligns with prior findings40,42,43.
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Fig. 5
Vertical profile (~ 0 to 80 km) of Q16DW in summer winds. Temporal variability of Q16DWE2 at (a) WU latitude (30.5° N), (b) JU latitude (54.6° N), and Q16DW amplitude at (c) WU (30.5° N, 114.6° E) and (d) JU (54.6° N, 13.4° E) in the altitude range of 0–80 km using MERRA-2 U. (e, f, g, h) represent the same as (a, b, c, d) but using MERRA-2 V. The white curve represents the 95% confidence level.
Three mechanisms proposed by previous investigators attempted to explain how Q16DW reaches the summer mesosphere. One suggests it originates in the winter hemisphere and propagates along the zero wind line to the summer mesosphere18,44,45. The other theory suggests that the Q16DW arises from oscillatory breaking of gravity waves modulated in the summer troposphere and lower stratosphere40,46. Additionally, Didenko et al. (2024)47 suggest that the Q16DW may also originate from nonlinear interactions between 4- and 5-day waves, which possess high phase speeds that allow them to penetrate the summer mesospheric easterlies. The present study is significant in this context as it presents the first observational evidence of the potential role of PW (Q2DW) in carrying the Q16DW signature from the winter to summer hemisphere mesosphere through modulation.
Plausible excitation source
Figure 6 exhibits the temporal variability of the Q16DWE2, and Q2DWW3 amplitude at an altitude of 50 km at the equator. The Q16DWE2 amplitude reveals its peak on 14 June. Similarly, the initial peak amplitude of Q2DWW3 is observed on 9 July. The red and black vertical dashed lines in Fig. 6 mark the initial peak amplitude day of the Q16DWE2, and Q2DWW3, respectively. The sustained high amplitude of the Q16DWE2 until the initiation of Q2DWW3 modulation suggests its possible role in causing the modulation at 50 km altitude. Interestingly, the 16-day modulation of Q2DWW3 becomes more apparent as Q16DWE2 begins to dissipate. This further suggests that the dissipating Q16DWE2 likely plays an appreciable role in modulating the Q2DWW3 component.
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Fig. 6
Temporal variability of the Q16DWE2, and Q2DWW3 waves at the inferred modulation origin. Temporal variability of Q16DWE2 (red), and Q2DWW3 (black) amplitude at an altitude of 50 km at the equator. The red dashed vertical line denotes the peak Q16DWE2 amplitude on 14 June. Similarly, the black dashed vertical line marks the initial peak amplitude of Q2DWW3, on 9 July. The red and black dotted horizontal line represents the 95% confidence level of Q16DWE2 and Q2DWW3, respectively. MERRA-2 V and U data are utilized for Q2DWW3 and Q16DWE2 analysis, respectively.
Next, we examined the global patterns of Q16DWE2, and Q2DWW3, along with the background zonal mean U conditions on the days of their peak amplitudes, to explore potential excitation sources, as shown in Fig. 7. Figure 7a and c illustrate the Q16DWE2 amplitude and the zonal mean U (ZMU) along the height-latitude section on 14 June. The white curve represents the 95% confidence level. The black curve indicates the zero ZMU line, while the magenta curve represents the critical layer. The critical layer is the region where the zonal phase speed of the wave becomes equal to the ZMU. At the critical layer, the wave can no longer travel upward. Instead, it gets absorbed or dissipates, leading to mixing and momentum transfer to the surrounding atmosphere48,49. Although critical layers typically dampen waves, unstable flows can turn them into wave sources10,50.
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Fig. 7
Height-latitude distribution of Q16DWE2, Q2DWW3, and the corresponding zonal mean zonal wind on the day of their respective peak amplitudes. Height latitude section of (a) Q16DWE2 amplitude on 14 June using MERRA-2 U, and (b) Q2DWW3 amplitude on 9 July using MERRA-2 V. (c,d) represent the same as (a,b) but of the ZMU on 14 June, and 9 July, respectively. The magenta curve represents the critical layer of the Q16DWE2 (a,c), and Q2DWW3 (b,d). The black curve represents the zero ZMU line. The initial peak amplitude day of the Q16DWE2, and Q2DWW3 is observed on 14 June, and 9 July 2025, respectively. The white curve represents the 95% confidence level.
The Q16DWE2 mainly occurs in the upper stratosphere and lower mesosphere (30–70 km) of the winter Southern Hemisphere (Fig. 7a), where it exists within regions of weak westerly winds (Fig. 7c), surrounding the core of the westerly jet near 50°S. Day-to-day variations in Q16DWE2 amplitude, critical layer, and ZMU are depicted in Movie S1 in Supplementary Information. Its amplification aligns with the intensification of winter westerly jet around 50 km altitude and 50°S, potentially drawing energy through baroclinic/barotropic instabilities. Upon closely monitoring the daily variability (Movie S1 in Supplementary Information), it seems that the intensification and poleward shift of the westerly jet contribute to the poleward migration of the critical layer, allowing Q16DWE2 presence across this line. Therefore, after the day of peak amplitude, the Q16DWE2 appears to extend beyond the critical layer at 50 km altitude near the equator and starts dissipating. Hence, this leakage across the critical layer seems crucial for initiating the modulation process, as the Q16DWE2 approaches Q2DWW3 (Fig. 7b) amplification near 50 km. Wu et al. (1996)51 suggested that winter PWs may trigger the summer Q2DW through their penetration into the summer stratosphere. In this connection, it can be comprehended that the observed long period modulation in the Q2DW in the present study is due to proximity of the Q16DWE2 near the equator where the Q2DWW3 is excited.
Figure 7b and d exhibit the same as Figs. 7a and c, but of the Q2DWW3 on 9 July. The Q2DWW3 appears to originate near the equator at around 50 km altitude, showing stronger amplitudes at higher altitudes (Fig. 7b). It is mainly confined between the zero-wind line and the critical layer, positioned equatorward of the boreal summer easterly jet (Fig. 7d). Movie S2 in Supplementary Information highlight daily variability in Q2DWW3 amplitude, showcasing the interaction with the background ZMU. The Q2DWW3 amplitude increases as strong easterly jets shift poleward, along with the intersection of the critical layer.
Overall, the winter westerly jet in the SH appears crucial in exciting the Q16DWE2, potentially through instability mechanisms. Similarly, the Q2DWW3 observed in the summer NH may be triggered by barotropic/baroclinic instabilities induced by the summer easterly jet, which aligns with previous studies10,52.
In the present study, we found the potential role of Q16DWE2 in driving the 16-day modulation of the Q2DW amplitude. This may occur through the modulation of the source processes that excite the Q2DWW3 component, as illustrated in Figs. 6 and 4b, c.
This hypothesis is supported by prior studies5,53,54, which have linked Q2DW activity in the summer stratopause region to strong PW activity in the winter hemisphere. PW breaking in the winter hemisphere can induce cross-equatorial mixing of Ertel’s potential vorticity, creating favorable conditions for inertial instability. The resulting momentum redistribution enhances the meridional curvature of the summer easterly jet50,55, promoting barotropic instability56, which further supports Q2DW growth.
In this context, Lieberman et al. (2021) reported strong planetary wave activity in the winter hemisphere during July 2014, creating conditions favorable for inertial instability. Their analysis identified dominant contributions from zonal wavenumber 1, along with a noticeable presence of zonal wavenumber 2 (PW2). Although the dominant wave period was not explicitly specified in the past study, it is plausible that the reported PW2 might have contribution from the Q16DWE2 in line with the present study. This may lend support to the inter-hemispheric coupling involving Q16DWE2, as proposed in the present study. Thus, modulation of the Q2DW likely begins near the equator, influenced by the critical layer of the winter hemispheric Q16DWE2.
Summary and conclusions
In the present work, we have potrayed a modulation of the Q2DW with a quasi-16-day period using meteor radar observations. The source of this modulation is found to be located at an altitude of 50 km near the equator, as found in the MERRA-2 data. The dominant Q16DWE2 wave in the winter hemisphere and its penetration across the critical layer likely initiates the modulation of the Q2DW in the summer hemisphere. The primary zonal wavenumber mode of the Q2DW, i.e., the Q2DWW3, show significant modulation with a quasi-16-day period.
No notable Q16DW is detected in the summer background winds, emphasizing the importance of Q2DWW3 in carrying the Q16DW signature from the near equator to the boreal summer mesosphere similar to the ISO. Interestingly, a Q16DW signature is observed in the upper MLT wind, coinciding with the altitude of Q2DW dissipation, further hinting at a potential link between the two phenomena.
In a nutshell, the present study provides a unique case of Q2DW modulation by a quasi-16-day period, highlighting its potential role in carrying the signature of the Q16DW from the austral winter to the boreal summer mesosphere.
Therefore, the findings of this study provide new insights into interhemispheric coupling mechanisms driven by PW. The observed modulation of the Q2DW by the Q16DW demonstrates how long-period PW signatures can propagate across hemispheres, even in the absence of direct local forcing. The present study highlights the role of long-period PW in influencing shorter-period PW across the hemispheric boundary, ultimately impacting the summer hemisphere MLT region.
Furthermore, our findings underscore the importance of incorporating PW modulation processes into whole-atmosphere models, as these processes facilitate momentum and energy transport from the stratosphere upward and across hemispheres. To build on these insights, future studies may investigate similar mechanisms over different seasons and regions to better understand the atmospheric conditions that drive such wave modulation. The specific research directions following the present work could be (1) identification of potential wave entities capable of transporting long-period wave signature, (2) study of suitable background conditions that support such phenomenon, (3) plausible dissipative processes that affect the interhemispheric propagation of the PWs. Exploring how these wave modulation processes evolve under climate change scenarios or during extreme weather events would provide valuable perspectives on their broader climatological significance.
Method
To analyze planetary wave activity in the middle atmosphere, we applied a combination of spectral analysis techniques to meteor radar wind data and MERRA-2 datasets.
Evolutionary Lomb-Scargle (ELS) periodogram
An ELS periodogram is estimated using the Lomb-Scargle technique applied to hourly wind data from meteor radar observations. A 21-day moving window, shifted hourly over the entire dataset, was used to capture time-varying periodicities. This window size effectively resolves sidebands arising from coupling with PW periods in the 2–20 day range, allowing detailed tracking of evolving features of Q2DW and the sidebands.
Wavelet spectral analysis
A wavelet transform is performed using the Morlet wavelet to identify the time-localized presence of dominant PWs in the radar-derived winds. This provided a time–frequency representation, revealing intermittent and evolving PW signatures in the MLT.
Combined Fourier–wavelet (CFW) technique
We employed the CFW method on wind fields in longitude-time space to identify the primary ZWN modes of the Q2DW and Q16DW. First, a Fourier transform along longitude yielded time series of spatial Fourier coefficients. Then, a wavelet transform was applied to these time series to obtain the time-resolved CFW spectrum. This method captures both the spatial structure and temporal evolution of PWs. ZWN 0 indicates zonally symmetric waves, while positive/negative ZWNs correspond to westward/eastward propagating components.
This combined approach enables robust detection and interpretation of planetary wave activity in both local and global datasets.
Acknowledgements
Authors GM and AG are supported by the Department of Space (Government of India). The authors gratefully acknowledge the Chinese Meridian Project for providing the useful data. The authors thank Nico Pfeffer and Matthias Clahsen (at IAP) for their vital help in maintaining the MMARIA Germany network. Authors are thankful to the editor and two anonymous reviewers for their useful comments to improve the manuscript.
Author contributions
GM and AG conceptualized the research. GM performed the analyses and prepared the manuscript. AG supervised the study, reviewed and edited the manuscript. PPB, RAB, TR, and JFC reviewed and edited the manuscript. PPB and JFC provided resources. RAB and TR managed data curation.
Data availability
The wind data from MMARIA Germany used in this study can be found under https://www.radar-service.eu/radar/en/dataset/txwdSdUlhffNgRYw?token=AsyfXxfDiHUVSODnUaYr. The WU meteor radar data can be accessed at https://data.meridianproject.ac.cn/data-directory/. The CA meteor radar datasets analyzed for the current study are available at Mitra, G. (2024)58. MERRA-2 data set utilized in the current study is available at https://gmao.gsfc.nasa.gov/reanalysis/MERRA-2/.
Code availability
The MATLAB implementations of the CFW method38 used to compute spectra in this study, is available at https://igit.iap-kborn.de/yamazaki/fourierwavelet (fourierwavelet v1.1). Additionally, the wavelet analysis software packages used for continuous wavelet transforms57 are accessible at: https://paos.colorado.edu/research/wavelets/.
Declarations
Competing interests
The authors declare that they have no competing interests.
Publisher’s note
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References
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Abstract
An interesting case of quasi-2-day wave (Q2DW) amplitude modulation with a quasi-16-day period is investigated using meteor radar winds and global reanalysis data during the 2019 boreal summer. The modulation is found to originate near the equator at 50 km altitude. Presence of a dominant eastward propagating quasi-16-day wave with zonal wavenumber 2 (Q16DWE2) in the austral winter across the zero-wind line near the equator initiates the modulation, as evident in the westward propagating quasi-2-day wave with zonal wavenumber 3 (Q2DWW3). Notably, while no significant Q16DW wave is detected in the boreal summer middle atmospheric winds, the primary Q2DWW3 mode (with amplitudes reaching ~8 m s−1) play a crucial role in carrying the Q16DW signature from the winter to the summer hemisphere. Additionally, the Q16DW appearance in the summer upper mesosphere and lower thermosphere (90–100 km altitude) that is near the dissipation altitude of the Q2DW corroborates a potential link between these two dynamical entities. Overall, the present study highlights a novel mechanism of interhemispheric coupling through planetary wave modulation, offering new insights into the global dynamics of the lower and middle atmosphere.
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Details
1 Space and Atmospheric Sciences Division, Physical Research Laboratory, Ahmedabad, India (GRID:grid.465082.d) (ISNI:0000 0000 8527 8247); Indian Institute of Technology, Department of Physics, Gandhinagar, India (GRID:grid.462384.f) (ISNI:0000 0004 1772 7433); Leibniz-Institute of Atmospheric Physics at the University of Rostock, Kühlungsborn, Germany (GRID:grid.10493.3f) (ISNI:0000 0001 2185 8338)
2 Space and Atmospheric Sciences Division, Physical Research Laboratory, Ahmedabad, India (GRID:grid.465082.d) (ISNI:0000 0000 8527 8247)
3 National Institute for Space Research, INPE, Heliophysics, Planetary Sciences and Aeronomy Division, São José dos Campos, Brazil (GRID:grid.419222.e) (ISNI:0000 0001 2116 4512)
4 Federal University of Campina Grande, Department of Physics, Campina Grande, Brazil (GRID:grid.411182.f) (ISNI:0000 0001 0169 5930)
5 Leibniz-Institute of Atmospheric Physics at the University of Rostock, Kühlungsborn, Germany (GRID:grid.10493.3f) (ISNI:0000 0001 2185 8338)