Migrating solar diurnal tidal variability during Northern and Southern Hemisphere Sudden Stratospheric Warmings

Abstract

In this study, the variability of the migrating solar diurnal (DW1) tide in the mesosphere-lower thermosphere (MLT) region during Northern and Southern Hemisphere (NH & SH) Sudden Stratospheric Warmings (SSWs) is investigated using Sounding of the Atmosphere using Broadband Emission Radiometry (SABER) temperature observations and reanalysis-driven Whole Atmosphere Community Climate Model with thermosphere and ionosphere extension (WACCM-X) simulations. The periods examined include four major NH SSWs that occurred in 2006, 2009, 2010 and 2013 and two SH SSWs that were observed in 2002 and 2019. Our analysis shows that the DW1 tide in both observations and simulations displays a reduction of amplitude at low-latitudes after the onset of NH and SH SSWs. As WACCM-X simulations qualitatively reproduce this feature of DW1 tidal variability common to both NH and SH SSWs, they have been used to examine the possible mechanism that could explain these observations in the DW1 tide. It is known that changes in the latitudinal shear of zonal winds at low-latitudes strongly affect the seasonal variation of the DW1 tide in the MLT. We show that SSW-associated changes in the latitudinal shear in the MLT could explain the observed variability of the DW1 tide during NH and SH SSWs.

Graphical Abstract

Introduction

Sudden stratospheric warmings (SSWs) are large-scale, transient and dynamically extreme meteorological events that are marked by a rapid rise in the polar stratospheric temperature together with the breakdown of climatological wintertime eastward winds (e.g., Scherhag 1952; Andrews et al. 1987; Baldwin et al. 2021). SSWs occur when the stratospheric polar vortex gets disrupted by the dissipation of large-scale upward propagating quasi-stationary planetary waves (QSPWs), which are forced from the troposphere (e.g., Matsuno 1971). As the eastward winds in the stratosphere act as a filter and only allow upward propagation of large-scale QSPWs with zonal wave numbers 1–3, the remaining QSPWs with higher zonal wave numbers are reflected back to the troposphere (Charney and Drazin 1961). The interaction of these upward propagating QSPWs with the stratospheric zonal mean flow results not only in the deceleration of the eastward winds but also induces a poleward flow, which descends over the polar stratosphere. The adiabatic heating associated with this descent results in the rapid rise of polar stratospheric temperature that manifests as an SSW. Depending on the extent of deceleration of the eastward zonal-mean zonal winds (ZMZW) in the polar stratosphere, SSWs are classified into ‘major’ and ‘minor’ warming events (e.g., WMO/IQSY 1964; Labitzke 1981). In the NH, a reversal of the ZMZW from eastward to westward direction at 60$^{\circ }$N and 10 hPa has been chosen as a criteria for identifying major SSWs whereas a minor SSW is identified when there is only an increase in polar stratospheric temperature without the reversal of ZMZW (e.g., Charlton and Polvani 2007; Butler et al. 2015). In the SH, a criteria analogous to the one in the NH has been used in literature for classifying major and minor SSWs. In addition to this classification, SSWs can also be distinguished based on the morphology of the polar vortex. Depending on the zonal wavenumber of the planetary wave forcing, the stratospheric polar vortex can either get displaced off the pole or split into child vortices (e.g., Charlton and Polvani 2007). The displacement and the splitting of the polar vortex is driven predominantly by the forcing of QSPWs with wave number 1 and 2, respectively. The occurrence of SSWs are common in the Northern Hemisphere (NH) but extremely rare in the Southern Hemisphere (SH). Major SSWs occur at an average rate of six events per decade in the NH (Charlton and Polvani 2007) but in the SH, only one major SSW and one minor SSW occurring during September 2002 and 2019, respectively, have so far been observed. The inter-hemispheric asymmetry in the occurrence of SSW has been attributed to the difference in planetary wave (PW) forcing due to orography and land-sea contrast in the two hemispheres (e.g., Waugh and Polvani 2010).

The SSW associated effects in the atmosphere are now well recognized to extend beyond the polar stratosphere and significant changes have also been witnessed in the mesosphere-lower thermosphere (MLT) and ionosphere regions (e.g., Pedatella et al. 2018). The warming of the winter polar stratosphere during SSWs is associated with the cooling of the winter polar mesosphere (e.g., Labitzke 1972). This mesospheric cooling happens due to the deceleration and potential reversal of the eastward stratospheric ZMZW during SSWs, which result in an increased eastward forcing due to gravity waves in the polar mesosphere that induces an upwelling and leads to adiabatic cooling at mesospheric altitudes (e.g., Holton 1983; Liu and Roble 2002; Zülicke and Becker 2013). The changes in gravity wave forcing in the mesosphere also modify the stratosphere-mesosphere residual circulation, which causes warming in the summer hemisphere mesosphere and a decrease in the occurrence of polar mesospheric clouds through inter-hemispheric coupling mechanisms (e.g., Karlsson et al. 2009; Körnich and Becker 2010). SSW related effects are also found in the lower thermosphere in the form of warming at polar and mid-latitudes (e.g., Goncharenko and Zhang 2008; Funke et al. 2010; Liu and Roble 2002) but the exact reasons behind this observation is yet to be fully ascertained.

Atmospheric tides have been found to play a key role in coupling the SSW effects to the upper atmosphere (e.g., Chau et al. 2009; Fejer et al. 2010; Goncharenko et al. 2010). Tides in the atmosphere are referred to as planetary-scale oscillations that have periods and sub-periods of a solar (24 h) or a lunar (24.84 h) day. Atmospheric solar tides form the primary components of tidal oscillations and are mainly thermally generated through the absorption of solar radiation by tropospheric water vapour and stratospheric ozone (e.g., Lindzen and Chapman 1969). In contrast, the relatively smaller atmospheric lunar tides are generated due to the gravitational interaction of the moon-Earth system (e.g., Sabine 1847). Tides that are sun- or moon-synchronous are termed as ‘migrating’ solar or lunar tides. Alternatively, tides that do not follow the motion of the moon or the sun are termed as ‘nonmigrating’. In literature, the shorthand notation xWs or xEs are used to denote a westward or eastward propagating tide, respectively, for which s is the zonal wavenumber. For diurnal, semidiurnal and terdiurnal oscillations, ‘D’, ‘S’ and ‘T’ replace ‘x’ and migrating diurnal, semidiurnal and terdiurnal tides are represented by DW1, SW2 and TW3, respectively.

During SSWs, it has been found that changes in the migrating semidiurnal solar (SW2) and lunar (M2) tides play an important role in the variability of MLT and ionosphere (e.g., Chau et al. 2012, and references therein). The SW2 enhancements during the SSWs are due to a combination of different factors, which arise due to SSW associated changes in stratosphere-mesosphere chemistry and ZMZW. These factors include changes in tidal propagation conditions (e.g., Jin et al. 2012), changes in stratospheric ozone distribution (e.g., Goncharenko et al. 2012; Siddiqui et al. 2019) and non-linear interaction with stationary planetary waves (e.g., Liu et al. 2010). The M2 enhancement is attributed to background zonal mean zonal wind changes, which shifts the secondary (Pekeris) resonance peak of the atmosphere towards the period of M2 tide (Forbes and Zhang 2012).

In addition to the variability in SW2 and M2 tides, SSW-driven changes can also be witnessed in a range of other migrating and nonmigrating tides. Along with the variability in DW1 and TW3 tides, the nonmigrating solar diurnal westward wave-2 (DW2), diurnal stationary (D0), semidiurnal westward wave-1 (SW1) and semidiurnal westward wave-3 (SW3) have been reported to show a strong response to SSW at MLT and ionospheric altitudes (e.g., Jin et al. 2012; Pedatella and Liu 2013; Lin et al. 2013; Lieberman et al. 2015; Sridharan 2017). These responses vary individually for the migrating and nonmigrating tides with differing level of changes seen during SSWs in each one of them. While the DW1 tide at MLT altitudes has been found to show a reduction at low-latitudes during the 2009 SSW from both Sounding of the Atmosphere using Broadband Emission Radiometry (SABER) temperature observations and coupled whole atmosphere model simulations (e.g., Jin et al. 2012; Pedatella et al. 2012; Sassi et al. 2013), the TW3 tide from SABER temperature observations has been found to enhance at low-to-mid-latitudes in the MLT region during the 2009 SSW (Jin et al. 2012). The TW3 enhancement at lower thermospheric altitudes had earlier been posited by Fuller-Rowell et al. (2010) in a simulation based study of the 2009 SSW. Besides the variability of solar diurnal and terdiurnal migrating tides, the variability of higher-order solar migrating tides at MLT altitudes have also been reported during SSWs (e.g., Gong et al. 2018, He et al. 2020). Using a network of mid-latitude specular meteor radars, He et al. (2020) found that the amplitudes of fourth (6 h), fifth (4.8 h) and sixth (4 h) harmonics of migrating solar tide quench after the SSW onset.

Although the SSW associated changes in migrating and nonmigrating tides have been well documented, the key mechanisms behind their variability, barring the SW2 and M2 tides, have not been thoroughly investigated. While earlier works such as by Sassi et al. (2013) have focused on the DW1 tidal variability during the 2009 NH SSW, there have been no further reports investigating the DW1 tidal variability during other NH SSWs or any SH SSWs in great detail. The objective of this study is to examine and understand the variability of the DW1 tide in the MLT region during multiple NH and SH SSWs. For this purpose, we use SABER temperature observations and reanalysis-driven Whole Atmosphere Community Climate Model with thermosphere and ionosphere extension (WACCM-X) simulations. The evolution of the DW1 tide is investigated during four NH SSWs and two SH SSWs in this study. For the NH SSWs, we select the 2006, 2009, 2010 and 2013 warming events and for the SH SSWs, we choose the 2002 and 2019 warming events in our analysis. The NH SSWs have been chosen in a way so as to include major SSWs that have occurred under varying solar flux conditions. The 2009 and 2010 NH SSWs took place under low solar flux levels while the 2006 and 2013 NH SSWs were realized under moderate-to-high solar flux conditions. By selecting these four events, we explore whether the MLT DW1 tide shows any discernible variability with varying solar flux levels during SSWs since it is known that the MLT DW1 tide shows higher amplitudes during low solar flux periods and lower amplitudes during high solar flux periods (e.g., Sridharan et al. 2010, Singh and Gurubaran 2017). In a similar manner, we select the 2002 and 2019 SH SSWs for our analysis since these two events are among the strongest SSWs that have ever happened in the SH with the 2002 and 2019 SH SSWs occurring under high and low solar flux conditions, respectively. In addition, we investigate whether the changes in the latitudinal shear of MLT zonal winds at low-latitudes, which are known to strongly affect the seasonal variation of the DW1 tide, could explain the observed variability of the DW1 tide during NH and SH SSWs. The structure of this paper is as follows. In "Data and methods" section, the data and methods used in this study are provided. The results are presented in "Results" section, which is followed by discussion in "Discussion" section. The conclusions from this work are presented towards the end.

Data and methods

MLT DW1 tide from SABER temperature measurements

The Sounding of the Atmosphere using Broadband Emission Radiometry (SABER) instrument onboard the National Aeronautics and Space Administration (NASA) Thermosphere Ionosphere Mesosphere Energetics and Dynamics (TIMED) satellite performs global measurements of the atmosphere by using a 10-channel broadband limb-scanning infrared radiometer, which covers the spectral range between 1.27 and 17 $\mu$m. The SABER limb scans use infrared CO$_{2}$ emissions at 4.3 and 15 $\mu$m to derive temperature profiles between 20–120 km (Remsberg et al. 2008). The TIMED satellite precesses in local time at a rate of $\sim$12 min/day and it covers a full 24-h cycle of local time in 60 days (e.g., Zhu et al. 2005). Tidal decomposition of SABER temperature data using standard spectral Fourier diagnostics or least-squares fitting approach therefore requires 60 days of combined ascending (asc) and descending (dsc) orbit nodes observations (e.g., Forbes et al. 2008; Pancheva and Mukhtarov 2011). The tidal amplitude that is obtained using this method represents an average over the 60 days period and is insufficient to capture tidal variability on shorter timescales (e.g., Lieberman et al. 2015; Pedatella et al. 2016). In case of diurnal tides, however, short-term variability can be inferred from an alternative mathematical approach commonly referred to as ‘tidal deconvolution’. This method does not require complete 24-h local time sampling of satellite data and has been utilized in earlier studies to investigate the short-term variability of various diurnal tides from SABER temperature data (e.g., Oberheide et al. 2003; Lieberman et al. 2015, Vitharana et al. 2019, Kumari and Oberheide 2020).

The tidal deconvolution method relies on the differencing between the daily measurements taken on the asc and dsc portions of the satellite orbit and can be applied at those latitudes where the local solar time difference between the asc/dsc orbit nodes is ideally $\sim$12 h. With the use of such differencing, the semidiurnal tidal components and low-frequency planetary-scale waves vanish in the asc-dsc difference fields (e.g., Oberheide et al. 2002, 2003). From the perspective of a quasi-Sun synchronous satellite, a diurnal tide with a zonal wavenumber s is viewed as one with a zonal wavenumber $s-1$ in case of westward propagation and as one with a zonal wavenumber $s+1$ in case of eastward propagation (Salby 1982). The amplitude of the DW1 tide is estimated from the vertical structure of the zonal mean component of the SABER asc-dsc difference fields as the DW1 tide is aliased to the zonal mean ($s=0$) from the satellite perspective (e.g., Lieberman 1991; Oberheide et al. 2000; Lieberman et al. 2015).

We apply this tidal deconvolution method to SABER observations to retrieve daily amplitudes of DW1 tide and present results based on a running 10-day average of the daily values. This averaging reduces the impact of spurious observations and occasionally large day-to-day variability in the estimated DW1 tide. The uncertainty in DW1 tidal amplitudes estimated by tidal deconvolution is <1 K (Lieberman et al. 2015), which arises partly because the SABER asc and dsc nodes are separated by $\sim$9 h in local time. When the asc-dsc difference fields are not separated by 12 h in local solar time then there is a potential for aliasing by semidiurnal tides. However, aliasing by semidiurnal tides has been found to be within the error limits at latitudes equatorward of 30$^\circ$ and at altitudes below 90 km (e.g., Vitharana et al. 2019). For a more detailed overview of the tidal deconvolution method, the readers can refer to Oberheide et al. (2002).

MLT DW1 tide from WACCM-X simulations

We employ the Whole Atmosphere Community Climate Model with thermosphere and ionosphere extension (WACCM-X version 2.1) (Liu et al. 2018) to perform the model simulations in this study. WACCM-X is the atmospheric component of the National Center for Atmospheric Research (NCAR) Community Earth System Model (CESM) (Hurrell et al. 2013) that extends from the surface to the upper thermosphere, with a model top boundary, depending on solar activity lying between 500 and 700 km. As WACCM-X is built upon the regular WACCM (version 4) (e.g., Marsh et al. 2013), it incorporates all the physical processes represented in WACCM4 up to the lower thermosphere. The horizontal spatial resolution of WACCM-X is 1.9$^\circ$ in latitude and 2.5$^\circ$ in longitude. In the vertical direction, WACCM-X uses a hybrid $\sigma$-p coordinate system, which is purely pressure based above 100 hPa. The vertical resolution for WACCM-X in log(p) coordinates varies from $\sim$0.16 in the troposphere and lower stratosphere to 0.25 in the mesosphere and thermosphere (see Fig. 1, Pedatella et al. 2019). The implementation of a coupled ionosphere with self-consistent ionospheric electrodynamics in WACCM-X is primarily based on the Thermosphere-Ionosphere-Electrodynamics General Circulation Model (e.g., Richmond et al. 1992; Qian et al. 2014). A more detailed description about the new developments incorporated in WACCM-X can be found in Liu et al. (2018). The ‘specified dynamics (SD)’ configuration of WACCM-X, commonly referred to as SD-WACCM-X, can be used to reproduce the atmospheric state during specific time periods by constraining the model toward meteorological reanalysis products. In the present study, we use the SD-WACCM-X configuration to relax the tropospheric and stratospheric dynamical fields (nudging up to $\sim$1 hPa) in the model toward NASA Modern Era Retrospective Analysis for Research and Applications (MERRA) version 2 (Gelaro et al. 2017).

Hourly outputs of neutral temperature from SD-WACCM-X simulations are used to extract the amplitude of the DW1 tide at MLT altitudes. At a particular geographic location, solar tidal oscillations can be represented in the following form:

$$\begin{aligned} \sum _{s=-5}^{s=5} \sum _{n=0}^{3} A_{n,s}(\theta ,h)\>cos(n\Omega t+s\lambda -\phi _{n,s}(\theta ,h)) \end{aligned}$$

(1)

where $\Omega =\frac{2\pi }{24h}$, t is universal time (UT) in hours, n denotes the harmonics and subharmonics of a solar day, s is the zonal wave number, $\lambda$ is the longitude. $A_{n,s}$ and $\phi _{n,s}$ represent the amplitude and phase of respective tidal components at latitude ($\theta$) and altitude (h), respectively. The tidal phase, $\phi _{n,s}$, is calculated with respect to $0^{\circ }$ longitude. For a westward propagating wave, $s>0$, while $s<0$ for an eastward propagating wave. We estimate daily amplitudes of the DW1 tide in SD-WACCM-X simulated neutral temperature by performing a least-squares fit to equation 1 with a sliding window of 10 days at each latitude. The 10-days sliding window is chosen for consistent comparison with the SABER DW1 tides. We present the DW1 tides that are estimated from SD-WACCM-X simulations and SABER temperature observations during the NH and SH SSWs in the following sections.

Fig. 1

The top panels present the daily zonal-mean temperature (K) averaged between 70$^\circ$N and 80$^\circ$N as a function of pressure levels from SD-WACCM-X simulations for (a) 2006, (b) 2009, (c) 2010 and (d) 2013 NH SSWs. The bottom panels present the SD-WACCM-X simulated daily zonal-mean zonal winds (m/s) at 60$^\circ$N as a function of pressure levels for the above-mentioned SSWs in e–h. The black dashed lines mark the day of polar vortex weakening (PVW) for the corresponding SSWs

Results

Zonal-mean variability

NH SSWs

Figure 1 presents an overview of dynamical conditions of the Arctic polar atmosphere using the temperature and wind outputs from SD-WACCM-X simulations during the 2006, 2009, 2010 and 2013 major NH SSWs. The top panels in Fig. 1 present the pressure-time plots of the zonal-mean temperature averaged between 70 and 80$^\circ$N for all these four major warming events (Fig. 1a–d). The black dashed lines in the figure mark the day of polar vortex weakening (PVW), which is a definition used for identifying the peak phase of SSW. As an alternative to the classical SSW definition, PVW has been used in recent studies to correlate the tidal enhancements in the MLT and ionosphere with the magnitude of the reversal of stratospheric zonal-mean zonal wind (e.g., Zhang and Forbes 2014; Chau et al. 2015; Siddiqui et al. 2015). The list of SSWs and their respective PVW dates are indicated in Table 1.

Table 1 List of NH and SH SSWs (year of occurrence) and their respective PVW (dd/mm) dates

The evolution of the stratopause during these SSWs bears a resemblance to each other with the most notable common feature being the rapid descent of the stratopause from its climatological position ($\sim$ 0.1 hPa) during the SSW onset. The descent of the stratopause begins around day -5 for the 2006 SSW, day 18 for the 2009 SSW, day 15 for the 2010 SSW and day 0 for the 2013 SSW. Among these four SSWs, the stratopause is seen to drop deepest during the 2009 SSW and the least during the 2010 SSW. During these four major SSWs, the stratopause descent is accompanied by its warming and followed by its breakdown and reemergence at a higher altitude. The rapid drop in the stratopause altitude leads to warming in lower altitudes, which happens before the stratopause breaks down in the peak phase of the SSWs (black dashed lines). Around this same time, another common feature seen in all four SSWs is cooling above 0.1 hPa in the mesosphere, which is known to accompany warming in the stratosphere (e.g., Zülicke et al. 2018). The breakdown in stratopause results in the formation of a nearly isothermal stratosphere as seen around day 30 for the 2006 SSW, day 35 for the 2009 SSW, day 40 for the 2010 SSW and day 20 for the 2013 SSW. Later, the stratopause is seen to reform with cooler temperatures and reappear as a well-defined structure in the recovery phase of each of the SSWs at an elevated altitude near 0.01 hPa (e.g., Siskind et al. 2007; Manney et al. 2009). The reformation of the stratopause at a higher altitude is referred to as elevated stratopause event and is attributed to mesospheric PW activity and non-orographic gravity wave (GW) drag after the SSWs (e.g., Chandran et al. 2011; Limpasuvan et al. 2012).

The bottom panels in Fig. 1 (Fig. 1e–h) present the daily zonal-mean zonal winds at 60$^\circ$N as a function of pressure levels from SD-WACCM-X simulations of the above-mentioned SSWs. Like zonal-mean temperature, we also observe a common feature in zonal-mean zonal winds during these SSWs, which happens to be the early appearance of westward ZMZW in the mesosphere that later descends through the stratosphere and eventually reaches the upper troposphere. The mesospheric wind reversals precede those in the stratosphere and are associated with the filtering of upward propagating GWs during SSWs (e.g., Hoffmann et al. 2002, 2007). The SSW-associated disturbance in stratospheric zonal winds changes the filtering conditions for upward propagating GWs, which results in only eastward propagating GWs reaching up to the mesosphere. As a result of this change in mesospheric forcing due to altered GW fluxes, a net eastward GW anomaly is introduced, which leads to upwelling and cooling in the polar mesosphere (e.g., Holton 1983).

From Fig. 1, we note that SD-WACCM-X simulations reproduce the temperature and wind structures of the SSWs in a consistent manner. The SD-WACCM-X simulated zonal-mean temperatures have been compared with Aura Microwave Limb Sounder (MLS) and SABER temperature observations during SSWs in earlier studies (e.g., Pedatella et al. 2014a, b) and a good agreement between observations and simulations have already been reported. A comparison between the simulated and observed zonal-mean temperatures have therefore not been presented in this study.

SH SSWs

Figure 2 gives an overview of dynamics of the Antarctic polar atmosphere during the 2002 and 2019 SH SSWs through the vertical time sections of the simulated zonal mean temperature averaged between 70 and 80$^\circ$S and zonal-mean zonal winds at 60$^\circ$S. The black dashed lines mark the days of PVW during the respective SSWs. In Fig. 2a, the descent of the stratopause during the 2002 SSW can be witnessed as it drops from a mean altitude of $\sim$48 km (1 hPa) around day 20 to $\sim$32 km (10 hPa) around day 26, which leads to warming in the lower stratosphere. Around this same period, the cooling of the mesosphere can also be seen above 0.1 hPa. From Fig. 2c, we notice that the westward ZMZW begin appearing in the mesosphere (above 0.1 hPa) since the beginning of September but the reversal of the mesospheric ZMZW remains transient and does not descend into the stratosphere until around day 22. Thereafter, the westward ZMZW descend from the mesosphere and eventually reach below 10 hPa level by day 24. In case of the 2019 SSW event, we see the descent and warming of stratopause between days 0 and 20 in Fig. 2b. The intensity of warming in the lower stratosphere ($\sim$10 hPa) is found to be stronger for this event in comparison to the 2002 SSW, which was also confirmed in an earlier study by Yamazaki et al. (2020). It is to be noted that unlike the four NH SSWs that we have studied, there is no development of elevated stratopause during the 2002 and 2019 SH SSWs. The readers may also note that not all SSWs in the NH display development of elevated stratopause. From Fig. 2d, the appearance of westward ZMZW in the mesosphere is seen around day 2 and it subsequently descends a week later into the stratosphere. Unlike the 2002 SSW, the westward ZMZW during the 2019 SSW do not reach down to the 10 hPa level so this event is classified as a minor warming.

Fig. 2

The top panels present the daily zonal-mean temperature (K) averaged between 70$^\circ$S and 80$^\circ$S as a function of pressure levels from SD-WACCM-X simulations for (a) 2002 and (b) 2019 SH SSWs. The bottom panels present the SD-WACCM-X simulated daily zonal-mean zonal winds at 60$^\circ$S as a function of pressure levels for both SSWs in c, d. The black dashed lines mark the day of polar vortex weakening (PVW) for the corresponding SSWs

MLT DW1 tidal variability

NH SSWs

Figure 3 shows the temporal evolution of DW1 tidal amplitude obtained from SABER temperature observations (upper panels) and SD-WACCM-X simulations (lower panels) at 90 km altitude during the 2006, 2009, 2010 and 2013 NH SSWs. The black dashed lines mark the corresponding PVW days for each SSW event. For all four periods shown in Fig. 3, the DW1 tide exhibits its well-known features with largest amplitude in temperature at low-latitudes along with an enhancement in its amplitude towards the end of February, which is part of its semi-annual variation in the MLT (e.g., Hays and Wu 1994; Vincent et al. 1998; Gan et al. 2014). We note that simulations are able to reproduce these aspects of temporal evolution of DW1 tide with great consistency for all the shown SSW periods but with reduced amplitudes. The underestimation of DW1 amplitude in WACCM-X simulations in the MLT as compared to that of in SABER temperature observations has been reported in many studies (e.g., Lu et al. 2012; Liu et al. 2018, 2021). The underestimation of simulated DW1 probably results due to an underestimation of the diurnal cycle in parameterized convection processes in WACCM-X (Lu et al. 2012). In Fig. 3, the DW1 tidal amplitudes also show a pronounced minimum associated with SSWs at low-latitudes, which is clearly seen in observations and reproduced in simulations. For the 2006 SSW event, the decline in DW1 can be seen between days 10 and 20 in the latitude range 0–15$^\circ$N in Fig. 3a. The DW1 tidal amplitude declines from a peak of $\sim$11 K around day 0 to a minimum of $\sim$9.5 K by day 14 before enhancing back to a maximum of $\sim$16 K by day 40 in Fig. 3a. The simulated DW1 tide for the 2006 SSW shows similar characteristics in Fig. 3e as in Fig. 3a with a decline of $\sim$1 K between 0 and 10$^\circ$N around day 10 and an enhancement beginning around day 30 following the peak of the SSW. During the 2009 SSW event, the DW1 tidal amplitude in Fig. 3b shows similar features as during the 2006 SSW with a marked decline around day 10 just prior to the SSW peak that lies between periods of DW1 enhancements. The DW1 amplitude declines from a peak value of $\sim$13 K around day 0 between 0-10$^\circ$N to $\sim$11 K around day 13 before enhancing back to $\sim$13 K levels by day 30. The simulated DW1 tide in Fig. 3f captures this observed DW1 tidal behavior in Fig. 3b with a decline of $\sim$1 K also seen around day 10 in the 0–10$^\circ$N latitude band in comparison to its peak value of $\sim$6 K around day 0. Following the SSW peak, the DW1 tidal amplitude in Fig. 3f enhances and reaches up to $\sim$10 K levels around day 40.

For the 2010 and 2013 SSWs as well, we witness similar DW1 tidal weakening around the PVW days in Fig.es 3c and 3d, respectively. For these two events, the DW1 tide also shows enhancement prior to and after the SSW peaks at low-latitudes. In case of 2010 SSW, the decline in DW1 tidal amplitude of $\sim$2 K is seen at low-latitudes between days 30 and 40 in Fig. 3c, whereas in case of 2013 SSW, the decline in DW1 amplitude of $\sim$3 K is recorded after the PVW day. The simulated DW1 tidal amplitudes in Fig. 3g and 3h reproduce the observed variability in DW1 tides during the 2010 and 2013 SSWs to a good extent and we notice a decline of $\sim$1 K and $\sim$2 K, respectively, in simulated DW1 tide during both these SSWs. The enhancements of DW1 tide prior to the PVW days and towards the end of February during 2010 and 2013 SSWs are also reproduced in simulations in Fig. 3g and h, albeit with lower amplitudes. From Fig. 3, we also find that the DW1 tide during these four SSWs displays similar amplitudes and any possible influence of solar flux levels is not clearly discernible.

Fig. 3

Daily amplitudes of DW1 tide (K) in SABER temperature observations and SD-WACCM-X simulations at 90 km altitude are presented during (a, e) 2006, (b, f) 2009, (c, g) 2010, (d, h) 2013 NH SSWs in the top and bottom panels, respectively. Note the difference in scale of the colorbars in the upper and lower panels

Fig. 4

Same as Fig. 3 except for (a, c) 2002 and (b, d) 2019 SH SSWs

Fig. 5

Daily amplitudes of DW1 tide (K) in SABER temperature observations are presented in upper panels for (a) 2010/2011 and (b) 2015/2016 NH non-SSW winters. In the lower panels, the DW1 tidal amplitudes (K) are presented for (c) 2006 and (d) 2009 SH non-SSW winters

SH SSWs

Figure 4 presents the temporal variability of DW1 tide at 90 km altitude during the 2002 and 2019 SH SSWs from SABER temperature observations (upper panels) and SD-WACCM-X simulations (lower panels). The black dashed lines mark the PVW days for both SSWs. For both these SH SSWs, the latitude-time structure of DW1 in SABER and SD-WACCM-X are found to be consistent with each other especially at low-latitudes. However, the amplitude of DW1 at the shown altitude is relatively lower ($\sim$50%) in simulations as compared to observations and the plausible reason for this underestimation of DW1 in SD-WACCM-X simulations has been discussed earlier in Section 2.1. For the 2002 SSW, the DW1 tide in SABER observations (Fig. 4a) is found to show enhancement centered around day 10 with peak amplitude reaching $\sim$13 K between 20$^\circ$S and 5$^\circ$N followed by a weakening of $\sim$2 K just prior to SSW onset between days 15 and 20. The DW1 tide enhances back to above 13 K levels post day 22 at low-latitudes and continues to gradually increase in October. The simulated DW1 tide for the 2002 SSW in Fig. 4c shows similar variability as in observations with peak enhancement reaching $\sim$8 K centered around day 10 at low-latitudes, which is followed by a weakening of $\sim$3 K between days 18 and 26 and a further enhancement in the beginning of October. For the 2019 SSW, the evolution of DW1 tide in SABER observations in Fig. 4b shows similar features as during the 2002 SSW with a prominent weakening in amplitude at low-latitudes close to the PVW day. In Fig. 4b, the DW1 amplitude declines from a peak amplitude of $\sim$14 K between 0 and 20$^\circ$S around day -10 to $\sim$9 K between days 10 and 20 and later gradually enhances at the beginning of October. For the 2019 SSW, the simulated DW1 tide in Fig. 4d reproduces the observed variability in Fig. 4b. A notable decline centered around day 10 is seen in the DW1 tide in Fig. 4d. The DW1 tidal amplitude in this figure declines from $\sim$6 K around day -5 to $\sim$3 K around day 10 before enhancing back to above $\sim$6 K levels in October.

From Figs. 3 and 4, we can note that the evolution of DW1 tide during NH and SH SSWs resemble each other, which is marked by a decline of DW1 tide around the PVW days. In the next section, we discuss the mechanism that could be responsible for this variability of DW1 tide during both NH and SH SSWs.

DW1 tidal variability during non-SSW NH & SH winters

The DW1 tidal variability during NH and SH SSWs were shown in Figs. 3 and 4, respectively. As a reference, we present the temporal evolution of DW1 tidal amplitudes during NH and SH non-SSW winters in Fig. 5. We select the 2010/2011 and 2015/2016 NH winters as both these periods were associated with strong stratospheric Arctic polar vortex and low PW activity (e.g., Hurwitz et al. 2011; Matthias et al. 2016). Similarly for SH winters, we choose the period between August and October in 2006 and 2009, as the Antarctic polar vortex was found to remain notably strong in these years (e.g., Zuev and Savelieva 2019). The DW1 tidal amplitude from SABER temperature observations during 2010/2011 and 2015/2016 NH winters are shown in upper panels in Fig. 5a and b, respectively. For both these periods, we notice that the DW1 tide has larger amplitudes at low-latitudes in February than in January, which is consistent with its seasonal variations. In Fig. 5a, the DW1 amplitude during the 2010/2011 NH winter remains around 12 K between 10$^\circ$N–10$^\circ$S in January and enhances to $\sim$20 K in February. During the 2015/2016 NH winter, the DW1 amplitude at low-latitudes in Fig. 5b enhances from $\sim$7 K in January to $\sim$10 K by mid-February and to $\sim$ 20 K towards the end of February. Unlike the DW1 tidal variability during NH SSWs in Fig. 3, we find no evidence of sharp decline in DW1 amplitudes at low-latitudes during both 2010/2011 and 2015/2016 NH winters. In the lower panels, the DW1 tidal amplitude from SABER temperature observations during 2006 and 2009 SH winters are shown in Fig. 5c and d, respectively. During both these periods, we find that the DW1 tide at low-latitudes peaks during the month of September with amplitudes reaching $\sim$15 K. During these periods as well, we do not find any sharp reduction in the DW1 tidal variability as we observed during the SH SSWs in Fig. 4. On comparing the DW1 tidal variability during non-SSW winters with those during SSW winters, we find that the short-term decline of DW1 tide in the MLT is a common feature associated with both NH and SH SSWs.

Fig. 6

The left y-axes in this figure show the temporal evolution of $R_{e}$ (black solid lines) during (a) 2006, (b) 2009, (c) 2010 and (d) 2013 NH SSWs while the right y-axes show the mean DW1 tidal amplitudes from SABER (purple dashed-dotted lines) and SD-WACCM-X (brown dashed lines) that are averaged between 30 S and 30 N at 90 km altitude. For comparison, the mean DW1 tidal amplitudes from SD-WACCM-X are scaled up by a factor of 2. The blue dotted lines show the climatological values of $R_{e}$ (clim_$R_{e}$) and the red dotted lines mark the standard deviation associated with clim_$R_{e}$ at ±2$\sigma$ levels

Fig. 7

Same as Fig. 6 except for (a) 2002 and (b) 2019 SH SSWs

Discussion

Following the numerical work of McLandress (2002), it is now known that the DW1 tide at MLT altitudes is sensitive to changes in latitudinal shear of the zonal-mean zonal winds in the MLT region. Due to the large phase speed of the DW1 tide ($c\sim 400$ m/s at the equator), the effect of changes in the zonal-mean zonal winds on the propagation of the DW1 tide seems unlikely. However, DW1 tide has been found to be strongly sensitive to the latitudinal shear in zonal-mean zonal wind in the MLT region and this shear effect is primarily responsible for its well-known semiannual variation, which is characterized by strong equinoctial and weak solsticial amplitudes (e.g., Hays and Wu 1994; Vincent et al. 1998). The latitudinal shear in the zonal-mean zonal winds introduces a zonal-mean vorticity (${\overline{\zeta }}$), which at low-latitudes can be large enough to be comparable to the Coriolis parameter (f). It is found that ${\overline{\zeta }}$ could affect the DW1 tide indirectly by changing the absolute zonal-mean vorticity ($\eta =f+{\overline{\zeta }}$) of the background atmosphere. This is qualitatively somewhat analogous to an enhancement or reduction of the Earth’s rotation rate, which ultimately determines the width of the latitudinal band or waveguide where the DW1 tide vertically propagates. According to the classical tidal theory, the waveguide for the DW1 tide is restricted near the equator and extends from 30$^\circ$N to 30$^\circ$S (Lindzen and Chapman 1969). Positive values of ${\overline{\zeta }}$ at some altitude result in a faster rotation rate ($\eta >f$), which narrows the waveguide for the vertically propagating DW1 tide while negative values of ${\overline{\zeta }}$ imply a slower rotation rate ($\eta <f$), which will result in broadening of this waveguide. This in turn will lead to reduction of DW1 tidal amplitude above this altitude in case of the former and an enhancement of DW1 tidal amplitude in case of the latter. Using a numerical model, McLandress (2002) applied this theory to show that the seasonal variation of latitudinal shear in the westward mesospheric ZMZW in the subtropics explains the observed semiannual variation of DW1 in the MLT. We suspect that this mechanism, which explains the variability of DW1 tide on seasonal time scales could also be used to explain the variability of DW1 tide on subseasonal time scales during NH and SH SSWs.

We calculate the ratio of absolute ($\eta$) and planetary vorticity (f) and define it as follows:

$$\begin{aligned} R=\frac{\eta }{f}=\frac{f+{\overline{\zeta }}}{f}=\frac{f-{\overline{u}}_y}{f} \end{aligned}$$

(2)

where, $f=2\Omega \>sin(\phi )$, $\Omega$ is the Earth’s rotation rate and $\phi$ is the latitude in degrees. On calculating and neglecting the zonal gradient, the zonal-mean vorticity (${\overline{\zeta }}$) simplifies to ${\overline{u}}_y$, which is the meridional gradient (y-direction) of the zonal-mean zonal wind (u).

In the NH, a negative meridional shear (${\overline{u}}_y<0$) will increase R, which will lead to narrowing of the waveguide and reduced DW1 amplitudes while a positive meridional shear (${\overline{u}}_y>0$) will reduce R, thus leading to broadening of the waveguide and enhanced DW1 amplitudes in the MLT. Numerical results of McLandress (2002) showed that R varies with maximum values near the solstices ($R\sim 1.5-2$) to minimum values near the equinoxes ($R\sim 0.6-0.8$). We calculate daily mean values of vorticity ratio, R, between 30$^\circ$S–30$^\circ$N (excluding the equator), which is then further averaged between 70 and 90 km altitude to obtain an effective R, which is henceforth referred to as $R_{e}$. This approach is similar to the one used by Sassi et al. (2013) to explain the DW1 tidal variability during the 2009 SSW.

In Fig. 6, we present the temporal evolution of $R_{e}$ and compare it with SABER and SD-WACCM-X mean DW1 tidal amplitudes at 90 km altitude that are averaged between 30$^\circ$S–30$^\circ$N during the (a) 2006, (b) 2009, (c) 2010 and (d) 2013 NH SSWs. The black solid line shows the $R_{e}$ for respective SSW intervals while the blue dotted line shows the climatological values of $R_{e}$ (clim_$R_{e}$), which are obtained from a 20-year long SD-WACCM-X run performed for the period 2001-2020. The standard deviation ($\sigma$) associated with clim_$R_{e}$ are also plotted in Fig. 6 in red dashed lines at ±2$\sigma$ levels. The SABER and SD-WACCM-X mean DW1 tidal amplitudes are plotted on the right y-axes in purple dashed-dotted lines and brown dashed lines, respectively, for each of the SSWs. The SD-WACCM-X mean DW1 tidal amplitudes are scaled up by a factor of 2 for plotting it within the same ordinate limits. For the 2006 SSW, it is seen in Fig. 6a that the $R_{e}$ values initially lie below the − 2$\sigma$ levels between days − 10 and 0 before enhancing and reaching climatological levels by day 10. Later $R_{e}$ declines slightly just before the peak phase of the 2006 SSW and then increases gradually up to day 30. A sharp decline in $R_{e}$ is seen after this day, which results in its values again being lower than the -2$\sigma$ levels between days 40 and 50. Thereafter, $R_{e}$ increases back to its climatological levels towards the end of February. Between days 0 and 20, the temporal variability of the SABER and SD-WACCM-X mean DW1 tidal amplitudes demonstrate a decline with increase in $R_{e}$. After day 30, when $R_{e}$ begins to decline steadily, the amplitude of both observed and modeled mean DW1 tides respond in an opposite manner and increase during this period. For the 2009 SSW, in Fig. 6b, we see a similar variability in $R_{e}$ as during the 2006 SSW with $R_{e}$ values being initially lower than − 2$\sigma$ levels between days − 4 and 10 before rising sharply and reaching above the + 2$\sigma$ levels around the peak day of the SSW. The $R_{e}$ values decline sharply again after day 20 and reach below − 2$\sigma$ levels between days 30 and 40 before increasing gradually and reaching back to climatological levels. During the sharp increase in $R_{e}$, the SABER and SD-WACCM-X mean DW1 tidal amplitudes reach their minimum between days 10 and 20 before increasing sharply just after the peak SSW phase, which coincide with the decline in $R_{e}$. Towards the end of February, the observed and modeled mean DW1 amplitudes follow their seasonal behavior and continue to increase with decreasing $R_{e}$. In case of the 2010 SSW, the $R_{e}$ values in Fig. 6c decline from their climatological levels around day − 10 to lower than − 2$\sigma$ levels between days 0 and 20 before sharply increasing during the peak SSW phase to higher than 2$\sigma$ levels around day 35. Another steady decline in $R_{e}$ follows and results in values reaching close to − 2$\sigma$ levels around day 55. From the SABER and SD-WACCM-X mean DW1 tidal amplitudes, we find an increase between days − 10 and 20 that coincide with the decrease in $R_{e}$ and a decline between days 21 and 40, which coincide with the rapid increase in $R_{e}$ during the peak SSW phase. After day 40, both observed and and modeled mean DW1 tidal amplitudes enhance with the continued decline in $R_{e}$. In Fig. 6d, the evolution of $R_{e}$ during the 2013 SSW is similar in characteristics to the three earlier discussed major NH SSWs. Around day − 10, the $R_{e}$ values are initially below the − 2$\sigma$ levels but increase steadily thereafter and reach values greater than 2$\sigma$ levels around day 20 after the peak SSW phase. A sharp decline in $R_{e}$ ensues after day 20 with its values again declining below the − 2$\sigma$ level around day 50 before recovering subsequently towards the end of February. To a large extent, the evolution of SABER and SD-WACCM-X mean DW1 tidal amplitudes during the 2013 SSW is also opposite to $R_{e}$ as enhancement in mean DW1 amplitude is seen with declining $R_{e}$ and a reduction with increase in $R_{e}$. As seen during earlier SSWs, the apparent decline in both observed and modeled mean DW1 tidal amplitudes during the 2013 SSW is coinciding with the increase in $R_{e}$ and its rapid enhancement is coinciding with the decrease in $R_{e}$. The readers may note that $R_{e}$ values during SSWs may reach their peaks earlier (as seen during 2006 and 2009 NH SSW) or later (as seen during 2010 and 2013 NH SSW) than the PVW date since the PVW date is only representative of the peak phase of the SSW and not of the dynamics in the MLT. It is understandable that the SSW-associated changes in the MLT zonal winds and subsequently in $R_{e}$ may vary in timing with the SSW-associated changes in the stratosphere, which is why we see the decline in DW1 tide to vary with respect to the PVW dates for different SSWs. For all the four NH SSWs, we also find that the variability of SABER and scaled-up SD-WACCM-X mean DW1 tidal amplitudes are consistent with each other.

As in Fig. 6, we present the temporal evolution of $R_{e}$ in Fig. 7 during the (a) 2002 and (b) 2019 SH SSWs and compare it with the SABER and SD-WACCM-X mean DW1 tidal amplitudes that are averaged between 30$^\circ$S–30$^\circ$N at 90 km altitude. The SD-WACCM-X mean DW1 tidal amplitudes presented in this figure are also scaled up by a factor of 2. In Fig. 7, we note that the climatological levels of $R_{e}$ are lower than in Fig. 6, which is expected as DW1 tides have larger amplitudes near the equinoxes due to lower $R_{e}$ values as opposed to the solstice periods when the $R_{e}$ values are comparably larger (e.g., McLandress 2002). In Fig. 7a, the $R_{e}$ values during the 2002 SSW are seen to decline from above climatological levels around day − 10 to below − 2$\sigma$ levels between days 0 and 10, which coincides with the increase in mean DW1 tidal amplitude during this time interval. A return back to climatological levels is witnessed in $R_{e}$ by day 20, which is followed by another decline that bottoms out around day 30. During this period, the SABER and SD-WACCM-X mean DW1 tidal amplitudes react in a contrary manner to $R_{e}$ as their decline coincide with increasing $R_{e}$ and vice-versa. By day 40, the $R_{e}$ values decline to climatological levels where they remain till the end of October. During this interval, as $R_{e}$ follows the declining climatological trend, an increase in the amplitude of SABER and SD-WACCM-X mean DW1 tides can be seen. In Fig. 6b, the $R_{e}$ values initially lie slightly below − 2$\sigma$ levels around day − 10 before steadily increasing to more than 2$\sigma$ level around day 15. Associated with this increase in $R_{e}$, rapid decline in SABER and SD-WACCM-X mean DW1 tidal amplitudes can be seen. Subsequently, $R_{e}$ levels decline sharply after this day and reach close to − 2$\sigma$ levels around day 35. Both the observed and modeled mean DW1 tidal amplitudes react in an opposite manner to this decline in $R_{e}$ and increase rapidly. Another episode of increase in $R_{e}$ is seen beginning around day 40, which coincide with the decline of SABER and SD-WACCM-X mean DW1 tidal amplitudes between days 40 and 50. Towards the end of October, as the $R_{e}$ values decline back to climatological levels, a gradual increase in both observed and modeled mean DW1 tidal amplitudes is seen during this time interval. From Figs. 6 and 7, we conclude that the temporal evolution of $R_{e}$ in the upper mesosphere, to a great extent, is opposite to the variability of the DW1 tidal amplitudes during both NH and SH SSWs. We calculate the Pearson’s correlation coefficients between $R_{e}$ and SABER and SD-WACCM-X mean DW1 tidal amplitudes shown in Figs. 6 and 7 and present them in Table 2. We note that both the observed and modeled mean DW1 tidal amplitudes demonstrate an anti-correlation with $R_{e}$, which is stronger for NH SSWs as compared to SH SSWs. The correlation coefficients between SD-WACCM-X mean DW1 tidal amplitudes and $R_{e}$ are only slightly higher than between SABER mean DW1 tidal amplitudes and $R_{e}$, which suggests that modeling results are consistent with observations and do not differ significantly.

Table 2 Pearson’s correlation coefficient (r) between $R_{e}$ and mean DW1 tidal amplitudes from SABER and SD-WACCM-X for the listed NH and SH SSWs

The anti-correlation between DW1 tidal amplitudes and SSW-associated low-latitude changes in MLT zonal-mean vorticity as implied by our results is plausible since there are numerous reports demonstrating significant changes in low-latitude MLT winds during SSWs ( e.g., Shepherd et al. 2007; Sathishkumar et al. 2009; Chen et al. 2012). In a case-study of the tropical MLT zonal wind changes during a minor NH SSW in February 1993, Shepherd et al. (2007) reported rapid deceleration and reversal of climatologically eastward zonal winds between 70 and 85 km using medium-frequency (MF) radar measurements from Tirunelveli (8.7$^\circ$N, 77.8$^\circ$E). During this event, the eastward zonal winds reversed to westward by declining from $\sim$ 40 m/s to $\sim$ −5 m/s over a 3 weeks period at around 80 km altitude prior to the onset of February 1993 NH SSW (see Fig. 3, Shepherd et al. 2007). Using the MF radar data at Tirunelveli, Sathishkumar et al. (2009) analyzed the evolution of tropical MLT zonal winds around 80 km altitude during the major NH SSWs in December 1998 and January 2006 and found them to decelerate and reverse from eastward to westward direction during the course of these SSWs (see Fig. 5, Sathishkumar et al. 2009). In the sub-tropics, the deceleration and reversal of MLT zonal winds between 80 and 90 km altitude from eastward to westward direction was also reported by Chen et al. (2012) during the 2001 NH major SSW using radar measurements from Wuhan (30$^\circ$N, 114$^\circ$W). They found that at these altitudes, the absolute change in MLT zonal winds could reach up to $\sim$60 m/s as it decelerated and turned westward within a 10 days period during the course of 2001 NH major SSW. These studies indicate that the SSW-associated effects extend far beyond the polar middle atmosphere and substantial changes in MLT zonal winds can even be observed at low-latitudes. It is therefore plausible that SSW-associated changes in MLT zonal winds at low-latitudes lead to changes in zonal-mean vorticity, which result in the enhancement or reduction of DW1 tidal amplitudes. By means of a diagram, we summarize this suggested mechanism in Fig. 8, which helps us to explain the evolution of DW1 tide during NH and SH SSWs.

Fig. 8

A simple diagram to explain a plausible mechanism behind the observed DW1 tidal variability during SSWs

Conclusions

The variability of the MLT DW1 tide during NH and SH SSWs is reported in the present study using SABER temperature observations and SD-WACCM-X simulations. We focused this work on examining the evolution of DW1 tide during four major NH SSWs that occurred in January in 2006, 2009, 2010 and 2013 and two SH SSWs that took place in September in 2002 and 2019. In our analysis, we use a ‘tidal deconvolution’ approach to estimate the DW1 tide in MLT region from SABER temperature observations. Results show that the observed DW1 tide displays reduced amplitude at low-latitudes after the onset of both NH and SH SSWs. To explain these results, we explore whether the SSW-associated changes at low-latitudes in latitudinal shear of MLT zonal winds, which strongly affects the seasonal variation of MLT DW1 tide, could be a reason for the decline of DW1 amplitudes during both NH and SH SSWs. Using SD-WACCM-X, we find that SSW-associated intraseasonal changes in the latitudinal shear of MLT zonal winds are comparable to the changes that happen on seasonal scales in the latitudinal shear of MLT zonal winds. We suggest that this latitudinal shear mechanism explains the observed decline of DW1 tide that is common to both NH and SH SSWs.