Formation of a Mesospheric Inversion Layer and the Subsequent Elevated Stratopause Associated With the Major Stratospheric Sudden Warming in 2018/19

Since 2004, following prolonged stratospheric sudden warming (SSW) events, it has been observed that the stratopause disappeared and reformed at a higher altitude, forming an elevated stratopause (ES). The relative roles of atmospheric waves in the mechanism of ES formation are still not fully understood. We performed a hindcast of the 2018/19 SSW event using a gravity‐wave (GW) permitting general circulation model that resolves the mesosphere and lower thermosphere (MLT) and analyzed dynamical phenomena throughout the entire middle atmosphere. An ES formed after the major warming on January 1, 2019. There was a marked temperature maximum in the polar upper mesosphere around December 28, 2018 prior to the disappearance of the descending stratopause associated with the SSW. This temperature structure is referred to as a mesospheric inversion layer (MIL). We show that adiabatic heating from the residual circulation driven by GW forcing (GWF) causes barotropic and/or baroclinic instability before the MIL formation, causing in situ generation of planetary waves (PWs). These PWs propagate into the MLT and exert negative (westward) forcing, which contributes to the MIL formation. Both GWF and PW forcing (PWF) above the recovered eastward jet play crucial roles in ES formation. The altitude of the recovered eastward jet, which regulates GWF and PWF height, is likely affected by the MIL structure. Simple vertical propagation from the lower atmosphere is insufficient to explain the presence of the GWs observed in this event.


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The stratopause descends during SSWs (e.g., Labitzke, 1981). After the onset of the SSWs of 2004SSWs of , 2006SSWs of , 2009SSWs of , 2012SSWs of , 2013SSWs of , 2018SSWs of , and 2019, the lowered stratopause became indistinct and then reformed at an altitude above its climatological height. This phenomenon is called an elevated stratopause (ES) (e.g., Manney et al., 2008Manney et al., , 2009Siskind et al., 2010). Several previous observational and numerical studies showed that gravity wave (GW) forcing (GWF) induces the formation and descent of the ES (e.g., Siskind et al., 2007Siskind et al., , 2010Thurairajah et al., 2014;Tomikawa et al., 2012). Thurairajah et al. (2014) provided observational evidence of the enhancement of GW activity after SSWs using global high-latitude temperature measurements from the Solar Occultation for Ice Experiment (SOFIE). Using a GW-permitting general circulation model (GCM) of the KANTO project (Watanabe et al., 2008), Tomikawa et al. (2012) analyzed a simulated major SSW event. They showed that positive PW forcing (PWF) leads to the quick recovery of the polar eastward jet after the major SSW (Orsolini et al., 2017), and negative GWF above the recovered jet contributes to the formation of the ES.
The crucial role of PWs in the initial phase of ES formation has also been suggested (e.g., Chandran et al., 2011Chandran et al., , 2013Limpasuvan et al., 2012Limpasuvan et al., , 2016. Limpasuvan et al. (2016) conducted a composite analysis of 13 SSW-ES events identified in the runs of the Whole Atmosphere Community Climate Model, Version 4 with specified dynamics (SD-WACCM) for 1990-2013. They showed that downward flow induced by negative PWF in the polar mesosphere and lower thermosphere (MLT) is responsible for ES formation. Several observational studies have pointed out that the amplitudes of PWs with zonal wavenumber E s = 1-2 increase in the MLT when an ES event occurs (e.g., Stray et al., 2015). However, it has also been indicated that PWF in the MLT is not necessarily strong during ES formation. Chandran et al. (2013) showed that in a few events in model simulations, the entire process of ES formation appears to be driven by GWF despite the climatological importance of PWF. The relative contributions of GWs and PWs to ES formation remain to be elucidated.
The ES phenomenon, which is accompanied by downwelling in the MLT, strongly influences downward material transport and thus the coupling between the MLT and the stratosphere (e.g., Randall et al., 2009). For example, NOx (=NO + NO 2 ) produced by energetic particle precipitation (EPP) in the MLT is transported into the stratosphere, especially during ES events that occur in early winter. In the region under the influence of the polar night, NOx is long-lived and causes ozone depletion in the stratosphere (e.g., Holt et al., 2013;Randall et al., 2009). This effect, referred to as the EPP indirect effect, is very important in chemistry-climate models because it affects the dynamics of the stratosphere (e.g., Siskind et al., 2015). Smith et al. (2018) also pointed out that the enhanced downward flow associated with ES events results in a downward shift in the maximum altitude of ozone concentrations.
However, most high-top models tend to underestimate downward material transport in the MLT during ES events (e.g., Orsolini et al., 2017;Randall et al., 2015). In addition, ES height is generally lower in the model than in observational data. These model biases are the results of the underestimation (overestimation) of downward motion in the upper (lower) mesosphere (e.g., Funke et al., 2017). Meraner et al. (2016) showed that the intensity of the parameterized nonorographic GW sources affects the height of GWF in the MLT. The modulation of the height of GWF can affect the amount of downward material transport. They reported that weaker GW sources in the parameterization yield a better agreement of simulations with observations.
To elucidate the relative importance of PWs and GWs in dynamical variation in the middle atmosphere associated with an SSW, the in situ generation of waves should be taken into consideration. Several studies showed that strong PW breaking causes the barotropic (BT) and/or baroclinic (BC) instability, which excites PWs (e.g., Baldwin & Holton, 1988;Greer et al., 2013;Hitchman & Huesmann, 2007). Smith (1996Smith ( , 2003 and Lieberman et al. (2013) suggested that momentum deposition by the GWs that have been filtered by planetary-scale wind structures in the stratosphere lead to in situ generation of PWs in the middle and upper mesosphere. On the basis of a case study of a boreal winter using the KANTO model, Sato and Nomoto (2015) suggested the importance of the interplay of GWs and PWs in the middle atmosphere. They provided evidence of in situ PW generation due to the BT/BC instability resulting from the generation of a potential vorticity (PV) maximum attributed to GWF. Positive and negative PWFs associated with the PW generation act to eliminate this PV maximum. Using the KANTO model,  showed that in the Antarctic winter mesosphere eastward 4-day waves are generated by the BT/BC instability which develops in the large-scale mean flow strongly distorted by GWF. Sato  showed that the BT/BC instability and shear instability caused by GWs originating from the lower atmosphere generate PWs and GWs in the mesosphere, respectively.
Most high-top GCMs include GW parameterizations. In general, GW parameterization schemes assume that GWs originate only from the lower atmosphere. In situ generation of GWs in the middle atmosphere is ignored in these parameterizations. Recently, Vadas and Becker (2018) suggested that momentum deposition associated with the breaking of orographic GWs generates secondary GWs in the stratosphere and lower mesosphere in the southern polar region in winter. In addition, most standard GW parameterizations also assume that GWs propagate only vertically. However, using the KANTO model, Sato et al. (2009Sato et al. ( , 2012 showed evidence of lateral propagation of GWs and provided theoretical explanations of the mechanisms involved. Conducting ray-tracing simulations, Yamashita et al. (2013) also suggested that high GW activity in the MLT during ES events observed by the Sounding of the Atmosphere using Broadband Emission Radiometry (SABER) on the Thermosphere, Ionosphere, Mesosphere Energetics Dynamics (TIMED) satellite is caused by poleward propagating GWs (Thurairajah et al., 2020). To understand the middle atmosphere dynamics in which behavior of the GWs is one of the key processes, state-of-the-art GW-permitting GCMs provide an effective approach.
In this study, we used a high-top and GW-permitting GCM to examine the SSW-ES event that occurred in January 2019. We focus on the relative roles of GWs and PWs to elucidate the mechanism of temperature variations in the middle atmosphere including the ES. Since GWs are explicitly resolved in the model, the in situ generation and lateral propagation of GWs are also simulated. The 2018/19 SSW event is classified as a mixture of displacement-type (s = 1) and split-type (s = 2) SSW (Rao et al., 2019). Three-dimensional analysis methods are applied wherever possible because zonal asymmetry is pronounced especially in the ES structures associated with displacement-type SSWs (Chandran et al., 2014;France & Harvey, 2013). The methods of analysis and details of the model used in this study are described in Section 2. In Section 3, the observed temperature variations associated with the SSW and their possible mechanisms are discussed. Section 4 focuses on the sources of PWs playing important roles in these mechanisms. Characteristics of both PWs and GWs observed in the middle atmosphere are shown in Section 5. Summary and concluding remarks are given in Section 6.

Methods and Model Description
In this study, we simulated the 2018/19 SSW event using the Japanese Atmospheric General circulation model for Upper Atmosphere Research (JAGUAR) (Watanabe & Miyahara, 2009). The model has 340 vertical layers from the surface to a geopotential height of approximately 150 km with a log-pressure height interval of 300 m throughout the middle atmosphere and a horizontal, triangularly truncated spectral resolution of T639 that has a minimum resolvable horizontal wavelength of ∼60 km (a latitudinal interval of 0.1875°). No parameterization for subgrid-scale GWs was used in this study.
It is considered that this model can resolve major part of GWs which can be inherently distributed over a wide horizontal wavelength range. Using continuous mesospheric wind observation data over 50 days from a mesosphere-stratosphere-troposphere radar called the PANSY radar at Syowa Station (69.0°S, 39.6°E), where PANSY stands for Program of the Antarctic Syowa MST/IS radar, Sato et al. (2017) showed that GW momentum fluxes are mainly associated with waves having long periods of several hours to a day at the southern high latitudes in summer. Using observational data from the PANSY radar, Shibuya et al. (2017) and Shibuya and Sato (2019) showed the GWs having such long periods are dominant also in the winter mesosphere and their horizontal wavelengths are greater than 1,000 km and vertical wavelengths of about 14 km. Ern et al. (2018) analyzed the satellite observation data and showed that dominant GWs in the middle atmosphere on average have horizontal wavelengths greater than 1,000 km and vertical wavelengths in excess of 10 km, although the observational filter problem remains. In the lower stratosphere, Sato (1994) showed that dominant inertia-GWs have horizontal wavelengths of 300-400 km based on 3-year observations by the MU radar (35°N, 136°E) in Japan. These dominant horizontal and vertical wavelengths are resolvable by the model used in the present study.
The KANTO model, which is a prototype of JAGUAR, is T213L256 GCM whose minimum resolvable horizontal wavelength is 180 km. Watanabe et al. (2008) showed that GW amplitudes simulated by the KANTO E z = ∼90 (∼90) km and the ES is at E z = ∼80 (80-85) km in the Aura MLS (SABER) data. Other temperature structures in the model results are generally consistent with the observation data as well.
Waves were divided into three components and analyzed separately: PWs having zonal wavenumber E s = 1-3, medium-scale waves (MSWs) having E s > 3 and total horizontal wavenumber E n < 21 and GWs having E n = 21-639. Figure 2 shows the time-height sections of EP flux divergence (EPFD) for respective wave components. The EPFD was smoothed with a lowpass filter with a cutoff of 1 day. During 23-31 December including the period when the MIL is present, GWF is strongly positive in the region of E z = 65-90 km. Around the time of the formation of the MIL, PWF is strongly negative OKUI ET AL.
10.1029/2021JD034681 6 of 22 This negative PWF is physically consistent with warming at the pole and MIL formation. Around 10 January when the ES is formed, GWF and PWF are negative above E z = 70 and 80 km, respectively, suggesting that both negative wave forcings are responsible for ES formation. The sources of PWs responsible for the formation of the MIL and subsequent ES are discussed in detail in Section 4. Because forcing by MSWs is always weak at any height or time, the following sections focus only on PWF and GWF.

Longitudinal Structure of the MIL and ES
As shown in previous studies (e.g., France & Harvey, 2013), the ES often has zonal asymmetry. To examine the longitudinal structure of the MIL and ES, the time-height sections at stations arranged along a latitude of 70°N at a fixed longitudinal interval of 45° are shown in Figure 3. The MIL is clearly observed at 15°W, 30°E, 75°E, 120°E, 165°E, and 150°W. The ES is observed at 75°E, 120°E, 165°E, 150°W, and 105°W.  Figures 4a and 4b, are located inside of the polar vortex. Thus, it is indicated that the MIL and ES are not an apparent phenomenon that is only seen in the zonal mean field associated with a shift of the polar vortex but is a real warming of the atmosphere inside of the polar vortex. Figure 5 shows the longitude-height sections at 70°N-80°N of temperature during the MIL and ES formation. The MIL appears in a thin layer at E z = ∼90 km in a longitude region of 100°E-180°-0° (Figure 5a), which is consistent with the SABER observation (Figure 5c). The ES is observed at E z = 75-85 km with slight dependence on the longitude (Figure 5d). This structure is consistent with the MLS and SABER (Figures 5e  and 5f). The temperature maximum of the ES is ∼250 K at E z = ∼80 km, 120°W. The longitude-height structure of PW propagation represented by 3D-flux-W and GWF   where † E denotes the GW components, during the MIL formation are shown in Figures 6a and 6b. Positive GWF is observed above the westward E u (red boxes in Figure 6b). The longitudinal distribution of GWF is consistent with the cold region at E z = 60-85 km (Figures 5a-5c) considering the downward control principle (Haynes et al., 1991). PWs propagating from the lower atmosphere are mostly attenuated below E z = 70 km. This is likely due to the nearly zero or westward E u     at E z = 40-80 km (the right panel in Figure 6a). According to the Charney and Drazin (1961) theorem, PWs cannot propagate upward in a westward wind. However, above E z = 75 km, strong upward PW propagation is observed at longitudes where the E T peak of the MIL is observed, which is denoted by cyan boxes in Figure 6a.   (Figure 8d). Generally, wave-induced residual mean vertical wind E w  is upward in the lower region on the poleward (equatorward) side of positive (negative) wave forcing (not shown, denoted by the lower arrow in Figure 8d). Above this region, downward E w  was observed (the upper arrow in Figure 8d). This 0 E w   seems due to tilted distribution of negative GWF which spread equatorward above this E w  < 0 region. These GWF and M E P     features suggest that the M E P     peak is a result of an increase in 2 E N due to the convergence of E w  at ∼40°N induced by GWF.  = ∼3,500 K becomes weak (Figure 8f). According to the quasi-geostrophic theory, a positive  EPFD is equivalent to a poleward PV flux, while a negative EPFD indicates an equatorward PV flux (e.g., Andrews et al., 1987). The observed PWF features suggest that the positive wave forcing is associated with the PW generation due to the BT/BC instability weakening the negative M y E P     , which is a necessary condition for the BT/BC instability. During this period, a M E P     peak becomes obvious from ∼50°N, E  = ∼5,500 K Figure 8f). It is slightly below the region with relatively high temperature, which is marked by the dashed line in Figure 8e. Thus, it is implied that this M E P OKUI ET AL.

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15 of 22 Section 3.2 (Figure 6c), PWs from the lower atmosphere hardly reach the MLT during 10-13 January. Thus, it is inferred that the in situ generated PWs contribute to the ES formation.
During 6-9 January, PWF is observed in the mesosphere despite the westward wind in the polar stratosphere. The longitude-height sections of 3D-flux-W 1 0 1 W E   F averaged over 60°N-70°N for 6-9 January are shown in Figure 11. The vectors represent the zonal and vertical components of the flux, the colors represent the vertical components of 1 0 1 W E   F and the contours represent the zonal wind averaged over 60°N-70°N at each longitude. The upward propagation of PWs occurs mainly in the region of 60°W-60°E, where the zonal wind has a westward-tilted structure at E z = 20-55 km. This structure is consistent with that of upward propagating PWs and similar situation was observed during the major SSW in February 2018 (e.g., Harada et al., 2019). Thus, the westward winds in this region can be regarded as part of the PWs. It is inferred that PWs propagate upward in the region of 60°W-60°E, even though E u     is westward.

Horizontal Structure
To examine the formation of the M E P     peak at ∼60°N, E  = 3,000-6,000 K ( E z = 60-80 km) during 6-9 January in terms of the horizontal structure, orthographic projection maps of M E P , GPH and 2 E N at E  = ∼4,000 K and 0.05 hPa ( E z = ∼70 km) are shown in Figure 12. In contrast to the results

Characteristics of PWs Generated in the Middle Atmosphere
To examine the PW periods, the longitude-time section of GPH deviation from zonal mean at 60°N-70°N, E z = 80 km is shown in Figure 13. During 21-24 December, when positive PWF appears north of ∼40°N at E z = 60-80 km (Figure 8g), stationary PWs with E s = 1 are dominant. During 25-28 December, when PWF is positive poleward of 55°N at E z = 67-82 km and the MIL is formed (Figure 3c), westward propagating PWs have periods of ∼6 days (indicated by the dashed line in Figure 13) and wavenumbers of E s = 1-2. During 10-13 January, when positive PWF is observed poleward of 60°N at E z = 35-80 km, PWs have periods of ∼24 days (the dash-dotted line) and wavenumbers of E s = 1.

Propagation of GWs
To examine the contribution of GWs which are generally ignored in GW parameterizations, the GWs which play crucial roles in the formation of the MIL and ES are further analyzed. Figure 14 shows  60°N (Figure 14d). Assuming normal distribution for E u     , the area between each pair of dashed curves encompasses 90% of the values of E u     . Figures 14a-14d are the profiles for GWs at 50°N for 17-20 December (Case A), 30°N for 21-24 December (Case B), 60°N for 2-5 January (Case C) and 60°N for 10-13 January (Case D), respectively. As discussed in Section 4.1, it is likely that  Right panel: variations with height of E u     averaged over the same latitudinal region. propagate upward through the prevailing westward wind in the stratosphere. Thus, the PWF is likely from PWs generated at >60°N, E z = 35-80 km during 10-13 January. These results indicate that both GWF and PWF played significant roles in the formation of the ES. Observed longitudinal structure of the polar temperature suggests that the zonally asymmetric ES was a warming inside of the polar vortex. The structure of the ES was likely to be determined by the zonally asymmetric GWF (Figure 16c).
Our results also suggest that the MIL structure may have affected the process of ES formation. The reformation of the mesospheric westward wind during 6-9 January prevented upward PW propagation. Without adiabatic heating associated with wave forcing, the latitudinal gradient of zonal mean temperature y E T     tends to decline gradually because of radiative relaxation in the polar night region. The height dependency  T     became strongly negative. The altitude of the recovered eastward jet was determined by y E T     via the thermal wind balance. Thus, the height of the eastward jet was probably modified by the MIL. The eastward jet affected the propagation of GWs and PWs and their forcings in the polar MLT, leading to the formation of the ES. In this way, it is likely that the height of the ES was affected by the MIL.
From the relationship between phase velocity spectra of GW momentum fluxes and the vertical profile of zonal-mean zonal wind, it is shown that vertical propagation from the lower atmosphere alone is insufficient to explain the presence of the GWs, which play important roles in the formation of the MIL and ES. It is suggested that a part of these GWs propagated laterally and/or were generated in the middle atmosphere. This result indicates that the assumptions generally underlying GW parameterizations are not necessarily appropriate for representing GWs in the MLT.
Results from the high-resolution JAGUAR are generally consistent with observations and enable quantitative analysis of the middle atmosphere dynamics including GWs. Although this study focused on the dynamics in the Northern Hemisphere, JAGUAR provides promising data that can be used to examine the mechanisms of various dynamical phenomena observed in the entire middle atmosphere, such as interhemispheric coupling (e.g., Körnich & Becker, 2010). All figures in this study were created using Dennou Club Library (DCL). This study benefitted from stimulating discussions at the International Space Science Institute (ISSI) Gravity Wave activity. The author (HO) is grateful to T. Kinoshita, M. Kohma and S. Noguchi for fruitful discussions. The study was supported by JST CREST (grant JPMJCR1663) and JSPS KAKENHI (grant JP21J20798). The hindcasts were performed using the Earth Simulator at the Japan Agency for Marine-Earth Science and Technology (JAMSTEC). This manuscript was grammatically edited by T. Tin from Edanz Group (https:// en-author-services.edanz.com/ac).