It is found that in the whole year from December 2012 to November 2013, the W1 Q16DW is extraordinarily intense at middle and high latitudes in the stratosphere of the NH in January, when a major SSW event is taking place. Next, we would like to investigate the relationship between the wave amplification and this major SSW event.
The World Meteorological Organization (WMO) defines a major SSW event as the gradient of the temperature from 60 N\(^\circ \) to the pole being positive and the reversal of the zonal-mean zonal wind at 10 hPa or below during wintertime. The day when the zonal-mean zonal wind reverses at 10 hPa is taken as the central date of the major SSW event. The major SSW event during the winter of 2012/2013 has been studied for several years (Wit et al. 2014, 2015; Coy and Pawson 2015). Here, we exhibit this event in detail by using the ERA-Interim data. Figure 5 displays the altitude-time cross-section of the zonal-mean temperature averaged from 60 \(^\circ \mathrm{N}\) to 90 \(^\circ \mathrm{N}\) and the zonal-mean zonal wind at 60 \(^\circ \mathrm{N}\) from November 2012 to March 2013. The stratospheric temperature rises rapidly after 1 January and reaches a maximum of 267 K at 1 hPa on 11 January. The rapid deceleration of the zonal-mean zonal wind at 60 \(^\circ \mathrm{N}\) starts when the stratospheric temperature increases rapidly, and then, the wind reverses and remains westward until approximately 27 January. The zonal-mean zonal wind reverses from eastward to westward at 10 hPa and 60 \(^\circ \mathrm{N}\) on 6 January, so we choose this day as the central date.
To classify the 2012/2013 SSW event, we present the evolutions of stratospheric PV (in units of PVU) and geopotential height around the central date from the ERA-Interim data. An overview of the vortex evolution in the middle (850 K, ~ 10 hPa) and lower (530 K, ~ 50 hPa) stratospheres during the 2012/2013 SSW event is shown in Fig. 6. The PV fields at 850 K (~ 10 hPa) together with the 10 hPa geopotential height show a clear synoptic evolution of the polar vortex in the top panel of Fig. 6. The strong polar vortex with high PV values accompanied by low geopotential heights (black contour) began to shrink and shift off the pole from 28 December 2012 to 2 January 2013, while the weak polar vortex with low PV values accompanied by high geopotential heights (white contour) shifted from low latitudes to middle latitudes. Then, the low PV region (accompanied by high geopotential heights) moved from middle latitudes to the pole, and the high PV region (accompanied by low geopotential heights) began to split on 7 January 2013. The vortex was completely split into two fragments on 12 January 2013. At the bottom panel, similar phenomena can be seen: the strong polar vortex with high PV values accompanied by low geopotential heights (black contour) shifted to the adjacent mid-high latitudes, and then, the vortex split into two fragments. In summary, the lower and middle stratospheric polar vortices first shifted off the pole and then split into two pieces, classifying this major SSW event as a complex event.
According to the results in “Seasonal, latitudinal and altitudinal variations of the W1 Q16DW”, we found that the W1 mode of the Q16DW was very energetic in January 2013. To further confirm the dominant traveling PWs in this SSW event, we applied the two-dimensional Fourier transform methods to the ERA-Interim data in January 2013. Figure 7 shows the frequency-wavenumber spectral results of the geopotential height, zonal wind and meridional wind at 1 hPa and 80 °N in January 2013. For each physical quantity, there are two conspicuous peaks at zero frequency with the same amplitudes, which represent the quasi-stationary PWs (Pogoreltsev et al. 2009). SPW1 is the strongest, which will be taken into consideration in the following analyses. In addition, there are significant spectral peaks in all three physical quantities, corresponding to the W1 mode of the Q16DW. For the geopotential height, zonal wind and meridional wind, the strongest spectral peaks have amplitudes of 308 \(\mathrm{m}\), 18.5 \({\mathrm{ms}}^{-1}\) and 19.4 \({\mathrm{ms}}^{-1}\), respectively. For the zonal wind and meridional wind, there are also spectral peaks corresponding to the s = − 1 mode of the Q16DW, which is much weaker than those for the W1 mode. Therefore, we still focus on the W1 mode in the following paper.
The above spectral analysis indicates that the W1 mode of the Q16DW is likely to be closely related to the 2012/2013 SSW event. To further clarify this relevance, we will display the W1 Q16DW activity during the 2012/2013 SSW event in detail in the following section. We fit the geopotential height, zonal wind and meridional wind data with the zonal wavenumber s = 1 from the equator to 80 \(^\circ \mathrm{N}\) in a 32-day window, and this window is moved from December 2012 to February 2013 with steps of 1 day to obtain daily values of the wave amplitudes and phases. Figure 8 presents the latitude-time structures of the W1 Q16DW amplitudes in the geopotential height, zonal wind and meridional wind at three pressure levels: 1 hPa, 10 hPa, and 30 hPa. For the geopotential height, the maximum amplitudes are centered near 70 \(^\circ \mathrm{N}\) at all levels, and the greatest value (930 \(\mathrm{m}\)) is located at 1 hPa. For the zonal wind, the maximum amplitudes are centered near 40–50 \(^\circ \mathrm{N}\) and near the Northern Pole, while for the meridional wind, the maximums are near the Northern Pole. The maximum zonal/meridional wind is 31.9/34.7 \({\mathrm{ms}}^{-1}\) and located near the Northern Pole. All the amplitudes in the geopotential height, zonal wind and meridional wind reach their maximums at high latitudes near the central date of the 2012/2013 SSW event, indicating that there is some close connection between the W1 Q16DW activity and the 2012/2013 SSW. Coy and Pawson (2015) found that the upward wave activity flux from the upper troposphere displaces the polar vortex in an SPW1 pattern. The vertical EP flux maximum from SPW2 at 100 hPa averaged over 30–90 \(^\circ \mathrm{N}\) is less than \(1\times {10}^{5}{kgs}^{-2}\), which is smaller than what is found during the previous split SSW events examined by Harada et al. (2010). Therefore, there may exist a wave that is expected to provide an additional forcing to split the polar vortex. The W1 mode is clearly amplified before and during the splitting of the displaced vortex, similar to the amplification of SPW2 described by Coy and Pawson (2015). This indicates that the W1 mode most likely contributes to the breakdown of the polar vortex.
On the central date, the maximum amplitude of geopotential height is found at 65 \(^\circ \mathrm{N}\). To determine the vertical propagation characteristics of the W1 mode, we show the profiles of the fitted amplitudes and phases of geopotential height at 65 \(^\circ \mathrm{N}\) in Fig. 9. The amplitude increases with height. It is worth noting that the phase exhibits a tendency of downward phase progression, indicating that the W1 mode wave propagates upward from lower stratosphere. In addition, the expected amplitude of the theoretical Lamb mode (dashed black line) is also plotted in Fig. 9 (left). We assume that the excepted amplitude has the same value as the actual amplitude at 30 hPa. The expected geopotential height amplitude change is proportional to \({e}^{(\kappa z/H)}\) based on the log-pressure vertical coordinate z, where \(\upkappa \) is the ratio of R the gas constant to \({c}_{p}\) the specific heat at constant pressure for air, and H is the scale height. The amplitude of the theoretical Lamb mode throughout the stratosphere shows a linear increasing trend. However, the actual geopotential height amplitude is much larger than the theoretical one, indicating that the W1 Q16DW is not a pure free mode wave, and there exists a wave source in the stratosphere.
The key mechanism for generating a major SSW event is the upward-propagating PWs from the troposphere into the stratosphere, which reverse the eastward winter stratospheric jet. The PW activity can also transport a large heat flux to the polar region, which leads to a warmer polar vortex. In our study, it was revealed that the strong W1 Q16DW occurred during the 2012/2013 SSW event. Therefore, we would focus on the interaction of the W1 mode wave with the mean flow in the stratosphere.
The EP flux and its divergence are used to investigate the propagation of eddy momentum and heat of waves and the wave forcing on the mean flow (Chen and Huang 2002; Chen et al. 2002; Tomikawa et al. 2012; Harda and Hirooka 2017; Rodas and Pulido 2017). In this paper, the transformed Eulerian-mean equations in spherical coordinates (Andrews et al. 1987) are applied:
$${\overline{u} }_{t}=-{\overline{v} }^{*}\left[\frac{1}{a\mathrm{cos}\varphi }{\left(\overline{u}\mathrm{cos }\varphi \right)}_{\varphi }-{f}_{0}\right]-{\overline{w} }^{*}{\overline{u} }_{z}+\frac{1}{{\rho }_{0}a\mathrm{cos}\varphi }\nabla \cdot \mathbf{F}$$
(2)
where \({\rho }_{0}\) is the air density, \(a\) is the radius of the Earth, \(\varphi \) is the latitude, \({f}_{0}=2\mathrm{\Omega sin}\varphi \) (\(\Omega =7.292\times {10}^{-5}{rad s}^{-1}\) is the Earth’s rotation rate) is the Coriolis parameter, and \(u\)/\(v\)/\(w\) is the zonal/meridional/vertical wind. Here, the zonal-mean fields and partial derivatives are denoted by overbars and subscripts, respectively. The left-hand side of Eq. (2) is the tendency of the zonal-mean zonal wind. The first and second terms on right-hand side represent accelerations associated with the residual velocities \({\overline{v} }^{*}\) and \({\overline{w} }^{*}\), which are defined as
$${\overline{v} }^{*}=\overline{v }-\frac{1}{{\rho }_{0}}{\left({\rho }_{0}\frac{\overline{{v }^{\mathrm{^{\prime}}}{\theta }^{\mathrm{^{\prime}}}}}{\overline{{\theta }_{z}}}\right)}_{z}$$
(3)
$${\overline{w} }^{*}=\overline{w }+\frac{1}{a\mathrm{cos}\varphi }{\left(\mathrm{cos}\varphi \frac{\overline{{v }^{\mathrm{^{\prime}}}{\theta }^{\mathrm{^{\prime}}}}}{\overline{{\theta }_{z}}}\right)}_{\varphi }$$
(4)
where \(\theta \) is the potential temperature. Here, perturbation quantities are denoted by primes. \(\mathbf{F}=\left(0,{F}^{\left(\varphi \right)},{F}^{\left(z\right)}\right)\) is the EP flux which is a vector in the meridional plane.
The meridional and vertical components of the EP flux in the spherical geometry can be expressed as follows:
$${F}^{\left(\varphi \right)}={\rho }_{0}a\mathrm{cos}\varphi \left(\frac{\overline{{v }^{^{\prime}}{\theta }^{^{\prime}}}}{{\overline{\theta }}_{z}}{\overline{u} }_{z}-\overline{{u }^{^{\prime}}{v}^{^{\prime}}}\right)$$
(5)
$${F}^{\left(z\right)}={\rho }_{0}a\mathrm{cos}\varphi \left\{\left[{f}_{0}-\frac{{\left(\overline{u}\mathrm{cos }\varphi \right)}_{\varphi }}{a\mathrm{cos}\varphi }\right]\frac{\overline{{v }^{\mathrm{^{\prime}}}{\theta }^{\mathrm{^{\prime}}}}}{{\overline{\theta }}_{z}}-\overline{{u }^{\mathrm{^{\prime}}}{w}^{\mathrm{^{\prime}}}}\right\}$$
(6)
The EP flux divergence is given by the following equation:
$$\nabla \cdot \mathbf{F}=\frac{1}{a\mathrm{cos}\varphi }\frac{\partial }{\partial \varphi }\left({F}^{\left(\varphi \right)}\mathrm{cos}\varphi \right)+\frac{\partial }{\partial z}{F}^{\left(z\right)}$$
(7)
The third term on the right side of Eq. (2) is defined as the zonal force per unit mass acting on the mean state \({{D}_{F}=\left({\rho }_{0}a\mathrm{cos}\varphi \right)}^{-1}\nabla \cdot \mathbf{F}\).
For the EP flux, the meridional component indicates the eddy momentum flux, and the vertical component represents the eddy heat flux. \({D}_{F}\) can represent the acceleration or deceleration of the zonal-mean flow. The EP flux divergence (positive value) is related to the eastward acceleration by wave activities, while convergence (negative value) is related to the westward acceleration.
Previous study has investigated the contributions of different waves to the EP flux and found that the EP flux is mostly due to the PWs in the stratosphere (Tomikawa et al. 2012). Hirooka (1986) found that the interference between traveling and quasi-stationary PWs can produce periodic changes of EP flux and its divergence, which in turn give rise to the vacillations in the basic flow. Since the amplitude of the traveling PWs is of the same order of magnitude as that of quasi-stationary PWs, Hirooka and Hirota (1985) indicated that the interference between traveling and quasi-stationary wave may plays an important role in the SSW event. The meridional wind amplitudes of W1 mode have comparable magnitudes with the quasi-stationary PWs described by Coy and Pawson (2015). Coy and Pawson (2015) revealed that SPW1 and SPW2 played a key role during this SSW event. Therefore, we speculate that the W1 mode may interact with the SPW1 during the 2012/2013 SSW event. This interaction would be discussed in detail in the following part. Hereafter, we use W1-SPW1 as the abbreviation for the “interaction between W1 Q16DW and SPW1”.
Referring to the previous work (Salby and Garcia 1987), we consider the simple two component frequency–wavenumber spectrum (referring to Fig. 7) and let \({x}^{^{\prime}}={x}_{Q16DW}^{^{\prime}}+{x}_{SPW1}^{^{\prime}}\). Here, \(x' = \left[ {u'}, {v'}, {w'}, {\theta'} \right]\). Then, the total EP flux field can be divided into two groups. The first group is the contribution from each spectral component, i.e., from the Q16DW and the SPW1, respectively. The second is contribution from the interaction of the two spectral components (representing by their cross terms), i.e., from W1-SPW1.
To clarify processes responsible for the zonal wind tendency during the SSW event, each term of Eq. (2) is evaluated. Figure 10 shows the time–pressure sections of the zonal wind tendency (\({\overline{u} }_{t}\)), the zonal wind acceleration due to \({D}_{F}\), and zonal momentum advection due to residual meridional and vertical velocities at 50–80 \(^\circ \mathrm{N}\). Here, the zonal wind acceleration due to \({D}_{F}\) is calculated from the total EP flux. The \({\overline{u} }_{t}\) is determined by the residual between the \({D}_{F}\) and momentum transport due to the meridional circulation. As shown in Fig. 10, \({D}_{F}\) and the meridional advection are dominant and tend to cancel each other during the 2012/2013 SSW event. Contributions of the vertical advection are quite small. As a result, the \({\overline{u} }_{t}\) is roughly given as a small residual between \({D}_{F}\) and the meridional advection. Before the central date, large negative EP flux divergences are observed in the middle and high stratosphere. Just after the central date, it is interesting that large negative and positive EP flux divergences appear above and below 2 hPa, respectively. Then, large EP flux convergences appear above 2 hPa. These large EP flux convergences are largely canceled by meridional advection. During the 2012/2013 SSW, the zonal wind tendency follows the sign of the \({D}_{F}\) in most of the height range. Therefore, the zonal wind tendency is roughly dominated by the EP flux divergence.
Figure 11 shows the time–pressure sections of \({D}_{F}\) due to quasi-stationary planetary waves/the interaction between quasi-stationary planetary waves and W1 Q16DW/W1 Q16DW at 50–80 \(^\circ \mathrm{N}\). In December, the convergence/divergence regions are dominated by quasi-stationary PWs below 2 hPa. Relatively small EP flux convergences from the interaction of quasi-stationary PWs with W1 Q16DW also occur in upper and middle stratosphere. Around the central date, it is worth noting that both quasi-stationary PWs and interaction component produce large EP flux convergence in the upper stratosphere. Moreover, both negative and positive \({D}_{F}\) from W1 Q16DW are particularly small and can be ignored. As a result, a large EP flux convergence associated with the interaction provides an additional contribution to the reversal of eastward wind. Therefore, the interaction between W1 Q16DW and quasi-stationary PWs plays an important role in this SSW event.
Here, we explore the effects of the interaction between the W1 Q16DW and quasi-stationary PWs on the mean flow during the 2012/2013 SSW by calculating the EP flux and its divergence. Figure 12 shows the zonal-mean zonal wind, EP flux vector and \({D}_{F}\) from W1-SPW1 on 26 December 2012, 31 December 2012, 5 January 2013, and 10 January 2013. All the strong EP flux vectors are concentrated in mid-high latitudes in the stratosphere. The EP flux vectors show upward propagation in the NH, which is consistent with the W1 mode propagation in Fig. 9. It can be clearly seen that the strong W1-SPW1 occurs in the lower stratosphere (below 10 hPa) and gradually extends upward on 5 January 2013. The EP flux vortex from W1-SPW1 become smaller after the central date. Note that the vertical EP flux from W1-SPW1 have the same order of magnitude as that from SPW2 described by Coy and Pawson (2015) at 100 hPa, which provides supplementary evidence for the contribution of the W1 to the splitting of the polar vortex. Importantly, a large heat flux (vertical component of EP flux) due to W1-SPW1 in Fig. 12 can be seen during the 2012/2013 SSW, which is consistent with the increased temperature. This finding indicates that W1-SPW1 may produce adiabatic warming in the stratosphere. Strong EP flux convergence of W1-SPW1 first occurs around high latitude (70–80 \(^\circ \mathrm{N}\)) on 26 December 2012, and then extends to low latitude (40 \(^\circ \mathrm{N}\)) on 5 January 2013. These observed strong eddy forcing regions lead to the deceleration and even reversal of the eastward winter stratospheric jet. It is worth noting that EP flux divergence region exists in the middle stratosphere below the upper stratosphere convergence region.
Figure 13 exhibits the W1 Q16DW amplitudes in the geopotential height, zonal wind and meridional wind. The selected four days in this figure are the same as those in Fig. 12. In the middle and upper stratosphere, the W1 Q16DW amplitudes in the geopotential height, zonal wind, and meridional wind is amplified at mid-high latitudes, which correspond to the strong EP flux in the Fig. 12.
According to the results and discussion above, the dynamic situation can be understood as follows: W1-SPW1 in the stratosphere may contribute greatly to the eastward jet reversal during this SSW event. In addition, this interaction also plays an important role in the stratospheric polar warming. Apparently, part of the W1 Q16DW in the stratosphere is the result of the upward-propagating wave from the low atmosphere. Since the W1 Q16DW is amplified in the stratosphere, there is also a wave source there, which is verified by the EP flux divergence region in the stratosphere. Thus, the W1 Q16DW in the stratosphere is the sum of the upward-propagating wave and the in situ excited wave, which is consistent with the results of Fig. 9.
Next, we explore the forcing mechanisms of the amplified W1 Q16DW in the stratosphere. The observed EP flux divergence region in the stratosphere is a key point of the wave forcing, indicating that there is indeed an in situ wave source. Thus, the possibility of in situ instability is considered and subsequently discussed. The effects of the mean flow on the propagation of the Q16DW can be quantified by the baroclinic and/or barotropic instability. Changes in the sign in the basic northward quasi-geostrophic potential vorticity gradient (\({\overline{q} }_{\varphi }\)) indicate the necessary conditions for the baroclinic and/or barotropic instability of the mean flow. To investigate this mechanism, we calculated \({\overline{q} }_{\varphi }\), which can be expressed in spherical coordinates as follows (Andrews et al. 1987):
$${\overline{q} }_{\varphi }=2\mathrm{\Omega cos}\varphi -{\left[\frac{{\left(\overline{u}\mathrm{cos }\varphi \right)}_{\varphi }}{a\mathrm{cos}\varphi }\right]}_{\varphi }-\frac{a}{{\rho }_{0}}{\left(\frac{{\rho }_{0}{{f}_{0}}^{2}}{{N}^{2}}{\overline{u} }_{z}\right)}_{z}$$
(8)
Here, \(N\) is the buoyancy frequency. The second and third terms of the right-hand side of Eq. (8) indicate the barotropic and baroclinic instability, respectively. The case when the second term of Eq. (8) dominates the third term is referred to as barotropic instability, and the opposite case is referred to as baroclinic instability.
To further determine the possible relationship between the amplified W1 Q16DW and the instability of the mean flow, Fig. 14 shows the altitude–latitude structures of \({\overline{q} }_{\varphi }\) on the same selected days as in Fig. 13. The blue and uncolored regions in Fig. 14 represent the possible mean flow instability regions. Note that the barotropic instability and/or baroclinic instability have roughly equal contributions to the mean flow instability in this case (not shown here). In the upper stratosphere, the W1 Q16DW in the geopotential height, zonal wind, and meridional wind is amplified in mid-high latitudes, which corresponds to the sign-changing region of \({\overline{q} }_{\varphi }\). The negative region of \({\overline{q} }_{\varphi }\) extends from the upper stratosphere to the lower stratosphere after the central date. In addition, there are significant amplitude regions for the geopotential height, zonal wind and meridional wind in Fig. 13. The distribution of the W1 Q16DW amplitude in the zonal wind is more consistent with the instability region than the meridional wind and geopotential height. This difference may be because the curvature terms of the zonal wind are closely related to the second and third terms on the right-hand side of Eq. (6).
In addition, a comparison of Figs. 12 and 14 clearly demonstrates that the negative regions of \({\overline{q} }_{\varphi }\) correspond to the regions where the eastward winter stratospheric jet reverses and remains westward. The large divergence region occurs where \({\overline{q} }_{\varphi }<0\). This result suggests that in situ instability causes the growth of W1 Q16DW accompanying the large positive EP flux divergence.
In summary, the observed barotropic and/or baroclinic instability of the mean flow in the stratosphere contributes significantly to the enhanced W1 Q16DW or may be an incentive source of the W1 Q16DW.