Observed Solar Cycle Variation of the Stratospheric QBO Generated in the Mesosphere and Amplified by Upward Propagating Waves

With an analysis of zonal wind observations over 40 years, Salby and Callaghan [1] showed that the Quasi-biennial Oscillation (QBO) at 20 km is modulated by 11-year solar cycle (SC) variations from about 12 to 20 m/s (Figure 2). The observations are reproduced qualitatively in a study with the 3D Numerical Spectral Model, which shows that the SC effect of the stratospheric QBO is produced by dynamical downward coupling originating in the mesosphere. In this modeling study, the SC period is taken to be 10 years, and a realistic heat source is applied varying exponentially with altitude: 0.2%, surface; 2%, 50 km; 20%, 100 km and above. The numerical results show that the variable solar radiation in the mesosphere around 65 km generates a hemispheric symmetric Equatorial Annual Oscillation (EAO), which is modulated by relatively large SC variations. Under the influence of wave mean flow interactions, the EAO propagates into the lower atmosphere and is the dynamical source or pacemaker for the large SC modulation of the QBO. The numerical results show that the upward propagating small-scale gravity waves from the troposphere amplify the SC modulations of the QBO and EAO in the stratosphere, part of the SC


Introduction
In several papers, the Quasi-biennial Oscillation (QBO) of the zonal circulation in the stratosphere around the equator has been linked observationally to solar cycle (SC) effects.
Following a study by Holton and Tan [2], Labitzke [3] [4] and Labitzke and van Loon [5] [6] discovered that the temperatures at northern polar latitudes in winter are positively and negatively correlated with the SC when the QBO is in its westward and eastward phase, respectively. Dunkerton and Baldwin [7] and Baldwin and Dunkerton [8] also found evidence of a correlation between the SC and phase of the QBO in the northern stratosphere.
The SC connection between the QBO and temperature variation in the polar region has been simulated in modeling studies. Matthes et al. [9] inserted rocketsonde data into their GCM to produce realistic QBO wind fields around the equator. With fixed eastward and westward QBO zonal winds for both solar maximum and solar minimum conditions, the model reproduces qualitatively the observed SC variations that characterize the polar stratosphere in winter.
The SC signatures at northern polar latitudes were also reproduced with a GCM [10] that simulates the QBO zonal winds with parameterized small-scale gravity waves.
The solar cycle (SC) variations in the temperature at polar latitudes are related to the phase of the QBO, and SC signatures are observed in the zonal winds near the equator where the QBO is generated. Salby and Callaghan [1]  showed that the westerly phase is 3 to 6 months longer during solar minimum than solar maximum. With the longer data record between 1950 and 2001 from FUB, Hamilton [11] reexamined the observed variations in the length of the period for the QBO zonal winds. The observations at 50 hPa confirmed the quasidecadal oscillation [1] but showed that the SC signature is not as clear in the longer 51-year data record. Between 1996 and 2001, the length of the QBO westerly increases with solar activity, in opposite phase to the preceding 40-year variations. Fischer and Tung [12] analyzed the data record of the lower stratosphere (70 to 15 [11], the derived length of the QBO period peaks during the solar minima in 1955, 1965, 1976 and 1986, but varies in opposite direction after 1996 with a sharp peak during the SC maximum in 2000. Salby and Callaghan [1] also analyzed the SC modulation of the QBO amplitude, which is the focus of the present paper. With the 40-year monthly data record (1956 to 1996) at 45 mb (20 km) supplied by FUB, they carried out a Fourier analysis to record the magnitude of the SC modulated zonal winds. In Salby and Callaghan [14] showed with an analysis of NCEP data covering 45 years that the QBO temperature variations at low latitudes are strongly correlated with the SC in support of their earlier findings. The 11-year SC signatures in the zonal wind and temperature variations have also been identified in 40  showed that their GCM produces longer QBO periods during solar minimum.
Cordero and Nathan [17] conducted a study with a 2½D model extending from about 15 to 30 km, in which the QBO is driven by prescribed Kelvin and Rossby gravity waves. In this model, the feedback from the SC induced variations of ozone influences the wave interaction to generate a SC modulation of the QBO amplitude, which varies in phase with the observed zonal winds reported by Salby and Callaghan [1]. The SC effects in the atmosphere have been studied with the NCAR Whole Atmosphere Community Climate Model (WACCM), which is a chemistry climate model that extends from the surface to the lower thermosphere. Matthews et al. [18] carried out a series of 20-year experiments with the WACCM3 model to study under the influence of the QBO the SC response of temperature and ozone in the middle atmosphere and its impact on the troposphere. The QBO was prescribed by adjusting the zonal winds to reproduce the observed durations of the eastward and westward phase. Kren et al. [19]  The observed SC modulation of the QBO in the stratosphere (Figure 2), presented by Salby and Callaghan [1], has been the impetus for a study with the 3D Numerical Spectral Model [20] [21] [22] that is reviewed and summarized in the present paper. It shows that the SC effect is spawned in the mesosphere. The variations in the UV radiation at higher altitudes generate in the zonal circulation a SC-modulated 12-month Equatorial Annual Oscillation (EAO). Amplified by wave interactions, the EAO propagates into the lower atmosphere and is the dynamical source for the SC modulation of the QBO.
Analysis of zonal wind data supplied by the National Centers for Environmental Prediction (NCEP) provides observational evidence for the EAO [23] [24] [25]. And the EAO is observed varying with the F10.7 cm solar flux [26].
The processes that generate the QBO and EAO with SC variations have in common that they are controlled by the unique dynamical properties of the equatorial region: 1) Without Coriolis force and related meridional circulation, the wave forcing is very efficient because it is only dissipated by the eddy viscosity [27]. As a result, the QBO and EAO zonal winds peak at the equator. 2) The eddy viscosity produces in the stratosphere time constants on the order of years, which controls in part the QBO period and favors the generation of SC related long-term variations.

Numerical Spectral Model
The Numerical Spectral Model (NSM) is fully nonlinear but is a mechanistic model without topography and ocean atmosphere interaction. The model was introduced by Chan et al. [28] [29] and Mengel et al. [30], and it has been applied to simulate and understand the dynamical features of the middle atmosphere e.g., [31] [32].
Discussed in considerable detail [22], the present 3D model is formulated in terms of vector spherical harmonics with zonal and meridional wave numbers limited to m = 4 and l = 12, respectively. Applying homogeneous boundary conditions, and with the initial conditions set to zero for all state variables, the model is integrated from the surface to 130 km with a small vertical step size of about 0.5 km.
An integral part of the NSM is that it incorporates the Doppler Spread Parameterization (DSP) for small-scale gravity waves (GW) developed by Hines [33] [34] [35] [36]; its application in the model is discussed in the appendix of Mayr et al. [37]. The DSP employs a spectrum of waves that interact with each other to produce Doppler spreading, which affects the interactions with the flow-of critical importance for generating the QBO. In the present model, a GW source is adopted that is isotropic, time independent, and peaks at the equator. The DSP is applied in the model under conservation of GW momentum, which requires that the nonlinear processes are accounted for that produce the interactions be-tween the GW and background winds. This requires that the model is integrated with a short time step close to 5 minutes to achieve convergence with Newtonian iteration. With an adjustable parameter, the DSP provides isotropic eddy diffusion rates, increasing with altitude, which is incorporated into the model under the assumption that the global variations can be ignored. In the present mechanistic model, the planetary waves are generated internally by instabilities without an imposed excitation source Mayr et al. [38]. The dynamical conditions around the tropopause, in part due to GW interactions, contribute significantly to the planetary waves in the middle atmosphere with amplitudes comparable to those observed. The model does not account for the planetary waves that are generated in GCMs by topography and convection.
In Figure 3 the computed monthly mean zonal wind velocities are shown near the equator, which are generated with the current 3D Numerical Spectral Model.
With a period of about 23 months, the amplitude of the QBO at 30 km is close to 20 m/s, and at 50 km the 6-month Semi-annual Oscillation is generated with velocities greater than 30 m/s.

Solar Cycle Modulated QBO
In the modeling study discussed here Mayr et al. [21], the solar cycle (SC) period is taken to be 10 years, and a realistic SC heat source is applied. The relative amplitude of the SC source increases exponentially with altitude: 0.2%, surface; 2%, 50 km; 20%, 100 km and above; illustrated in Figure 4   The above discussed QBO zonal wind velocities peak at the equator. Away from the equator, the oscillation is dissipated by the meridional circulation, which generates SC variations in the temperature at high latitudes. In Figure   5(a) the temperature spectrum is shown at 84˚ latitude. A sharp amplitude maximum is generated at h = 16 for the QBO period of 22.5 months, and the 10year SC signatures are pronounced at h = 13 and 19 (16 ± 3). The synthesis of the spectral features is presented in Figure 5(b). It shows that the computed SC modulation of the QBO is pronounced in the lower stratosphere, and is relatively large in the troposphere below 10 km with values close to 1 K during solar maximum.

Solar Cycle Modulated Equatorial Annual Oscillation (EAO)
The QBO is generated in the model with a large SC modulation (Figure 4(c)).
And the question is how the SC effect is transferred to the QBO.
The 10-year SC forcing must go through the seasonal variations, and the Semi-annual Oscillation (SAO) seemed to be the answer. Like the QBO, the SAO peaks at the equator and is amplified by wave interactions. And in their seminal theory for the QBO, Lindzen and Holton [27] invoked the SAO to seed the QBO.
But a numerical search for SC signatures in the SAO proved the effect to be weak and erratic.
The model generates a 12-month annual oscillation in the zonal winds, which is modulated with a pronounced SC variation [20].   (Figure 4(b)).
In Figure 6(b) the synthesis is presented for the spectrum of the 10-year SC modulation of the EAO, h = 30 with h = 30 ± 3. The EAO slowly propagates down with a velocity of about 3 km/month, confirmed by observations e.g., [25].
The SC modulation of the EAO is very large in the upper stratosphere around 45 km, and it is in phase with the SC and with the QBO variation (Figure 4(c)).
Apparently, the EAO is guiding and stimulating the SC modulation of the QBO, a pivotal role of the SC mechanism discussed. As shown in Figure 6   synthesis of the spectrum in Figure 7(b) shows that the symmetric AO propagates down from the mesosphere to produce temperature variations around 1K near the tropopause, in phase with the SC forcing.

Generation of SC-Modulated EAO
What is the mechanism that generates the SC-modulated Equatorial Annual Oscillation (EAO) in the model? Addressing this question [22], Figure 8  SC oscillation and the dominant anti-symmetric annual oscillation (h = 30; Figure   8(a)) can produce the hemispheric symmetric SC-modulated EAO shown in Figure   6 which is the source and origin of the large SC variations generated in the model.

Amplification by Wave Interaction
Gravity wave (GW) interactions with the zonal winds play a central role in generating the QBO and EAO at equatorial latitudes. Shown in a numerical study [22], the GW momentum source (MS) further increases the SC modulations of the equatorial oscillations. In this analysis, the wave MS is normalized at each altitude to a dimensionless maximum value of 10, which preserves the relative SC variations.
The spectral features for the wave MS of the QBO at h = 16 and h = 16 ± 3 (not shown) are mirror images of the zonal wind oscillations. With a synthesis of the spectrum, the MS for the QBO is presented in Figure 9(a). It shows that the MS varies by about a factor of 2 at 40 km, in phase with the solar forcing.
The spectrum for the MS of the EAO also produces the salient features that  describe the SC modulation of the zonal winds, and the synthesis of the spectrum is presented in Figure 9(b). It shows that the MS varies with the SC by about a factor of 4 at 40 km.
The upward propagating small-scale GW amplify the SC modulations of the QBO and EAO, part of the SC mechanism.
The above-discussed mechanism shows that the following processes are involved in generating the SC modulation of the stratospheric QBO: (1) Solar forcing produces in the mesosphere a 10-year SC oscillation (h = 3, Figure 8(a)), which is hemispheric anti-symmetric (opposite phase in the two hemispheres).
(2) Non-linear interactions between this anti-symmetric SC oscillation and the large and dominant anti-symmetric 12-month annual oscillation (h = 30, Figure  8(a)) can produce the symmetric SC modulated Equatorial Annual Oscillation (EAO) shown in Figure 6. (3) Like the QBO, the symmetric EAO propagates down into the lower atmosphere under the influence of wave interactions that amplify the zonal wind oscillations. (4) And gravity wave interactions amplify the SC modulations of the QBO (Figure 9(a)) and EAO (Figure 9(b)). (5) The wave amplified EAO is the dynamical source and pathway for the large SC modulation of the QBO in the lower stratosphere, in qualitative agreement with the observations shown in Figure 2 [1].

Solar Cycle Modulated NCEP Equatorial Annual Oscillation (EAO)
The temperature and zonal wind variations supplied by the National Centers for Environmental Prediction (NCEP) provide observational evidence for the SC modulated EAO [26].
In this review of the earlier study, the NCEP data are employed from the National Center for Atmospheric Research (NCAR) Reanalysis R-1 [39], which cover the years from 1958 to the present. The R-1 data represent the zonal-mean temperature and zonal wind variations extending from the surface to 31 km, which are produced by balloon-borne radiosonde observations assimilated with GCM simulations [39] [40]. Satellite measurements after 1978 improved the global coverage, but produced a jump in the NCEP temperatures near the tropopause and around 31 km [41] [42].
The The NCEP data discussed cover the years from 1958 to 2006. For this time span, the amplitude spectrum of the F10.7 flux is dominated by the harmonics h = 4 and 5 ( Figure 10(a)), corresponding to SC periods of 12 and 9.6 years respectively. Fourier analysis shows that the SC periods appear in the hemispheric symmetric equatorial annual oscillation of the zonal winds ( Figure 10(b)), mainly below 20 km. In the temperature spectrum at the pole (Figure 10(c)), the SC signatures are pronounced and extend from about 10 to 25 km.
In Figure 11 Figure 6(b) for the EAO model results, we present in Figure 11(b) for the 48-year NCEP data the synthesis of the zonal wind harmonics, h = 48 with (48 ± 4) and (48 ± 5), identified in Figure 10  in the NCEP zonal winds mimic those of the solar cycle. Above 18 km however, the modulation pattern in Figure 11(b) is highly variable and has no resemblance to the solar flux index. The filtered AO temperature modulations in the polar region are presented in Figure 11(c) and show that around 10 km there is a resemblance to the SC variability. At the pole, the variations are much larger than those generated at the equator (see Figure 6(c) of Mayr et al. [26].

Summary and Conclusions
Salby and Callaghan [1] have shown from an analysis of 40 years of zonal wind measurements that the QBO in the lower stratosphere is modulated by a large 11-year solar cycle (SC) variation in phase with the 10.7 cm solar flux ( Figure 2).
The SC variation of the QBO is reproduced in the present modeling study that is cillation (EAO) that is modulated by the SC (Figure 6). The SC-modulated EAO is the dynamical source or pacemaker for the SC modulation of the QBO. Like the QBO (Figure 4), the EAO propagates down into the lower atmosphere under the influence of wave interactions that amplify the oscillations. And gravity-wave interactions amplify the SC modulations of the QBO (Figure 9(a)) and EAO (Figure 9(b)). The large SC variations in the lower stratosphere are generated by dynamical downward coupling amplified by wave mean flow interactions. Around the equator, the dynamical conditions for the zonal winds are unique [27]. Without the Coriolis force and related meridional circulation, the wave mean flow interactions are very effective because they are only dissipated by eddy diffusion. As a result, the QBO is generated with large zonal winds and large SC variations.
Generated by the meridional circulation, the signature of the SC-modulated QBO zonal winds extend to high latitudes to produce measurable temperature variations in the stratosphere and troposphere ( Figure 5(b)). The observed SC effects in polar temperatures have been linked to the equatorial QBO e.g., [3] [7] [9].
The numerical results show that the EAO also generates in the polar region SC variations (Figure 7(b)). The oscillations propagate down from the upper stratosphere and may be related to the Arctic Oscillation, which is a mode of variability that is sensitive to SC influence (e.g., Kodera [43]; Thompson and Wallace [44]; Baldwin and Dunkerton [45]; Ruzmaikin and Feynman [46]; Lee and Hameed [47]; Lee et al. [48]).
NCEP Reanalysis data of the temperature and zonal winds from 1958 to 2006 [39] provide observational evidence of the EAO with SC variations around 11 years [26]. The spectral features of the 48-year data record contain SC signatures with periods of 9.6 and 12 years ( Figure 10). And below 20 km, the EAO variations mimic the varying maxima and minima of the 10.7 cm solar flux ( Figure  11).