1. The equatorial QBO affects the polar stratosphere during winter with the easterly phase of the QBO (e-QBO) creating the condition for a more perturbed and warmer polar vortex [Holton and Tan, 1980, 1982; Baldwin and Dunkerton, 1999, Ruzmaikin et al., 2005]. Therefore, the variation of the QBO period has additional significance, especially with respect to the timing of its phase relative to the northern winter [Baldwin et al. 2001]. Model QBO and Comparison with NCEP The THINAIR (Two and a Half dimensional INterActive Isentropic Research) is a chemical-radiative-dynamical model. The model has zonally averaged dynamics and includes the three longest planetary waves, which are prescribed by observations at the tropopause level [Kinnersley and Harwood, 1993]. The QBO-source term in the momentum equation uses parameterization of wave momentum fluxes from Kelvin, Rossby-gravity and gravity waves [Kinnersley and Pawson, 1996]. These momentum sources also force the SAO above the QBO. UARS/SOLSTICE spectral irradiance observation is used as the 11-year solar cycle. Figure 1 (a) presents the modeling e-QBO and w-QBO duration versus pressure from 10 to 50 hPa under the SC- mean conditions. Near 10 hPa, the QBO period is dominated by its easterly phase. The e-QBO duration decreases and the w-QBO duration increases until they are about equal near 50 hPa. Figure 1 (b) shows the corresponding behavior in the NCEP reanalysis and demonstrates that the model has the correct behavior as compared to the reanalysis data. Solar-cycle Induced Jumps of the Quasi-Biennial Oscillation Period in Perpetual Solar Forcing Modeling Experiments Le Kuai 1, Runlie Shia 1, Xun Jiang 2, Ka-Kit Tung 3, Yuk L. Yung 1 1 Division of Geological and Planetary Sciences, California Institute of Technology, Pasadena, CA 91125 2 Jet Propulsion Laboratory, California Institute of Technology, 4800 Oak Grove Drive, Pasadena, CA 91109 3 Department of Applied Mathematics, University of Washington, Seattle, WA 98195 Figure 1. (a) Composite mean of e-QBO duration (*) and w-QBO duration (+) versus pressure from the THINAIR model. (b) Same as (a) from NCEP reanalysis. JAN Abstract Using THINAIR model, we examine the mechanism of solar-cycle modulation on the Quasi-biennial Oscillation (QBO) period. Observational evidence for the existence of such a modulation--an anti-correlation between the westerly QBO duration and the solar flux--is controversial because it is found only during a period (1960s to early 1990s) contaminated by volcano aerosols. However, this correlation in the longest available record was found to be near zero. In modeling, longer period runs without volcano influence can be obtained. The solar-cycle effect on the QBO period is rather subtle and complicated, with phase locking, beating and non-stationary behaviors. The experiments are run with perpetual solar minimum/maximum conditions, which help us capture the features in the realistic case of periodic forcing. Both in our model and observed data, the QBO period is constant with height. Under low solar forcing, the QBO period is phase-locked to a multiple (4) of Semi-Annual Oscillation (SAO) period. As solar forcing increases, the QBO period jumps with quantized multiple of the SAO periods, from 24 to 30 or 36 months. Because of this non-stationarity even under constant solar-cycle forcing, QBO periods do not respond one-to-one to changing solar flux in the realistic case of periodic solar-cycle forcing. Therefore the statistical significant QBO-solar relationship cannot be established without a much longer observational record. The mechanisms for solar modulation of QBO period are also discussed. Figure 2. Fourier power spectra of the 70-year zonal wind time series from the THINAIR model; black line for 1×SC-min case; red line for 1×SC- max case; blue line for 2×SC-max case. (a) at potential temperature level 712 K (~15 hPa); (b) 595 K (~ 26 hPa); In Figure 3 we plot the QBO period as a function of the solar index in units of solar flux (one unit represents one half of the difference of solar flux between the SC-max and SC-min). This establishes that the period of the QBO generally increases as the solar flux increases, contrary to the finding of previous authors that the period reaches a maximum during SC-min. An interesting feature revealed in Figure 3 (a) is the tendency of the QBO period to phase-lock with the 4 SAO periods (so that it is also phase-locked with the annual cycle). Once the QBO period was locked in a 24 months at 2 × SC-min, further reduction of the solar flux to 3 × SC-min does not seem to be able to change its period, thus forming a flat ledge in Figure 3 (a). In the other cases, the averaged QBO period increases when perturbed by increasing solar fluxes. Above 30 hPa, it is the easterly duration which varies with solar flux (Figure 3 (b) and (c)), while below 30 hPa it is the westerly duration that varies with solar flux (Figure 3 (d)), consistent with the observational result of Fischer and Tung [2007]. Figure 3. (a) QBO period as a function of solar-cycle forcing obtained using the THINAIR model for five levels from 7-80 hPa. Lines overlap, showing that the period does not change with height. Composite mean of e-QBO duration (*) and w-QBO duration (+) versus solar forcing (b) 10 hPa, (c) 20 hPa, (d) 50 hPa. Figure 4. Time-height section of the equatorial monthly-mean zonal wind component (in m s -1 ) from the THINAIR model simulation. The individual QBO period is synchronized with SAO near stratopause. The black line is the zero-wind line. (a) 2×SC-min perpetual condition; (b) 1×SC-min perpetual condition; (c) SC-mean perpetual condition; (d) 1×SC- max perpetual condition; (e) 2×SC-min perpetual condition. (f) under realistic periodic solar-cycle forcing from 1×SC-min to 1×SC-max. Solar Cycle Influence on the QBO Period With the time-dependent oscillatory solar forcing, determining the QBO period is not straightforward, since the period itself is changing with the solar cycle. However, with fixed solar forcing, the QBO period can be determined using its Fourier spectrum. We perform the simulation with the 1× to 3× SC-min/SC-max conditionand the SC mean conditions. Figure 2 shows the Fourier spectrum of the 70-year time series of the QBO zonal wind at equator at various altitudes. The period of the QBO was showed to be independent on height. The results reveal a QBO Period of 25.08 months for 1×SC-min (black line), 31.85 months for the 1×SC-max (red line) and 36.01 months for the 2×SC-max (blue line) conditions. Thus, the period of the QBO is unambiguously lengthened as the solar fluxincreases. As pointed out by previous authors (Lindzen and Holton [1968]; Dunkerton and Delisi, [1997]), the SAO’s alternating easterly and westerly shear zones serve to “seed” the QBO below. In particular, the onset of the westerly phase of the QBO is tied to the downward propagation of the westerly phase of the SAO. A QBO period starts with the zero-wind line associated with the westerly shear zone of the SAO descending into the QBO region below, and ends when next such westerly descent occurs, to replace the easterly QBO below, at a multiple of SAO period later. In this way the QBO period is quantized in units of SAO period. Panel (a) in Figure 4 shows the simplest case, a QBO period locked in 4 SAO periods for 2×SC-min. Panel (b) shows the case for 1×SC-min. The QBO period comprises 4 SAO periods most of the time, and occasionally there is one or two QBO periods consisting of 5 SAO periods. As a result, the average QBO period is 25.08 months. Apparently the solar forcing is not strong enough to force the QBO period into 5 SAO periods permanently. There is also the possibility that an odd multiple of SAO periods is not stable with respect to annual-cycle perturbation. Panel (d) shows the result with 1×SC-max condition. Similar to the 1×SC-min case, the time series is also non-stationary. A QBO period can comprise of mostly 4 and 6 and occasional 5 SAO periods, yielding an average QBO period of 31.85 months. Panel (c) shows the case of SC-mean (without solar-cycle forcing) and it appears to behave approximately as the average of 1×SC-min and 1×SC-max cases, with an average period of 28.59 months, which comprises mostly 5 and 4 SAO periods with an occasional 6 SAO periods. Panel (e) shows the behavior for 2×SC-max, where the QBO period time series becomes stationary again and phase-locked into 6 SAO periods. Mechanisms for solar modulation of QBO period. The partition of the whole QBO period into its easterly and its westerly parts in the lower stratosphere depends on the equatorial upwelling rate of the global Brewer-Dobson circulation. The isentropic stream-function for the Brewer- Dobson circulation in the stratosphere in January shows a strengthened Brewer-Dobson circulation during SC-max conditions as compared to SC-min conditions (figure 5). Under the SC-max conditions the planetary waves are more focused to mid and high latitudes, and there are more Stratospheric Sudden Warmings in the polar stratosphere during late winter [Camp and Tung, 2007]. Consequently the polar stratosphere is warmer and the Brewer-Dobson circulation is more downward in mid to high latitudes JAN [Cordero and Nathan, 2005]. This could remotely force a stronger upwelling branch of the Brewer-Dobson circulation over the equator, which then slows the descent of the QBO shear zone and extends the QBO period. Because the QBO- induced secondary circulation is also upward for the easterly phase at the equator, the e-QBO is more vulnerable to slowing and eventual stalling, which usually occurs near 30 hPa [Plumb and Bell, 1982 (a), 1982 (b)]. Below the stalling level, the westerly phase persists without being replaced by the descending easterlies, leading to a longer westerly duration. This explains why the descent of the easterly shear zone is more vulnerable to stalling. In this model there is no local heating due to volcanic aerosols, and so the anomalous upwelling over the equator shown here is remotely forced by the breaking of planetary waves in the extra-tropics. The prolongation of the westerly phase of the QBO in the lower stratosphere is an important feature of the observed decadal variation of the QBO period because it delays the onset of the next westerly descent into the stratosphere by filtering out the westerly waves. In the absence of the westerly wave momentum deposition, the easterly duration is lengthened in the upper stratosphere. In the observational result of Fischer and Tung [2007], the decadal variation of the easterly duration at 15 hPa is tied to that of the westerly duration at 50 hPa. This feature is also seen in this model. A second mechanism is local radiative heating by the increased solar flux in SC-max as compared to the SC-min. In this model the UV radiation of the solar cycle forcing interacts with ozone most strongly in the stratopause region, and the resulting diabatic heating affects the seeding of the QBO by the SAO. This solar perturbation serves to “kick” the QBO period from one SAO multiple into another, higher (on average) multiple. To test this hypothesis, we make another run by switching off the solar cycle-ozone feedback. Ozone in the model is then not allowed to change as solar cycle changes, but other interaction with dynamics are still allowed. In the non-interactive case, ozone is fixed at the SC-mean case, but the solar flux is increased to 1×SC-max. The average period is 29.80 months without ozone feedback. The behavior is non-stationary, and lie between the SC-mean (with an average period of 28.59 months) and 1×SC-max (with an average period of 31.84 months) case with ozone feedback. Discussion and Conclusions It is well known that the polar stratosphere in winter is significantly more perturbed when the equatorial QBO is easterly than when it is westerly [Holton and Tan, 1980, 1982; Baldwin et al, 2001]. A mechanism that can affect the period of the equatorial QBO, by altering the timing of the phase of the QBO relative to the polar winter will therefore have a significant impact on the circulation of the entire stratosphere. The 11-year solar cycle has often been cited as able to modulate the equatorial QBO period, especially its westerly duration in the lower stratosphere. In the present model where there is no volcanic influence and long runs are possible, we have established that the QBO period is lengthened during solar maxima. We also find that such an effect is difficult to establish without a long time record because of the presence of non-stationary behavior, whereby the QBO period can change even if the solar flux is held constant. To understand the mechanism of solar-cycle modulation of the QBO period, model runs with perpetual solar conditions are performed. We find a tendency of the QBO period to synchronize with the SAO period. That the observed mean period (e.g. 28 month) is not always a multiple of six months can be partially explained by the fact that the QBO period is non-stationary even when the solar forcing is constant. Two exceptions occur at 24 months and 36 months, forced by 2  SC-min forcing and 2  SC-max conditions. These two periods are more stable because there is also a synchronization with the annual cycle. In between these two cases there are temporary (non-stationary) quantum jumps of the QBO period by a SAO period when the stratopause region is perturbed by the solar cycle, yielding non-integer multiples of the SAO period as the average period of the QBO. In the model two mechanisms are responsible for the solar influence of the QBO period: a radiative perturbation of the SAO-QBO transition region when ozone production is enhanced by the increased solar flux; a dynamical mechanism which increases the strength of the Brewer-Dobson circulation. The work reported here is a preliminary study of the influence of the solar cycle on the QBO period using the THINAIR model. Further study is needed on the cases driven by a realistic time-dependent solar cycle forcing. More simulations will be performed to study the influence of volcanic aerosols on QBO to explain the puzzling results between 1960 and 1995. Ultimately, the results obtained here must be verified in a three-dimension general circulation model such as the Whole Atmosphere Community Climate Model (WACCM) [Garcia et al., 2007]. Figure 5. (a) Mass stream function on isentropic surfaces in units of 10 9 kg s -1 under 1×SC- min condition. (b) The difference between the composites of the 1×SC-max and 1×SC-min. Both figures are for Jan.