Quasi-biennial Oscillation was first discovered by Reed in 1961 and independently by Veryard and Ebdon.
QBO is observed in the equatorial mean zonal wind in the stratosphere. The QBO signal is also found in the mesosphere but the largest amplitude is observed in the lower stratosphere. The easterly and westerly zonal wind regimes altered regularly with averaged period of 28 months. The QBO period has interannual variability, ranging from 22 to 34 months. The time-height cross section show it first appears above 30 km, the easterly and westerly QBO regimes propagate downwards at a rate of 1 km/month. The oscillation is symmetric about the equator with maximaamplitude of about 20 m/s, and an approximately Gaussian distribution in latitude with a half-width of about 12 degree. The QBO signal is also found in the ozone and temperature and can be transported to polar region.
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A lot of previous work has been done to study the QBO mechanism and its influence on the climate.However, there are two characteristics of the observed behavior of the QBO have been underempahsized by previous modeling and observational discussions. First is its synchronization with the SAO in the upper stratosphere and the second is the random quantum jumps of the QBO period by one multiple of the SAO period.
There are also a lot of debates on the 11-year solar cycle modulation of the QBO period. The different authors studies the observational data with different time range. They found there is anti-correlation between the solar radiation and length of QBO period from 1960s until the beginning of 1990s. However, two these paper Hamliton 2002 and Fischer and Tung 2007 indicate an in-phase relation is found during the years before and after these period. The volcanic aerosols is most possible response to cause the anti-correlation in the period. During the period in-phase relation was found, no major volcano occurred. Then the clear stratosphere can show us a true relation between the solar radiation and the QBO periods. Furthermore, the available observational data is still not long enough for the 11-year solar cycle. Therefore, there is difficulty to get the true relation between the solar forcing and qbo period using observational data only.
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Fortunately, the modeling experimentsprovide us the opportunity for further study. The advantages of using model include first, it can provide longer time period. The previous work examine the observations can only have 4 complete solar cycles data at most. Furthermore, without the volcanic aerosol influence, the model can provide us a clear relation between solar forcing and QBO periods. Finally, the experiments under solar radiation perpetual conditions can help us easily determine the solar forcing modulation on the QBO periods.
The model used in this study is two and a half dimensional interactive isentropic research model. It includes the chemical-radiative and dynamical interaction. The isentropic vertical coordinate have 29 layers from ground to 100 km. 19 grid points from pole to pole is calculated.
The QBO-source term in the momentum equation uses parameterization of wave momentum fluxes from Kelvin, Rossby-gravity and gravity wave. These momentum sources also force the SAO above the stratosphere.
First of all, I’d like to show the synchronization of QBO with SAO in the observational data. Here are the time and pressure cross section of ERA-40 mean zonal wind at equator. The upper two panels are the raw data for 45 year recodes from 70 hpa up to 1 hpa. Since above the stratosphere, both the QBO and SAO exit, the present of the QBO makes parts of the SAO difficult to see. During a QBO easterly phase, the w-SAO and e-SAO are imbedded in an easterly background and only show up as relative easterly maxima and minima. The regular alternating e-SAO and w-SAO are seen when we remove the QBO by averaging over every each 12 months during the year in the entire ERA-40 record. It is showed in the last two panels in the upper stratosphere. Below 5 hPa, the raw data was kept to show the QBO. From these two bottom plots, it is showed that w-QBO always starts with a w-SAO above and descends to the lower stratosphere. One period of the QBO terminates when the next w-QBO starts similarly with descent of another w-SAO. Why it is always w-SAO, but not the e-SAO that initiates a QBO? Since the equatorial upper stratosphere is easterly without the SAO, the e-SAO does not introduce a zero-wind line, but the w-SAO does. A zero-wind line is where enhanced wave-man flow interaction occurs. Therefore, at and immediately below the zero-wind line introduced by the w-SAO, westerly wave momentum is deposited, causing the descent of the westerly shear zone. The next w-QBO starts when the westerly waves are allowed to propagate up again from the lower to the upper stratosphere. Since a QBO period always starts and terminates with a w-SAO, the period of the QBO should be an integer multiple of the SAO period.
To verify this, we measured the QBO period at 5 hPa by counting the number of SAO period in figure a. The solid line indicates the 11 year solar cycle variations, scale on the right side. There is no obvious correlation or anti-correlation between solar cycle and qbo periods.
Figure b is the histogram of the number of occurrences when the QBO period is 4- or 5-SAO in the 45-year ERA-40 data. The reported mean period of 28 months for the QBO during this period is an average of 6 QBO each lasting 4-SAO periods and twelve QBO when each is 5-SAO periods.
Figure c shows two examples of vertical structures of QBO periods.The starsare the qbo during the year 1997 and crosses are qbo occurred in 1962. There are less than 2 months variability for QBO period with height. The diamonds are the mean qbo periods on different levels. It is almost constant with height. The mean QBO period is about 28 months.
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Next, I will first show the model run with solar varying case. Even in a 200-year long run, the period of the QBO does not settle down to a fixed number. The behavior of the QBO period in the model is quite similar to the observation discussed above.
The QBO period jumps from 4 to 5 SAO periods in a non-stationary manner.
The number of 5-SAO periods is about equal to the number of 4-SAO periods in long term run. For example, 90 out of 176 QBO are synchronizedwith 4 SAO and the rest 86 QBOs are synchronized with 5-SAO. However, in different smaller time segments of about 45 years from the model, the distribution can shift. Here, we showed 3 pieces of 45 year segmentsfrom 200-year run. We choose 45 years to correspond to the period of ERA-40 data.The segment in figure b has about the same number of 4-SAO and 5-SAO, which is similar to the distribution of long term run. However, during the period in figure c, there are less 4-SAO and 5-SAO. It displayed the similar distribution as in the ERA-40 data. In figure d, it shift to more 5-SAO than 4-SAO.
Then look at the period in Panel c, it also showed little relation with the 11-year solar cycle, small very aviation of qbo period with height. It’s average QBO period is also about 28 month.
An additional interesting result is that the jumps in the QBO period that we see in the ERA-40 data, is not only seen in our model result with a periodic solar cycle forcing, but is also present in runs with perpetual solar forcing.
The non-stationary jumps in QBO period are not a result of the variable solar-cycle forcing, but are a property intrinsic to the QBO phenomenon itself.
The intrinsic period of the QBO is determined by the internal dynamics of the wave-mean flow system. Here are the 4 cases with decreasing waving force from a to d. It shows the QBO periods shift to more synchronization of 5-SAO under the decreasing of wave forcing. Plume 1977 gave a simple formula that the period T is proportional to the cube of the phase speed c of the forcing wave and inversely proportional to the magnitude of the wave forcing F. Therefore, when the wave forcing is increased, there are more QBO synchronized with 4 SAO than 5 SAO to shorten the mean QBO period.
Using ERA-40 data, which extends to the stratopause region and encompasses both the SAO and QBO, we find that the period of the QBO is always an integer multiple of the SAO period.
The w-QBO always corresponds to a w-SAO above. On an eastward rotating planet, the equatorial upper stratosphere has an easterly bias in the absence of the SAO. The initial of the w-QBO would have become more difficult in the absence of the SAO.
We have also shown that since there is very little variation of the QBO period in the vertical, the same synchronization with the SAO should also hold throughout the stratosphere.
A second interesting feature of the observed behavior of the QBO period is its random jumps between 4-SAO and 5-SAO periods. This non-stationary behavior is not due to the fact of the solar-cycle forcing, because the same behavior remains when we perform a run under the perpetual solar-mean forcing.
An alternative explanation is that the magnitude of wave forcing in our current climate determine the intrinsic QBO mean period lies between 4-SAO and 5-SAO. To maintain synchronization with the SAO period, the QBO jumps in a non-stationary way so that a long-term average is about 28 months.
If this explanation is correct, then we should be able to find a different behavior for a different wave forcing, either larger or smaller than the value for the current climate, so that the intrinsic period is an integer multiple of the SAO, 24 months or 30 months. Then the QBO period actually locks into 4- or 5-SAO periods.