Updated observation and theory of the quasi-biennial zonal wind oscillation(QBO) in the equatorial stratosphere

By Chih-Wen(Jason) Hung

1. Introduction

The quasi-biennial oscillation (QBO) in the equatorial lower stratosphere is an interesting periodic oscillation in atmosphere. This term paper will present the updated studies of QBO in recent years. A briefly review of QBO observation and theory are in Section 2. QBO simulated by General Circulation Model is in Section 3. The model simulation of QBO associated with extratropical Planetary Rossby waves is in Section 4. Finally, concluding remarks are given in Section 5.

2. A review of QBO observation and theory

The quasi-biennial oscillation(QBO) in the mean zonal winds of equatorial stratosphere is a very well known periodic oscillations in atmosphere. The period of this oscillation is about(a little over) two years and zonally symmetric easterlies and westerlies alternate regularly. According to previous analysis of observation(Fig1), we have known the following observed features:
1. Zonally symmetric easterly and westerly wind regimes alternate regularly with periods varying from about 24 to 30 months(Holton,1992). The fastest obsevedoscillation had a period close to 20 months(1959-1961) and the slowest was 36 months(1984-1987), while the mean period was 28.2 months(Pawson et al 1993b);about 5 cycles in 12 years(Maruyama,1997).
2. Successive regimes first appear above 30Km (~10 hPa), but propagate downward at a rate of 1Km/month. The downward propagation occurs without loss of amplitude between 30 Km and 23 Km(10 hPa ~ 35 hPa)(Holton,1992),but below this level, the westerly wind regimes propagate smoothly downward with little variation between cycles; however, the descending easterlies are often subject to a delay(Kinnersley et al 1996).Because of this stalling of easterlies, the time between maximum easterlies and maximum westerlies is much shorter than the other way around(Naujokat,1986). Otherwise, the easterlies are generally stornger than the westerlies.The asymmetrical descent rate of the easterly and westerly shear zones is one of the most notable properties of the QBO.
3. The amplitude of QBO is between 40 and 50 m/s. The maximum amplitude is near 20 hPa(Naujokat 1986).
those observed features gave us a very good concept of the phenomenon of QBO.However, many researchers tried to find a theory to explain it and use model to simulate this periodic oscillation in lower equatorial stratosphere.
1.Coupling with the SAO of zonal wind in the upper stratosphere(Lindzen & Holton,1968) This theory assumes the SAO(Semi-Annual Oscillation) in the upper stratosphere plays an important role in lower stratosphere QBO. The semiannual oscillation at about 40 Km is needed, and the vertically propagating equatorial gravity waves carry the vertical eddy momentum and can be absorbed above the critical level(assume below 19Km, there will be no absorption of gravity waves).In this theory,the important factor of QBO is come from upper stratosphere.
2.Kelvin wave & mixed Rossby-gravity waves provide the zonal momentum sources (Holton & Lindzen,1972) This theory assumes the vertically propagating equatorial Kelvin wave and mixed Rossby-gravity waves provide the zonal momentum source of QBO and are dissipated by Newtonian cooling. The Rossby-gravity waves of zonal wave number 4 and a period of about 4.5 days are discovered by Yanai and Maruyama(1966); The Kelvin waves of zonal wavenumber 1 or 2 and a period of about 15 days are found by Wallace and Kousky(1968). The eastward propagating Kelvin wave provides the needed source of westerly momentum, and the westward propagating mixed Rossby-gravity wave provides easterly momentum.However, the westerly Kelvin waves tend to be damped in westerly shear zones, and the easterly mixed Rossby-gravity wave is damped in easterly shear zones.
Plumb(1984) used this simple concept to explain the QBO oscillation very well.The total cycle of QBO is explained as following:<1>Kelvin wave provides the westerly momentum and increase the westerly shear zone <2>When the shear zone in atmosphere become strong westerly, the Kelvin wave tend to be damped and mixed Rossby-gravity wave can propagate upward well <3>Mixed Rossby-gravity wave provide the easterly momentum upward and increase the easterly shear zones <4>When the shear zones in atmosphere become strong easterly,the mixed Rossby-gravity wave tends to be damped and Kelvin wave can propagate upward well <5>go back to step<1>.

3. Updated observation of QBO

1 El Nino & QBO
Maruyama & Tsuneoka(1988) noted that the rapid descent of QBO westerly was accompanied with the El Nino. The El Nino event enhanced Kelvin wave activities, it maybe possible to explain the rapid westerly wind descent. If the El Nino event suppressed mixed Rossby-gravity wave activities, it maybe possible to explain the preceding long westerly wind phase and short easterly phase. El Nino event are cosidered to work partly on the descent rate of westerly phase. All slower descents were out of El Nino event.
We can find the El Nino event related to longer westerly in 1965,1968,1976,1979,1982/83, 1986/87 and 1991/92, and shorter easterly in 1982/83 and 1987.
2 The eruption of Volcano, Pinatubo, Philippines
The QBO-related temperature oscillation can be found, if we seperated by removing annual variations and the mean temperature profile. We can see the QBO easterlies related to positive temperature oscillation exhibits a irregular variation sometimes. In 1991, the eruption of volcano Pinatubo, Philippines(June 15, 1991) caused the descending nagative anomaly is suddenly interrupted. The regular anomaly is about 2C, but the warming by the eruption was about 4C at most(Maruyama,1997).

4. QBO simulated by General Circulation Model

Recently, many studies used different models to simulate QBO in the equatorial lower stratosphere. Takahashi et al(1997) demonstrated a very well QBO-like oscillation in a general circulation model(GCM). They used the first version of the Center for Climate System Research/National Institude for Environmental Studies (CCSR/NIES) atmospheric general circulation model. The horizontal resolution of this model is T21 with 60 layers of vertical resolution (500m).
The westerlies of the QBO-like oscillation in this model is forcing by Kelvin wave and easterward propagating gravity wave; the easterlies are due to westward-propagating n=1 equatorial gravity waves, random westward-propagating gravity waves and Rossby waves propagating from mid-latitudes in the northern hemisphere to the equatorial region.
The result of this model simulation is quite well, but still have little differences from the observed QBO. The period of the simulated oscillation is 1.5 years( a little shorter than "quasi-biennial") and the height of the oscillation is slightly higher than real. This is related to the general weakness of easterly phase and caused the easterly phase is too high. On the other hand, the westerly phase of the oscillation (maximum westerly is about 20 m/s) is stronger than the easterly (maximum easterly is about -15 m/s) in this model. That's exactly reverse of the observed QBO --- Easterly is stronger than westerly.
In this model, Rossby waves propagating from the mid-latitudes to equatorial region play a role in QBO-like oscillation. On average, the contribution of the easterly acceleration due to Rossby waves from mid-latitude is about half (-0.5 x 10 m/s )the vertical wave momentum flux, but the magnitude of the easterly flux is still smaller than the westerly flux.

5. The model simulation of QBO associated with extratropical Planetary Rossby waves

The recent QBO studies tend to take extratropical stratospheric westward Rossby waves into account, because extratropical Rossby waves have been observed at the equator(Hitchman et al, 1987), although most equatorward radiating Rossby waves are absorbed at low latitudes, but the absorption process must not be complete.
However, it has long been known that laterally propagating extratropical Rossby waves do not play a major role in forcing the QBO(Wallace & Holton, 1968), but it is still possible that extratropical Rossby wave contribute to the QBO's momentum budget in some ways.
Recent study by O'Sullivan(1997) shows the incident extratropical Rossby waves radiating to the tropics during the QBO's westerly phase remarkably unaffect to QBO westerly jet. He used a global shallow water model to examine the pattern of wave absorption at low latitude during the westerly wind phase of the QBO. The important conclusion is the QBO is unforced and free to evolve in respone to Rossby wave absorption. However, how about the situation when the stratosphere is the easterly wind phase of the QBO? Does extratropical Rossby waves play an important role?
A study of Kinnersley & Pawson(1996) is another research of extratropical Rossby waves in the QBO. They didn't only just focus on the role of extratropical Rossby waves, but also the asymmetrical descent rate of QBO, because in original Holton-Lindzen(1972) model of QBO, they can't explain the descending easterlies are often subject to a delay. Kinnersley & Pawson(1996) used a 2 1/2D model to simulate this assymmetrical descent rate of the easterly and westerly shear zones. The basic concept of this study is to take extratropical planetary waves into account, not just only have tropical waves.
The 2 1/2D model is an isentropic zonally averaged chemical-radiative-dynamical model which coupled to a 3-D planetary wave model that is used to compute the horizontal wave fluxes that used by the zonally averaged model.
The study assumes that tropical Kelvin wave is the forcing of the QBO westerly winds and tropical mixed Rossby-gravity wave is the forcing of the QBO easterly winds. However, tropical gravity wave and extratropical planetary wave are taken into account.
This model includes gravity wave drag above 35 Km, the annual cycle in the incoming solar flux, lower level forcing as Holton-Lindzen(1972) model, and extratropical planetary waves.
In order to demonstrate the extratropical planetary wave can play an important role of the observed stalling of the descent rate of the easterly wind regimes. In this study, they simulate the all same incoming forcing except extratropical planetary waves at the first. The result of the QBO without planetary waves shows a regular downward propagation of both easterly and westerly wind regimes. The period of this oscillation is arround 20 months. This is quite well if the stalling of easterlies are neglected.
Secondly, they introduce the planetary waves into the model. It leads to a stalling of more than one year in the descent rate of the easterly wind regimes, but only about 2 months longer in the westerly wind regimes. Not only did the stalling happen for westerlies, but also in the model at about 20 Km.
The westerlies still propagate downward smoothly because the vertical advection term is much smaller than the equatorial wave forcing due to the large cancellation between QBO induced cooling and planetary-wave-induced heating.
On the other hand, the stalling of easterlies is the most interesting part of this study. We need to note that this result is achieved in the model without any asymmetric or seasonally varying equatorial wave forcing and is due to the strengthening of the planetary-wave-induced equatorial heating rates by the QBO heating anomaly.
When the atmosphere is during easterly descent, the enhanced heating is "observed" in this model due to combine with the QBO easterlies induced heating and the equatorial heating induced by the extratropical planetary wave. When the heating rate is not weak, the vertical wind shear is increased due to the impact of vertical advection. Then, the accelerations of the easteerly descent tend to be smaller and cause the stalling.
Otherwise, why can this model produce the stalling only under 20 Km? the answer is the QBO heating anomaly is in general much smaller than the control heating rate at 30 Km. However, at 20 Km, it is about the same size. This causes the vertical advection in the easterly descent phase increase until it balances the wave drag, and a stalling occurs.

6. Conclusion

The observation of QBO is a routine job for weather center and the height-time figure can be made easily and show us this periodic oscillation very well. The El Nino related to the QBO will be investigated in the near future. The eruption of volcano can be another topics for us to see how this kind of irregilar warming affect on the QBO.
The development of model simulation has moved from 2D model to 2 1/2D and 3D models. Some 2D model already can simulate the QBO very well. Recently, Kinnersley & Pawson(1996) 2 1/2D model has successfully produced the QBO oscillation and the stalling of the descent rate of the easterly wind regimes with the effect of extratropical planetary waves. Takahashi et al(1997) get the QBO-like oscillation by General Circulation Model, although there are some results are different from the real such as "The westerlies are stronger than easterlies" and "The period of the QBO oscillation is just 1.5 years" in this model. However, it is quite well to obtain the QBO-like oscillation by GCM simulation, because it is harder than the 2D model.
The recent studies of QBO tend to take extratropical planetary waves into account. Even it is not a major forcing of tropical QBO, but still affect on the descent rate. The extratropical planetary waves become one of the QBO forcing is parts of the reasons 3D QBO simulation become important on this topics.


Hitchman, M.H. C.B. Leory, J.C. Gille, and P.L. Bailey,1987: Quasi-stationary zonally asymmetric circulations in the equatorial middle atmosphere, J. Atmos. Sci., 44,2219-2236.
Holton,J.R.,and R.S.Lindzen,1972:An updated theory for the quasi-biennial oscillation of the tropical stratosphere. J. Atmos. Sci.,29,1076-1080.
Kinnersley, J.S.,and S. Pawson, 1996: The descent rates of the shear zones of the equatorial QBO. J. Atmos. Sci.,53,1937-1949.
Maruyama, T. and Y. Tsuneoka, 1988: Anomalously short duration of the easterly wind phase of the QBO at 50hPa in 1987 & its relationship to an El Nino event. J.Meteor. Soc. Japan,66,629-634.
Maruyama,T.,1997: The quasi-biennial oscillation(QBO) and equatorial waves - a historical review. Paper in Meteo. & Geophys. 48, 1-17.
Naujokat, B.,1986: An updated of the observed quasi-biennial oscillation of the stratospheric winds over the Tropics. J. Atmos. Sci.,43,1873-1877.
O'Sullivan, Donal,1997: Interaction of extratropical Rossby waves with westerly quasi-biennial oscillation winds, J. Geophys. Res., 102,19461-19469.
Pawson, S.,K. Labitzke,R. Lenschow, B. Naujokat, B.Rajewski, M. Wiesner, and R.-C. Wohlfahrt, 1993b: Climatology of the Northern Hemisphere stratosphere derived from Berlin analyses. Part 1: Monthly means. Meteorologische abhandlungen (Neue Folge),Verlag von Dietrich Reimer,141pp.
Takahashi, M., N. Zhao & T. Kumakura,1997: Equatorial waves in a General Circulation Model simulating a quasi-biennial oscillation. J. Meteor. Soc. Japan, 75,529-539.
Wallace, J.M.,and J.R. Holton,1968: A diagnostic numerical model of the quasi-biennial oscillation. J. Atmos. Sci.,25,280-292.