# The Quasi-biennial Oscillation (QBO)

This web page shows the Quasi-biennial Oscillation (QBO) near real-time and historical behavior over the satellite-era (1980-present). Daily plots are updated at least once per day, while monthly plots are updated on the 2nd of the following momth.

## Introduction

The Quasi-biennial Oscillation (QBO) is a tropical, lower stratospheric, downward propagating zonal wind variation, with an average period of ~28 months. The importance of the QBO is that it dominates the variability of the tropical lower stratospheric meteorology [Wallace, 1973]. The QBO is also important for seasonal forecasting, and the QBO controls stratospheric ozone and water variability that can modulate surface ultra-violet (UV) and infrared (IR) radiation.

Ebdon [1960] and Reed et al. [1961] independently first detected the QBO in the early 1960s. Tropical radiosonde wind observations that document the QBO have been made continuously since 1953 [e.g., Naujokat, 1986], and these early observations are available as a continuous time series to the present at the Freie Universitat of Berlin.

A comprehesive QBO summary (with a description of the cause of the QBO) can be found in Baldwin et al. [2001].

Data herein are from radiosondes, NASA GSFC/GMAO assimilated data, and NASA satellites. The radiosondes are from the Meteorological Service Singapore Upper Air Observatory (station code 48698). The station is located at 1.34041N, 103.888E at an altitude of 21m.

The assimilated data are from the Modern-Era Retrospective analysis for Research and Applications, Version -2 (MERRA-2). MERRA-2 provides data beginning in 1980 and runs a few weeks behind real time [Gelaro et al., 2017]. The structure, dynamics, and ozone for the QBO in MERRA-2 is documented in Coy and Wargan [2016].

These plots also reveal the QBO disruption that occured from late 2015 through about February 2017 [Newman et al., 2016; Osprey et al., 2017]. A more complete dynamical explanation of the disruption can be found in Coy et al. [2017] with another paper describing the deceleration as being caused by a very strong wave packet Lin et al. [2019]. The impact on ozone, water, etc., can be found in Tweedy et al. [2017].

## Zonal winds

### Singapore sonde 1980-present QBO from monthly mean zonal wind

The plot is made by: 1) reading all daily sondes for the full month (generally twice per day at 0Z and 12Z), 2) vertically interpolating the zonal wind to missing levels (no extrapolation to levels above balloon burst altitudes), and 3) time interpolating for missing levels above the top of the balloon profile. The thick dotted line shows the tropopause calculated from the thermal lapse rate. Units are meters per second (m/s).

As above, but with annual cycle removed and a 5-month Gaussian smoothing, and the high-res PDF.

### MERRA-2 1980-present QBO monthly mean zonal wind at the Equator

The plot is generated from the monthly mean MERRA-2 zonal mean winds. The thick dotted line shows the tropopause calculated from the thermal lapse rate. The noted easterly and westerly phases are derived from the Singapore sonde above. Units are meters per second.

MERRA-2 zonal wind plot as above (png) (or high-rese PDF), but winds are detrended and the annual cycle removed.

### The last 3 years of the QBO from the Singapore sonde daily zonal wind

The plot shows the daily zonal mean winds from the twice per day (0Z and 12Z) Singapore radiosondes. Each sonde is interpolated to a 0.5km vertical grid. Above the burst altitude, either MERRA-2 or GEOS-FP data are used to fill this vertical grid. The black line shows the tropopause as computed from the lapse rate. Units are meters per second.

### MERRA-2 1980-present QBO monthly mean zonal wind versus latitude

#### 40 hPa

The latitudinal structure of the zonal mean wind from MERRA-2 at 40hPa. These data INCLUDE the annual cycle in order to show how the QBO phase connects to mid-latitude, mid-winter westerlies. Units are meters per second.

#### 10 hPa

As above, but for 10 hPa.

### The EOFs of the 1980-present QBO from the Singapore sonde monthly mean winds

The plot shows the phase diagram of the two leading modes of the calculated empirical orthogonal functions (EOF). The EOFs represent the major components of the QBO variability, and have been calculated following [Wallace et al., 1993]. The EOFs were derived from the 1979-present deaseasonalized monthly mean Singapore radiosonde zonal winds (shown above). The first two EOFs show the circular polarization that is characteristic of the QBO in the counter-clockwise rotation. On the rim of the figure are the simple reconstructuions of the zonal wind profile for the various phases. The last 3 calendar years are colored. This plot was recently shown in Tweedy et al. [2017]. Units are meters per second.

Most of the plots on this page have superimposed easterly (E) and westerly (W) points. These E and W points are derived from this EOF-1 and EOF-2 phase diagram above. The W (E) points are calculated when the phase angle is 45 (225) degrees, corresponding to a dominant westerly (easterly) in the 70-10 hPa part of the stratosphere.

## Temperatures

### Singapore sonde temperature QBO from monthly mean data

The plot is generated by: 1) reading in monthly mean temperatures, 2) detrending the temperature time series, 3) subtracting off the annual cycle at all levels, and 4) smoothing the data with a 1-2-1 Gaussian filter (effectively removing variability with periods of 2 months or less. The thick dotted line shows the tropopause calculated from the thermal lapse rate. Units are Kelvin.

### MERRA-2 temperature QBO from monthly mean data at the Equator

As with the zonal winds, the T plot is generated by taking the monthly mean MERRA-2 zonal mean temperature, and then subtracting the long-term monthly mean, and then performing a linear detrending of the residual temperature. The thick dotted line shows the tropopause calculated from the thermal lapse rate. Note that the QBO wind peaks tend to fall along the "zero" temperature lines. Units are Kelvin.

### The last 3 years of the temperature QBO from the Singapore sonde daily

The plot shows the daily zonal mean temperatures from the twice per day (0Z and 12Z) Singapore radiosondes. Each sonde is interpolated to a 0.5km vertical grid. Above the burst altitude, either MERRA-2 or GEOS-FP data are used to fill this vertical grid. The 3-year time average profile is subtracted from the data (annual cycle is still embedded in the plot). The tropopause is shown as the black line (computed from the lapse rate). Units are Kelvin.

### MERRA-2 temperature (deseasonalized) QBO from monthly mean data versus latitude

#### 40 hPa

As with the zonal winds, the T plot is generated by taking the monthly mean MERRA-2 zonal mean temperatures, and then subtracting the long-term monthly mean, and then linearly detrending the residual temperature. The easterly (E) and westerly points are as shown in the Singapore zonal winds, and are defined by the EOF-1 and EOF-2 phase diagram above. Units are Kelvin.

Same plot, but 90S-90N PNG file, or high-res PDF

#### 10 hPa

As above, but for 10 hPa.

Same plot, but 90S-90N PNG file, or high-res PDF

## Vertical velocity (W*)

### MERRA-2 W* QBO from monthly mean data at the Equator (2S-2N)

As with the zonal winds, the W* plot is generated from MERRA-2 zonal mean values. The annual cycle and the linear trend of the 1980-present time series are both removed, and the values are band pass filtered with a Gaussian filter (9-45 months). The thick dotted line shows the tropopause calculated from the thermal lapse rate. The QBO is well correlated in the post-1999 period, but relatively poor prior to that date. This is probably related to the increased assimilation of satellite data in the post-1999 period.

### MERRA-2 W* QBO from monthly mean data versus latitude

#### 40 hPa

As described above. The easterly (E) and westerly points are as shown in the Singapore zonal winds, and are defined by the EOF-1 and EOF-2 phase diagram above. Units are millimeters per second.

#### 10 hPa

As above, but for 10 hPa.

## Zonal mean wind momentum budget

The zonal mean zonal wind budget is from MERRA-2. Daily files at 0, 6, 12, and 18Z from 2000-present are used, annual cycle is computed and removed from all terms. Smoothing is applied with a 21-day 1/2 amplituded Gaussian filter. Trends are not removed. Data are cosine-weighted averages from 5S to 5N. Plot includes (see equations below): a) the zonal mean wind tendency; b) the total momentum terms from the resolved data; and individual momentume terms: c) the mean vertical momentum advection; d) the mean horizontal momentum advection; e) the horizontal eddy momentum flux; and f) the vertical eddy momentum flux.

Transformed Eulerian Mean (TEM) zonal mean wind tendency equation is taken from Andrews et al. [1987]. Overbars indicate zonal mean averages, primes indicate deviations from the zonal mean, $$\phi$$ is latitude, $$\rho$$ is density, $$a$$ is the Earth's radius, $$f$$ is the Coriolis parameter, and $$[u, v, w]$$ represent the zonal, meridional, and vertical winds, while $$t$$ is time.

Eliassen-Palm flux $$= \boldsymbol{\vec{F}} = [ F^{(\phi)}, F^{(z)} ]$$

$$F^{(\phi)} = \rho_{o} a \, {\cos\phi} \; (\overline{u}_z \overline{v^\prime\theta^\prime} / \overline{\theta}_z - \overline{u^\prime v^\prime}), \; F^{(z)} = \rho_{o} a \, {\cos\phi} \, \{ \; \, [f-(a \, \cos\phi)^{-1}(\overline u \cos\phi)_{\phi} ] \; \overline{v^\prime\theta^\prime} / \overline{\theta}_z - \overline{u^\prime w^\prime} \}$$

Residual Circulation (denoted by * superscript) $$= \boldsymbol{\vec{v}^*} = [ \overline{v}^*, \overline{w}^*]$$

$$\overline{v}^* = \overline{v} - \rho_{o}^{-1}(\rho_{o} \overline{v^\prime\theta^\prime} / \overline{\theta}_z)_z, \; \overline{w}^* = \overline{w} + (a \, {\cos\phi})^{-1}(\cos\phi \, \overline{v^\prime\theta^\prime} / \overline{\theta}_z)_{\phi}$$

$$\overline u$$ tendency equation = $$\overline u_t = - \overline v^* [( a \, \cos\phi )^{-1} (\overline u \cos\phi )_\phi -f ] - \overline w^* \overline u_z + (\rho_{o} a \, \cos\phi)^{-1} \nabla \cdot \boldsymbol{\vec{F}} + X$$

### Momentum (5S-5N) versus pressure

The full terms for the plot below are:

(a) $$\frac{\partial \overline u}{\partial t}$$

(b) $$- \overline v^* [( a \, \cos\phi )^{-1} (\overline u \cos\phi )_\phi -f ] - \overline w^* \overline u_z + (\rho_{o} a \, \cos\phi)^{-1} \nabla \cdot \boldsymbol{\vec{F}}$$

(c) $$- \overline w^* \overline u_z$$

(d) $$- \overline v^* \, [ \, ( a \, \cos\phi )^{-1} (\overline u \cos\phi )_\phi -f \, ]$$

(e) $$(\rho_{o} a^2 {\cos^2\phi})^{-1} \frac{\partial}{\partial \phi}(F^{(\phi)} \cos\phi)$$

(f) $$(\rho_{o} a^2 {\cos^2\phi})^{-1} \frac{\partial F^{(z)}}{\partial z}$$

Colors represent accelerations (red) and decelerations (blue) . The thick black lines are zero wind lines of the zonal mean zonal wind average, and the westerly (W) and easterly (E) phases are noted. The tropopause is shown as the thick red dotted line.

This momentum budget is not complete, since it does not include the parameterized gravity wave drag term, the wet momentum deposition term, and the assimilation increments.

### Momentum versus latitude

The latitudinal structure of the zonal mean zonal wind budget from MERRA-2 at 40hPa. Units are meters per second per day. Daily files at 0, 6, 12, and 18Z from 2000-present are used, annual cycle is computed and removed from all terms. Smoothing is applied with a 21-day 1/2 amplituded Gaussian filter. Trends are not removed.

#### 40 hPa

As above, but for 40 hPa.

#### 10 hPa

As above, but for 10 hPa.

## Ozone

### Total ozone from TOMS/OMI versus latitude (deseasonalized)

The plot is generated by: 1) reading in monthly mean total ozone, 2) subtracting off the annual cycle at all levels, 3) detrending the total ozone time series with a linear term over the entire time series, and 4) smoothing the data with a 1-2-1 Gaussian filter (effectively removing variability with periods of 2 months or less. The white "stipes" are data voids (e.g., in 1995 nd 1996), while the white spots (e.g., 30N in early 1985) show where the anomalies exceed the color scale maximum or minimum. The easterly (E) and westerly points are as shown in the Singapore zonal winds, and are derived (see text with EOF figure) from the EOF-1 and EOF-2 phase diagram above. Units are Dobson Units (DU).

### Daily total ozone (last 3 years) from TOMS/OMI versus latitude (deseasonalized)

The plot is generated by: 1) reading in 3-years of daily zonal mean total ozone, 2) reading in the 1979-2017 daily zonal mean data and creating a 365-day climatology, 3) subtracting this annual cycle climatology from the 3-years of daily data, 4) applying a Gaussian smoothing filter with a 6.7 day 1/2 amplitude (i.e., high frequency features are smoothed out). Units are Dobson Units (DU).

### MLS Ozone versus pressure

Ozone versus pressure at the equator from the NASA JPL Microwave Limb Sounder (MLS) on the NASA Aura satellite. Each day's MLS ozone is read, and all profiles within 2.5 degrees of the equator are averaged together to produce the daily ozone profiles. The annual cycle is subtracted from the profiles, and missed profiles are added by temporal linear interpolation. A Gaussian smoothing is applied (1/2 amplitude = 10.1 days) to remove higher frequency structure. The easterly (E) and westerly points are as shown in the Singapore zonal winds, and are derived (see text with EOF figure) from the EOF-1 and EOF-2 phase diagram above. Units are parts per million (ppmv).

### MLS Ozone versus latitude (deseasonalized) QBO from monthly mean data versus latitude

#### 56 hPa

As above for the MLS ozone vertical profile. The data are binned into 5 degree boxes from 45S to 45N. The easterly (E) and westerly points are as shown in the Singapore zonal winds, and are derived (see text with EOF figure) from the EOF-1 and EOF-2 phase diagram above. Units are parts per million (ppmv). The easterly (E) and westerly points are as shown in the Singapore zonal winds, and are defined by the EOF-1 and EOF-2 phase diagram above. Units are Kelvin.

#### 26 hPa

As above, but for 26 hPa.

#### 6.8 hPa

As above, but for 6.8 hPa.

## Water (H2O)

### Water (H2O) versus pressure from MLS

Water (H2O) versus pressure at the equator from the NASA JPL Microwave Limb Sounder (MLS) on the NASA Aura satellite. Each day's MLS water is read, and all profiles within 2.5 degrees of the equator are averaged together to produce the daily water (H2O) profiles. The annual cycle is subtracted from the profiles, and missed profiles are added by temporal linear interpolation. A Gaussian smoothing is applied (1/2 amplitude = 30 days) to remove higher frequency structure. The easterly (E) and westerly points are as shown in the Singapore zonal winds, and are derived (see text with EOF figure) from the EOF-1 and EOF-2 phase diagram above. Units are parts per million (ppmv).

The QBO in water is different than most QBO structures because of the impact of the QBO forced temperature anomalies at the tropical tropopause. There is still downward progression of the QBO above 10 hPa. This behavior is explained by Kawatani et al. [2014] using these same MLS data.

The H2O tape recorder (H2O without deseasonalization), and the high-res pdf version.

### Water (H2O) versus latitutde from MLS

MLS water vapor is gridded into 5 degrees bins. The annual cycle is removed, missed is filled with linear interpolation, data are detrended, and Gaussian smoothing is applied (1/2 amplitude = 14 days) to remove higher frequency structure. The easterly (E) and westerly points are as shown in the Singapore zonal winds, and are derived (see text with EOF figure) from the EOF-1 and EOF-2 phase diagram above. Units are parts per million (ppmv).