Modeling theModeling thequasi-biennial oscillations quasi-biennial oscillations

of the zonal wind in the equatorial stratosphere.

Kulyamin D.V.

MIPT, INM RAS

Quasi-biennial oscillations (QBO)

• Period ~ 22 to 33 months (average - 28 months)• Zone of propagation: 80 to 10 mb (20 – 40 km) with maxima of amplitudes about 30 m/s at 20 to

10 mb• Slow downward propagating (at speed ~ 1 km per month)• Tendency for a seasonal preference in the phase reversal (probable synchronization problem)

Latitudinal structure of QBO

Zonal wind at 20 mb• Narrow equatorial zone ( ~ 6° northward and southward of the equator).• Distribution of QBO amplitudes is approximately symmetric about the equator

QBO influence on the circulation of atmosphere• modulating the propogation of extratropical waves

• has influence on generation and circulation of ozone and on other chemical constituents

• interaction with other low-frequency processes (El Niňoo–Southern Oscillation (ENSO) etc.)

• affect variability in the mesosphere (by selectively filtering waves that propagate upward)

• affect the strength of Atlantic hurricanes.

QBO anomaly in ozone:

(a) Full anomalies defined as deseasonalized and detrended over 1979–1994, and (b) the QBO component derived by seasonally varying regression analysis.

Contour interval is 3 DU, with 0 contours omitted and positive values shaded.

The basic theory of the QBOThe basic theory of the QBOMain task - the simulation of the QBO in the atmospheric Main task - the simulation of the QBO in the atmospheric general circulation models (GCM)general circulation models (GCM)(only few climate models are now able to reproduce QBO)(only few climate models are now able to reproduce QBO)

The QBO general mechanismThe QBO general mechanism::

nonlinear interaction between the mean flow and equatorial waves nonlinear interaction between the mean flow and equatorial waves propagating upward (with periods unrelated to that of resulting QBO)propagating upward (with periods unrelated to that of resulting QBO)

Conditionally all equatorial waves are divided into two groups• large-scale waves (trapped equatorial Kelvin waves, mixed Rossby–gravity waves, and long inertia–gravity waves, periods - about 1 to 10 days, zonal wavelengths about1000 km) in GCM - internal process

• small-scale gravity waves (periods << 1 day, zonal wavelengths - 10 to 1000 km) in GCM - a subgrid-scale process, is solved by a parameterization of gravity-wave drag

Concept of the mechanism for the QBO generationConcept of the mechanism for the QBO generation

Schematic representation of the evolution of the mean flow in Plumb’s [1977] analog of the QBO.

Simulation of the QBO inLow-Parameter ModelsLow-Parameter Models

Investigation of QBO formation by interaction of two types of waves with mean flow

•The mechanism of the interaction of long waves with mean flow at critical levels (based on the low-parameter model of R. Plumb): obtaining realistic OBQ and determination of key parameters responsible for its period and other characteristics

•The mechanism of the interaction of short gravity waves with mean flow (based on the parameterization, proposed by C. Hines): investigation of the possibility to obtain the OBQ with realistic characteristics, using only gravity-wave drag

•Investigation of the relative role of different scales equatorial waves in the QBO formation in model, combined two mechanisms.

Simulation of the QBO through interactionSimulation of the QBO through interactionof of long waves long waves with the mean flowwith the mean flow

The QBO formation is considered on the basis of the interaction of large-scale equatorial waves with the mean flow at critical levels (layers)

Model general equations:2

2

00 0

0 20

1,

[0, ], 0, 0, ( ),

( ) ' ' exp ' .( )

n

n

z tz H

z

n n n

u F u

t z z

uz H u u u z

z

NF z u w F dz

k u c

Main assumptions used in the Plumb model: the equations of a two-dimensional (x,z) viscous Boussinesq fluid in the gravity-force field with thermal cooling.

the equations in terms of stream function and buoyancy:

Solved using WKB-approximation

2

2

( ) ( , ) ( ) 0,

( , ) 0.

BJ

t xB

J B N Bt x

2 waves differing only in the directions of phase velocity are used as a wave forcing

1 2c c c

1 2k k k

1 2 0(0) (0)F F F

The results of a numerical experiments with Plumb model of QBO

• obtained oscillations close to realistic QBO

• obtained the experimental dependence of the oscillations period and the model parameters• real values of long-wave energy are not enough for the QBO formation• in modeling the process of interaction at the critical level the vertical resolution is of

primary importance• the vertical-diffusion process is significant for QBO formation

0

kcT A

F

0( , , , )A N H Z - dimensional coefficient of proportionality (which may depend on other model parameters)

height-time section

The QBO mechanism by gravity-wave drag is carried out with a simple one-dimensional model analogous to Plumb by parameterization (developed by C. Hines)

Model general equation – the evolution of the zonal mean flow at the equator

2

2

1 GWFu u

t z z

20 0( ) ( ) ( ( ) ( ))GW iC iCF z z kC m z m z

- the momentum flux from gravity-wave drag, calculated by parameterization algorithm

The main ideas of parameterization is based on the theory of the Doppler shift of the middle portion of the spectrum of gravity waves toward higher vertical wave numbers:

• - dispersion relation, based on the assumption of isotropy of wave velocity

• - the condition of non obliteration of gravity wave

• Statistical fudge factors:

• necessary conditions for the value of critical heights for any initial-spectrum element

• linear spectrum:

1 1Nm k v

Nz

1 2 ˆ, ( )m N v z

min min

20 0 0 0 0( ) ( ) ( ) / ( ) ( ) ( ) /

iCritical iCritical

i i

m m

GW i i i i i

m m

F z v z v z k m dm z z k P m m dm

10 1 0( )[ ( ) ( ) ( )]iCm N z u z u z v z

GWF

Simulation of the QBO through interactionSimulation of the QBO through interactionof of gravity wave drag gravity wave drag parameterizationparameterization

The results of a numerical experiments with gravity-wave drag model of QBO

Boundary conditions:

0

max

0

max

( ) 0,

( ) 0

( ) 0,

( ) 0

GW

GW

Z

u z

u z

F z

F z

z

20 min

1T B

k m

• as a result of parameters varying we obtained oscillations with the characteristics are close to realistic QBO

• obtained the experimental dependence of the oscillations period and the model parameters

• range of the model parameters under which the decision was in the form of a limit cycle is small

• period-parameters dependence is highly sensitive to fluctuations in model parameters

• to obtain realistic QBO characteristics of gravity waves are greatly overrated compared to actual values

The results of a numerical experiments with gravity-wave drag model of QBO

height-time section

The model include both QBO mechanism by long waves - mean flow interaction and gravity-wave drag

2

2

1 ( )P GWu F F u

t z z

0 20

( ')( ) ( ) ( )exp ' , 1,2

( ( ') )

z

P nn n n

N zF z z F z dz n

k u z c

20 0( ) ( ) ( ) ( ( ) ( )).GW iC iCF z z z kC m z m z

Simulation of the QBO through the combined interaction of Simulation of the QBO through the combined interaction of gravity and planetary wavesgravity and planetary waves with zonal flow with zonal flow

Model general equations:

The main results of combined modeling1. With realistic values of the long waves energy and gravity-wave drag parameters obtained

oscillations closed to observed QBO.

2. The main interaction of long equatorial waves with the zonal flow occurs in the lower stratosphere and produces own oscillations there (fig. 1). These waves play major role in QBO period formation.

3. Gravity-wave drag occurs in the upper stratosphere, gravity waves play a minor role in the period formation (fig. 2).

height-time sectionsFig. 1 Fig. 2

Main task – making a GCM which simulates realistic QBO

Simulation of the QBO inSimulation of the QBO inGeneral Circulation Models (GCM) of INM RASGeneral Circulation Models (GCM) of INM RAS

• The model of INM RAS 2°х2.5°х39 – used as a basis, includes parameterization of gravity-wave drag, rough vertical resolution (not satisfies the condition for realization of the interaction of long waves with the mean flow)

• Is not able to reproduce QBO (only annual cycle)

• The model of INM RAS 2°х2.5°х80 – a new version of model with high vertical resolution, built for realization of two QBO formation (vertical resolution in the stratosphere is about 500 m)

Numerical experiments were performed on clusters of INM RAS and MIPT

It is necessary to obtain QBO in GCM with realistic characteristics (both QBO mechanisms are realized: gravity-wave drag and long waves - mean flow interaction)

height-time section of zonal wind from ERA40 reanalysis of observations for 10 years

The results of a numerical experiments to simulate QBO in GCMThe results of a numerical experiments to simulate QBO in GCM

The results of a numerical experiments to simulate QBO in The results of a numerical experiments to simulate QBO in GCM INM RAS 2°GCM INM RAS 2°х2.5°х80 х2.5°х80

For the GCM 2°х2.5°х80 obtained realistic QBO (by varying vertical diffusion parameter)

height-time section of zonal wind

The spectral characteristics of the QBO from the observational data and modeling data of GCMGCM INM RASINM RAS 2°х2.5°х80 2°х2.5°х80

Basic research methods: spectral analysis, histograms

ERA40 reanalysis

Height 50 mb 20 mb 10 mb 5 mb

Mean period 28.6 mon 27.8 mon 28.3 mon 12.7 mon

Standard deviation of period value 4.7 mon 4.9 mon 4.3 mon 8.2 mon

The duration of the westerly QBO phase 16.8 mon 14.2 mon 14.4 mon 6.6 mon

The duration of the easterly QBO phase 11.6 mon 14.2 mon 13.9 mon 5.9 mon

GCM INM RAS 2°х2.5°х80

Height 50 mb 20 mb 10 mb 5 mb

Mean period 28.5 mon 28.2 mon 25.3 mon 15.9 mon

Standard deviation of period value 1.5 mon 2 mon 7.3 mon 7.6 mon

The duration of the westerly QBO phase 14.3 mon 13.5 mon 14.5 mon 9.6 mon

The duration of the easterly QBO phase 13.5 mon 14.8 mon 10.9 mon 6.2 mon

Data:- ERA40 reanalysis- numerical experiment with the GCM INM RAS 2°х2.5°х80

QBO period is calculated as:

The table gives the mean values and standard deviation of periods, calculated as differences between the transitions through zero value for the filtered data series

The spectrum of the zonal wind at the equator by the ERA40 the ERA40 reanalysis datareanalysis data

The most intense spectral peaks observed in the stratosphere with the value of the period ~ 28-29 months (QBO), as well as in the mesosphere, the relevant SAO and annual cycle

height-period section

The spectrum of the zonal wind at the equator by the GCM INM the GCM INM RAS 2°х2.5°х80RAS 2°х2.5°х80

The GCM spectra is similar to the observations: intense peaks corresponding to the SAO and the annual cycle in the mesosphere and broad spectral peak of the QBO with a maximum at T ~ 28 months, the spread period, the QBO peak is narrower than the observational

ConclusionConclusion• Two mechanisms of the QBO formation are considered (through

the interaction of planetary waves with the mean flow at critical levels and through gravity-wave drag) on the base of low-parameter models. It is shown that each type of waves can generate oscillations of the zonal velocity, similar to the observed QBO.

• On the base of numerical experiments dependences of the oscillations characteristics and models parameters are gotten in both cases. The conditions necessary for the realization of the QBO in GCM are obtained (ground - high spatial resolution).

• It is shown that with the combined inclusion of two wave sources leading role in the QBO period formation play by the planetary waves, gravity waves also play a minor role

ConclusionConclusion• New version of INM GCM 2°х2.5°х80 with high vertical

resolution are built

• In the INM GCM 2°х2.5°х80 become possible to reproduce the QBO very close to observations. This is a key result of the study.

• It is shown that INM GCM 2°х2.5°х80 generally satisfactory reproduces the main spectral characteristics of the QBO