Transcript Моделирование квазидвухлетних колебани

Modeling the
quasi-biennial oscillations
of the zonal wind in the
equatorial stratosphere.
Kulyamin D.V.
MIPT, INM RAS
Quasi-biennial oscillations (QBO)
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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
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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
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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 QBO
Main task - the simulation of the QBO in the atmospheric general
circulation models (GCM)
(only few climate models are now able to reproduce QBO)
The QBO general mechanism:
nonlinear interaction between the mean flow and equatorial waves
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 gravitywave drag
Concept 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 in
Low-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 interaction
of long waves with the mean flow
The QBO formation is considered on the basis of the interaction of largescale equatorial waves with the mean flow at critical levels (layers)
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.

B
(  )  J ( ,  ) 
  (  2 )  0,
t
x
B

 J ( B, )  N 2
  B  0.
t
x
the equations in terms of stream
function and buoyancy:
Solved using WKBapproximation
Model general equations:
u
1
F n
2 u
 
 2 ,
t
 n z
z
z  [0, H ], u
z 0
 0,
u
z
2 waves differing
only in the
directions of phase
velocity are used
as a wave forcing
c1  c2  c
 0, u
zH
t 0
 u0 ( z ),


N
Fn ( z )    u 'n w 'n    F0 exp  
dz '.
2
0 k (u
c)


z
k1  k2  k
F1 (0)   F2 (0)  F0
The results of a numerical experiments with Plumb model of QBO
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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
kc
T  A
 F0
A(  , N , H , Z0 )
- dimensional
coefficient of
proportionality (which
may depend on other
model parameters)
height-time section
Simulation of the QBO through interaction
of gravity wave drag parameterization
The QBO mechanism by gravity-wave drag is carried out with a simple onedimensional model analogous to Plumb by parameterization (developed by C. Hines)
u
1 FGW
2 u
2




F


(
z
)

(
z
)
kC
(
m
(
z
)

m
2
GW
0
0
iC
iC ( z ))
t
 z
z
Model general equation – the evolution of the zonal mean flow at the equator
FGW - 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:
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Nm1  k 1- dispersion relation, based on the assumption of isotropy of wave velocity
v
 N - the condition of non obliteration of gravity wave
z
• Statistical fudge factors:   m  N , v( z)   ˆ
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1
2
• necessary conditions for the value of critical heights for any initial-spectrum element
miC  N ( z0 )[1  u( z)  u( z0 )  v( z)]1
• linear spectrum:
FGW 
miCritical

mi min
 ( z0 )v( z0 )v( z0 )k / mi dmi   ( z0 ) ( z0 )2 k
miCritical

mi min
P(mi ) / mi dmi
The results of a numerical experiments with gravity-wave drag model of QBO
• 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
Boundary conditions:
u ( z0 )  0,
u ( zmax )  0
FGW ( z0 )  0,
FGW ( z )
0
z Z max
1
T  B
2
k 0 mmin 
The results of a numerical experiments with gravity-wave drag model of QBO
height-time section
Simulation of the QBO through the combined interaction of
gravity and planetary waves with zonal flow
The model include both QBO mechanism by long waves - mean flow interaction and gravity-wave drag
Model general equations:
u
1  ( FP  FGW )
2u

 2
t

z
z
 z

N ( z ')
FP ( z )   ( z) Fn ( z0 )exp 
dz ', n  1,2
0 k (u ( z ')  c ) 2
n
n
n


FGW ( z)   ( z0 ) ( z0 )2 kC(miC ( z)  miC ( z)).
The main results of combined modeling
1. 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).
Fig. 1
height-time sections
Fig. 2
Simulation of the QBO in
General Circulation Models (GCM) of INM RAS
Main task – making a GCM which simulates realistic QBO
• 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
The results of a numerical experiments to simulate QBO in GCM
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
GCM INM RAS 2°х2.5°х80
height-time section of zonal wind
For the GCM 2°х2.5°х80 obtained realistic QBO (by varying vertical diffusion parameter)
The spectral characteristics of the QBO from the observational data and modeling data of
GCM INM RAS 2°х2.5°х80
Basic research methods: spectral analysis, histograms
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
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
The spectrum of the zonal wind at the equator by the ERA40
reanalysis data
height-period section
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
The spectrum of the zonal wind at the equator by the GCM INM
RAS 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
Conclusion
• 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 lowparameter 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
Conclusion
• 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