MODELLING OF COUPLING OF THE TROPOSHERE AND STRATOSHERE CIRCULATION - - PowerPoint PPT Presentation

MODELLING OF COUPLING OF THE TROPOSHERE AND STRATOSHERE CIRCULATION V.KRUPCHATNIKOFF, I. BOROVKO Institute computational mathematics and mathematical geophysics SB RAS and Novosibirsk State University

e - mail: vkrup@ommfao1.sscc.ru, irina@ommfao1.sscc.ru The Workshop

• Profs. Kabanov M. and V. Lykosov

International Conference : “CITES-2007” Tomsk, Russia, 20-25 July, 2007

• Acknowledgements. The work was supported by RFFI № 05-05 - 64989

Contents

• Dynamic interaction between a stratosphere and troposphere, in particular, connected with planetary waves, can

render essential influence on variations of tropospheric circulation with time scales from several days about several months. Climatology of extratropical stratospheres it is defined by intensity of a polar vortex, which is connected, with gradients rate of temperature.

• Recently there is decrease of temperature of the top layers of an atmosphere, contrast between a tropical and

polar stratosphere and, accordingly, a temperature gradient decreases. Therefore the question on how changes of a polar vortex influence a condition of the bottom layers of an atmosphere represents essential interest.

• So, for example, in work in M.Ambaum and B.Hoskins 2003, using daily and monthly average data, has been

established communication between variations surface pressure, strength of polar vortex and tropopause altitude, increasing of polar vortex connected with low tropopause over Iceland and high tropopause over Arctic.

• High tropopause altitude is connected with strength and twisting of column of air and small drop of surface

pressure in polar region. However, we have no deep understanding of mechanism of interaction of atmosphere and stratosphere.

• The sensitivity of the tropospheric extratropical circulation to thermal perturbations of the polar stratosphere is

examined in general circulation model with zonally symmetric forcing and boundary conditions. For sufficiently strong cooling of the polar winter stratosphere, the winter-hemisphere tropospheric jet shifts poleward at the surface; this is accompanied by decreasing in surface pressure at high latitudes in the same hemisphere.

Polar vortex

Longitudinally averaged longitudinal component of wind in troposphere and stratosphere for January (Northern Hemisphere winter) The winter hemisphere has strong eastward jets in the stratosphere - the “polar vortex”, (W.J. Randel, 1992)

Polar vortex (cont.)

Using monthly mean data, daily data, and theoretical arguments, relationships between surface pressure variations associated with the North Atlantic Oscillation (NAO - NAM), tropopause height, and the strength of the stratospheric vortex are established (M. AMBAUM, B. J. HOSKINS, 2002) (a) First PC of mean SLP; (b) First PC of PV at θ = 500K and

Structure and composition of Northern Annular Modes (NAM)

Composit structures in a field of the wind, corresponding to high and low index NAM; Elliasen - Palma flux which specifies a direction distribution of waves and transport of the zonal moment and poleward, and it divergence, (Hartmann et al. 2000.)

Structure and composition of Northern Annular Modes (NAM) (cont.)

Correlation between time series at each level of measurements NAM with the data on 10 hPa. It can be interpreted as propagation of a phase from top to down

Structure and composition of Northern Annular Modes (NAM) (cont.)

The global spectral model T42L41

( )

ξ τ ξ µ λ µ ζ

n n f u v

k F F t

2 2

1 1 1 ∇ − − − ∂ ∂ − ∂ ∂ − = ∂ ∂

( )

( )

D k D p T V U F F t D

n n f s R v u 2 2 2 2 2 2

1 ln 1 2 1 1 ∇ − − −         + Φ + − + ∇ − ∂ ∂ + ∂ ∂ − = ∂ ∂ τ µ µ λ µ

( ) ( ) ( )

T k T T p T T T D T v T u t T

n n R R

′ ∇ − − − + + ∂ ∂ − ′ ⋅ + ′ ∂ ∂ − ′ ∂ ∂ − − = ∂ ′ ∂

2 2

1 1 1 τ ω κ σ σ µ λ µ &

σ σ µ λ µ ∂ ∂ − − ∂ ∂ − ∂ ∂ − − = ∂ ∂ & D p V p U t p

s s s

ln ln 1 ln

2

T − = ∂ Φ ∂ σ ln

Уравнение для вихря уравнение для дивергенции уравнение термодинамики уравнение неразрывности уравнение квазистатики

λ σ σ ζ ∂ ∂ ′ − ∂ ∂ − =

s u

p T U V F ln &

( )

µ µ σ σ ζ ∂ ∂ − ′ − ∂ ∂ − − =

s v

p T V U F ln 1

2

&

R R

α τ / 1 =

f

τ

• масштаб времени радиационного выхолаживания

масштаб времени релеевского трения (считается бесконечно большим везде, кроме подстилающей поверхности )

Simulation Characteristics

( ) ( ) ( ) ( ) ( )

σ ϕ ω ϕ ω ϕ σ

1 2

1 , T T TR + − =

( )

) / ln(

1 T

H T T σ σ σ Γ + =

K T 210

0 ≈

Г = 0.0, 2.5, 4.0

The Eliassen - Palm fluxes. Downward control (Haynes P., et al., 1990)

'

' 2 ' ' ' ' ' ' ' ' '

1 ( ) 2

g

D q Q q q v q q Q t y v q F u v F v f d d z ρ ρ θ ρ = ∂ ∂ + = ∂ ∂ = ∇   −     =   Θ     ur  ur

(a) Г=0.0 (b) Г=4.0 (b)-(a)

Downward control

(a) Zonal mean zonal wind, (b) Г=2.5, Г=4.0 (b) Zonal mean temperature, Г=2.5, Г=4.0 (c) Zonal mean SLP, Г=2.5, Г=4.0

Lapse rate

The zonal-mean lapse rate in the free troposphere is relatively uniform (about 6.5 K/km) and varies only weakly with season—observations that motivated the assumption of a fixed thermal stratification in quasigeostrophic theory. Regions of smaller lapse rate (statically more stable stratification) are seen near the surface in the subtropics and in high latitudes, particularly in winter. At the tropopause, the lapse rate decreases, in many regions to zero or less, marking the transition from the troposphere to the more stably stratified stratosphere. What distinguishes the troposphere and stratosphere kinematically is that the bulk of the entropy the atmosphere receives by the heating at the surface is redistributed within the troposphere, whereas only a small fraction of it reaches the stratosphere.

Extratropical thermal stratification

One reason why our understanding of the extratropical thermal stratification is incomplete is that in quasigeostrophic models the thermal stratification of the atmosphere is taken to be fixed. Quasigeostrophic models have formed the basis for studies of extratropical dynamics over the past decades and have led to some of the most important insights in dynamical meteorology (e.g., the theory

• f Rossby waves and baroclinic instability).

But because they do not allow dynamics to affect the thermal stratification, quasigeostrophic models are poorly suited for studying the processes that determine the thermal stratification. With today’s computational resources, however, we are in a position to study the maintenance and variability

• f the extratropical thermal stratification by systematic experimentation with general circulation models that are

not based on quasigeostrophic assumptions. There are distinguishing between radiative and dynamical constraints on the thermal stratification. Radiative constraints express the balance of incoming and outgoing radiant energy fluxes in atmospheric columns, plus any dynamical energy flux divergences in the columns. Dynamical constraints express balance conditions based on dynamical considerations, such as that moist convection maintains the thermal stratification close to a moist adiabat or that baroclinic eddy fluxes satisfy balance conditions derived from the mean entropy and zonal momentum balances.

Extratropical thermal stratification

2 __

1 U ξ ξ βλ = >

4 5 3 5

D β ε

−



1 2 2 ;

, D g NH fU N z θ ε τ τ θ ∂   = =   ∂   

3 3 2 3 3 2 3

1 _ _ D

• r

D D y z θ θ βλ ξ β τ

−

    ∂ ∂ ⇒     ∂ ∂       

Extratropical thermal stratification

Components of geostrophic mass flux along isentropes

(T. SCHNEIDER AND C. C. WALKER,2006)

(a) geostrophic eddy mass flux (b) geostrophic mean mass flux

( ) ( ) ( )

5 5 2

' ' ' ' _ _ ' ' v w along surfaces y z w y z θ θ θ θ θ θ θ θ

−

    ∂ ∂ − ⇒     ∂ ∂         ∂ ∂     ∂ ∂      

( )

10 7 6 7

_ ' ' If w D z z y y θ θ θ θ θ         ∂ ∂ ∂ ∂ ⇒ ⇒         ∂ ∂ ∂ ∂            Extratropical thermal stratification

Extratropical thermal stratification. Isentropic slope

3 7 3 7 s

I y z y I y z y

θ θ

θ θ θ θ θ θ

−

      ∂ ∂ ∂ =       ∂ ∂ ∂             ∂ ∂ ∂ =       ∂ ∂ ∂        

Extratropical thermal stratification. Isentropic slope

1.The model simulation show that “downward control” is a key mechanism of tropospheric response; stratospheric eddy driving responds as to gently wave the troposphere and troposphere then responds in strong way with eddy feedbacks.

• 2. The question of what determines the thermal stratification is

the question of what determines the dynamical equilibrium between radiative processes and dynamical entropy transport.

Conclusion

Many Thanks!