Climatology of the effective diffusivity in the middle atmosphere - - PowerPoint PPT Presentation

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ENVIROMIS-2006 Tomsk, Russia, 1-8 July 2006 S.Kostrykin, Institute of Numerical Mathematics RAS, Moscow, Russia G.Schmitz, Leibniz-Institute of Atmospheric Physics, Kühlungsborn, Germany

Climatology of the effective diffusivity in the middle atmosphere based on GCM winds

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• long-lived chemical species: N2O, H2O, CH4, O3
• dynamical factor is dominated
• chemical factor is dominated

spacial distribution of stratospheric gases atmospheric dynamics chemical (photochemical) reactions

adv chem chem adv

t t t t << <<

Main factors for the gas distribution in the stratosphere

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How to characterize average tracer mixing?

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Definition of the effective diffusivity through Lagrangian contours

q dt dq ∆ = κ

Eulerian framework (point)

      ∂ ∂ ∂ ∂ = ∂ ∂ A q A t q

eff

κ

Tracer induced framework (contour)

Nakamura, JAS, 52, 1995

1) 2D-isentropic non-divergent motion (neglecting diabatic circulation) 2) Passive tracer (long-lived chemical component)

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, | | 1 | |

2

dl q dl q Le

∫ ∫

∇ ⋅ ∇ =

Effective diffusivity: Equivalent length:

2

1         = ∂ ∂ − ≡ L L q r F

e e d eff

κ ϕ κ

L L Le ≥ ≥

NP

Average diffusive flux:

∫ ∇

− = dl n q L Fd r κ 1

e

r L ϕ π cos 2

0 =

analogy with definition of usual diffusivity

n r

d

F r

Definition of the effective diffusivity through Lagrangian contours

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Advection-diffusion problem

• realistic winds from INM middle atmospheric climate model with horizontal resolution -

5x4° and time step – 3 hour

• integration on the 21 isentropic levels from 400K up to 5000K with resolution 1x0.8°
• initial distribution of tracer – zonally symmetric, linear with latitude
• period of integration 6 years
• no explicit diffusion is used, therefore the source of diffusion is only numerical scheme

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Comparison of the model winds with UARS data

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CIP – cubic interpolated profile scheme

• development - Yabe et al., 1991
• more stable modification - Kostrykin, 2001
• semi-Lagrangian, 3d-order in space for exact trajectories
• stable for flows with Lipshitz number less than 1, or

where τ − time step, u – wind field, Ω – integration area

• conserves following the particle trajectory values of function and its gradient
• to achieve an exact conservation of mass and monotonicity the special

correcting procedures are applied.

The numerical advection scheme

1 || || max < τ x u d d

Ω

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Climatology of the effective diffusivity

ln 2 ln

L Le

num eff =

=

κ κ

ξ

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Climatology of the effective diffusivity

Lower stratosphere Middle stratosphere Upper stratosphere Lower mesosphere

ln 2 ln

L Le

num eff =

=

κ κ

ξ

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Ozone zonal waves observed by POAM II

colour - 100[χ(λ)−<χ>]/<χ>, where χ(λ) − ozone mixing ratio 55°N-65°N, <>-zonal average dots – denotes position of air parcel moving zonally with mean zonal wind (Hoppel et all, GRL, 26, 1999)

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Results of numerical experiments with INM GCM

colour - 100(q(λ)-<q>)/<q>, where q(λ) - tracer mixing ratio 55°N-65°N, <> - zonal average

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Tracer advected by INM GCM winds

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Tracer advected by INM GCM winds

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sources of the enhanced mixing breaking waves slow waves propagating from the troposphere fast waves mainly generated due to instability

• f the mean flow

break near critical line break near critical line

= u

c u =

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Wave-breaking and the effective diffusivity

num eff

κ κ

ln

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Wave-breaking and the effective diffusivity

• line of the

wave- generating areas zero-line of the gradient of quasi-geostrophic potential vorticity

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Summary

• discrepancies from previous analyses of the climatology of the effective

diffusivity in the stratosphere can be explained by the difference in the numerical advection scheme and input GCM data

• existence of the “frozen” filamentary tracer structures in the summer

midlatitudes of the middle and upper stratosphere is shown

• first time a climatology of the effective diffusivity in the lower mesosphere

is obtained

• the structure of the effective diffusivity can be explained by the wave-

breaking of the planetary waves

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Numerical diffusivity

2 2

2 1 q t q

num ∇

− = ∂ ∂ κ

Evolution equation for the tracer variance

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Plan

• Description of the effective diffusivity approach
• Details of the numerical experiments and comparison of the model

winds with UARS data

• Climatological mean of the effective diffusivity in the stratosphere and

lower mesosphere

• Example of sensitivity of the effective diffusivity to the numerical

advection scheme

• Wave-breaking of the planetary waves and the effective diffusivity