in the stratosphere (CLaMS):

(1)

Lagrangian modeling of mixing and chemistry

in the stratosphere (CLaMS):

Comparison with ER2 and satellite observations

CLaMS - Chemical Lagrangian Model of the Stratosphere

P. Konopka

Research Centre J ¨ulich, ICG-I: Stratosphere, Germany

P.Konopka@fz-juelich.de

(2)

Acknowledgments:

CLaMS group:

Danny McKenna (now at NCAR, Boulder),

Rolf Müller, Jens-Uwe Grooß, Gebhard Günther, Paul Konopka, Hildegard-Maria Steinhorst, Stephan Bausch, Carsten Lemmen Modeling support:

Yvan Orsolini (NILU, Oslo), Glenn Carver (University of Cambridge), Olaf Morgenstern (MPI, Hamburg), Yasuhiro Sasano (NIES, Tsukuba), Richard Swinbank (UKMO),

Joanna Haigh (Imperial College, London) Experimental data:

CRISTA-Team:

Martin Riese, Dirk Offermann, Reinhold Spang, Volker Küll (University of Wuppertal) ...

SOLVE-THESEO-Team:

James Elkins (University of Colorado), Hans-Jürg Jost (NASA, Moffett Field), Geoffrey Toon (JPL, Pasadena), Andreas Engel, Ulrich Schmidt (University of Frankfurt), Erik Richard (Bay Area Environmental Research Institute, Sonoma), David Fahey, Peter Popp (NOAA, Boulder),....

(3)

Objectives:

Stratospheric transport and its modeling (CLaMS)

Deformation-induced mixing in 2d and 3d formulation Adjusting of mixing parameters on the observations SOLVE-THESEO-2000

Impact of mixing on the chemistry

(4)

Stratosphere

[km] [hPa]

45

10

1

200 1

Equator

North pole South pole

Troposphere Stratosphere

Tropopause 800 K

600 K 450 K

400 K 350 K

2 3

Main dynamical properties:

Tropics: main flux into the stratosphere High latitudes: main flux from the stratosphere

Weak vertical velocities (radiative equilibrium) adiabatic motion of air parcels

stable stratification

Horizontal motion: chaotic advection, 2d-turbulence, very weak mixing

(5)

Stratosphere

[km] [hPa]

45

10

1

200 1

Equator

600 K 450 K

400 K 350 K

2 3

Tropics: main flux into the stratosphere High latitudes: main flux

from the stratosphere

Weak vertical velocities (radiative equilibrium) adiabatic motion of air parcels

(6)

Stratosphere

[km] [hPa]

45

10

1

200 1

Equator

600 K 450 K

400 K 350 K

2 3

Tropics: main flux into the stratosphere High latitudes: main flux from the stratosphere Weak vertical velocities (radiative equilibrium)

adiabatic motion of air parcels stable stratification

(7)

Stratosphere

[km] [hPa]

45

10

1

200 1

Equator

600 K 450 K

400 K 350 K

2 3

Weak vertical velocities (radiative equilibrium)

adiabatic motion of air parcels

stable stratification Horizontal motion: chaotic advection,

2d-turbulence, very weak mixing

(8)

Stratosphere

[km] [hPa]

45

10

1

200 1

Equator

600 K 450 K

400 K 350 K

2 3

Weak vertical velocities (radiative equilibrium)

adiabatic motion of air parcels

(9)

Stratosphere

TROPOSPHERE

SUMMER

LOWER STRATOSPHERE

winter hemisphere summer hemisphere

SUBVORTEX

LOWERMOST STRATOSPHERE

LOWERMOST STRATOSPHERE 450

Strong large-scale stirring + poleward & downward transport Large-scale

descent Large-scale ascent

Weak large-scale stirring + weak poleward & downward transport

VORTEX

POLAR SURF ZONE

TROPICAL RESERVOIR

stratosphere-troposphere exchange Large-scale descent and two-way

30

0 60

1000

30

20

Latitude 400

380

300

30 Pole 60

10

0 300

100 30 10

Pressure (hPa)

350

Pole

Height (km)

850

600

Holton diagram (from Haynes and Shuckborough, JGR, 2000)

(10)

Why CLaMS ?

„Political” motivation:

ozone depletion (vortex and mid-latitudes) water vapor trends ?

global change, its influence on the stratospheric composition, circulation.

stratosphere-troposphere exchange ....

„Physical” motivation:

a reliably CTM for the stratosphere

dynamical properties from meteorological analysis (UKMO, ECMWF) but chemistry is still open

understanding of small-scale processes:

mixing, transport barriers, age of air, coupling between mixing and chemistry Lagrangian view allows to avoid some Eulerian disadvatenges (high numerical diffusion, weak understanding of mixing and coupling between chemistry and dynamics)

...

(11)

Stratospheric Turbulence

Spatial scales: horizontal: 500 m – 50 km, vertical: 100 - 500 m

Stratospheric flow stably stratified flow in radiative equilibrium, weak turbulence

(12)

Stratospheric Turbulence

Stratopause

Tropopause 12 km

50 km

[K]

Temperature

Potential Temperature z

stratified:

,

, horizontal velocity vertical velocity

raditive equilibrium: entropy S const potential temperature :

adiabatic processes ( ) const

(13)

Stratospheric Turbulence

air parcel

stably stratified (linear stability theory)

with

- Brunt Väisälä frequency ( 2..5 minutes), S - vertical shear ( 5 m/s per 1 km) active turbulence very seldom, 2-5% of the the observed volume (Lilly et al, 1974,

(14)

Stratospheric Turbulence

k [1/m]

Turb.

kinetic Energy E

−5/3 k

weak turbulence

Kolmogorov scale cascade (1941)

for homogeneous, isentrop and stationary turbulence

(large scale eddies dissipate into smaller and smaller eddies)

(15)

Lagrangian View of Transport

along the trajectories

Mixing Chemistry

Advection

Chemistry Advection

driven by given wind fields

Tracer

transport = Advection

(reversible) + Mixing

(irreversible) Isentropic coordinates:

Small vertical velocities

adiabatic motion of air parcels 2d description

[km] [hPa]

45

10

1

200 1

Equator

600 K 450 K

400 K 350 K

2 3

(16)

Lagrangian View of Transport

along the trajectories

Mixing Chemistry

Advection

Chemistry Advection

driven by given wind fields

Tracer

transport = Advection

(reversible) + Mixing

(irreversible)

Isentropic coordinates:

Small vertical velocities

adiabatic motion of air parcels 2d description

[km] [hPa]

45

10

1

200 1

Equator

600 K 450 K

400 K 350 K

2 3

(17)

Components of CLaMS

Diabatical Correction (Morcrette scheme)

Meteorological Data (ECMWF, UKMO)

Initialisation

(2d model, satellite data, PV correlation)

Photolysis

Heterogeneous Chemistry

Trajectory model (4^th order Runge− Kutta)

Chemistry model ASAD

40 species 112 Reactions

Lagrangian Mixing

The CLaMS model system

McKenna et al., JGR, 2002, 107, 10.1029/2000JD000114, 10.1029/2000JD000113

(18)

Lagrange versus Euler

Lagrange (irregular grid)

!!""

##$$

% %

% %& &

& &

' ' ' '

( ( ( () )

) )

* *

* *+ + + +

+ + + +

, , , ,

- - - -

. . . .

. . . . / / / / / / /

/ / / / / / /

0 0 0 0 0 0 0

1 1

1 12 2

2 2

3 3 3 3

4 4 4 4

4 4 4 45 5 5 5 5

5 5 5 5 5

6 6 6 6 6

r(t)

mixing (exchange of mass) is under control

Euler

(regular grid)

777777777777777777777777777777777777777777777777777777 888888888888888888888888888888888888888888888888888888

9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9: : : : : : : : : : : : : : : : : : : : : : : : : : :

; ; ; ;

< < < <

< < < < = = = =

= = = =

> > > >

> > > > ? ? ? ?

? ? ? ?

@ @ @ @

@ @ @ @ A A A A A

A A A A A

B B B B B

C C C

C C CD D

D D

D D E E E E

E E E E

F F F

F F F G G G

G G G

H H H

H H H I I I I

I I I I

J J J J

K K

K KLLLLLLLL M M M M

M M M M

N N N

N N N O O O O

O O O O

P P P P

P P P P Q Q Q Q

Q Q Q Q

R R R R

S S S S S

T T T T

T T T T U U U U U

U U U U U

V V V V

V V V V W W W W

W W W W

X X X X

X X X X Y Y Y Y Y

Y Y Y Y Y

Z Z Z Z Z

mixing is determined by the numerical diffusion

(19)

Grid Adaptation Mixing

A C B

quasiuniform distribution of air parcels

Voronoi triangulation next neighbors sheared flow

hours

A C B

D

grid adaptation =

regridding of the deformed grid new air parcels

interpolations (num. diffusion) mixing

(20)

Grid Adaptation Mixing

A C B

Voronoi triangulation next neighbors

sheared flow

hours

A C B

D

grid adaptation =

regridding of the deformed grid new air parcels

interpolations (num. diffusion) mixing

(21)

Grid Adaptation Mixing

A C B

Voronoi triangulation next neighbors

sheared flow

hours

A C B

D

grid adaptation =

regridding of the deformed grid

new air parcels

interpolations (num. diffusion)

mixing

(22)

Lyapunov Exponent

r₀

t=t₀

Consider an air parcel sur- rounded by a small circle of ra- dius .

t=t + t r r

+

−

0

After a time and for sufficiently small values of , the circle is deformed into an ellipse with minor and major axes and

Definition: (Lyapunov exponent)

for sufficiently small and Incompressible flows ( )

(23)

Lyapunov Exponent

r₀

t=t₀

Consider an air parcel sur- rounded by a small circle of ra- dius .

t=t + t r r

+

−

0

After a time and for sufficiently small values of , the circle is deformed into an ellipse with minor and major axes and

Definition: (Lyapunov exponent)

for sufficiently small and Incompressible flows (

)

(24)

2d-CLaMS: Dynamically Adaptive Grid

Before the advection step

A C B

Determine nearest neighbors (e.g. for point A), - mean distance between air parcels

Set the critical Lyapunov exponent and the time step (free parameter) Define

After the advection step

A C B

D

If , then a new grid point D is inserted midway between A and B (insertion)

If , then grid points A and C are removed and a new grid point is intro- duced midway between the positions of A and C (merging)

(25)

2d-CLaMS: Dynamically Adaptive Grid

Before the advection step

A C B

Determine nearest neighbors (e.g. for point A), - mean distance between air parcels

Set the critical Lyapunov exponent and the time step (free parameter) Define

After the advection step

A C B

D

If , then a new grid point D is inserted midway between A and B (insertion)

If , then grid points A and C are removed and a new grid point is intro- duced midway between the positions of A and C (merging)

(26)

3d-CLaMS:Overlapping Layers

vertical (cross-isentropic) velocities from the radiation scheme (Morcrette scheme), temperature profiles (ECMWF, UKMO) and HALOE climatology (O , H O,...)

boundary conditions (same PV-tracer correlations as at the beginning of the simulation)

Θ[K]

Lat., Lon.

400 450 500 550 600 650 700

350

z

r

∆

o Θ[K]

Lat., Lon.

∆z Θ[K]

Lat., Lon.

∆z

New parameter: - thickness of the layer

or

, – aspect ratio

- mean horizontal distance between the next neighbours

- mean vertical distance between air parcels in the layer

(27)

3d-CLaMS:Overlapping Layers

Θ[K]

Lat., Lon.

400 450 500 550 600 650 700

350

z

r

∆

o

Θ[K]

Lat., Lon.

∆z Θ[K]

Lat., Lon.

∆z

or

, – aspect ratio

(28)

3d-CLaMS:Overlapping Layers

Θ[K]

Lat., Lon.

400 450 500 550 600 650 700

350

z

r

∆

o

Θ[K]

Lat., Lon.

∆z

Θ[K]

Lat., Lon.

∆z

or

, – aspect ratio

(29)

Flow Deformations Mixing

CLaMS-2d – mixing is driven by the horizontal deformations (strain)

CLaMS-2d – mixing is driven by the horizontal deforma- tions (strain)

CLaMS-3d – in addition, ver-

tical shear contributes to

mixing

(30)

Flow Deformations Mixing

CLaMS-2d – mixing is driven by the horizontal deforma- tions (strain)

CLaMS-3d – in addition, ver-

tical shear contributes to

mixing

(31)

Properties of Mixing in CLaMS

driven by the horizontal (strain) and vertical (shear) deformations in the flow

inhomogeneous in time and space

implicit (i.e. due to numerical diffusion in the adaptive advection algorithm)

adjustable:

- critical Lyapunov exponent

- grid adaptation frequency

- mean horizontal distance between the neigboring air parcels

- mean vertical distance between the air parcels

(32)

CLaMS Studies for the CRISTA Period:

CRISTA-1 data: N O, 4-12, November 1994 hor/vert resolution

200/2.5 km

Begin of CLaMS-2d simulation: October, 20, 1994,

700 K

Initilization derived from PV-N O correlation observed bei CRISTA between 4th anf 6th November.

CLaMS-2d resolution:

200 km, UKMO winds Free (mixing) parameters:

critical deformation

and mixing frequency

(33)

Mixing versus CRISTA-1 Observations

CRISTA observations

(November, 10, 1994)

(34)

Mixing versus CRISTA-1 Observations

CRISTA observations (November, 10, 1994)

CLaMS-2d

no mixing

(35)

Mixing versus CRISTA-1 Observations

CRISTA observations (November, 10, 1994)

CLaMS-2d

mixing too strong

(36)

Mixing versus CRISTA-1 Observations

CRISTA observations (November, 10, 1994)

CLaMS-2d

adjusted mixing

(37)

Tracer Transport in Terms of PDFs

Synoptic map of N O derived from CRISTA observations between 4th and 6th November

−200 −100 0 100 200

∆ N2O [ppbv]

0.0001 0.0010 0.0100 0.1000

PDF

CRISTA observations

Gaussian fit Exponential tails, p=0.63

CRISTA observations Gaussian fit

Exponential tails, p=0.63

PDF – probability density function of N O differences between observations separated by 150 250 km

“fat” tails inidicate filaments and 2d-turbulence

(38)

Tracer Transport in Terms of PDFs

−200 −100 0 100 200

∆ N2O [ppbv]

0.0001 0.0010 0.0100 0.1000

PDF

CRISTA observations

Gaussian fit Exponential tails, p=0.63

CRISTA observations Gaussian fit

Exponential tails, p=0.63

PDF – probability density function of N O differences between observations separated by 150 250 km

“fat” tails inidicate filaments and 2d-turbulence

(39)

CLaMS-2d versus CRISTA PDFs

0.0001 0.0010 0.0100 0.1000

PDF

∆t=6 h r₀=200 km

Critical λ [day c

] −1 4.5 4.0 3.0 2.0 1.5 CRISTA

Critical λc [day⁻¹] 4.5 4.0 3.0 2.0 1.5 CRISTA

0.0001 0.0010 0.0100 0.1000

PDF

∆t=12 h

Critical λ [day c

] −1 3.0 2.0 1.5 1.2 0.8 CRISTA

Critical λc [day⁻¹] 3.0 2.0 1.5 1.2 0.8 CRISTA

−300 −200 −100 0 100 200 300

∆ N 0.0001

0.0010 0.0100 0.1000

PDF

∆t=24 h

Critical λ [day c

] −1 , no mixing ∞ 1.2 0.8 0.6 0.5 CRISTA

Critical λc [day⁻¹] ∞, no mixing 1.2 0.8 0.6 0.5 CRISTA

How inhomogeneous is stratospheric mixing?

only 10% of the flow is affected by mixing

long-lived vortex remnants in re-

gions with

(CLaMS-3d, in situ observations

)

(40)

CLaMS-2d versus CRISTA PDFs

0.0001 0.0010 0.0100 0.1000

PDF

λ_c=∞

0.0001 0.0010 0.0100 0.1000

PDF

λ_c=3.0 day⁻¹

∆t=6 h

0.0001 0.0010 0.0100 0.1000

PDF

λ_c=1.5 day⁻¹

∆t=12 h

−300 −200 −100 0 100 200 300

∆ N2O [ppbv]

0.0001 0.0010 0.0100 0.1000

PDF

λ_c=0.8 day⁻¹

∆t=24 h

Hor. scale r

0

200 km 100 km 65 km 45 km

Hor. scale r0

200 km 100 km 65 km 45 km Hor. scale r0

200 km 100 km 65 km 45 km

How strong is the PDFs dependence on the model resolution ?

fractal behavior of CLaMS-2d PDFs

(Konopka et al., submitted to JAS)

(41)

SOLVE-THESEO-2000

Considered period:

3d - 01.12.1999 - 20.03.2000 CH , H1211, O

(tracer),

digital tracer (vortex=1, mid-latitudes=0) 2d - 10.02.2000 - 20.03.2000

4 levels: 400, 425, 450, 475 K full chemistry

ECMWF winds, Adjusted mixing (

=1.2), Horizontal resolution

up to 80/40 km (3d/2d) Intialization:

ER-2, POAM, HALOE, OMS, TRIPLE

(42)

Mixing versus ^{in situ} Data

ER2 flight on March 11, 2000

0.6 0.8 1.0 1.2 1.4 1.6

CH4 [ppmv]

0.6 0.8 1.0 1.2 1.4 1.6

CH4 [ppmv]

mixing=0

0.6 0.8 1.0 1.2 1.4 1.6

CH4 [ppmv]

0.6 0.8 1.0 1.2 1.4 1.6

CH4 [ppmv]

adj. mixing

09:00 10:00 11:00 12:00 13:00 14:00 15:00 time [UTC]

0.6 0.8 1.0 1.2 1.4 1.6

CH4 [ppmv]

0.6 0.8 1.0 1.2 1.4 1.6

CH4 [ppmv]

strong mixing

ACATS CLaMS

CH along the flight track

(43)

Adjusted Mixing (in situ Observation)

Spatial variability of the simulated time series :

09:00 10:00 11:00 12:00 13:00 14:00 15:00 time [UTC]

0.6 0.8 1.0 1.2 1.4 1.6

CH4 [ppm]

0.6 0.8 1.0 1.2 1.4 1.6

CH4 [ppm]

no mixing

09:00 10:00 11:00 12:00 13:00 14:00 15:00 time [UTC]

0.6 0.8 1.0 1.2 1.4 1.6

CH4 [ppm]

0.6 0.8 1.0 1.2 1.4 1.6

CH4 [ppm]

Exp, ARGUS CLaMS

adjusted mixing

09:00 10:00 11:00 12:00 13:00 14:00 15:00 time [UTC]

0.6 0.8 1.0 1.2 1.4 1.6

CH4 [ppm]

0.6 0.8 1.0 1.2 1.4 1.6

CH4 [ppm]

mixing too strong

(44)

Adjusted Mixing (in situ Observation)

Spatial variability of the simulated time series :

09:00 10:00 11:00 12:00 13:00 14:00 15:00 time [UTC]

0.6 0.8 1.0 1.2 1.4 1.6

CH4 [ppm]

0.6 0.8 1.0 1.2 1.4 1.6

CH4 [ppm]

no mixing

09:00 10:00 11:00 12:00 13:00 14:00 15:00 time [UTC]

0.6 0.8 1.0 1.2 1.4 1.6

CH4 [ppm]

0.6 0.8 1.0 1.2 1.4 1.6

CH4 [ppm]

Exp, ARGUS CLaMS

adjusted mixing

09:00 10:00 11:00 12:00 13:00 14:00 15:00 time [UTC]

0.6 0.8 1.0 1.2 1.4 1.6

CH4 [ppm]

0.6 0.8 1.0 1.2 1.4 1.6

CH4 [ppm]

mixing too strong

(45)

Adjusted Mixing (tracer correlations)

no mixing

adjusted mixing

(minimal) mixing too strong

- Deviation from H1211/CH correlation,

means a perfect agreement between CLaMS and observations.

(46)

Adjusted Mixing (tracer correlations)

no mixing

adjusted mixing

(minimal)

mixing too strong

- Deviation from H1211/CH correlation,

means a perfect agreement between CLaMS and observations.

(47)

Adjusted Mixing

1

Spatial variability γ 10

Deviation from H1211/CH4 correlation ε _0.5 _0.75 _1.0 _1.5 _2.0 _∞_λ

c∆t=

300 km 200 km 150 km 100 km mixing too

strong mixing too weak

Conclusions:

Mixing improves tracer transport studies only for km

Best agreement with satellite and in situ observations for:

(CRISTA) (ER-2) Note: only the product could be fixed

Adjusted aspect ratio:

Inhomogeneous (in time and space), deformation-induced mixing, scale collapse driven by large-scale isentropic deformations with:

Effective diffusivity of the order m /s

(48)

Adjusted Mixing

1

Spatial variability γ 10

Deviation from H1211/CH4 correlation ε _0.5 _0.75 _1.0 _1.5 _2.0 _∞_λ

c∆t=

300 km 200 km 150 km 100 km mixing too

strong mixing too weak

Conclusions:

Mixing improves tracer transport studies only for km

Best agreement with satellite and in situ observations for:

(CRISTA) (ER-2) Note: only the product could be fixed

Adjusted aspect ratio:

Inhomogeneous (in time and space), deformation-induced mixing, scale collapse driven by large-scale isentropic deformations with:

Effective diffusivity of the order m

/s