Stochastic parameterization of gravity waves

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Stochastic parameterization of gravity waves

F. Lott, A. de la Camara, L. Guez, A. Hertzog, P. Maury Laboratoire de Météorologie Dynamique, Paris.

1)Motivation and Formalism 2)Offline and online results

3) Validation against observations

EGU, 2014

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1) Motivation and formalism

Mesoscale GWs transport momentum from the lower atmosphere to the stratosphere and

mesosphere

GWs significantly contribute to driving the Brewer-Dobson

circulation, the QBO, etc.

GWs break and deposit momentum to the mean flow

- Density decrease with altitude - Critical levels

To incorporate these effects and have a realistic atmosphere, all ESMs and GCMs have GWD parameterizations.

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Classical arguments to justify stochastic schemes:

Palmer et al. 2005, Shutts and Palmer 2007,

for GWs: Piani et al. (2005, globally spectral scheme) and Eckerman (2011, multiwave scheme)

⃗F=

∑

_n^∞₌₁ ^Cn

2 ⃗F_n

∑

_n^∞₌₁ ^Cn

2=1

where

1) Motivation and formalism

Fourier series at the basis of the subgrid scale waves parameterization, are replaced by stochastic series where the GWs momentum fluxes are written:

1) The spatial steps ∆x and ∆y of the unresolved waves are not well defined. The time scale of the GWs life cycle t is certainly larger than the time step (t) of the model, and is not well defined either.

2) The mesoscale dynamics producing GWs is not well predictable (for the mountain gravity waves see Doyle et al. MWR 11).

I

Few waves (say M=8) are launched each δt=30mn, but their effect is redistributed over ∆t=1day: around 400 waves can be active at the same time (if needed)!

This excellent spectral resolution is a benefit of the method.

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For the F_n we use the linear theory and treat each waves independently from the others.

Passage from one level to the next:

m= N

∣

k^⃗_n

∣

Ω=ω_n−⃗k_n⋅⃗u Ω

⃗ k

_n

, ω

_n

Wavenumber and frequency chosen randomly:

∆^{z, G}_uw^{, S}_c^{, k}^*^,µ: Tunable parameters

F⃗_n(z+dz)= ⃗k_n

∣

^k^⃗n

∣ Θ

(^{Ω (}z+δ z)⋅Ω(z))

Min (

^∣^⃗^Fⁿ⁽^z⁾^∣^e⁻²^μ^ρΩ^m³^δ^z^, ^ρ^r^∣²^Ω^N³^∣ ^e^−(z^+δ^z^)/^H ^S²^c

∣

^k^⃗^k^∗2n 4

∣ )

Critical level EP theorem

with dissipation Breaking

1) Motivation and formalism

Intrinsic frequency and vertical wavenumber:

⃗F_nl=ρ_r k⃗_n

∣^k^⃗n∣

(

^G^b⁽¹⁻^cos⁸^{φ) +} ^G^uw^∣^k^⃗ⁿ^∣^N²^e^−m^Ωnⁿ²^Δ^z²

3

(

^ρ^{R L}r H c^W_p

)

²^P^r²

)

GWs due to convection:

P_r is the precipitation

Stochastic background flux to represent

GWs from fronts

Launched Fluxes:

G_b: Chosen out of a log-normal distribution

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Lott and Guez, JGR 2013 CGWs

stress

CGWs drag

Same zonal mean stress

Real precip. Stress amplitude (CI=2mPa) Uniformized precip. Stress amplitude (CI=2mPa)

Eq 30N 60N 90N

30S 60S

90S0 60E 120E 180E 60W 120W 0 60E 120E 180E 60W 120W

Real precip. du/dt *e(-z/2H), CI= 0.1 m/s/d Uniformized precip. du/dt *e(-z/2H), CI= 0.1 m/s/d

Eq 30N 60N 30S

60S 60S 30S Eq 30N 60N

More drag near and above stratopause Slightly less drag in the QBO region

50 60

40 30 20 10

50 60

40 30 20 10

0.15 0.25 0.35 0.45

0.05 0.05 0.15 0.25 0.35 0.45

2) Offline and online results

Benefit of having few large GWs rather than a large ensemble of small ones Exemple of the GWs due to convection:

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LMDz version with 80 levels, dz<1km In the stratosphere

QBO of irregular period with mean around 26month, 20% too small amplitude

Westerly phase lacks of connection with the stratopause SAO

Lott and Guez, JGR13

a) LMDz with convective GWs LMDz+CGWs

b) MERRA

1000 100

10 20 1 0.1 1000 100

10 20 1 0.1

1990 1992 1994 1996 1998

2 4 6 8

2) Offline and online results

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3) Validation against observations

Hertzog et al. 2012 JAS Dewan&Good 1986 JGR

Show intermittent GW fluxes

Hertzog et al. (2012).

Obs. of GWs traveling in packets

Property used in global “spectral schemes”

Hines (1997), Warner&McIntyre (2001), Scinocca (2003)

70's-90's observations (vertical soundings) Recent balloon and satellite obs.

Long-term averages of vertical profiles show well- defined vertical wavenumber spectra

Van Zandt (1982), Fritts et al. (1988), Fritts&Lu (1993)

Property justifying stochastic schemes

Lott et al. (2012), Lott&Guez (2013)

Likely produce narrow-banded periodograms

Use of stochastic multiwave schemes

Does our scheme generate realistic GW momentum flux intermittency andvertical spectra??

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CONCORDIASI (2010)

Rabier et al. 2010 BAMS

19 super-pressure balloons launched from McMurdo, Antarctica, during Sep and Oct 2010.

The balloons were advected by the wind on a isopycnic surface at ~ 20 km height.

3) Validation against observations

Instruments on board sampled the interior of the stratospheric polar vortex every 30 s for an

averaged period of 2 months.

Dataset of GW momentum fluxes (as by Hertzog et al. 2008)

www.lmd.polytechnique.fr/VORCORE/Djournal2/Journal.htm

GWs from the scheme:

Offline runs using ERAI and GPCP data corresponding to the

Concordiasi period.

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3) Validation against observations

The stochastic scheme parameters can be tuned to produce fluxes as intermittent as in balloon observations.

Intermittency of GW momentum flux

de la Cámara et al. 2014, in preparation.

Remember that intermittency is important because it produces GW breaking at lower altitudes (Lott&Guez 2013)

In order to parameterize GWs issued from fronts, we add a stochastic background flux with

log-normal distribution to the convective GWs:.

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3) Validation against observations

Vertical spectra of GWs energy

Average of periodograms The observed “universal spectra” can be obtained with a “multiwave scheme” as a superposition of individual periodograms

of GW packets.

Remember that In order to parameterize GWs issued from fronts, we add a stochastic background flux with

log-normal distribution to the convective GWs.

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3 ) Validation against observations

What cause the intermittency?

Sources, like P² for convection or ξ² for fronts have lognormal distributions (P precipitation, ξ relative vorticity)

For waves produced by PV see Lott et al.~(2012)

Results for intermittency suggest to relate the GWs to their sources

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Summary and conclusions

Advantages of stochastic multiwaves methods:

- Very high spectral resolution, which is good for the treatments of critical levels;

- Very cheap cost; Easy to relate to the convective (and may be frontal) sources.

It helps produce a realistic QBO in our model (but this may be more related to the relation with the sources)

Evaluations of vertical spectra show that we can reconcile “multiwaves” and “globally spectral” parameterizations.

Validation against balloon shows that the observed intermittency result from:

(i) filtering by the background flow (as expected from past studies) (ii)Relation with the sources (precipitations and fronts)

Next work:

Relate the GWs to their frontal sources (e.g. ξ², see theory in Lott et al.~2010, 2012).

Extent stochastic methods to mountain GWs !

Evaluate the impacts of stochastic parameterizations on the varibility in the middle atmosphere