Intermittency from a stochastic parameterization of gravity waves and relation with Vorcore and Pre-Concordiasi observations

Intermittency from a stochastic parameterization of gravity waves and relation with Vorcore and Pre-

Concordiasi observations

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

ISSI

1) Motivation and Formalism

2) Off-line tests with ERA-Interim and GPCP 3) Online results with LMDz

4) Validation against observations 5) Summary and conclusions

Bern, April 2014

For the w'_n we use the linear WKB theory of hydrostatic monochromatic waves

w '

=ℜ { ^{w }

^{ z  e}

^e

}

WKB passage from one level to the next with a small dissipation :

m= N∣^k∣

 =−k⋅u

w 

, k

, l

, 

S_c, k^* , µ: Tunable parameters EP-flux:

Fzdz= k

∣^k∣^{sign }









Critical level EP theorem

with dissipation Breaking

1) Motivation and formalism

w '=

∑

∑

where

Instead of using a triple Fourier series, which is at the basis of the subgrid scale waves parameterization, we use a stochastic series:

Subgrid scale precipitation over the gridbox considered as a stochastic series

P '_r=

∑

[

]

We take

∣

∣

Distributing the related diabatic forcing over the vertical via a Gaussian function yields the EP-flux at the launch level (see also Beres et al.~(2004), Song and Chun (2005):

G_uw tuning parameter of the CGWs amplitude

The k_n's are chosen randomly between 0 and k*

F_nl=_r k_n

∣k^_n∣

∣k^_n∣²e^−mn2z2

N _n³ G_uw





n

,_n=_n−k_n⋅U

The ω_n's are chosen randomly between 0 and k_nC_max

Tuning parameter max phase speed

z tuning parameter or scale of the heating depth

1) Motivation and formalism

a) Precipitation Kg.s^-1.day^-1

b) Surface Stress amplitude (mPa)

30S 30N Eq 60N 90N

60S 90S

30S 30N Eq 60N 90N

60S

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

0

180 120W 60W

120E 60E

0

30S 30N Eq 60N 90N

60S 90S

30S 30N Eq 60N 90N

60S 90S

7 6 5 4 3 2 1 0

8 10 4 2

0 6

mPa Kg.s^-1.day^-1

30 26 22 16 12 8 4

42 36 30 24 18 12 6

Precipitations and surface stresses averaged over 1week (1-7 January 2000) Results for GPCP data and ERAI G_uw=2.4, S_c=0.25,

k*=0.02km^-1, m=1kg/m/s

Dt=1day and M=8

Dz=1km (source depth~5km)

2) Offline tests with ERAI and GPCP

The CGWs stress is now well distributed along where there

is strong precipitations It is stronger on average in the

tropical regions, but quite significant in the midlatitudes.

The zonal mean stress comes from very large values issued

from quite few regions.

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 tests with ERAI and GPCP

Benefit of having few large GWs rather than a large ensemble of small ones:

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

3) Online results with LMDz

Relatively good spread of the periods taking into account that it is a forced

simulation with climatological SST (no ENSO)

Periods related to the annual cycle (multiples of 6 months) are not favoured:

probably related to the weak relations with the SAO

Histogram of QBO periods

Lott and Guez, JGR13

3) Online results with LMDz

No negative impacts on other climatological aspects of the model

January zonal mean zonal wind

CGWs improve the phase at the stratopause

CGWs reduce easterly biases in the subtropics summer mesosphere

(1) LMDz+CGWs

MERRA

(2) LMDz without CGWs

LMDz+CGWs

MERRA

LMDz without CGWs

Impact: (1) – (2)

100 10 1 0.1

100 10 1 0.1

100 10 1 0.1

100 10 1 0.1

1000

100 10 1 0.1

1000

100 10 1 0.1

1000 100

10 1 0.1

Eq 30N 60N 1000 30S

60S

90S 90N 90S 60S 30S Eq 30N 60N 90N

Eq 30N 60N 30S

60S

90S 90N

Eq 30N 60N 30S

60S

90S 90N

FEB

1979 APR JUN AUG OCT DEC

FEB 1979

APR JUN AUG OCT DEC

FEB 1979

APR JUN AUG OCT DEC

20 60 85

-10 -35 -50 -75

-90 5 45

20 60 85

-10 -35 -50 -75

-90 5 45 -90 -75 -50 -35 -10 5 20 45 60 85

20 60 85

-10 -35 -50 -75

-90 5 45

15 35 45 -5

-15 -25 -35

-45 5 25 55

-55

3) Online results with LMDz

SAO:

ERAI 21, 11 cases

LMDz+CGWs 10 cases

LMDz without CGWs 10 cases 20S

20N

Eq

20S 20N

Eq

20S 20N

Eq

80E 0

80W 40W 40E

80E 0

80W 40W 40E

80E 0

80W 40W 40E

Composite of Rossby-gravity waves with s=4-8 Temp (CI=0.1K) and Wind at 50hPa & lag = 0day

Equatorial waves:

Remember also that when you start to have positive zonal winds, the planetary scale Yanai wave

is much improved (the composite method is

described in Lott et al. 2009)

Lott et al. 2012 GRL

3) Online results with LMDz

4) 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??

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.

4) 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

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

GWs from the scheme:

Offline runs using ERAI and GPCP data corresponding to the

Concordiasi period.

4) 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.

In order to parameterize GWs issued from fronts, we add a stochastic background flux with log-normal distribution to represent the frontal GWs

.

⃗F_nl=ρ_r k⃗_n

∣^k⃗_n∣

(

3

(

)

)

Midlatitude

confinement GWs due to convection

The idea here is just to replace the Hines~(1997) globallly spectral scheme by a stochastic multiwave scheme

4) 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:.

4) 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.

de la Cámara et al. 2013, in preparation.

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

log-normal distribution to the convective GWs.

4) Validation against observations

60 55 50 45 40 35 30 25 20 15 10 5

40 35 30 25 20 15 10 5

-0.65 -0.25 0.15 0.55 -0.13 -0.05 0.03 0.11 -17.5 -7.5 2.5 12.5 22.5 -17.5 -7.5 2.5 12.5 22.5

July 2010 du/dt (m/s/day) CGWD

July 2010 du/dt (m/s/day) Hines (1997) param.

de la Cámara et al. 2013, in preparation.

We need to verify that the multiwave stochastic scheme gives GW drag

comparable to that given by the operational scheme

(here the Hines 1997 global spectral

scheme) _H^eig

ht (km)Height (km)

30S Eq 30N

90S Eq 90N

30S Eq 30N

90S Eq 90N

CI=0.1m/s/d CI=0.02m/s/d

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

log-normal distribution to the convective GWs.

4) Validation against observations

de la Cámara et al. 2013, in preparation.

The tendencies on the zonal mean flow are also comparable with those obtained in recent runs with GW-resolving GCM

Watanabe et al. 2010 JGR

60 55 50 45 40 35 30 25 20 15 10 5

Height (km)

90S Eq 90N

Jul 2010 du/dt (m/s/day) CGWD Jul du/dt (m/s/day) GW-resolving GCM

4) Validation against observations

de la Cámara et al. 2013, in preparation.

Significancy of intermittency

A small number of large waves carrying abount the same amount of stress when enteringnin the stratosphere then a large amount of small waves, will break at

low altitudes.

Here an exemple where the launching background fluwes is uniformized in latitude longitude and times before the waves are launched.

Uniformized Log-

normal

4) Validation against observations

de la Cámara et al. 2013, in preparation.

What cause the intermittency?

Just the filtering by the wind (Hertzog et al. 2012)

Reasonnable but may be at higher altitudes than the balloons

At low altitude a log-normal distribution of mom. Fluxes needs log-normal distributions of the launched fluxes.

4 ) Validation against observations

Sources in ξ^2,

where ξ is vorticity:

Simulations to support these parameterizations:

Reeder and Griffiths (1995)

4 ) Validation against observations

Sources in ξ^{2, where} ξ is vorticity:

General setup: A 3D (x,y,z) PV anomaly advected in a rotating (f =cte), stratified (BV freq N=cte) shear flow (vertical shear ^=cte).

For the 2D and 3D results: Lott, Plougonven and Vanneste, JAS 2010, 2012.

4 ) Validation against observations

Sources in ξ^{2, where} ξ is vorticity:

4 ) Validation against observations

de la Cámara et al. 2013, in preparation.

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

4 ) Validation against observations

Courtesy de la Cámara today!

Sources, like P² yield larger momentum fluxes in the SH

Simpler than using a “threshold” on the frontogenesis function

Exceeds 0.045 (K2 (100km)-2 h-1), GWF=1.5 mPa!

Justification : the relation between frontal characteristics and wave amplitude have not been established to date (a 2010 paper))

−

(

∂ λ∂θ

) (

∂ϕ

) (

∂v

∂ λ +1 a

∂u

∂ ϕ+utanϕ a

)

F=−

(

∂ θ

∂λ

)

(

∂u

∂ λ− v tanϕ

a

)

⁽

∂ θ

∂ ϕ

)

(

∂v

∂ ϕ

)

4 ) Validation against observations

Sources in ξ^{2, where} ξ is vorticity:

5) 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.

We have shown that it helps produce a realistic QBO in our model, without being detrimental to other other features of the large scale flow.

We have also shown that we can potentially reconcile the “multiwaves” techniques and the

“globally spectral” techniques, via evaluation of spectra issued from the multiwaves techniques.

All the validations are done looking at the large scale zonal mean flow, but we have also analysed the inderect effects of the parameterized waves on the large scale waves.

Stochastic schemes can easily be tuned against in situ observations in off-line modes. This yields interesting result concerning intermittency:

It is in part cause by intermittency related to the sources (precipitations and fronts) It makes GWs act at much lower altitude then when less intermittent

Offline results often translate well online

5) Summary and conclusions

The future:

Relate the waves to their frontal sources (for instance using the spontaneous emission theory in Lott Plougonven and Vanneste (JAS2010, 2012).

In this theory the momentum fluxes due to the waves are related to the square vorticity, and this yields realistic statistics of GWs emission as well (as convection does by the way see de la Camara Lott and Hertzog 2014)

Extent stochastic methods to mountain GWs !

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