1) A stochastic parameterization of gravity waves: formalism, tests in a GCM, and validation against observations

A stochastic parameterization of gravity waves:

formalism, tests in a GCM, and validation against observations

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

Stochastic parameterisation in weather and climate models

1)

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

4) Validation against observations 5) Summary and conclusions

Paris, September 2013

Stochastic parameterization of GWs, formalism, tests and validation

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:

waves with positive (negative) intinsic phase speed accelerate

(decelerate)

- Density decrease with altitude - Critical levels

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

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)

w ' = ∑

^C

w '

∑

^C

2

= 1

where

tochastic parameterization of GWs, formalism, tests and validation

1) Motivation and formalism

The

C'

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 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).

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

:

For the w'_n we next use the linear WKB ravity wave theory and treat their breaking as if each wave was were doing the entire wave field: they are viewed as independent realizations.

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

, 

chosen randomly

S

, k

, µ :

Fzdz= k

∣^k∣^{sign }









Critical level EP theorem

with dissipation Breaking

Stochastic parameterization of GWs, formalism, tests and validation

1) Motivation and formalism

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

This excellent spectral resolution is a benefit of the method.

The redistribution is done via an AR-1 protocol which forces to keep the GWs tendency:









∑

z

∂z

At each time we launch M new waves and degrade the probability of all the others by the AR-1 factor (∆t-δt)/∆t

C_n²=





∑

Lott et al. GRL 2012

tochastic parameterization of GWs, formalism, tests and validation

1) Motivation and formalism

Subgrid scale precipitation over the gridbox considered as a stochastic:

P '_r=

∑

^[

^]

We take

∣ ^{P }

∣ ^{= P}

Distributing the related diabatic forcing over the vertical via a Gaussian function yields the EP-flux at the launch level (as in 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

∣

∣

∣

∣

N _n³ G_uw





^∣

^∣

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

Stochastic parameterization of GWs, formalism, tests and validation

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)

tochastic parameterization of GWs, formalism, tests and validation

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

Stochastic parameterization of GWs, formalism, tests and validation

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

tochastic parameterization of GWs, formalism, tests and validation

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

Stochastic parameterization of GWs, formalism, tests and validation

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

Stochastic parameterization of GWs, formalism, tests and validation

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

Stochastic parameterization of GWs, formalism, tests and validation

3) Online results with LMDz

tochastic parameterization of GWs, formalism, tests and validation

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.

Stochastic parameterization of GWs, formalism, tests and validation

4) Validation against observations

Instruments on board permit to evaluate GWs momentum fluxes

( 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.

tochastic parameterization of GWs, formalism, tests and validation

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

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

Stochastic parameterization of GWs, formalism, tests and validation

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.

tochastic parameterization of GWs, formalism, tests and validation

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.

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)

Height (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

Stochastic parameterization of GWs, formalism, tests and validation

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

tochastic parameterization of GWs, formalism, tests and validation

Summary and conclusions

Advantages of stochastic multiwaves methods:

- Very high spectral resolution: good for treatments of critical levels;

- Very cheap cost; Easy to relate to the convective sources.

Disadvantages:

Breaking far from critical levels is not well described by linear theory, In this sense, the globally spectral methods (Hines (1997), Warner and McIntyre (1997)) are may be more adapted.

But: Global spectral schemes are also quite incorrect since:

Spectra are the superposition of individual periodograms, each

realisation is not supposed to realize the entire spectra, this becomes a problem when we relate to sources.

It helps produce a realistic QBO in our model, without being detrimental to other other features of the large scale flow.

we can reconcile the “multiwaves” techniques and the “globally spectral”

techniques, via evaluation of spectra issued from the multiwaves techniques.

Stochastic parameterization of GWs, formalism, tests and validation

Summary and conclusions

Few current issues:

Improve the GWs spectra produced by convection Relation with frontal sources

(today rather empitical or uniform bckground);

better based on theory “Geostrophic adjustment forced by a frontogenetic function”

Impact of intermittency on larger-scale variability

(direct and indirect impacts of GWs on Sudden Stratospheric Warmings)

GWs sensitivity and impact on climate changes

(now that we relate them to sources)