Non-orographic gravity waves parameterizations

1) Stochastic GWs scheme and application to convection 2) Impact on the middle atmosphere circulation

3) Preparing CMIP6

Non-orographic gravity waves parameterizations

François Lott, flott@lmd.ens.fr

Laboratoire de Météorologie Dynamique, Ecole Normale Supérieure, Paris

A. de la Camara, D. Cugnet, L. Fairhead, L. Guez, A. Hertzog, F. Hourdin, P. Levan, P. Maury, R. Plougonven, J. Vanneste⁽⁺⁾

(+) University of Edimburgh

Classical arguments: see Palmer et al. 2005, Shutts and Palmer 2007, for the GWs: Piani et al. (2005, globally spectral scheme) and Eckeman (2011,

multiwaves scheme)

1) The spatial steps ∆x and ∆y of the unresolved waves is not a well defined concept (even though they are probably related to the model gridscales x δy). The time scale of the GWs life cycle t is certainly larger than the time step (t) of the model, and is also not well defined.

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

These calls for an extension of the concept of triple Fourier series, which is at the basis of the subgrid scale waves parameterization to that of stochastic series

:

w ' = ∑

^C

w '

∑

^C

=1

where

The

C'

Non-orographic gravity waves parameterizations

1) Stochastic GWs parameterization schemes and application to convection

For the w'_n we use linear WKB theory of hydrostatic GWs, and treat the breaking as if each w'_n was doing the entire wave field (using Lindzen (1982)'s criteria for instance):

w '

=ℜ { ^{w }

^{ z  e}

^e

}

WKB passage from one level to the next with a small dissipation (Eliasen Palm flux):

m= N ∣ ^⃗ k ∣

Ω =− k⋅ u

chosen randomly

S

, k

:

Fzdz= k

∣^_k∣^{sign }









Critical level Eliasen-Palm theorem

with dissipation Breaking

Vertical wavenumber Intrinsic frequency

Few waves (say M=8) are launched at each physical time step (δt=30mn), but their effect is redistributed over a longer time scale (∆t=1day), via an AR-1 protocole:









∑

z

∂ z

k

,l

ω

Non-orographic gravity waves parameterizations

1) Stochastic GWs parameterization schemes and application to convection

P '=

∑

[

]

^{∣ P }

^{∣ = P}

The subgrid scale standard deviation of the precipitation equals the gridscale mean Distributing the related diabatic forcing over a depth ∆z it is quite easy to place the forcing in the right hand side of a “wave” equation:

New tuning parameter (could be a random number)

k

,l

, 

F_nl=_r k_n

∣

∣

∣

∣

N _n³ G_uw





m_n=N

∣

∣

_n ,_n=_n−k_n⋅U EP-flux at the launch level:

ρc_p

(

)

k² ŵ _zz+N²ŵ = R L_w

ρH c_p P̂ e^−z2/Δz2 Δ z

Non-orographic gravity waves parameterizations

1) Stochastic GWs parameterization schemes and application to convection

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)

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.

Non-orographic gravity waves parameterizations

1) Stochastic GWs parameterization schemes and application to convection

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

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

Offline tests with ERAI and GPCP

Non-orographic gravity waves parameterizations

1) Stochastic GWs parameterization schemes and application to convection

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

Online results with LMDz

Non-orographic gravity waves parameterizations

2) Impact on the middle atmosphere circulation

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

Online results with LMDz

Non-orographic gravity waves parameterizations

2) Impact on the middle atmosphere circulation

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

SAO:

Non-orographic gravity waves parameterizations

2) Impact on the middle atmosphere circulation

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)

Zero longitude line arbitrary

Lott et al. 2012 GRL

Non-orographic gravity waves parameterizations

2) Impact on the middle atmosphere circulation

Lott et al. 2012 GRL

Composite of Kelvin waves with s=1-6

Temp (CI=0.5K) and Wind at 50hPa & lag = 0day

LMDz + CGWs

LMDz without CGWs

20N ERAi

20N

20N

20S 20S 20S

20S Eq.

Eq.

Eq.

Eq.

120W 120W 120W

120E 120E 120E 0

0

0

Equatorial waves:

Remember that when you have

No QBO, the zonal winds are negative, , the

planetary scale Kelvin wave Becomes to strong

(the composite method is described

in Lott et al. 2009)

Zero longitude line arbitrary

Non-orographic gravity waves parameterizations

2) Impact on the middle atmosphere circulation

Including the frontal waves, see next presentation, now it is the subgrid scale vorticity which is considered as a “white” stochastic series:

Non-orographic gravity waves parameterizations

3) Preparing CMIP6

q '=

∑

[

]

^{∣ q ̂}

^{∣ = ∣ q}

^∣

Grilles testées:

Extension à 80km dz~1km en strato 64 niveaux en tout

Depuis la résolution est retournée à 72 puis

à 80 niveaux verticaux mais les points gagnés ont été mis dans la couche

limite

Non-orographic gravity waves parameterizations

3) Preparing CMIP6

Lott and Guez (2013) 80 levels

56 levels

64 levels

.

4xCO2 +4K SST experiments, results for October (month of the SH stratospheric vortex break-up)

Present Climate Future Climate

Break-up delayed

Surface Impact

Difference future-present

with GWs sources Zonal mean

zonal wind

80km

50km

20km 0km

80km

50km

20km 0km

80km

50km

20km 0km 80km

50km

20km 0km

Difference future-Present

without GWs sources

Non-orographic gravity waves parameterizations

3) Preparing CMIP6

Present Climate Future Climate

80km

50km

16km 0km 80km

50km

16km 0km

1 3 5 7 9 11 13 15 17 19 Years

1 3 5 7 9 11 13 15 17 19 Years

GWs with sources

GWs without sources

4xCO2 +4K SST experiments, Quasi-Biennial Oscillation

Non-orographic gravity waves parameterizations

3) Preparing CMIP6

Weakening and lengthening consistent

with other models

Kawatani and Hamilton (2011) Weakening only, consistent

with CMIP5 models and Observations (historical period)

Kawatani and Hamilton (2013) Some models, like MPI-MR predicts Shorter periods in 4XCO2

(Schirber et al. 2014)

Non-orographic gravity waves parameterizations

3) Preparing CMIP6

2xCO2 +2K SST experiments, Quasi-Biennial Oscillation

Impact on the stratospheric warmings, via the shaping of the polar vortex before warmings (splitting versus displacement, see Albers and Birner 2014)

Relation with the EU project ARISE2?

Will this physically based stochastic approaches increase the spread of climate simulations?

For instance via an improvement of the year to year variability of the SH stratospheric winter vortex breakdown?

Now that the GWs are tied to the tropospheric weather, we can address their contribution to the climate change in the middle atmosphere,

But there are still large uncertainties on the robustness of the response

Non-orographic gravity waves parameterizations

Perspectives