Gravity waves:

introduction and global view

Peter Preusse

ECMWF, 2 September 2015 – p. 1

Structure of middle atmosphere

✇ dudt − fv + 1

ρ∂p∂x = X

✇ steady state, zonal mean: ⇒ −fv = X

✇ X by planetary waves and gravity waves

Decelleration of westerlies induces poleward circulation

ECMWF, 2 September 2015 – p. 2

GW impact on middle atmosphere

QBO

summer winter

surface temperatures,

precipitation(via QBO, circulation, NAO)

Brewer-Dobson

circulation-trend

cold summermesopause

Brewer-Dobson

circulation

tro

po

sp

here

str

ato

sp

here

meso

sp

here

radiative forcing

PSC

mesospheric circulation

cirrus, dehydration(direct and indirect)

Red: Processes which are driven to >50 % by GWsPurple: Indirect effects

ECMWF, 2 September 2015 – p. 3

General circulation → polar troposphere

Sigmond and Scaife, J. Clim., 2010

Sensitivity on the strength of GW momentum flux

ECMWF, 2 September 2015 – p. 4

QuasiBiennialOscillationQBOAfter:

B. Naujokat

ECMWF, 2 September 2015 – p. 5

QBO → tropospheric weather

from Marshall and Scaife, JGR, 2009

Difference of mean winter temperature between QBOphases in NCEP/NCAR reanalysis data.

ECMWF, 2 September 2015 – p. 6

gravity wave=

buoyancy wave6=

gravitational wave

ECMWF, 2 September 2015 – p. 7

Isolated Airparcel

temperature profileof backgroundatmosphere

air parcel

Γ

∆Τ

∆ρ

z

T

g

ECMWF, 2 September 2015 – p. 8

Plane Wave

cφ

warmco

lddownupward

ECMWF, 2 September 2015 – p. 9

Plane Wave

warmwarm

colddown

λx

λz

cφ

upward

upward

ECMWF, 2 September 2015 – p. 9

Plane Wave

s

dx

dz

φ

φ

warmco

ldwarm

λ x

λ z

upward

downward

upward

cφ air parcel

r

Ngr

avity

F

restorin

g force

F

ω2 =k2hN

2

k2h +m2(1)

ECMWF, 2 September 2015 – p. 9

Dispersion relation

The full dispersion relation in 3D, including exponentialdensity decrease and Earth rotation is:

ω2 =(k2 + l2)N2 + f2

(

m2 + 1

4H2

)

k2 + l2 +m2 + 1

4H2

≃ ω2 =k2hN

2

k2h +m2+ f2 (2)

This implies

N2 > ω2 > f2 (3)

⇒ phase velocity and group velocity

~cφ =ω

|~k|

(

k

|~k|,l

|~k|,m

|~k|

)

, ~cg =

(

∂ω

∂k,∂ω

∂l,∂ω

∂m

)

(4)

ECMWF, 2 September 2015 – p. 10

Plane Wave

warmwarmdown

λx

λz

cφ

upward

upward

cold

cg

Fpx = ρ(1− f2

ω2 )u′w′; X = −1

ρ∂∂zFpx

ECMWF, 2 September 2015 – p. 11

Wave clouds at Juelich

ECMWF, 2 September 2015 – p. 12

Wave clouds at Juelich

ECMWF, 2 September 2015 – p. 13

Saturation AmplitudeToo large amplitudes result in convectively instable layers.

Wave solution:

N2 > 0 ⇔ Γ = −10K

km<

∂(T + T sin(mz))

∂z(5)

⇒ Maximum stable amplitude:

Tmax =N2T

gm=

N2T

g2πλz (6)

Doppler shift

ω = ωgb − ~kh~U (7)

ω2 =k2hN

2

m2⇒ λz =

∣

∣

∣

∣

2πc− U||

N

∣

∣

∣

∣

(8)

ECMWF, 2 September 2015 – p. 14

The key quantitiesVery simplified:

✇ The momentum flux decides how much drag can beexerted

✇ The phase speed decides where the drag is exerted✇ The direction decides whether the drag accelerates or

decelerates the background flow

ECMWF, 2 September 2015 – p. 15

CRISTA-1 (1994)

Eckermann and Preusse, Science, 1999

F ∝ λz

λh(T ′)2

ECMWF, 2 September 2015 – p. 16

Absolute values of momentum fluxCRISTA-2, August 1997 F ∝ λz

λh(T ′)2

Absolute Values of Momentum Flux [mPa]

60N

40N

20N

Equ

20S

40S

60S

180W 150W 120W 90W 60W 30W 0 30E 60E 90E 120E 150E 180E

60N

40N

20N

Equ

20S

40S

60S

180W 150W 120W 90W 60W 30W 0 30E 60E 90E 120E 150E 180E

CRISTA Warner & McIntyre

Ern et al., JGR, 2004Orr et al., J. Clim., 2010 :GW scheme in ECMWF confined by CRISTA

ECMWF, 2 September 2015 – p. 17

HIDLS: Annual cycle for 2006

Ern et al., JGR, 2011

ECMWF, 2 September 2015 – p. 18

ECMWF global data and HIRDLS

abs.

GW

mom

entu

m fl

ux [m

Pa]100

10

1

0.1

0.01

Preusse et al., ACP, 2014

✇ Single day vs. whole month✇ General good agreement✇ Low latitudes: Satellites show hot spots over continents

ECMWF, 2 September 2015 – p. 19

Yonsei Convective GW Source

Choi et al., JGR, 2009ECMWF, 2 September 2015 – p. 20

Yonsei Convective GW Source

Song and Chun, JAS, 2005

Trinh et al., in preparation ECMWF, 2 September 2015 – p. 21

10 years of SABERla

titud

e [d

eg]

SABER GW momentum flux [ 10-3 Pa ]

50

-50

0

JAJOJAJOJAJOJAJOJAJOJAJOJAJOJAJOJAJO2002 2003 2004 2005 2006 2007 2008 2009 2010

1.80

1.35

0.90

0.45

0.00

z = 30.0 km

λz= 5-25 km

Ern et al., JGR, 2011 ECMWF, 2 September 2015 – p. 22

SABER: poleward shiftla

titud

e [d

eg]

SABER GW momentum flux [ 10-3 Pa ]

z = 70.0 km

50

-50

0

JAJOJAJOJAJOJAJOJAJOJAJOJAJOJAJOJAJO2002 2003 2004 2005 2006 2007 2008 2009 2010

0.10

0.08

0.06

0.04

0.020.00

λz= 5-25 km

Ern et al., JGR, 2011 ECMWF, 2 September 2015 – p. 23

QBO is wave-driven

wind u+c-c

Wave drag is exerted in the direction of phase speed c

= 2 c-u Nzλ π

cf. Lindzen and Holton, A theory of the Quasi-Biennial Oscillation, JAS,1968

ECMWF, 2 September 2015 – p. 24

QBO forcing

Ern et al., JGR, 2014

ECMWF, 2 September 2015 – p. 25

QBO forcing

Ern et al., JGR, 2014

ECMWF, 2 September 2015 – p. 26

Comparison of GCM and measurements

SPARC gravity wave initiative(reinstated in 2008; lead Joan Alexander).

A Comparison Between Gravity Wave Momentum Fluxes inObservations and Climate Models

Marvin A. Geller, M. Joan Alexander, Peter T. Love,Julio Bacmeister, Manfred Ern, Albert Hertzog, Elisa Manzini,Peter Preusse, Kaoru Sato, Adam A. Scaife, and Tiehan Zhou

J. Clim., 2013

ECMWF, 2 September 2015 – p. 27

Zonal mean climatologies

✇ general agreement of shape✇ quantitative agreement (better factor 2) in winter vortex✇ indicates problem at summer high latitudes

ECMWF, 2 September 2015 – p. 28

ECMWF, 2 September 2015 – p. 29

Findings and challenges

✇ General shape of global distribution bymodulation of tropospheric GWs by background windindividual sources such as orography, convection,spontaneous adjustmentlarge GWMF in southern winter: source still not fullyexplained

✇ sources need to be quantified✇ QBO driving seams clear, but direction could induce

artifacts✇ vertical gradient, propagation and dissipation need

good accuracy measurements

ECMWF, 2 September 2015 – p. 30

Infrared limb imaging from space

✇ 3D images of GWs✇ vertical resolution

about 1.0 km✇ temperature

precision0.5-1.0 K

✇ sources bybackwardray-tracing

ECMWF, 2 September 2015 – p. 31

Assessment

By simulated measurements (limb soundings) throughECMWF data fields:

✇ Infrared limb imaging will be able to measure all threekey quantities:

GW momentum fluxdirectionphase speed (inferred)

✇ zonal mean net GWMF accurate to ∼30 %✇ independent values at several altitudes throughout

entire stratosphere

ECMWF, 2 September 2015 – p. 32

Summary✇ Gravity waves are important for e.g. QBO and

Brewer-Dobson circulation and thus for climateprojection

✇ Gravity wave sources include: orography, convection,spontaneous adjustment, ?

✇ Oblique propagation is important → parametrisation vsresolved?

✇ GCM ↔ observations: General distributions betweenmodels and measurements are coarsly realistic

✇ Uncertainty ranges are large (factor 2 at best (e.g.30km, SH winter), order of magnitude at worst).

✇ 3D distributions from limb imager would be mostimportant break-through

ECMWF, 2 September 2015 – p. 33

Coupling by propagating waves

Global equation of motion (wind):

du

dt− fv +

1

ρ

∂p

∂x= X (9)

Separate into large scale u and GWs u′, u = u+ u′.Acceleration for u by GWs:

X = −1

ρ

∂

∂zFpx (10)

Pseudomentum flux:

Fpx = ρ(1−f2

ω2)u′w′ (11)

ECMWF, 2 September 2015 – p. 34