1

The middle atmosphere and the parametrization of

non-orographic gravity wave drag

Peter Bechtold and Andrew Orr

2

Literature

• Holton, 2004: An introduction to Dynamic Meteorology, AP• Ern, M., P. Preusse, M.J. Alexander & C.D. Warner, 2004: Absolute values of

gravity wave momentum flux derived from satellite data. J. Geophys. Res., 109, D20103, doi:10.1029/2004JD004752

• Ern, M., P. Preusse & C.D. Warner, 2006: Some experimental constraints for spectral parameters used in the Warner and McIntyre gravity wave parameterization scheme. Atmos. Chem. Phys., 6, 4361-4381.

• Mc Landress, C. & J.F. Scinoccia, 2005: The GCM response to current parameterizations of nonorographic gravity wave drag. J. Atmos. Sci., 62, 2394-2413.

• Scinocca, J.F, 2003: An accurate spectral nonorographic gravity wave drag parameterization for general circulation models. J. Atmos. Sci., 60, 667-682.

• Warner, C.D & M.E. McIntyre, 1996: On the propagation and dissipation of gravity wave spectra through a realistic middle atmosphere. J. Atmos. Sci., 53, 3213-3235.

• Orr, Bechtold, Scinnoca, Ern, Janiskova, 2010 : JCL (see Lecture Note)• P. Bechtold et al. ECMWF Newsletter No 120, summer 2009

• Temperature decrease in the Troposphere is due to adiabatic decompression

• Midlatitude upper-tropospheric Jet form due to strong temperature gradient between Pole and Equator.

• The temperature in the Stratosphere increases due to the absorption of solar radiation by ozone

P (hP

a)

Typical Temperature and Zonal Wind profiles for July at 40S, together with the distribution of the 91-levels in the IFS. Tp denotes the Tropopause, Sp the Stratopause, the model top also corresponds to the Mesopause

Structure of the Atmosphere:

Troposphere & Stratosphere

CO2 and O3 zonal mean concentrations from GEMS as used in Cy35r3

SPARC

July climatology

• As heating due to ozone starts to decrease with height, so does the temperature

• Radiative heating/cooling of summer/winter hemispheres causes air to rise/sink at the summer/winter poles, inducing a summer to winter pole meridional circulation

• Coriolis torque induced by meridional circulation to produce easterly/westerly jets in the summer/winter hemispheres

• The large Coriolis torque implies the existence of some eddy forcing to balance the momentum budget. This is provided by the breaking/dissipation of vertically propagating planetary waves, and small-scale non-orographic gravity waves. GWs transport energy and momentum vertically

• Planetary waves add extra drag in the winter stratosphere, particularly northern winter (this is resolved by the model)

Structure of the Atmosphere: Stratosphere & Mesosphere

From Lindzen (1981)

Pronounced waviness in profiles due to gravity wavesVertical wavelength ~12km

Radiosonde observations of gravity waves

8OW 4OW 0O 4OE 8OE 12 OE 16 OE 20 OE 24 OE

60.5N1000

900800700600500

400

300

200

1009080706050

40

30

20

10

Cross section of - 19980317 1200 step 24 Expver F9I20.05 H-IFS 1279 Vertical velocity w

8OW 4OW 0O 4OE 8OE 12 OE 16 OE 20 OE 24 OE

60.5N1000

900800700600500

400

300

200

1009080706050

40

30

20

10

Cross section of - 19980317 1200 step 24 Expver F9I20.05 NH-IFS 3999 Vertical velocity w

(plotted at 1279 equivalent)

Jiang et al. 2005Seasonal climatology of gravity waves from UARS MLS

Latitudinal and seasonal dependence

Although no such thing as a gravity wave source climatology

Sources of (non-orographic) gravity waves: convection, fronts, jet-stream activity

Gravity wavesVertical wavelengths: 1-10s kmHorizontal wavelengths: 10s-1000s kmUnresolved or under-resolved by the IFS

Wave representation

( )

ˆ( , , ) ( ) cos( );

ˆ( , , ) ( )

; int

i k x mz t

g

t x z z k x mz t

t x z z e

frequency

k horizontal wavenumber

m vertical wavenumber

c horizontal phase speedk

c group velocityk

kU c c U rinsic frequency

and phas

e speed

What is a “ non-orographic” gravity wave?

Orographic gravity waves are supposed to be stationary (ω=0 => zero horizontal phase speed)

Non-orograpgic gravity waves are non-stationary, and therefore have non-zero phase speed. The parametrization problem is therefore 5-dimensional!

Depending on gridpoint j, height z, wavenumber k, frequency ω, and direction Φ

( , , , , )j z k

• Define a launch spectrum

• Define the relation between ω and κ. This is called the dispersion relation, and depends on the equation system (hydrostatic or non-hydrostatic shallow water) used to derive the waves (see Appendix in convection Lecture Note).

• Define in which physical space one wants to propagate the wave spectrum: either ω-κ coordinate frame or -m resp.

-m coordinate frame. For practical reasons one wants to have conservative

propagation from one level to the other as long as there is no dissipation.

• Define dissipation procedure, i.e. critical level filtering + some adhoc nonlinear dissipation mechanism to account for wave braking as amplitude increases with height due to decreasing density.

How to proceed for a simple parametrization

c

2 2 2 22

2 2 2

2 2

2 2

(1 / )

(1 / )

/ 0 ( )

/ 0 ( )

k N Nm

f

N hydrostatic wave dynamics

f no rotation

Dispersion relation for gravity waves

2

2

2

222

~~ c

NNkm

Wavelike solutions exist for

For simplicity we only consider hydrostatic, non-rotational waves which also allows to ignore the effect of back reflection of waves

Wavelike solutions exist for and critical level filtering occurs when the intrinsic phase speed approaches zero

2 0

2 2 2f N

Gravity wave source: launch globally constant isotropic spectrum of waves at each grid point as function of, for example, c. Assume constant input momentum flux

Consist of spectrum of waves via hydrostatic non-rotational dispersion relation

2

2

2

222

~~ c

NNkm

UcckUkmhz

~;~;2

;2

U: background wind; N: buoyancy

N

EW

S

Net input momentum flux = 0

Rely on realistic winds to filter the upward propagating (unrealistic) gravity wave source.

Physically based gravity wave scheme

Simplified hydrostatic non-rotational version of Warner and McIntyre (1996) scheme (Scinocca, 2003) - WMS

ts

ps

mm

N

m

mBmE

1

~),~,(ˆ

20

0

1. In any azimuth, φ, the launch spectrum is specified by the total wave energy per unit mass,

2. This is chosen to be the standard form of Fritts and VanZandt (1983), which in space is

3. It is assumed to be separable in terms of and .

4. The dependence on is

5. With

6. is a transitional wavenumber estimated to correspond to in the troposphere (Allen and Vincent, 1995)

7. The ‘tail spectrum’ is largely independent of time, season, and location (VanZandt, 1982)

0E

~m

** for ˆ and for ˆ mmmEmmmE ts

m ~

m

1, 3, 1 5 / 3s t p

km 32 z*m

large-m (small vertical scale) waves saturate at low altitudes

Increase in wave energy as the waves propagate vertically

m-3 slope

Larger scale wave saturate at progressively greater heights

3/5~

Observations: Fritts and VanZandt (1983) and VanZandt (1982)

Convective instabilities and dynamic (shear) instabilities (+ other not well understood processes) act to limit gravity wave amplitudes – gravity wave saturation

t=3

p=5/3

Theoretical considerations set 1≤p≤5/3 (Warner and McIntyre (1996))

unsaturated saturated

sm tm

m

Wav

e m

om

entu

m f

lux

• The characteristic vertical wavenumber m*, separating the saturated and unsaturated slopes is 2π/ 2km, with 2km the characteristic vertical wavelength.

• There is one free parameter in the scheme that allows to shift the saturation curve (dashed blue curve) to the right, with the result that non-linear dissipation is occuring at greater heights. As we will se, and as documented in the literature, this has important consequences for the simulation of the QBO

1) Specify in terms of momentum flux spectral density, using group velocity rule

2) Where

3) are not invariant to vertical changes in U(z) and N(z) (i.e. dependent variables). Hence spectral elements in space are also not invariant. Consequently are not conserved for conservative propagation, i.e. Eliassen-Palm theorem

4) Chose space to describe the vertical propagation of the wave field

5) Use dispersion relationship to remove out dependence on , and integrate out dependence on , which gives (Scinocca, 2003)

00F

dynamics chydrostatifor /~/~ mmcgz

~ and m

),~,(ˆ~),~,( 0000

mEk

cmF gz

),~,( and ˆ000 mFE~ and m

c

3

2

)(1

1),(

s

p

N

Ucmc

Uc

N

UcAcF

p

fNBmA

pp

2

2203

where the constant A is all terms which are independent of height

0 0 and U U U c c U

m ~

Non-hydrostatic limits (more physically realistic)

2( , , )( , , ) ( , , );

( , , )

m mF c J F m J

c N

Galilean Transform

At the launch level we have

Which sets an absolute lower bound for critical level absorption of .

If on the next vertical level z1(>z0) U increases such that

then waves with phase speeds in the range

encounter critical level absorption and the

momentum flux corresponding to these phase speeds is

removed from

How to do critical level absorption

0 1U c U

0 0U

0c

1 0U U

( , )F c N

S

EW

U0

Convective instabilities and dynamic (shear) instabilities (+ other not well understood processes) act to limit gravity wave amplitudes – gravity wave saturation

Results in the “universality” of the GW spectrum m-3 (Smith et al. 1987)

WMS scheme deals with non-linear dissipation in an empirical fashion by limiting the growth of the GW spectrum so as not to exceed saturated spectrum ~m-3.

1) Achieved by specifying a saturation upper bound on the value of the wave energy density at each level with the observed m-3 dependence at large-m

2) Which can be expressed as

3) Unlike the unsaturated spectrum, , the saturated spectrum is not conserved, ,and so decreases in amplitude with height as a result of diminishing density. This limits to a saturation condition

psat Nm

mCmE

~),~,(ˆ 2

3

p

sat

c

Uc

N

UcBCcF

2

),(

F satFF

),(),( cFcF sat

Parameter specification1) t=3 (fixed)2) p=1 (or 3/2 ; observed/theoretical )3) s=1 (or 0,1; s=1 most common, ie positive slope required)4) m* (= , see Ern et al (2006))5) C* (=1; raising this raises the height momentum is

deposited)6) φ =4 (number of azimuths, although can have 8, 16, …)

7) z0 (launch level; Ern et al. (2006) suggests either 450 hPa or 600 hPa)

8) input momentum flux into each azimuth is set to 3.75 x10-3 (Pa)

3/51 p

Ern, Preusse, and Warner, ‘Some experimental constraints for spectral parameters used in the Warner and McIntyre gravity wave parameterization scheme’, Atmos. Chem. Phys., 6, 4361-4381, 2006

00F

km2/2

Procedure1) Check for critical level absorption, i.e. if U increases such that

then waves with phase speeds in the range

2) Phase speeds which survive critical level absorption propagate conservatively to next level

3) Possible nonlinear dissipation is modelled by limiting the momentum flux

4) Implies for , that the momentum flux corresponding to these phase speeds is removed from and deposited to the flow in this layer, and that is set equal to .

5) Repeat procedure for subsequent layers and all azimuths

6) Results in momentum flux profiles used to derive the net eastward, , and northward, momentum flux

7) The wind tendency (i.e. gravity wave drag) in each of these directions is given by the vertical divergence of the momentum flux

Discretize speeds phase using cnc

min max0.25 m/s; 100 m/s; 20 50cc c n

)()( 01 zUzU

)()( 10 zUczU

),(),( cFcF sat

),~( cF

satF),~( cF

EFNF

p

FFg

t

VU NE

,,

Co-ordinate stretch applied: higher resolution at large-c (i.e. small-m)

Evaluation: Run ensemble of T159 (125 km) 1-year climate runs and compare mean circulation and temperature structure against SPARC dataset

• Cy35r2 (operational from 10 March 2009). Uses so called Rayleigh friction, a friction proportional to the zonal mean

wind speed, to avoid unrealistically high wind speeds (polar night jet) in middle atmosphere. The trace gas climatology (CO2, CH4 etc) consist of globally constant values, apart

from ozone

• Cy35r3 (became operational September 2009) includes a new trace gas climatology (GEMS reanalysis + D. Cariolle

fields), zonal mean fields for every month, and the described non-orographic gravity wave parametrisation

January

NH

July

SH

Polar winter vortex

ERA

Cy35r2

Operational since March 2009

Cy35r3

Operational in summer 2009 with GWD + GHG

SH wintertime vortex is quasi-symmetric, but not NH polar vortex, due to braking quasi-stationary Rossby waves emanating in the troposphere

Distinguishing between resolved and unresolved (parametrized) waves.

the Eliassen Palm flux vectors

• EP Flux vectors give the net wave propagation for stationary Rossby waves (derived from quasi-geostroph. eq.)

• Stationary Rossby waves are particularly prominent in the NH during winter. They propagate from the troposphere upward into the stratosphere

1* * * *cos , cos /

; ; .

*

& 1992, .388

EPVector R u v f R v p

f Coriolis latitude pot temperature

denote anomalies from zonal mean

Peixoto Oort p

ERA40

Resolved stationary Rossby waves: EP-Fluxes in Winter

Cy35r3-ERA40

Stationary Rossby waves are particularly prominent in the NH during winter. They propagate from the troposphere upward into the stratosphere

ERA40

Resolved stationary Rossby waves: EP-Fluxes in Summer

Cy35r3-ERA40

35r2

SPARC

July climatology

30

35r3

SPARC

July climatology

U Tendencies (m/s/day) July from non-oro GWD

32Comparison of observed and parametrized GW momentum flux for 8-14 August 1997 horizontal distributions of absolute values of momentum flux (mPa) Observed values are for CRISTA-2 (Ern et al. 2006). Observations measure temperature fluctuations with infrared spectrometer, momentum fluxes are derived via conversion formula.

Momentum fluxes from CRISTA campaign compared to parametr non-orogr GW momentum

fluxes

33

Total = resolved +parametrized (orograph+non-orograph.) wave momentum flux

Conclusions from comparison against SPARC & ERA-Interim reanalysis

• Polar vortex during SH winter quasi symmetric, but asymmetric NH winter polar vortex, due to vertically propagating quasi-stationary Rossby waves (linked to mountain ranges)

• In Cy35r2 (no GWD parameterization) SH polar vortex too strong, westerly polar night Jet is wrongly tilted with height, large T errors in mesosphere. Jet maximum in summer hemisphere easterly jet at wrong height (at stratopause instead of mesopause)

• In Cy35r3 improved tilt of the polar Jet with height towards the Tropics, allover improved winter hemisphere westerly and summer hemisphere easterly jets. The smaller warm bias around the stratopause is due to the improved greenhouse gas climatology

• Results qualitatively similar for January, invert NH and SH

35r2

SPARC

January climatology

35r3

SPARC

January climatology

U Tendencies (m/s/day) January from non-oro GWD

The QBO

Prominent oscillations in the tropical middle atmosphere are

• A quasi bi-annual oscillation in the stratosphere, and a

• Semi-annual oscillation in the upper stratosphere and mesosphere

These oscillations are wave induced. Whereas the waves are moving upward, these oscillations propagate downward. Why ? Waves deposit momentum at critical level, wind changes, and so does the critical level, etc

In the following 6-year integrations are carried out with Cy35r2, Cy35r3, and one sensitivity experiment with Cy35r3, but shifting the saturation spectrum to the right ->shifting wave braking to higher altitudes.

QBO : Hovmöller from free 6y integrations

=no nonoro GWD

Resolution dependent resolved gravity-wave activity as seen in Omega field (Pa/s) August 2006

Resolution dependence: Monthly mean parameterized (non-orographic & orographic ) & resolved momentum fluxes (mPa) August 2006

42

Resolution dependence Cy35r3 August