Mountain Waves entering

the Stratosphere

Mountain Waves entering the Stratosphere: New aircraft data analysis techniques from T-Rex

Ronald B. Smith, Bryan WoodsYale University

New Haven, Connecticut

J. Jensen*, W. Cooper*, J. D. Doyle**, Q. Jiang**, V. Grubisic***[* National Center for Atmospheric Research, Boulder, CO;

**Naval Research Laboratory, Monterey, CA, ***Desert Research Institute, Reno, NV]

[Support from the National Science Foundation]

Outline• T-Rex Events (march/April 2006)• Potential and Kinetic energy• Sensitivity to Mountain Top Winds• Wave spectra with altitude• Wind and stability profiles• Layering of Mechanical Bernoulli and Ozone• Summary and future work

[Warning: Beware of speculation. This project is only a few weeks old.]

Microwave Limb ScannerJiang et al

Global pattern ofGravity Waves in the upperatmosphere

Frequency w > 1 m s-1 and Mean TKE> 2 m2 s-2

COAMPSClimate(Doyle)

Tropopause

Wind

Final GV Flight Table for T-Rex RF IOP Date JD Track

/actual Wmax**

Del WI

DWS MS Feature

01 1 M2 61 B 1.5 4 17 Smith 02 2 M5 64 C 1.5 18 Smith 03 3 M9 68 A/265 5 12 Smith Leg differences 04 4 M14 73 B/245 5 12 31 Smith 05 6 M25 84 B/260 9 17 32 Doyle Short Train & leg

diff 06 9 A2 92 B/245 1.5 3 Cooper Leg Diff 07 IC A7 97 IC* Grubisic 08 10 A9 99 B/245 3 8 Grubisic Periodic W& leg

diff 09 13 A15 105 B 2 6 Grubisic 10 13 A16 106 B/245 10 20 Grubisic Easter Event 11 14 A21 111 C Cooper? 12 15 A26 116 B/210

? 5 Cooper Easterly flow,

Jiang (* Intercomparison flight; ** eyeball)

Dashed Line = North Leg Solid Line = South leg

Note shorter wavelength ~15km

dxdyvuKH

)''()2/( 22

dxdywKZ 2')2/(

dxdyTgPE '')2/(

Wave Energy Components

)0()(

)()(

0

dssU

sws

s

Vertical Kinetic Energy (J/m2)

0

20

40

60

80

100

120

140

0 2 4 6 8 10 12 14

Research Flight (RF#)

Ve

rtic

al K

E

(times 1000) Each point is a leg

Sensitivity

0

10

20

30

40

50

60

70

80

0 5 10 15 20 25 30

Windspeed @700hPa (m/s)

Ver

tic

al

KE

(J

/m2

)Threshold?

Lemoore and Visalia soundings

Each point is a flight

Horizontal Kinetic Energy (J/m2)

0

100

200

300

400

500

600

700

800

900

0 2 4 6 8 10 12 14

Research Flight (RF#)

Ho

rizo

nta

l Kin

eti

c E

ne

rgy

Each point is a leg

Potential Energy (J/m2)

-2000

0

2000

4000

6000

8000

10000

0 2 4 6 8 10 12 14

Research Flight (RF#)

Po

ten

tia

l En

erg

y

Computed from the product of theta and displacement perturbation

BigWaves (RF4,5,10) Potential Energy (J/m2)

-5000

0

5000

10000

15000

20000

0 2000 4000 6000 8000 10000 12000 14000 16000

Altitude (m)

Po

ten

tia

l E

ne

rgy

(J/

m2

)

Wave Energy Comparison

• Observation – Vertical KE ~ 40 J/m2– Horizontal KE ~ 400 J/m2– Potential Energy ~ 4000 J/m2 (stratosphere)

• Interpretation– Wave energy concentrated in the stratosphere– Observations not consistent with vertically

propagating or trapped waves “rooted” in the troposphere

– Horizontal KE may be enhanced by Bernoulli layering

Wavelength 20 km

10km

VerticalVelocitySpectrum

9km 11km 13km

RF10

9km 11km 13km

RF10

North

South

9km 11km 13km

RF4

North

South

9km 11km 13km

RF4

North

South

Vandenberg Windspeed Profiles:Big Wave Events(RF4,5,10)

[Note oscillations in the stratosphere]

Vandenberg Theta Profiles:Big Wave Events(RF 4,5, 10)

Scorer Parameter from quadratic fits

0.00E+00

5.00E-08

1.00E-07

1.50E-07

2.00E-07

2.50E-07

3.00E-07

3.50E-07

4.00E-07

4.50E-07

5.00E-07

0 5000 10000 15000 20000 25000

Altitude (m)

Sc

ore

r P

ara

me

ter

(m-2

)

Ksquared for Lamda =15km

Gravity wave region

April 16, 2006

Scorer Parameter from quadratic fit

22 /)( UNzS

0ˆ)(ˆ 2 wkSwZZ

Conserved Variable Diagram for a racetrack

Dashed line = North Leg Solid line = South Leg

.)2/1()( 2 constgZUpPB

Mechanical Bernoulli Function for compressible steady flow

GPS altitudeMinor contributoras the A/C tries tofly at constant pressurealtitude

Dual Conserved Variable Plots(RF4; March 14, 2006; Leg @41kft)

Ozone Mechanical Bernoulli*

Wave #1 @41kft

352

354

356

358

360

362

364

366

368

370

372

0 50 100 150 200 250 300

Ozone (ppb)

Theta

(K)

Wave #1 @ 41kft

352

354

356

358

360

362

364

366

368

370

372

352300 352350 352400 352450 352500 352550 352600 352650 352700 352750 352800 352850

Bernoulli (m2/s2)

Theta

(K)

[using GPS altitude]

Conclusions• The new GV aircraft is effective in monitoring

stratospheric gravity waves. • March/April 2006 was an active period for storms hitting

the Sierras• 3 large gravity wave events out of 8 Track B flights• Wave energy is concentrated in the stratosphere• Typical wavelength there is ~15km• Wave location suggests Sierra causation• 2-D and steadiness are imperfect and variable• Wave amplitude very sensitive to mountain top winds• Strong wave events have similar wind environments

(with a stratospheric critical level)

Linear Theory

• Criterion for linear waves is nearly satisfied

2.0/50/02.0*500/2

smmUNPMAX

•Vertically propagating gravity waves should have KE = PE at each level (equipartition)

•Trapped waves should have PE concentrated in the active stable layer

Speculations on wave dynamics

• Waves are “rooted” in the stratosphere– Wave energy distributions are not consistent

with vertically propagating or conventional trapped waves.

– Potential energy is concentrated in the stratosphere

– Scorer parameter exceeds the wavenumber only in the stratosphere

– Generation mechanism unknown; probably non-linear

Free surface (Critical layer?)All the potential energy is here.

UMT website

Speculations on layering

• Vertical advection by waves allows diagnosis of ozone layering and dynamic “Bernoulli Layering”

• GPS altitude is required for Bernoulli function determination (new!)

• Bernoulli Layering correlates with ozone layering in the stratosphere

• Layering may represent isentropic interleaving of stratospheric air masses, prior to the wave encounter

• Bernoulli layering contributes a false signal to the horizontal wave kinetic energy.

Future work

• Improve GV instrument calibrations– Compute wave energy flux using GPS altitude– Improved wave energy density computations– Momentum fluxes– Improved Bernoulli computations

• PV computations using Crocco’s theorem• Analysis of soundings• Compare observations with linear wave theories• Test non-linear theories of wave regeneration, undular

bores, and critical level reflection and/or decoupling• Determine the role of the critical level

Big Waves (RF4,5,10)Vertical Kinetic Energy (J/m2)

0

20

40

60

80

100

120

140

0 2000 4000 6000 8000 10000 12000 14000 16000

Altitude (m)

Ver

tic

al

Kin

eti

c E

ne

rgy

(J

/m2

)

(Smith, 1985)

Other aircraft profiles:OzoneAir densityWater Vapor

Each point is a racetrack

delta WI

0

5

10

15

20

25

0 2 4 6 8 10 12 14

Flight number

Wm

ax-W

min

(m

/s)

Each point is one racetrack

Big Wave Events (RF4,5,10)Aircraft Racetrack Data

y = -3E-07x2 + 0.0043x + 33.241R2 = 0.3747

0

10

20

30

40

50

60

0 2000 4000 6000 8000 10000 12000 14000 16000

Altitude (m)

Ave

r. W

ind

spee

d (

m/s

)

Big Wave Events (RF4,5,10)Aircraft Racetrack Data

y = 2E-06x2 - 0.042x + 501.97R2 = 0.8289

310

320

330

340

350

360

370

380

0 2000 4000 6000 8000 10000 12000 14000 16000

Altitude (m)

Th

eta

(K

)

Aircraft Profiles:All Big Wave Events(RF4,5,10)

Each point is a racetrack