Dr. Robin RobertsonSchool of PEMSUNSW@ADFA

Canberra, Australia

Vertical Mixing from ROMS: Spectral Response of

Velocities

Indonesian Throughflow

Domain Transects

0 500 1000 1500 2000

Distance (km)

0

500

1000

1500

2000

Dis

tan

ce (

km)

110 115 120 125 130 135 140

Longitude

-20

-15

-10

-5

0

5

10

La

titu

de

0

500

1000

2000

4000

6000

8000

(m )

Australia

Timor Sea

HalmaheraSea

IndianOcean

Mak

assa

r S

trai

t

Timor Sea

Arafura Sea

Maluku Sea

BandaSea

MakassarPacific Ocean

Flores Sea

Indonesian Seas Model Domain

Ombai Strait

Borneo(Kalimmantan)

(m)

Sulaw esiSea

Elevation Fields

0 500 1000 1500 2000

Distance (km)

0

500

1000

1500

2000

Dis

tan

ce

(km

)

0

10

20

30

40

50

60

70

80

90

100

125

150

Land

0 500 1000 1500 2000

Distance (km)

0

500

1000

1500

2000

(cm)

(o )Land

M2

Elevation Amplitudes M2

Phase Lags

0 500 1000 1500 2000

Distance (km)

0

500

1000

1500

2000

Dis

tan

ce

(km

)

0 500 1000 1500 2000

Distance (km)

0

500

1000

1500

2000

K1

Elevation Amplitudes K1

Phase Lags

0

45

90

135

180

225

270

315

Rms differences:

M2 7.6 cm

S2 5.8 cm

K1 11.7cm

O1 8.8 cm

With site 8 excluded

Isotherm Fluctuations

Vertical Mixing

• Internal Waves are a significant mixing mechanism – 3.2 TW (TW=1012 W) [Garrett, 2003]

• Interest in estimates of vertical mixing• Measurements

– Difficult and expensive– Small scale– Episodic

• From Models – Depends on the parameterization used

Vertical Mixing ParameterizationsIn ROMS

• Many available in Roms– Mellor-Yamada 2.5 level turbulence closure (MY2.5)– Kpp – Large-McWillamns-Doney (LMD)– Brunt-Väisälä Frequency Based (BVF)– Pacanowski-Philander (PP)– General Ocean Mixing (GOM)– Generic Length Scale (GLS)

- - -l• generic

Evaluated the Performance of these

Mixing Parameterizations

• Internal Tidal model for Fieberling Guyot• Accessible data set for both velocities and

dissipation• Good agreement for major axes of

semidiurnal tidal ellipses between model estimates and observations

Domain

•

-128.2 -128.0 -127.8 -127.6 -127.4

Longitude

32.0

32.2

32.4

32.6

32.8L

atit

ud

e

500

1000

1500

2000

2500

3000

3500

4000

W ater Depth

(m)

taken from Smith and Sandwell [1997]

B2

B3

F2

F3F4,F5 C

R3

R2 P

Comparison to Observations:Observations

Model Results32 42.05 N128 2.70 W

32 28.64 N127 50.44 W

32 28.27 N127 48.57 W

32 26.56 N127 46.16 W

32 9.30 N128 0.49 W

32 25.75N127 50 W

32 24.61 N127 47.57 W

Major Axis (cm s -1 )

B2 F2 R2 C B3F3R3

4 8

0

1000

2000

De

pth

(m

)

4 8 120 4 4 8 12 4 8 4 8 12 4 8 12 4 8

P32 26.56 N127 46.70 W

4 8 12

0

1000

2000

De

pth

(m

)

8 160 4 8 16 8 16 4 8 12 4 8 120 4 8

K 1

M 2

4 8

0

1000

2000

De

pth

(m

)

8 160 4 4 8 8 16 4 8 8 16 4

Mean

rms: 7.1 cm s-1

rms: 6.5 cm s-1

rms: 3.7 cm s-1

Baroclinic Tides

Bottom

-4000

-2000

0

Dep

th (

m)

(cm s -1 )

32.0 32.2 32.4 32.6 32.8

Latitude

-4000

-2000

0

De

pth

(m

)

-4000

-2000

0

32.0 32.2 32.4 32.6 32.8Latitude

-4000

-2000

0

127o 51.4'W

127o 41.0' W

127o 51.4'W

127o 41.0'W

M2

M2

K1

K1

00.511.522.533.544.555.56

Velocity Dependence:

Vertical Mixing Parameterization

0.5

1.5

2.5

3.5

4.5

5.5

Bottom

(cm s -1 )

-4000

-2000

0

Dep

th (

m)

-4000

-2000

0

De

pth

(m

)

32.4 32.6 32.8

Latitude

-4000

-2000

0

De

pth

(m

)

32.4 32.6 32.8

Latitude

LMDMY

LMDSSCW

PP

GOM

32.4 32.6 32.8

Latitude

GLS: gen

GLS: k-

GLS: k-

-4000

-2000

0

BVF

GLS: k-kl

Diffusivity of Momentum:

Vertical Mixing Parameterizatio

n

1E-005

1E-004

1E-003

Bottom

(m 2 s -1 )

-4000

-2000

0

Dep

th (

m)

-4000

-2000

0

Dep

th (

m)

32.4 32.6 32.8

Latitude

-4000

-2000

0

Dep

th (

m)

32.4 32.6 32.8

Latitude

LMDMY

LMD-SSCW

PP

GOM

32.4 32.6 32.8

Latitude

GLS: gen

GLS: k-

GLS: k-

-4000

-2000

0

BVF

GLS: k-kl-4000

-2000

0

Dep

th (

m)

Obs.

GW

, 2

004

P, 1

99

7

Vertical Diffusivities Averaged over the Region

• MY25* 1.1x10-4 m2 s-1

• GOM 7.0x10-5 m2 s-1

• BVF 3.4x10-3 m2 s-1

• LMD* 1.9x10-4 m2 s-1

• LMD-SCCW 1.7x10-4 m2 s-1

• PP 4.8x10-5 m2 s-1

• GLS- kkl 1.7x10-3 m2 s-1

• GLS- k 1.7x10-3 m2 s-1

• GLS- k* 9.9x10-5 m2 s-1

• GLS- gen* 8.9x10-5 m2 s-1

Is there really no difference

in the velocities?

• Maybe the tidal frequencies aren’t the place to look

• Vertical mixing transfers energy from tides to high frequencies, especially harmonics

0.5

1.5

2.5

3.5

4.5

5.5

Bottom

(cm s -1 )

-4000

-2000

0

Dep

th (

m)

-4000

-2000

0

De

pth

(m

)

32.4 32.6 32.8

Latitude

-4000

-2000

0

De

pth

(m

)

32.4 32.6 32.8

Latitude

LMDMY

LMDSSCW

PP

GOM

32.4 32.6 32.8

Latitude

GLS: gen

GLS: k-

GLS: k-

-4000

-2000

0

BVF

GLS: k-kl

Spectral Response

•Background Location

•Follows Garrett-Munk spectra (N=5 cph)

0.0001 0.001 0.01 0.1 1

0.1

1

10

100

1000

10000

Sp

ec

tra

l De

ns

ity

((

cm

s-1

)2 /h

r-1)

0 .0001 0.001 0.01 0.1 1Frequency (hr -1)

0.1

1

10

100

1000

10000S

pe

ctr

al D

en

sit

y

((c

m s

-1)2 /

hr-1

)

419 m

1419 m

0.0001 0.001 0.01 0.1 1

0.1

1

10

100

1000

10000

Sp

ec

tra

l De

ns

ity

\(

(cm

s-1

)2 /h

r-1)

719 m

U obsV obsU modelV modelGM Spectrum N=5 cph

Leads to 2 questions

• Why do the spectra follow Garrett-Munk? • Which one is the best performer?

Garrett-Munk and Vertical Diffusion

•

•Vertical Diffusion plays a big role in spectral shape

•Is not responsible for the transfer of energy between frequencies or energy cascade

•Does remove the higher frequency energy

•Background location

Black – with vertical diffusion

Red – without vertical diffusion

What about Higher

Frequencies?•

• Diurnal and Semidiurnal tidal peaks clearly visible

•0.04 hr-1 (24 hr)

•0.08 hr-1 (12 hr)

•GOM has increased energy at highest frequency (midlevel)

Focusing on Higher

Frequencies

• Internal Wave Generation Site

Normalizing by MY25

• Internal Wave Generation Site

Focusing on Higher

Frequencies• Background Site

Normalizing by MY25

• Background Site

Observations

• Correlation between high vertical diffusivity and low spectral energy

• GOM showed enhanced energy at high frequencies; exceeded the 95% confidence

• PP shows very weak vertical diffusivity• BVF, GLS-kkl, and GLS- have high

average KM

• MY25 has bump in energy at high frequency end

• Differences at tidal frequencies are small• Differences occur in high frequencies.

Summary

• All 10 vertical mixing schemes generated spectra roughly following G-M– Believed to be due to non-linear interactions

and the vertical mixing parameterization

• No answer as to which is “best”• Best performers are: GLS-, GLS-gen then MY25, LMD

– Based on matching • tidal velocities• Dissipation: both with depth and area average• Spectral response

•

The End:Time for Discussion