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