Post on 10-Mar-2018
Effects of surface waves Effects of surface waves
on airon air--sea momentum and sea momentum and
energy fluxes and ocean energy fluxes and ocean
response to hurricanes response to hurricanes
Isaac GinisIsaac Ginis
University of Rhode IslandUniversity of Rhode Island
Collaborators: Yalin Fan and Collaborators: Yalin Fan and TetsuTetsu HaraHara
July 17, 2007July 17, 2007
OutlineOutline
1.1. Energy and momentum flux budget Energy and momentum flux budget across airacross air--sea interfacesea interface
–– Uniform wind Uniform wind –– Hurricanes Hurricanes
2.2. WindWind--wavewave--current interaction in current interaction in hurricanes hurricanes
3.3. Case study: Hurricane Ivan (2004) Case study: Hurricane Ivan (2004)
Wind-Wave-Current Interaction
Wind stressWind stress(momentum flux from air)(momentum flux from air)
Surface wavesSurface waves
AtmosphereAtmosphere
OceanOcean
Ocean currentsOcean currents
URI Coupled WaveURI Coupled Wave--Wind (CWW) ModelWind (CWW) Model
•• Near the peak : Near the peak : WAVEWATCH III (WW3) modelWAVEWATCH III (WW3) model..•• High frequency part : High frequency part : Equilibrium Spectrum modelEquilibrium Spectrum model of Hara and of Hara and
Belcher (JFM, 2002)Belcher (JFM, 2002)
maxk0k
2k
1k
mink
1k∆
3k
2k∆ 0k∆
123
vk
High frequency partNear peak
Wave Boundary Layer (WBL) modelWave Boundary Layer (WBL) modelof Hara and Belcher (JPO, 2004)of Hara and Belcher (JPO, 2004)
025 - max-1
Explicitly calculates wave-induced stress
Full wave spectrum
Wind profile and drag coefficientWind profile and drag coefficientover any given seasover any given seas
20 30 50U10 (m/s)
400
Powell et al. (2003) Large & Pond (1981)WW3 (upper and lower bound)
3
1
Our results (upper and lower bound)
5
4
2C
D *
1000
Bulk, 0.0185
Drag Coefficient in Drag Coefficient in the CWW modelthe CWW model
•• At high wind speeds, CAt high wind speeds, Cdd levels levels off and even decrease with wind off and even decrease with wind speedspeed
Extrapolation of Large & Pond (1981)’s formula
Constant zch (0.0185)
Upper and lower bounds of Cd from all earlier exp.
GPS GPS sondesonde observation under various observation under various hurricanes (Powell et al., 2003). hurricanes (Powell et al., 2003).
Roughness Length and Drag Coefficients Roughness Length and Drag Coefficients Parameterizations based on CWW Parameterizations based on CWW
1. Modeling of air-sea fluxes in hurricanes
Effect of surface gravity waves on air-sea fluxesc
c
c c
Ocean Currents
EFair = EFc + (EFgrowth + EFdivergence)
( )divergencegrowthcair ττττ rrrr++=
Horizontal wave propagation
(EFdivergence , )divergenceτrWave growth
( EFgrowth, )growthτr
1. Modeling of air1. Modeling of air--sea fluxes in hurricanessea fluxes in hurricanes
Air-sea flux calculationsWind Field
τc=τair - τwEFc = EFair - EFw
Momentum & energy fluxτair=f(ψ(θ,k),β(θ,k))EFair=f(ψ(θ,k),β(θ,k))
Wave information ψ(θ,k), Hs, L, T, …
Downward Energy and Momentum
Flux Budget Model
Ocean Model
Ocean ResponseU, T, …U
Atmospheric observations(wind speed, Uw ) Coupled Wind-Wave
Boundary Layer Model
Traditional parameterization Momentum flux ( )
Energy flux (EFair )wwdairair UUCvv ρτ =
airτr , EFair
Ocean Model
2. Energy and momentum flux budget across air2. Energy and momentum flux budget across air--sea interfacesea interfaceUniform wind experiments
Fetch limited (space variation) experiment
Duration limited (time variation) experiment
Steady and homogenous wind: 10, 20, 30, 40, 50 m/s
Steady and homogenous wind: 10, 20, 30, 40, 50 m/s
30o
2. Energy and momentum flux budget across air2. Energy and momentum flux budget across air--sea interfacesea interface
TimeDependent
FetchDependent
Uniform Wind experiments: Momentum and energy fluxes
|τc| / |τair| x 100%
|τc| / |τair| x 100%
EFc / EFair x 100%
EFc / EFair x 100%
= cp/u* = cp/u*
= cp/u* = cp/u*
2. Energy and momentum flux budget across air2. Energy and momentum flux budget across air--sea interfacesea interface
Uniform wind: Energy flux into currents (EFc) as a function of u*
This studyThis study: EF: EFc c ~ ~ ρρairair |u|u**||3.53.5
gray circle – fetch dependent
Black circle – time dependent
Previous studies: EFc ~ ρair |u*|3
2. Energy and momentum flux budget across air2. Energy and momentum flux budget across air--sea interfacesea interface
Hurricane experiments
Wind Field (m/s)
Longitude
Win
d sp
eed
(m/s
)
0m/sTSP = 5m/s
10m/s
Latit
ude
10
20
3
0
40
0 9 18
Holland Hurricane Wind Model
Input parameters:Input parameters:Maximum wind speed (MWS)Radius of MWS (RMW)Central & environmental sea-level pressure
2. Energy and momentum flux budget across air2. Energy and momentum flux budget across air--sea interfacesea interface
Hurricane experiments
0m/sTSP = 5m/s
10m/s
TSP0m/s
TSP5m/s
Hs
(m)
Hs
(m)
Hs
(m)TSP
10m/s
Cg
(m/s
)C
g(m
/s)
Group Velocity
Wave Field
2. Energy and momentum flux budget across air2. Energy and momentum flux budget across air--sea interfacesea interface
Hurricane experiments: Stationary Case (TSP = 0 m/s)
|τc| / |τair| x 100% EFc / EFair x 100%RMW RMW
RMW RMW
Wind Speed Profile
Longitude
Latit
ude
2 3 4 5 6 7 82
3
4
5
6
7
8
0
2
4
6
8
10
12
14
16
18
20
7 8 9 10 1122
22.5
23
23.5
24
24.5
25
25.5
26
→ τair
→ τc
Longitude
Latit
ude
TSP = 10m/s
7 8 9 10 1117.5
18
18.5
19
19.5
20
20.5
21
21.5
→ τair
→ τc
Longitude
Latit
ude
TSP = 5m/sTSP = 5 m/s TSP = 10m/s
2. Energy and momentum flux budget across air2. Energy and momentum flux budget across air--sea interfacesea interfaceHurricane experiments: Moving cases (TCP = 5 m/s and 10 m/s)
τairτc
τairτc
7Nm-2 7Nm-2
Longitude
Latit
ude
100
9896
92
94100
⏐τc⏐/⏐τ
air⏐ x 100%
7 8 9 10 1122
23
24
25
26
80
90
100
110
120
Longitude
Latit
ude
τair
− τc
7 8 9 10 1122
23
24
25
26
0
0.2
0.4
0.6
0.8
1
Longitude
Latit
ude
τair
− τc
7 8 9 10 11
18
19
20
21
0
0.2
0.4
0.6
0.8
1
Longitude
Latit
ude
100
99 98
97 95
93
⏐τc⏐/⏐τ
air⏐ x 100%
7 8 9 10 11
18
19
20
21
80
90
100
110
120
TSP = 5 m/s TSP = 10 m/s(N/m2) (N/m2)
(%) (%)
Hurricane experiments: Moving cases (TCP = 5 m/s and 10 m/s)
Longitude Longitude
Longitude Longitude
Latit
ude
Latit
ude
Latit
ude
Latit
ude
2. Energy and momentum flux budget across air2. Energy and momentum flux budget across air--sea interfacesea interface
|τc| / |τair| x 100% |τc| / |τair| x 100%
|τair - τc| |τair - τc|
Longitude
Latit
ude
7 8 9 10 11
18
19
20
21
0
5
10
Longitude
Latit
ude
7 8 9 10 11
18
19
20
21
0
2
4
6
8
10
Longitude
Latit
ude
7 8 9 10 1122
23
24
25
26
0
5
10
Longitude
Latit
ude
7 8 9 10 1122
23
24
25
26
0
2
4
6
8
10
Longitude
Latit
ude
82
91
97
100
6 7 8 9 10 11 12
21
22
23
24
25
26
27
70
75
80
85
90
95
100
105
110
Longitude
Latit
ude
91
94
97
100
6 7 8 9 10 11 1216
17
18
19
20
21
22
23
70
75
80
85
90
95
100
105
110
EFair – EFc
EFc/EFairx100%
Hurricane experiments: Moving cases (TCP = 5 m/s and 10 m/s)
2. Energy and momentum flux budget across air2. Energy and momentum flux budget across air--sea interfacesea interface
Longitude Longitude
Longitude Longitude
Latit
ude
Latit
ude
Latit
ude
Latit
ude
TSP = 5 m/s TSP = 10 m/s
EFc/EFairx100%
EFair – EFc
3. Wind3. Wind--wavewave--current interaction in hurricanescurrent interaction in hurricanes
airτr
cτr
Control (one-way interaction,
fluxes from air)Exp. A
(one-way interaction,fluxes into currents)
Exp. B (two-way interaction,
partial)
Exp. D (fully coupled)
Exp. C (two-way interaction,
partial)
Momentum & energy flux
τair=f(ψ(θ,k),β(θ,k))
EFair=f(ψ(θ,k),β(θ,k))
cτr
Ocean response in Control Experiment
τair Currents W at 90 m
3. Wind-wave-current interaction in hurricanes
Ocean response in Control Experiment
3. Wind3. Wind--wavewave--current interaction in hurricanescurrent interaction in hurricanes
a b
Initial Tprofile
Sea Surface Temperature anomalyTemperature, TKE profile
RMW 2RMW
TKET TKE
T
3. Wind3. Wind--wavewave--current interaction in hurricanescurrent interaction in hurricanesMomentum Flux ratio
τc in A / τair in Control τair in B / τair in Control
τair in C / τair in Control τc in D / τair in Control
Exp A(one way)
Exp C(two wayPartial)
Exp B(two way)
Exp D(fully coupled)
3. Wind3. Wind--wavewave--current interaction in hurricanescurrent interaction in hurricanesDifferences in surface current
τair in C / τair in Control τc in D / τair in Control
Exp A(one way)
Exp B(two way)
Exp C(two wayPartial)
Exp D(fully coupled)
Longitude
Latit
ude
(a) Control − A
6 8 10 1225
27
29
31
33(ms−1)
0
0.1
0.2
0.3
0.4
0.5
Longitude
Latit
ude
(b) Control − B
6 8 10 1225
27
29
31
33(ms−1)
0
0.1
0.2
0.3
0.4
0.5
Longitude
Latit
ude
(c) Control − C
6 8 10 1225
27
29
31
33(ms−1)
0
0.1
0.2
0.3
0.4
0.5
Longitude
Latit
ude
(d) Control − D
6 8 10 1225
27
29
31
33(ms−1)
0
0.1
0.2
0.3
0.4
0.5
3. Wind3. Wind--wavewave--current interaction in hurricanescurrent interaction in hurricanes
τair in C / τair in Control τc in D / τair in Control
Exp A(one way)
Exp B(two way)
Exp C(two wayPartial)
Exp D(fully coupled)
Longitude
Latit
ude
6 8 10 12
26
28
30
32
(oC)
0
0.1
0.2
0.3
0.4
0.5
0.6
Longitude
Latit
ude
6 8 10 12
26
28
30
32
(oC)
0
0.1
0.2
0.3
0.4
0.5
0.6
Longitude
Latit
ude
6 8 10 12
26
28
30
32
(oC)
0
0.1
0.2
0.3
0.4
0.5
0.6
Longitude
Latit
ude
6 8 10 12
26
28
30
32
(oC)
0
0.1
0.2
0.3
0.4
0.5
0.6
Longitude Longitude
Longitude Longitude
A – Control B – Control
C – Control D – Control
Differences in the Sea Surface Temperature cooling
3. Wind3. Wind--wavewave--current interaction in hurricanescurrent interaction in hurricanes
A – Control B – Control
C – Control D – Control
Temperature and TKE profiles
15 20 25−250
−200
−150
−100
−50
0
T (oC)
Z (
m)
(a) T profile at a
ControlExp. DInitial
0 0.05 0.1−250
−200
−150
−100
−50
0
q2 (m2s−2)
Z (
m)
(b) q2 profile at a
ControlExp. D
15 20 25−250
−200
−150
−100
−50
0
T (oC)
Z (
m)
(c) T profile at b
ControlExp. DInitial
0 0.05 0.1−250
−200
−150
−100
−50
0
q2 (m2s−2)
Z (
m)
(d) q2 profile at b
ControlExp. D
3. Wind3. Wind--wavewave--current interaction in hurricanescurrent interaction in hurricanesImpact of wind-wave-current interaction on the wave field
Exp. C Exp. D
RMW
3. Wind3. Wind--wavewave--current interaction in hurricanescurrent interaction in hurricanesFrequency spectrum for different experiments
3. Wind3. Wind--wavewave--current interaction in hurricanescurrent interaction in hurricanesWW3 2-D spectrum in two locations
−0.04 −0.02 0 0.02 0.04−0.04
−0.02
0
0.02
0.04
East Wave Number (radm−1)
(a)
Nor
th W
ave
Num
ber
(rad
m−
1 )(a) L1: Contr & A
17.05 m358.69 m
0
0.1
0.2
0.3
0.4
0.5
0.6
−0.04 −0.02 0 0.02 0.04−0.04
−0.02
0
0.02
0.04
East Wave Number (radm−1)
(b)
Nor
th W
ave
Num
ber
(rad
m−
1 )
(b) L1: B
14.58 m304.22 m
0
0.1
0.2
0.3
0.4
0.5
0.6
−0.04 −0.02 0 0.02 0.04−0.04
−0.02
0
0.02
0.04
East Wave Number (radm−1)
(d)
Nor
th W
ave
Num
ber
(rad
m−
1 )
(c) L2: Contr & A
16.82 m365.78 m
0
0.1
0.2
0.3
0.4
0.5
0.6
−0.04 −0.02 0 0.02 0.04−0.04
−0.02
0
0.02
0.04
East Wave Number (radm−1)
(d)
Nor
th W
ave
Num
ber
(rad
m−
1 )
(d) L2: B
14.74 m316.81 m
0
0.1
0.2
0.3
0.4
0.5
0.6
3. Wind3. Wind--wavewave--current interaction in hurricanescurrent interaction in hurricanesExplanation of the ocean current effect on wave spectrum
( ) 0=∂∂
∂∂
−−+∂∂
xU
kNkUCU
xN
tg
Steady state equation of wave action conservation:
0>∂∂
xU
0<∂∂
xU
kNk∂∂
for x < 0
for x > 0.
is always negative
4. Case study: Hurricane Ivan (2004)4. Case study: Hurricane Ivan (2004)Ivan track and reconnaissance flight tracks
Flight tracks/Scanning Radar Altimeter measurementsNASA/Goddard space flight center & NOAA/HRD
Exp. A: WAVEWATCH III wave model (operational model)Exp. B: Coupled wind-wave model Exp. C: Coupled wind-wave-current model
4. Case study: Hurricane Ivan (2004)4. Case study: Hurricane Ivan (2004)
3000 m
50 m
2400 m
Scanning Radar Altimeter (SRA) measurements
4. Case study: Hurricane Ivan (2004)4. Case study: Hurricane Ivan (2004)HRD H*wind
4. Case study: Hurricane Ivan (2004)4. Case study: Hurricane Ivan (2004)Wind swath and sea surface temperature
Significant Wave Height Swaths
Exp. A
Exp B
Exp C
Longitude
4. Case study: Hurricane Ivan (2004)4. Case study: Hurricane Ivan (2004)
Exp. A: WAVEWATCH III wave model (operational model)Exp. B: Coupled wind-wave model Exp. C: Coupled wind-wave-current model
4. Case study: Hurricane Ivan (2004)4. Case study: Hurricane Ivan (2004)Surface wave field & flight track
Distance to eye (km)
Dis
tanc
e to
eye
(km
)
300m
−200 −100 0 100 200−200
−150
−100
−50
0
50
100
150
200
(m)
0
2
4
6
8
10
12
14September 9 18:00 UTC
Distance to eye (km)
Dis
tanc
e to
eye
(km
)
2ms−1
−200 −100 0 100 200−200
−100
0
100
200
x10−4ms−1
−4
−2
0
2
4
0 100 200 3000
100
200
300
Dire
ctio
n (o )
spectrum number
0 100 200 3000
100
200
300
400
spectrum number
dom
inan
t wav
e le
ngth
(m
)
0 100 200 3000
5
10
15
spectrum number
Sig
nific
ant w
ave
heig
ht (
m)
HRAExp. AExp. BExp. C
4. Case study: Hurricane Ivan (2004)4. Case study: Hurricane Ivan (2004)Wave parameter comparisons between model and SRA data
Dominant Wave Length Significant Wave Height
Wave Direction
Left-rear Right-rear
SRA
SRA data number
SRA data number SRA data number
Vertical velocity
Distance to eye (km)
Dis
tanc
e to
eye
(km
)
300m
−200 −100 0 100 200−200
−150
−100
−50
0
50
100
150
200
(m)
0
2
4
6
8
10
12
14
Wave spectrum comparisons
−0.06 −0.03 0 0.03 0.06
−0.03
0
0.03
0.06
East Wave Number (radm−1)
Nor
th W
ave
Num
ber
(rad
m−
1 )
SRA
Sept. 0971067
15.5N
−72.14W
261m7.32m
−0.06 −0.03 0 0.03 0.06−0.06
−0.03
0
0.03
0.06
East Wave Number (radm−1)N
orth
Wav
e N
umbe
r (r
adm
−1 )
9.04 m222.1 m
Exp. C
−0.06 −0.03 0 0.03 0.06−0.06
−0.03
0
0.03
0.06
East Wave Number (radm−1)
Nor
th W
ave
Num
ber
(rad
m−
1 )
10.77 m261.4 m
Exp. B
−0.06 −0.03 0 0.03 0.06−0.06
−0.03
0
0.03
0.06
East Wave Number (radm−1)
Nor
th W
ave
Num
ber
(rad
m−
1 )
11.81 m295.6 m
Exp. A
0
0.05
0.1
0.15
0.2
0
0.05
0.1
0.15
0.2
0
0.05
0.1
0.15
0.2
0
0.05
0.1
0.15
0.2
Location ofSpectrum
Comparison
4. Case study: Hurricane Ivan (2004)4. Case study: Hurricane Ivan (2004)
ConclusionsConclusions•• For momentum flux calculations at the airFor momentum flux calculations at the air--sea interface, sea interface,
the effect of time variation of the wave field is small but the effect of time variation of the wave field is small but the effect of spatial variation is important. Both effects, the effect of spatial variation is important. Both effects, however, are important for energy flux calculations.however, are important for energy flux calculations.
•• The surface wave effects on the airThe surface wave effects on the air--sea fluxes are most sea fluxes are most significant in the rearsignificant in the rear--right quadrant of the hurricane and right quadrant of the hurricane and consequently reduce the magnitude of subsurface currents consequently reduce the magnitude of subsurface currents and sea surface temperature cooling to the right of the and sea surface temperature cooling to the right of the storm track. storm track.
•• WaveWave--current interaction reduces the momentum flux into current interaction reduces the momentum flux into currents mainly due to the reduction of wind speed input currents mainly due to the reduction of wind speed input into the wave model relative to the ocean currents. into the wave model relative to the ocean currents.
•• The improved momentum flux parameterization, together The improved momentum flux parameterization, together with wavewith wave--current interaction is shown to improve forecast current interaction is shown to improve forecast of significant wave height and wave energy in Hurricane of significant wave height and wave energy in Hurricane Ivan. Ivan.
Energy and Momentum Flux Budget Model
( )E g d dw= ∫∫ ρ ψ ω θ θ ω,
EF EF EFxx
EFyy
Etc air= − +
⎛⎝⎜
⎞⎠⎟ +
∂∂
∂∂
∂∂
( )∫∫ ⋅⋅= ωθθθωωψρ ddM wx cos,
( )∫∫ ⋅⋅= ωθθθωωψρ ddM wy sin,
( )∫∫ ⋅⋅= ωθθθωψωρ ddCMF gwxx2cos,
( )∫∫ ⋅⋅= ωθθθθωψωρ ddCMF gwxy sincos,
( )∫∫ ⋅⋅= ωθθθωψωρ ddCMF gwyy2sin,
( )∫∫ ⋅⋅= ωθθθθωψωρ ddCMF gwyx cossin,
⎥⎦
⎤⎢⎣
⎡
∂∂
+⎟⎟⎠
⎞⎜⎜⎝
⎛∂
∂+
∂∂
−=t
My
MFx
MF xxyxxxairxc __ ττ
⎥⎦
⎤⎢⎣
⎡
∂
∂+⎟⎟⎠
⎞⎜⎜⎝
⎛∂
∂+
∂
∂−=
tM
yMF
xMF yyyyx
yairyc __ ττ
Energy Flux Budget
( )EF gC d dx w g= ⋅ ⋅∫∫ ρ ψ ω θ θ θ ω, cos
( )EF gC d dy w g= ⋅ ⋅∫∫ ρ ψ ω θ θ θ ω, sin
Momentum Flux budget
Wave component
ψ(ω,θ) wave spectrum
Cg group velocity
ρw water density