effects of surface waves on air-sea momentum and energy ... · pdf fileon air-sea momentum and...

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*


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


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


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


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


|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)


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


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


Exp A(one way)

Exp B(two way)



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



Exp A(one way)

Exp B(two way)



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


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


(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


(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


(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


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


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


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


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


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


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


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

effects of surface waves on air-sea momentum and energy ... · pdf fileon air-sea momentum and...

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