Effect of Surface Waves on Air-Sea Momentum Flux in Tropical cyclones

1
Effect of Surface Waves on Air-Sea Momentum Flux
in Tropical cyclones
Isaac Ginis Il Ju Moon Tetsu Hara Biju
Thomas Graduate School of Oceanography Universit
y of Rhode Island
Collaboration H. Tolman (EMC/NCEP) E. Walsh
(ETL/NOAA) S. Belcher (UR, UK)
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Air-Sea Fluxes
Height
Air
Air
Interface
C
Sea
Water
C
The vertical fluxes of any variable (c, i.e.,
wind speed) are assumed to be driven by the
difference in variable across the air-sea
interface with transport velocity, U
T
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Air-Sea Momentum Flux (Wind Stress)
Wind Profile

• Air side controlled flux
• The transport velocity is
• usually parameterized as

0
U
Height
Air
U
Water
where U is the mean horizontal wind speed at
height 10m and C is the bulk transfer
coefficient (or drag coefficient)
10
D
4
Drag Coefficient Surface roughness
Using the logarithmic wind profile in neutral
condition, where z is the surface roughness
length and u is the friction velocity (
) we obtain
Height
log(z)
0

Wind speed, U
A non-dimensional roughness length is called the
Charnock Coefficient
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Simple Bulk Parameterization

• Drag coefficient is a function of wind speed
• Charnock coefficient is constant

Most widely used in atmospheric and oceanic models
Drag Coefficient, Cd
Drennan et al. (2003)
Wind Speed
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Parameterizations including wave age

• In real ocean, drag coefficient is not a simple
  function of wind speed.
• This is mainly because the state of sea surface
  is not determined by local wind condition but by
  history of wind forcing (i.e. surface waves).
• The most common way to find the relationship
  between momentum flux and surface waves is to use
  Charnock coefficient and wave age.

Wave age

• is the phase speed of dominant waves
  (at the spectral peak)
• States of growth of wind waves relative to
  local wind forcing
• Young sea or growing sea, Old sea or mature sea

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Charnock Coefficient vs Wave age
Swell
Wind waves
Charnock coefficient
0.0185
Laboratory
Field
Adapted from Jones Toba (2001)
Inverse wave age

• The relationship is far from conclusive!!!

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Numerical Investigation of the Effect of Surface
Waves on Air-Sea Momentum Exchange
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Coupled Wave-Wind (CWW) Model
Two dimensional wave spectrum

• Near the peak WAVEWATCH III (WW3) model.
• High frequency part Equilibrium Spectrum model
  of Hara and Belcher (2002)

Full wave spectrum
Near peak
High frequency part
Wave Boundary Layer (WBL) model of Hara and
Belcher (2004)
Explicitly calculates wave-induced stress
0
1
2
3
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- max
-1
Wind profile and drag coefficient over any given
seas
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1. Uniform Wind Experiments
3000 km
10 45 m/s
1500 km
Spatially homogeneous northward winds
72h
Significant wave height

1. Mature seas

At 72 h after the onset of wind when wave field
becomes fully developed and steady state
2. Growing seas
Mean wave length
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Drag Coefficient vs Wind Speed
Constant Charnock Coefficient (0.0185)
Observation-based formulas
Mature sea (72h)
Young sea (01h)
Cd at mature sea increases with wind speed
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Charnock Coefficient vs. Wave age
Wind speed
Charnock Coefficient
At mature seas
Constant 0.010.02 Is true coefficient only if
waves are fully developed!
old
young
Wave age
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2. Hurricane Conditions
A hurricane produces severe and complex ocean
waves
Waves under Hurricane Isabel (2003)
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Idealized Hurricane Experiments
An axisymmetric hurricane wind moves northward
with the translation speed of 0, 5, 10 m/s

• Arrows
• wind direction
• Contours wind speed
• Maximum wind speed 45 m/s

After a spinup time of 72 h, a quasi steady state
is achieved
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0 m/s 5 m/s 10 m/s
0 m/s 5 m/s
10 m/s

• Contour Hs
• Arrow wave
• direction
• Arrow length
• wavelength

Significant wave height

• Complex, multimodal spectrum
• Peak freq. of the wind energy input

Input wave age
In the rear-left quadrant zch is reduced
significantly as HTS increases.
Charnock coefficient
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Scatterplot of Drag Coefficient vs Wind Speed

Relative position from the storm center
Constant zch (0.0185)
5 m/s 10 m/s
Mature seas
Young seas (uniform wind)

• Drag in the front-right quadrant monotonically
  increases with the wind speed, which is similar
  to mature sea results of uniform wind.
• Drag in the rear-left quadrant tends to level
  off or even decrease at high higher winds
  especially for the fast-moving hurricane. This
  trend is similar to the young sea results of
  uniform wind experiment.

(i)
(j)
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Drag Coefficient in Different Models
0 m/s
5 m/s
10 m/s
CWW
Bulk
WW3
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Comparisons with observations

• At high wind speeds, Cd levels off and even
  decrease with wind speed

Upper and lower bounds of Cd from all earlier exp.
(Charnock Coefficient0.0185)
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Wave-Wind Simulations in Real Hurricanes
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Scatterplot of Charnock Coefficient vs Wave Age
Toba et al. (1990)
Because of large scatter, it is difficult to find
a unique relation ship between zch and wage
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Scatterplot of Drag Coefficient vs Wind Speed

• Drag coefficient levels off at very high wind
  speeds
• This is consistent with recent field
  observations and the previous idealized hurricane
  simulations.
• Under hurricane wind forcing waves are extremely
  young at high wind speeds and the young waves
  produce small drag.
• This explains why drag coefficient levels off at
  high wind speed.

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3. Hurricane Wind Forecast Problem The GFDL
operational model underestimates winds in strong
hurricanes
Observations
Model
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Computation of Momentum Flux in the GFDL
hurricane model

• Universal function of Hicks (1975)
• Roughness length is computed using Charnock
  formula

U(z)
Constant Charnock Coefficient!
Roughness length
Saturation mixing ratio, bulk Richardson number
stable
unstable

• Iteration using Hicks functions (Hicks, 1975)
• L (Monin-Obukhov length)
• Drag Coefficient, Cd

• Updated roughness length
• 10-m Wind speed, U(10)

Momentum flux
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Scatterplot of Cd and Ch vs Wind Speed in the
GFDL Operational Model
Cd
Ch
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Developing a Coupled Hurricane-Wave-Ocean Model
Atmosphere
GFDL(WRF) Hurricane Model
Wind Air Temp.
Flux
Wind Air Temp.
SST
Wave Boundary Model
SST Current
Wave Spectra
Flux
Flux
Currents,
NCEP WAVEWATCH III

POM (HYCOM)
Elevations, SST

• GFDL model (black) C, M, F
• POM (blue) OW, OE
• WAVEWATCH-III (red) WL, WS

Ocean
Waves
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(Very) Preliminary results Hurricane Isabel 06Z
12 Sept, 2003
Sea Surface Temperature
Sea Surface Currents
Surface Waves
Surface Winds
Surface Stresses
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Scatterplot of Cd and Ch vs Wind Speed in the
Coupled Hurricane-Wave-Ocean Model
Cd
Ch
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Spatial Distribution of the Drag Coefficient
Uncoupled
Coupled
Wave fields
Difference
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Spatial Distribution of the Drag Coefficient
Uncoupled
Coupled
Wave fields
Difference
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Track and Intensity Forecasts Hurricane Isabel
06Z 12 Sep
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Improvements in the Hurricane Wind Structure
Forecasts
Uncoupled
Coupled
Difference
HRD Wind
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Conclusions

• 1. Uniform Wind Experiments
• Mature seas
• The Charnock coefficient is estimated to be about
  0.01 ? 0.02 and the drag coefficient increases as
  wind speed increases, which are within the range
  of previous observational data.

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Conclusions
2. Idealized and real hurricane experiments

• As the hurricane translation speed increases,
  higher, longer and more developed waves in the
  right front quadrant of the storm track produce
  higher sea drag lower, shorter and younger waves
  in the rear left quadrant produce lower sea drag.
  
• Drag coefficient levels off at high wind speeds
  under tropical cyclones. This tendency is
  consistent with the recent observations.

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Conclusions
3. Coupled Hurricane-Ocean-Wave experiments

• We have developed a coupled hurricane-wave-ocean
  coupled model by coupling the GFDL hurricane
  model with the WAVEWATCH III wave model and a
  wave boundary layer model.
• Preliminary simulations indicate that the
  hurricane intensity and structure can be
  significantly effected by explicit simulations of
  surface waves.

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Characteristics of wave model in coupled model

• 1. Use of high-resolution wind inputs in
  time/space near storm center
• Every time step (12 min), wind is updated using
  GFDL wind
• Spatial resolution of wave model 1/12o by
  1/12o
• 2. Continuously-moving ice coverage areas (for
  economical calculation)
• Every time step (12 min), wave calculation areas
  (6o by 6o) that are not covered by ice are
  defined using storm center positions estimated
  from GFDL model.
• Here, momentum fluxes of smaller areas (5o by
  5o) are transferred to GFDL model.
• 3. Considering current-wave interactions
• Current and elevation data from ocean model will
  be used to consider current-wave interactions