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The Wave Model (ECWAM) Slide 1
2. The WAM Model:
Solves energy balance equation, including Snonlin
WAM Group (early 1980’s) State of the art models could not handle rapidly varying
conditions. Super-computers. Satellite observations: Radar Altimeter, Scatterometer,
Synthetic Aperture Radar (SAR) .
Two implementations at ECMWF: Global (0.5 0.5 reduced latitude-longitude).
Coupled with the atmospheric model (2-way).Historically: 3, 1.5 then 0.5 (Future: 0.36)
Limited Area covering North Atlantic + European Seas (0.25 0.25) Historically: 0.5 covering the Mediterranean only.
Both implementations use a discretisation of 30 frequencies 24 directions (used to be 25 freq.12 dir.)
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The Wave Model (ECWAM) Slide 2
2.1. Energy Balance for Wind Sea
Summarise knowledge in terms of empirical growth curves.
Idealised situation of duration-limited waves ‘Relevant’ parameters:
, u10(u*) , g , , surface tension, a , w , fo , t
Physics of waves: reduction to
Duration-limited growth not feasible: In practice fully-developed and fetch-limited situations are more relevant.
, u10(u*) , g , t
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The Wave Model (ECWAM) Slide 3
Connection between theory and experiments:wave-number spectrum:
Old days H1/3
H1/3 Hs (exact for narrow-band spectrum)
2-D wave number spectrum is hard to observe frequency spectrum
One-dimensional frequency spectrum
Use same symbol, F , for:
)()( kNkF
)(d2 kFkmo
24 sH
dd),(d)(dd),(2 kkkFkkFF
),(),(2 kFv
kF
g
),(d)( 21 FF
)(,),(,)( FFkF
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The Wave Model (ECWAM) Slide 4
Let us now return to analysis of wave evolution:Fully-developed:
Fetch-limited:
However, scaling with friction velocity u is to be preferred
over u10 since u10 introduces an additional length scale, z
= 10 m , which is not relevant. In practice, we use u10 (as
u is not available).
)/(/)(~
10510
3 gufuFgF
constant/~ 410
2 umg oconstant/10 gup
)/,/(/)(~ 2
1010510
3 uXggufuFgF
)/(/~ 210
410
2 uXgfumg o
)/(/ 21010 uXgfgup
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The Wave Model (ECWAM) Slide 5
JONSWAP fetch relations (1973):
guuXgXumg po /,/~
,/~10
210
410
2
~
X~
Empirical growth relations against measurements
Evolution of spectra with fetch (JONSWAP)
Hz
km
km
km
km
km
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The Wave Model (ECWAM) Slide 6
Distinction between wind sea and swell
wind sea: A term used for waves that are under the effect of their
generating wind. Occurs in storm tracks of NH and SH.
Nonlinear.
swell: A term used for wave energy that propagates out of storm
area. Dominant in the Tropics. Nearly linear.
Results with WAM model: fetch-limited. duration-limited [wind-wave interaction].
guuXgXumg po /,/~
,/~10
210
410
2
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The Wave Model (ECWAM) Slide 7
Fetch-limited growth
Remarks:
1. WAM model scales with u
Drag coefficient,Using wind profile
CD depends on wind:
Hence, scaling with u gives different results compared
to scaling with u10.
In terms of u10 , WAM model gives a family of growth
curves! [u was not observed during JONSWAP.]
2*
210 ,/ uuCD
guzz
C oo
D /,)/10(ln *
2
10u
DC
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The Wave Model (ECWAM) Slide 8
Dimensionless energy:
Note: JONSWAP mean wind ~ 8 - 9 m/s
Dimensionless peak frequency:
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The Wave Model (ECWAM) Slide 9
2. Phillips constant is a measure of the steepness of high-frequency waves.
Young waves have large steepness.
100
0
p
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The Wave Model (ECWAM) Slide 10
Duration-limited growth
Infinite ocean, no advection single grid point.
Wind speed, u10 = 18 m/s u = 0.85 m/s
Two experiments:
1. uncoupled: no slowing-down of air flow Charnock parameter is constant ( = 0.0185)
2. coupled:slowing-down of air flow is taken into account by a parameterisation of Charnock parameter that depends on w:
= { w / } (Komen et al.,
1994)
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The Wave Model (ECWAM) Slide 11
Time dependence of wave height for a reference runand a coupled run.
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The Wave Model (ECWAM) Slide 12
Time dependence of Phillips parameter, p , for
a reference run and a coupled run.
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The Wave Model (ECWAM) Slide 13
Time dependence of wave-induced stress for a reference run and a coupled run.
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The Wave Model (ECWAM) Slide 14
Time dependence of drag coefficient, CD , for
a reference run and a coupled run.
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The Wave Model (ECWAM) Slide 15
Evolution in time of the one-dimensional frequencyspectrum for the coupled run.
spec
tra
l den
sity
(m
2/H
z)
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The Wave Model (ECWAM) Slide 16
The energy balance for young wind sea.
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The Wave Model (ECWAM) Slide 17
The energy balance for old wind sea.
0-2
-1
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The Wave Model (ECWAM) Slide 18
2.2. Wave Forecasting
Sensitivity to wind-field errors.
For fully developed wind sea:
Hs = 0.22 u102 / g
10% error in u10 20% error in Hs
from observed Hs
Atmospheric state needs reliable wave model.
SWADE case WAM model is a reliable tool.
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The Wave Model (ECWAM) Slide 19
Verification of model wind speeds with observations
+ + + observations —— OW/AES winds …… ECMWF winds
(OW/AES: Ocean Weather/Atmospheric Environment Service)
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The Wave Model (ECWAM) Slide 20
Verification of WAM wave heights with observations
+ + + observations —— OW/AES winds …… ECMWF winds
(OW/AES: Ocean Weather/Atmospheric Environment Service)
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The Wave Model (ECWAM) Slide 21
Validation of wind & wave analysis using satellite & buoy.
Altimeters onboard ERS-1/2, ENVISAT and Jason
Quality is monitored daily.
Monthly collocation plots
SD 0.5 0.3 m for waves (recent SI 12-
15%)
SD 2.0 1.2 m/s for wind (recent SI 16-
18%)
Wave Buoys (and other in-situ instruments)
Monthly collocation plots
SD 0.85 0.45 m for waves (recent SI 16-
20%)
SD 2.6 1.2 m/s for wind (recent SI 16-
21%)
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The Wave Model (ECWAM) Slide 22
Problems with buoys:
1. Atmospheric model assimilates winds from buoys (height ~ 4m) but regards them as 10 m winds [~10% error]
2. Buoy observations are not representative for aerial average.
Problems with satellite Altimeters:
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The Wave Model (ECWAM) Slide 23
Quality of wave forecast
Compare forecast with verifying analysis.
Forecast error, standard deviation of error ( ), persistence.
Period: three months (January-March 1995).
Tropics is better predictable because of swell:
Daily errors for July-September 1994Note the start of Autumn.
New: 1. Anomaly correlation
2. Verification of forecast against buoy data.
N.H. Tropics S.H.
tHs1 0.08 0.05 0.08