Slide 1The Wave Model (ECWAM) 2. The WAM Model: Solves energy balance equation, including S nonlin WAM Group (early 1980s) State of the art models could.

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.)

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

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

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

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

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

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

The Wave Model (ECWAM) Slide 8

Dimensionless energy:

Note: JONSWAP mean wind ~ 8 - 9 m/s

Dimensionless peak frequency:

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

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)

The Wave Model (ECWAM) Slide 11

Time dependence of wave height for a reference runand a coupled run.

The Wave Model (ECWAM) Slide 12

Time dependence of Phillips parameter, p , for

a reference run and a coupled run.

The Wave Model (ECWAM) Slide 13

Time dependence of wave-induced stress for a reference run and a coupled run.

The Wave Model (ECWAM) Slide 14

Time dependence of drag coefficient, CD , for

a reference run and a coupled run.

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)

The Wave Model (ECWAM) Slide 16

The energy balance for young wind sea.

The Wave Model (ECWAM) Slide 17

The energy balance for old wind sea.

0-2

-1

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.

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)

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)

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%)

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:

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