Wind Wave and Storm Surge Workshop Halifax 16-20/06/03 Wind Wave and Storm Surge workshop-Halifax...

Wind Wave and Storm Surge Workshop Halifax 16-20/06/03

Wind Wave and Storm Surge workshop-Halifax 16-20/06/03

SWELL WAVES : concepts and basis

Jean-Michel LefèvreMeteo-France

Marine and [email protected]

Aknowledgement to Jaak Monbaliu from UKL for having provided some of the material


Spatio-temporal analysis

integration time

Azim

uth

Variation of backscatter intensity with short duration within the

integration time

Expected correlation to only apply on long

duration patterns (longer waves)

Look filters

Bright targets only on one look

from Chapron et al., presented at the ASAR calibration review, ESEC 10-11 Sept. 2002


ASAR level 2b products, from Chapron et al.

External wind direction information used (ECMWF), requires minimum wind speed, not high wind speeds (<20 kts)


1-day altimeter sampling (from Queffeulou)


• Real aperture radar system at Ku-band (13.6 GHz)

• scanning in incidence (0 à 10° every 2°), Conical scanning of 360°(in azimuth)

• Nadir look : similar use as an altimeter (wind/Hs)

• Off-nadir look : estimation directional wave spectrum (complement SAR)

• 50-70 m wavelength for wind sea; minimum detectable wave height of 1 m for swell

SWIMSAT Project, Hauser et al., submitted to ESA in 2002,

• Angle of incidence combination

various spatial scales (50x50 km; 90x90 km)

•access to other parameters (wave slopes)

Better than SAR for detecting shortest waves (SAR limited to long waves Above 150-200 m wavelength) but much lower resolution (SAR: 5x10 km)


Swell measurements

– In situ • Buoys• Platforms• Sea bed (Pressure gauges)

– Remote sensed• Ground: Coastal radars or sky-wave radars (HF)• Ship : X-band navigation radars• Air-Plane : Microwave radars• Satellite : Microwave, SAR (Ku and C bands) – RAR

(Ku band)


how to define a swell ?

• Waves travelling out of their generation area

waves travelling faster than the wind speed : C> U. cos(-)

– C is the phase speed– U is the 10m wind speed is the wave direction is the wind direction


Swell properties

• A swell has a low stepness and a high wave age, C/U (>1)

Relatively small interactions with other wave components and with the wind

Linear wave theory « well » appropriate to describe swell


air-water boundary interaction

a) coupled wind waves

b) forced waves

c) free waves (Dean & Dalrymple, 1991; their fig 3.4)

Linear wave theory


boundary value problem specification for periodic water waves

(Dean & Dalrymple, 1991; their fig 3.7)

SUMMARY


progressive linear wave

)(cos2

tkxH

)sin(cosh2

)(coshtkx

kh

zhkHg


shallow water waves

deep water waves

ghT

LC

k 2

22

2

2

gk2 20 2

Tg

LL

Tg

CC20


asymptotes to hyperbolic functions(Dean & Dalrymple, 1991; their fig

3.12)


Time series of displacement (from Massel figure 3.2)

Two waves superposition

Many waves superposition


from Massel figure 1.3

)(t

0

)cos(n

nnn ta


Determination of wave spectraFourier Analysis

0

)sincos()()(n

nn tnbtnatft

For a time-interval t to t + T

where = 2/T, b0 is zero and a0 is the mean of the record


N

n

tinnntinnn eiba

eiba

tf0 22

)(

in the complex domain

N

Nn

tinenFtf )()(

Tt

t jiij dttftfT

C )()(1

)(

The covariance function

its Fourier transform = power spectrum

2

11111 )()(1

)( nFdeCT

nTt

t

in


analytical expressions

PIERSON-MOSKOWITZ SPECTRUM

4

52

4

5exp)(

PM

gS

10

213.0u

gPM

JONSWAP SPECTRUM

4

52

4

5exp)(

PM

gS

22

2

2

)(exp

p

p


JONSWAP experiment


Type of spectra amplitude in function of frequency energy in function of frequency energy density in function of frequency directional spectra

Shape of the spectrum broad narrow single peaked double peaked


DIRECTIONNAL WAVE SPECTRA

WIND SEA CASES



SWELL CASES



CROSS SEAS


Comparison between wave spectra:with a cut-off of 0.1 Hz; Long=282 deg;lat=-26 deg

0 100 200 3000.05

0.1

0.15

0.2

wave direction (degrees)

frequ

ency

(H

z)

WAM-FG

0

10

20

30

0 100 200 3000.05

0.1

0.15

0.2


frequ

ency

(H

z)

ASSIMILATED

0

5

10

15

20

0 100 200 3000.05

0.1

0.15

0.2


frequ

ency

(H

z)

ASAR-ENVISAT

0

5

10

15

0 0.1 0.2 0.3 0.40

5

10

15

20

frequency (Hz)

ener

gy d

ensi

ty (

m2 /H

z)

long=282 deg; lat=-26 deg

WAMASSIASAR

May 3, at 6:00


Wave statistics

N

nHHP )ˆ(

N

iirms H

NH

1

21

Hp : average of the largest pN waves (N is the number of waves, p > 1)

H1/3 : average of the highest third of the waves significant wave height

Hmax : maximum wave height


narrow banded spectrum for the swell

large number of sinusoids, but statistically independent frequencies near a common value

The result is a Rayleigh distribution for the wave heights:

2)/ˆ()ˆ( rmsHHeN

nHHP

wave height exceeded by n waves out of a total N:

n

NHH rms lnˆ


wave heights

• significant wave height• maximum wave height• mean wave height

• zero upcrossing or downcrossing• mean wave period• peak period

wave periods


Partitionning of the wave spectrum

-150 -100 -50 00.05

0.1

0.15

0.2

0.25

direction (degrees)

freq

uenc

y (H

z)

wave spectrum

0

0.5

1

1.5

2

2.5

3

3.5

Partition 2

Partition 1

Partition 4

Partition 3

For each partition, mean parameters are computed(energy, direction, frequency)


Existing tools


•All ocean waves move along great circle tracks.

•A great circle is the shortest distance between two points on a sphere. •When swell travels great distances over ocean, the great circle track may by markedly different than a straight line on your specific map projection.

•One needs to know the track to estimate the distance from the incoming swell and the time of arrival!

Great circle track


Swell track

Nb: Ceci n’est pas une image instantanée, 10 jours de mesures ont été utilisés.


• The distance D over a great circle track betweenen two points can be calculated from the following formula, knowing the coordinates of the departure point (LAT1,LON1) et arrival point (LAT2,LON2).

D=Rcos-1 ((sinLAT1sinLAT2)+(cosLAT1cosLAT2cos(LON1-LON2))

• Where R is the Earth’s radius. The angle C of the starting track from a meridian is given by:

C=tan-1 (sin(LON1-LON2)/(cosLAT1tanLAT2-sinLAT1cos(LON1-LON2))


Swell decayThe main factors for swell decay are:

• angular dispersion

- It depends on the width of the generating area

• longitudinal dispersion (difficult to estimate manually)

- It depends on the shape of the spectrum

• other factors such as whitecaping, non-linear wave-wave interactions, opposite winds may have small impact compared to the above factors since the swell’steepness is small. However, since swell may travel over very long distances, the wave-wave interaction can shift the wave spectrum (see Lavrenov book) and. Also because the earth is a sphere, swell can collect energy from other the generation area far from it!!! (see Lavrenov book)


ANGULAR AND LONGITUDINAL DISPERSION

1+2+3+…1

2

3


Dispersive waves in deep water

Cg is depends on wave lenght

Swell decay. At a fixe point, far from the generation area, the SWH is progressively increasing due to the superposition of the incoming wave components while the significant wave period is decreasing, just after the first components arrived (their is first a jump in the period): longitudinal dispersion.

Generation area Swell area


Angular dispersion factor (%) for swell energy (not wave height!)

example : Due to angular dispersion, a 6 m swell should reduce to 0,2½ x 6 2,7 m at a distance of 3X in the initial wind direction.

Angular dispersion calculation


How do wave models perform for predicting swell

• Different physics and numerics : long time integration + numerical approximations (propagation scheme + wave spectrum discretisation may lead to significant errors)

Intercomparison study using several wave models (WAM, WW3,VAG) with same winds


Areas of interest

• East Coast of US – (wind sea dominant)• West Coast of US (swell + wind sea)• European Coast (swell + wind sea)• Tropics –Hawaii (swell dominant in winter) • Mediterranean sea (see Ardhuin et al.)


Oper. Hind.

Hawaii area, february 2002

ECMWF WAM/ECMWF VAG2/ECMWF

NCEP WW3/NCEP WAM/ECMWF WW3/ECMWF

VAG3/ECMWF

VAG1/ECMWFVAG/MFMF ECMWF


US East coast, february 2002


First results

• For high swell events, dissipation term is important.

• For weak and moderate swell having travelled over long distances, no significant differences where found with the various models in term of SWH.

• But periods must be also checked.

Keys for model improvements


How improving swell forecast in theCaribbean sea ?


Nesting high resolution wave models (0.1°) to deal with the Caribbean’s island channels.

How to improve swell forecast in the Caribbean sea ?


Spatiale resolution 1°x1° - Max 102h, 4 runs per day

Modèle VAG – Domaine : Globe


61° 60° 59° 58° 57° 56° 55°62°63°64°65°

12°

13°

14°

15°

16°

17°

18°

19°

20°

Saint-Martin

Saint-Barthélémy

Guadeloupe

Martinique

Sainte-Lucie

Saint-VincentBarbade

Grenadines

Grenade

Dominique

Montserrat

Antigua

Barbuda

Saint-Kitts

Nevis

Vierges

St-Croix

Anguilla

21°

domaine résolution 15'

domaine résolution 05'

domaine résolution 01'Guadeloupe

domaine résolution 01'Martinique

Over seas territories

Hurricane wave model implementation for the Caribbean's islands


DRAUPNER - 1 january 1995 (from Statoil)

-10.00

-5.00

0.00

5.00

10.00

15.00

20.00

0 300 600 900 1200

DRAUPNER - 1 january 1995 (from Statoil)

-10.00

-5.00

0.00

5.00

10.00

15.00

20.00

150 210 270 330 390 450

LINEAR ?


http://www.mpc.ncep.noaa.gov/perfectstorm

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Continent

Ocean

# Ship accidents

0 3000 6000 Kilometers

Ship Accidents (1995-1999, Lloyd´s after Det Norske Veritas)


• Still some work for wave people!

Wind Wave and Storm Surge Workshop Halifax 16-20/06/03 Wind Wave and Storm Surge workshop-Halifax...

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Transcript of Wind Wave and Storm Surge Workshop Halifax 16-20/06/03 Wind Wave and Storm Surge workshop-Halifax...