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.
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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 OceanographyJean-Michel.Lefevre@meteo.fr
Aknowledgement to Jaak Monbaliu from UKL for having provided some of the material
Wind Wave and Storm Surge Workshop Halifax 16-20/06/03
Wind Wave and Storm Surge Workshop Halifax 16-20/06/03
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
Wind Wave and Storm Surge Workshop Halifax 16-20/06/03
ASAR level 2b products, from Chapron et al.
External wind direction information used (ECMWF), requires minimum wind speed, not high wind speeds (<20 kts)
Wind Wave and Storm Surge Workshop Halifax 16-20/06/03
1-day altimeter sampling (from Queffeulou)
Wind Wave and Storm Surge Workshop Halifax 16-20/06/03
• 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)
Wind Wave and Storm Surge Workshop Halifax 16-20/06/03
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)
Wind Wave and Storm Surge Workshop Halifax 16-20/06/03
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
Wind Wave and Storm Surge Workshop Halifax 16-20/06/03
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
Wind Wave and Storm Surge Workshop Halifax 16-20/06/03
air-water boundary interaction
a) coupled wind waves
b) forced waves
c) free waves (Dean & Dalrymple, 1991; their fig 3.4)
Linear wave theory
Wind Wave and Storm Surge Workshop Halifax 16-20/06/03
boundary value problem specification for periodic water waves
(Dean & Dalrymple, 1991; their fig 3.7)
SUMMARY
Wind Wave and Storm Surge Workshop Halifax 16-20/06/03
progressive linear wave
)(cos2
tkxH
)sin(cosh2
)(coshtkx
kh
zhkHg
Wind Wave and Storm Surge Workshop Halifax 16-20/06/03
shallow water waves
deep water waves
ghT
LC
k 2
22
2
2
gk2 20 2
Tg
LL
Tg
CC20
Wind Wave and Storm Surge Workshop Halifax 16-20/06/03
asymptotes to hyperbolic functions(Dean & Dalrymple, 1991; their fig
3.12)
Wind Wave and Storm Surge Workshop Halifax 16-20/06/03
Time series of displacement (from Massel figure 3.2)
Two waves superposition
Many waves superposition
Wind Wave and Storm Surge Workshop Halifax 16-20/06/03
from Massel figure 1.3
)(t
0
)cos(n
nnn ta
Wind Wave and Storm Surge Workshop Halifax 16-20/06/03
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
Wind Wave and Storm Surge Workshop Halifax 16-20/06/03
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
Wind Wave and Storm Surge Workshop Halifax 16-20/06/03
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
Wind Wave and Storm Surge Workshop Halifax 16-20/06/03
Wind Wave and Storm Surge Workshop Halifax 16-20/06/03
JONSWAP experiment
Wind Wave and Storm Surge Workshop Halifax 16-20/06/03
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
Wind Wave and Storm Surge Workshop Halifax 16-20/06/03
DIRECTIONNAL WAVE SPECTRA
WIND SEA CASES
Wind Wave and Storm Surge Workshop Halifax 16-20/06/03
DIRECTIONNAL WAVE SPECTRA
SWELL CASES
Wind Wave and Storm Surge Workshop Halifax 16-20/06/03
DIRECTIONNAL WAVE SPECTRA
CROSS SEAS
Wind Wave and Storm Surge Workshop Halifax 16-20/06/03
Wind Wave and Storm Surge Workshop Halifax 16-20/06/03
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
wave direction (degrees)
frequ
ency
(H
z)
ASSIMILATED
0
5
10
15
20
0 100 200 3000.05
0.1
0.15
0.2
wave direction (degrees)
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
Wind Wave and Storm Surge Workshop Halifax 16-20/06/03
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
Wind Wave and Storm Surge Workshop Halifax 16-20/06/03
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
Wind Wave and Storm Surge Workshop Halifax 16-20/06/03
wave heights
• significant wave height• maximum wave height• mean wave height
• zero upcrossing or downcrossing• mean wave period• peak period
wave periods
Wind Wave and Storm Surge Workshop Halifax 16-20/06/03
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)
Wind Wave and Storm Surge Workshop Halifax 16-20/06/03
Existing tools
Wind Wave and Storm Surge Workshop Halifax 16-20/06/03
•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
Wind Wave and Storm Surge Workshop Halifax 16-20/06/03
Swell track
Nb: Ceci n’est pas une image instantanée, 10 jours de mesures ont été utilisés.
Wind Wave and Storm Surge Workshop Halifax 16-20/06/03
• 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))
Wind Wave and Storm Surge Workshop Halifax 16-20/06/03
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)
Wind Wave and Storm Surge Workshop Halifax 16-20/06/03
ANGULAR AND LONGITUDINAL DISPERSION
1+2+3+…1
2
3
Wind Wave and Storm Surge Workshop Halifax 16-20/06/03
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
Wind Wave and Storm Surge Workshop Halifax 16-20/06/03
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
Wind Wave and Storm Surge Workshop Halifax 16-20/06/03
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
Wind Wave and Storm Surge Workshop Halifax 16-20/06/03
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.)
Wind Wave and Storm Surge Workshop Halifax 16-20/06/03
Oper. Hind.
Hawaii area, february 2002
ECMWF WAM/ECMWF VAG2/ECMWF
NCEP WW3/NCEP WAM/ECMWF WW3/ECMWF
VAG3/ECMWF
VAG1/ECMWFVAG/MFMF ECMWF
Wind Wave and Storm Surge Workshop Halifax 16-20/06/03
Wind Wave and Storm Surge Workshop Halifax 16-20/06/03
Wind Wave and Storm Surge Workshop Halifax 16-20/06/03
US East coast, february 2002
Wind Wave and Storm Surge Workshop Halifax 16-20/06/03
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
Wind Wave and Storm Surge Workshop Halifax 16-20/06/03
How improving swell forecast in theCaribbean sea ?
Wind Wave and Storm Surge Workshop Halifax 16-20/06/03
Nesting high resolution wave models (0.1°) to deal with the Caribbean’s island channels.
How to improve swell forecast in the Caribbean sea ?
Wind Wave and Storm Surge Workshop Halifax 16-20/06/03
Spatiale resolution 1°x1° - Max 102h, 4 runs per day
Modèle VAG – Domaine : Globe
Wind Wave and Storm Surge Workshop Halifax 16-20/06/03
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
Wind Wave and Storm Surge Workshop Halifax 16-20/06/03
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 ?
Wind Wave and Storm Surge Workshop Halifax 16-20/06/03
http://www.mpc.ncep.noaa.gov/perfectstorm
Wind Wave and Storm Surge Workshop Halifax 16-20/06/03
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)
Wind Wave and Storm Surge Workshop Halifax 16-20/06/03
• Still some work for wave people!
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