comet winter weather workshop 2001 canadianhurricanecentre waves with tropical cyclones how big can...
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COMET Winter Weather Workshop 2001
CanadianCanadianHurricaneHurricaneCentreCentre
Waves withWaves withTropical CyclonesTropical Cyclones
How How BigBigCan They Get?Can They Get?
(size matters)(size matters)
Pete BowyerPete BowyerProgram Manager
COMET Winter Weather Workshop 2001
Between Oct. 91 and Sept. 95, EC’s East CoastNOMAD buoys reported some extraordinary waves events, with the 100-year waves being greatly exceeded 3 times in those 4 years
COMET Winter Weather Workshop 2001
As it turned out, As it turned out, Hurricane Luis became—arguably—Hurricane Luis became—arguably—
the most important storm forthe most important storm forthe wave forecasting programs inthe wave forecasting programs in
Canada because the extreme waves of Canada because the extreme waves of a Nomad weather buoy on thea Nomad weather buoy on the
Scotian Slope were corroboratedScotian Slope were corroboratedby the finest hurricane-researchby the finest hurricane-research
ship money can buy...ship money can buy...
COMET Winter Weather Workshop 2001
the QEII Luxury Linerthe QEII Luxury Liner
COMET Winter Weather Workshop 2001
LUIS AND THE BUOYSLUIS AND THE BUOYS
Aug.28 - Sep.11, 1995Aug.28 - Sep.11, 1995Aug.28 - Sep.11, 1995Aug.28 - Sep.11, 1995
COMET Winter Weather Workshop 2001
Hurricane LuisHurricane Luis
Sept.10, 1995Sept.10, 1995 9 p.m. EDT9 p.m. EDT
Tracking at >40Tracking at >40knots throughknots throughMaritime watersMaritime waters
...no longer...no longerjust a hurricanejust a hurricane
4414144141
4413944139
44137 missing44137 missing
COMET Winter Weather Workshop 2001
Buoy 44137 - Wind SpeedBuoy 44137 - Wind SpeedBuoy 44137 - Wind SpeedBuoy 44137 - Wind Speed
Sept. 10Sept. 10 Sept. 11Sept. 11
Maximum wind speedMaximum wind speed
Mean wind speedMean wind speed
COMET Winter Weather Workshop 2001
Buoy 44137 - Wave Height & PeriodBuoy 44137 - Wave Height & PeriodBuoy 44137 - Wave Height & PeriodBuoy 44137 - Wave Height & Period
Maximum wave heightMaximum wave height
Significant wave heightSignificant wave height
PeriodPeriod
Sept. 10Sept. 10 Sept. 11Sept. 11
COMET Winter Weather Workshop 2001
Buoy 44139 - Wind SpeedBuoy 44139 - Wind SpeedBuoy 44139 - Wind SpeedBuoy 44139 - Wind Speed
Sept. 10Sept. 10 Sept. 11Sept. 11
Maximum wind speedMaximum wind speed
Mean wind speedMean wind speed
COMET Winter Weather Workshop 2001
Buoy 44139 - Wave Height & PeriodBuoy 44139 - Wave Height & PeriodBuoy 44139 - Wave Height & PeriodBuoy 44139 - Wave Height & Period
Maximum wave heightMaximum wave height
Significant wave heightSignificant wave height
PeriodPeriod
Sept. 10Sept. 10 Sept. 11Sept. 11
Maximum wave heightMaximum wave height
COMET Winter Weather Workshop 2001
Buoy 44141 - Wind SpeedBuoy 44141 - Wind SpeedBuoy 44141 - Wind SpeedBuoy 44141 - Wind Speed
Maximum wind speedMaximum wind speed
Mean wind speedMean wind speed
Sept. 10Sept. 10 Sept. 11Sept. 11
COMET Winter Weather Workshop 2001
Buoy 44141 - Wave Height & PeriodBuoy 44141 - Wave Height & PeriodBuoy 44141 - Wave Height & PeriodBuoy 44141 - Wave Height & Period
Maximum wave heightMaximum wave height
Significant wave heightSignificant wave height
PeriodPeriod
Sept. 10Sept. 10 Sept. 11Sept. 11 Sept. 12Sept. 12
Upper-limitUpper-limitof buoyof buoy
capabilitycapability
COMET Winter Weather Workshop 2001
Luis and the QEII Sept.10, 1995 9 p.m. EDTLuis and the QEII Sept.10, 1995 9 p.m. EDT
QEIIQEII
4414144141
4413944139
44137 missing44137 missing
COMET Winter Weather Workshop 2001
50N
60W
45N
40N
44142
44137
44139
NW20 3.5 m
55W
44141
NW25 4 m
SE355 m
W50 4 m
SW142.5 m
SW95 9 m
WSW130 29 mW60
7 m
Height ofthe storm
50W 45W
S142 m
40W
SW121.5 m
SW16 2 m.
.
..
03Z
09Z
21Z
LUIS AND THE QUEENLUIS AND THE QUEEN
COMET Winter Weather Workshop 2001
HURRICANELUIS
Sept. 10-11, 1995
85 knots
10 / 06Z
2585 knots
10 / 12Z
10 / 18Z
85 knots
95 knots
11 / 00Z
11 / 06Z
105 knots
32
38
39
COMET Winter Weather Workshop 2001
Max ReportedMax ReportedSig. WavesSig. Waves17+ metres17+ metres
66
55
44
33
22
77 88
99
1010
HURRICANELUIS
Sept. 10-11, 1995
85 knots
10 / 06Z
2585 knots
10 / 12Z
10 / 18Z
85 knots
95 knots
11 / 00Z
11 / 06Z
105 knots
32
38
39
Wave Field atWave Field atSept.11 - 01ZSept.11 - 01Z
**QEIIQEII
COMET Winter Weather Workshop 2001
Sept. 11,Sept. 11, 3 a.m.3 a.m.
Luis crossesLuis crossesthe Avalon...the Avalon...
leaving buoyleaving buoy4413744137limping.....limping.....
and manyand manycruise-shipcruise-shippassengerspassengersreelingreeling
QEIIQEII
4414144141
441394413944137 missing44137 missing
COMET Winter Weather Workshop 2001
With the buoy report validated by theWith the buoy report validated by theQEII, we could now redirect ourQEII, we could now redirect ourenergies from energies from debating the datadebating the data
to to trying to understand it.trying to understand it.
This has led us back to the drawingThis has led us back to the drawingboard to examine more closely,board to examine more closely,
“what makes big waves?”“what makes big waves?”
With the buoy report validated by theWith the buoy report validated by theQEII, we could now redirect ourQEII, we could now redirect ourenergies from energies from debating the datadebating the data
to to trying to understand it.trying to understand it.
This has led us back to the drawingThis has led us back to the drawingboard to examine more closely,board to examine more closely,
“what makes big waves?”“what makes big waves?”
COMET Winter Weather Workshop 2001
Basics of WavesBasics of Waves
= cT= cT
COMET Winter Weather Workshop 2001
SPEED OF WAVES IN WATERSPEED OF WAVES IN WATER
c = g tanh 2d 2 ( )[ ]
g = gravitational constant
= wavelength
d = water depth
In deep water, d /gets very large, sotanh (big #) , therefore,
( )
12
12
COMET Winter Weather Workshop 2001
SPEED OF WAVES IN WATERSPEED OF WAVES IN WATER
c = g tanh 2d 2 ( )[ ]
g = gravitational constant
= wavelength
d = water depth
In shallow water, d /gets small, sotanh (small #) small # , therefore,
( )
12
12
COMET Winter Weather Workshop 2001
SPEED OF WAVES IN DEEP WATERSPEED OF WAVES IN DEEP WATER
Since= cT= cT c = gTc = gT 22
= gT= gT 22
22
Therefore, speed (c) and wavelength () are only a function of period (T).
Since the speed is a function of the period,deep water is a “dispersive” medium.
COMET Winter Weather Workshop 2001
BASIC DEEP WATER WAVE FORMULAEBASIC DEEP WATER WAVE FORMULAE
c = gT 2
c (m/s) = 1.56 T (sec)c (kts) = 3.03 T (sec)
(m) = 1.56 T (sec)(ft) = 5.12 T (sec)
S = H = H (m) 1.56 T (sec)
2
2
2
COMET Winter Weather Workshop 2001
COMPOSITION OF COMPOSITION OF WAVESWAVES
Any observed wave pattern on the ocean can be shown to be comprised of a number of simple waves, which can differ from each other in height, wavelength and direction. The above profile is the result of two waves differing in only.
COMET Winter Weather Workshop 2001
COMPOSITION OF COMPOSITION OF WAVESWAVES
In reality, In reality, the sea is a the sea is a superpositiosuperposition of many n of many wave sets.wave sets.
COMET Winter Weather Workshop 2001
WAVE GENERATION & DECAYWAVE GENERATION & DECAY
W ind
Energy Input
Angular Spreading Dispersion
Friction & air resistance W hitecapping
W ave-bottom interaction ** Surf Breaking **
* Dissipation *
Energy Loss
Non-linear w ave-w ave interactions
* Energy Shift *
COMET Winter Weather Workshop 2001
WIND-WAVES...depend on:WIND-WAVES...depend on:
Wind speed - the speed of the wind
Fetch - the area of sea surface over which a wind of constant direction (within 30o) and steady speed is, or has been blowing
Duration - the length of time the wind persists from a certain fetch
COMET Winter Weather Workshop 2001
WAVE ENERGY vs. WIND WAVE ENERGY vs. WIND SPEEDSPEED
Wave energy is very sensitive to wind speed:
Wave Energy (Wave Height)
Wave Height (Wind Speed)
Wave Energy (Wind Speed)
2
2
4
Focus of the Best Wave Model “I.T.W.S.”Focus of the Best Wave Model “I.T.W.S.”
COMET Winter Weather Workshop 2001
SIGNIFICANT WAVE HEIGHTSSIGNIFICANT WAVE HEIGHTS
HHsigsig V V22 tanh [ tanh [ (F/V (F/V22))aa]]
V = wind speedV = wind speedF = fetch lengthF = fetch length
““Law of Diminishing Returns”Law of Diminishing Returns”is at workis at work
COMET Winter Weather Workshop 2001
WIND
FETCH of the wind
SEA CHANGINGTO SWELL
FULLY DEVELOPEDSEARIPPLES CHOP
WIND WAVES
COMET Winter Weather Workshop 2001
THE WAVE THE WAVE SPECTRUMSPECTRUM
For a simple sine wave, the energy is proportional to the square of the wave height. However, the real sea is a combination of many sinewaves of varying and T. The simplest way of
determining the “energy” of the sea is to examine the relative amounts of energy contained within different period ranges in the sea surface. The plot here of energy vs. frequency (1/T) is a typical energy (or wave) spectrum.
ENERGY
PERIOD
COMET Winter Weather Workshop 2001
WAVE SPECTRA FOR WAVE SPECTRA FOR DIFFERENT WIND SPEEDSDIFFERENT WIND SPEEDS
As wind speed isincreased, not onlyis more energyavailable (higherwave heights), butlonger waves(longer period orlower frequency) arealso present. Also,the period ofmaximum energyshifts to longerperiod waves.
SP
EC
TR
AL
EN
ER
GY
60 20 10 5
PERIOD (sec)
40 knots
30 knots
20 knots
COMET Winter Weather Workshop 2001
STATISTICAL DESCRIPTION STATISTICAL DESCRIPTION OF WAVE HEIGHTSOF WAVE HEIGHTS
H = significant wave height = average height of highest 1/3 waves in record (corresponds roughly to visually observed heights)
H = average of all height values .625 H
H = average height of (1/n)th highest waves
H = 1.3 H
H = 1.8 to 2.2 times the H
SIG
SIGAV
SIG
1/n
1/10
MAX SIG
COMET Winter Weather Workshop 2001
WAVE GROUPSWAVE GROUPS
Although individual crests advance at a speed correspondingto their wavelength (as a coherent unit), the group advances at its own speed, called the GROUP SPEED....Cg.
The group speed is the speed at which the energy propagates(moves with the speed of the “middle” of the pack...slower thanleading waves and faster than trailing waves.)
The energy is equally split between KE and PE, however, theKE is associated with movement of particles in nearly closedorbits....therefore, the KE is not propagated. The PE isassociated with net displacements of particles and this movesalong with the wave at the wave speed.
COMET Winter Weather Workshop 2001
WAVE GROUPSWAVE GROUPS
Therefore, only 1/2 of the energy (PE) is propagated at the wave speed which is the same as the total energy moving at 1/2 of the wave speed.
C (kts) = C = C (kts) = C = 1.51 T 1.51 T (sec)(sec) 22
gg
COMET Winter Weather Workshop 2001
Period (sec) Group Speed (kts)5 86 97 118 129 14
10 1511 1712 1813 2014 2115 2316 2417 2618 2719 2920 30
6m waves developedby a marginal gale
Long swell well aheadof a storm system
16m “fully-developed”seas in a big storm
TYPICALTYPICALWAVEWAVE
PERIODSPERIODS
COMET Winter Weather Workshop 2001
Bretschneider Wave CalculatorBretschneider Wave Calculator
COMET Winter Weather Workshop 2001
STATIONARY FETCHES - STATIONARY FETCHES - Example 1Example 1
Coast-lines - The fetch at point B is the distance AB. The fetch at point D is the distance CD. Since AB > CD, a wind from the coast would generate greater waves at B than at D because of the proximity of the coastline.
COMET Winter Weather Workshop 2001
Curvature - The fetch at point B is limited by the curvature of the flow upwind. The fetch is now the distance upwind from B to the point where the wind direction becomes more than 30o different from that at B.
STATIONARY FETCHES - STATIONARY FETCHES - Example 2Example 2
COMET Winter Weather Workshop 2001
Fanning out of flow The fetch at point B is limited by the fanning out of the isobars upstream, therefore giving decreasing wind speeds. In this case, the criterion that is recommended is for wind-speed reductions > 20%.
STATIONARY FETCHES - STATIONARY FETCHES - Example 3Example 3
COMET Winter Weather Workshop 2001
Moving FetchesMoving Fetches
Most interesting wind systems are not stationary.
Determining fetches in a moving system can be complex and time consuming.
COMET Winter Weather Workshop 2001
Waves withWaves withMoving FetchesMoving Fetches
Pete Bowyer & Al MacAfeePete Bowyer & Al MacAfeeCanadian Hurricane CentreCanadian Hurricane Centre
COMET Winter Weather Workshop 2001
XO
CycloneMotion
WIND
WINDW
IND
WIN
D
11
22
33 44
COMET Winter Weather Workshop 2001
Time T0
PB
..
.
PA
PC . PD
.PE
Winds Perpendicularto Fetch Motion
XO
1
COMET Winter Weather Workshop 2001
Time T1
PB
.
PA
PC...
..
. PD
.PE.
.
Waves from Waves from PPA A & P& PCC & P & PEE
grew for less thangrew for less than1 time-step1 time-step
before movingbefore movingoutside the fetchoutside the fetch
Waves fromWaves fromPPB B & P& PDD
have grown forhave grown for1 time-step1 time-step
Winds Perpendicularto Fetch Motion
XO
1
COMET Winter Weather Workshop 2001
Time T2
PB
.
PA
PC.....
...
. PD
.PE.
.
.
.
Waves fromWaves fromPPBB moved outside moved outside
the fetch afterthe fetch after1 time-step1 time-step
Waves from PWaves from PDD
grew for almost grew for almost 2 time-steps2 time-steps
Winds Perpendicularto Fetch Motion
XO
1
COMET Winter Weather Workshop 2001
Winds Perpendicularto Fetch Motion
Time T0
PB
..
.
PA
PC .PD
.PE
XO
2
COMET Winter Weather Workshop 2001
Time T1
PB
..
.
PA
PC .PD
.PE
..
...
Waves from Waves from PPA A & P& PDD & P & PEE
grew for less thangrew for less than1 time-step1 time-step
before movingbefore movingoutside the fetchoutside the fetch
Waves fromWaves fromPPC C & P& PBB
have grown forhave grown for1 time-step1 time-step
Winds Perpendicularto Fetch Motion
XO
2
COMET Winter Weather Workshop 2001
Time T2
PB
..
.
PA
PC .PD
.PE
...
.....
.
.
Waves fromWaves fromPPBB moved outside moved outside
the fetch afterthe fetch after1 time-step1 time-step
Waves from PWaves from PCC
have grown for have grown for 2 time-steps2 time-steps
Winds Perpendicularto Fetch Motion
XO
2
COMET Winter Weather Workshop 2001
Time T3
PB
..
.
PA
PC .PD
.PE
....
....
.....
..
Waves from PWaves from PCC
grew for moregrew for morethan 2 time-stepsthan 2 time-steps
before movingbefore movingoutside the fetchoutside the fetch
Winds Perpendicularto Fetch Motion
XO
2
COMET Winter Weather Workshop 2001
Time T0
PB..PC . PD
.PE
PA.
XO3
Winds OpposingFetch Motion
COMET Winter Weather Workshop 2001
Time T1
PB..PC . PD. .
.
Waves from PWaves from PC C & P& PDD
grew for 1 time-stepgrew for 1 time-step
Waves fromWaves fromPPE E & P& PB B & P& PAA
grew for less thangrew for less than1 time-step1 time-step
before movingbefore movingoutside the fetchoutside the fetch
. .. PE
PA..
.
XO3
Winds OpposingFetch Motion
COMET Winter Weather Workshop 2001
Time T2
PB
..
.
PA
PC . PD
.PE. .
.. .
. .
..
.
Waves from PWaves from PC C & P& PDD
moved outside themoved outside thefetch before growingfetch before growing
for evenfor even2 time-steps2 time-steps
XO3
Winds OpposingFetch Motion
COMET Winter Weather Workshop 2001
Winds WithFetch Motion
Time T0
PB..PC . PD
. PA
.PE
XO 4
COMET Winter Weather Workshop 2001
Time T1
PB
..
.
PA
PC . PD
.PE
. .
.. .
Waves from PWaves from PAA
fell behind thefell behind thefetch beforefetch before
even 1 time-stepeven 1 time-step
Winds WithFetch Motion
XO 4
COMET Winter Weather Workshop 2001
Time T2
PB
..
.
PA
PC . PD
.PE
.. .
....
. ..
Waves from PWaves from PEE
grew for more thangrew for more than1 time-step but1 time-step but
were then outrunwere then outrunby the fetchby the fetch
Winds WithFetch Motion
XO 4
COMET Winter Weather Workshop 2001
Time T3
PB
..
.
PA
PC . PD
.PE
..
.
..
.
..
...
..
..
Waves fromWaves fromPPC C & P& PBB & P & PDD
are still growingare still growingafter 3 time-stepsafter 3 time-steps. . . although those. . . although those
from Pfrom PBB will soon be will soon be
outrun by theoutrun by thefetchfetch
Winds WithFetch Motion
XO 4
COMET Winter Weather Workshop 2001
Time T4
PB
..
.
PA
PC . PD
.PE
..
..
..
..
..
..
..
..
..
..
Waves fromWaves fromPPC C & P& PDD
are still growingare still growingafter 4 time-stepsafter 4 time-steps
Winds WithFetch Motion
XO 4
COMET Winter Weather Workshop 2001
Time T5
PB
..
.
PA
PC . PD
.PE
..
..
.
..
..
.
..
..
..
..
..
..
..
.
Waves fromWaves fromPPDD were finally were finally
outrun by the fetchoutrun by the fetchafter more thanafter more than
4 time-steps4 time-steps
Waves fromWaves fromPPCC are still growing are still growing
after 5 time-stepsafter 5 time-steps
Winds WithFetch Motion
XO 4
COMET Winter Weather Workshop 2001
XO
CycloneMotion
WIND
WINDW
IND
WIN
D
11
22
33 44
“Fetch Reduction”always occurs inQuadrants 1-2-3. . . as long as thecyclone is moving
COMET Winter Weather Workshop 2001
XO
CycloneMotion
WIND
WINDW
IND
WIN
D
11
22
33 44
“Fetch Enhancement”may occur inQuadrant 4
. . . depending on thespeed of the cyclone
COMET Winter Weather Workshop 2001
Waves Moving in Waves Moving in Same DirectionSame Directionas Their Stormas Their Storm
Potential for Potential for ResonanceResonance
COMET Winter Weather Workshop 2001
Fetch movingmuch fasterthan waves
Mid-latitudesystems
A
COMET Winter Weather Workshop 2001
Fetch movingmuch fasterthan waves
Mid-latitudesystems
AWaves moving
much fasterthan fetch
Tropical stormsin the tropics
B
COMET Winter Weather Workshop 2001
Fetch movingmuch fasterthan waves
Mid-latitudesystems
AWaves moving
much fasterthan fetch
Tropical stormsin the tropics
BSome wavesin harmonywith fetch
Strong windsystems in
mid-latitudes
C
COMET Winter Weather Workshop 2001
Fetch movingmuch fasterthan waves
Mid-latitudesystems
AWaves moving
much fasterthan fetch
Tropical stormsin the tropics
BPerfect
Waves-StormResonance
The REALREAL“Perfect Storms”
DSome wavesin harmonywith fetch
Strong windsystems in
mid-latitudes
C
COMET Winter Weather Workshop 2001
Fetches moving withFetches moving withconstant speedconstant speed
COMET Winter Weather Workshop 2001
All of theAll of thewaves quicklywaves quicklyoutrun the slow-outrun the slow-moving stormmoving stormsystemsystem
The steady-stateThe steady-statesolution issolution isreached inreached in7+ hours.7+ hours.
COMET Winter Weather Workshop 2001
Most of theMost of thewaves stillwaves stilloutrun theoutrun theslower movingslower movingstorm systemstorm system
The steady-stateThe steady-statesolution issolution isreached inreached in10+ hours.10+ hours.
COMET Winter Weather Workshop 2001
Waves leavingWaves leavingthe trailing edgethe trailing edgeof the fetch areof the fetch areoutrun by theoutrun by thewind system . . .wind system . . .however, allhowever, allothers move outothers move outahead.ahead.
The steady-stateThe steady-statesolution issolution isreached inreached in17+ hours.17+ hours.
COMET Winter Weather Workshop 2001
Most waves areMost waves aresoon outrun by thesoon outrun by theinitially quicker initially quicker moving wind moving wind system . . .system . . .however, waveshowever, wavesstarting at thestarting at theleading edge “hold leading edge “hold on long enough” on long enough” until their speeduntil their speedcatches up to thecatches up to thesystem speed . . .system speed . . .and eventuallyand eventuallyoutruns the system.outruns the system.
Steady state isSteady state isreached in 30 hrs.reached in 30 hrs.
COMET Winter Weather Workshop 2001
All waves areAll waves arequickly outrunquickly outrunby the muchby the muchquicker windquicker windsystem . . . andsystem . . . andgrowth is verygrowth is verylimited.limited.
The steady-stateThe steady-statesolution issolution isreached in reached in under 5 hours.under 5 hours.
COMET Winter Weather Workshop 2001
Maximum waveMaximum wavegrowth occursgrowth occursfor a constantfor a constantsystem speed of system speed of 20.7 knots. All20.7 knots. Allspeeds greaterspeeds greateror less than thisor less than thiswill result inwill result inlower wavelower waveheights.heights.
The steady-stateThe steady-statesolution is notsolution is notreached untilreached until34 hours.34 hours.
COMET Winter Weather Workshop 2001
Even for speedsEven for speedsonly slightlyonly slightlygreater, theregreater, thereis a significantis a significantdifference indifference inthe resonancethe resonanceof the storm-of the storm-waves system.waves system.
COMET Winter Weather Workshop 2001
Consider . . .Consider . . .- a fixed fetch length (eg. 50 nmi)- a fixed fetch length (eg. 50 nmi)- fixed wind speed throughout fetch - fixed wind speed throughout fetch (eg. 50 kts)(eg. 50 kts)
What is the relationship between What is the relationship between fetch-enhancement and storm speed?fetch-enhancement and storm speed?
COMET Winter Weather Workshop 2001
Storm-Wave Resonance CalculatorStorm-Wave Resonance Calculator
COMET Winter Weather Workshop 2001
COMET Winter Weather Workshop 2001
COMET Winter Weather Workshop 2001
COMET Winter Weather Workshop 2001
Fetch Enhancement
Fetch Reduction
COMET Winter Weather Workshop 2001
Fetch Reduction
Enhancement
Significant Enhancement
Extreme Enhancement
COMET Winter Weather Workshop 2001
Maximum Significant Wave Height for Storm Speed vs Wind Speed50 nm Fetch Area
0
5
10
15
20
25
30
1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49
Storm Speed (kt)
Max
imu
m S
igW
ave
Hei
gh
t (m
)
Wind 20
Wind 30
Wind 40
Wind 50
Wind 60
Wind 70
Wind 80
Wind 90
Wind 100
COMET Winter Weather Workshop 2001
Maximum Significant Wave Height vs Wind Speed at Optimum Storm Speed for 50 nm Fetch Area
y = 0.3216x - 3.65
R2 = 0.9984
0
5
10
15
20
25
3020 24 28 32 36 40 44 48 52 56 60 64 68 72 76 80 84 88 92 96 10 0
Wind Speed (kt)
Max
imu
m S
igW
ave
Hei
gh
t
plot Cg and overlaythink lagrangian frame of reference (not Eulerian)
COMET Winter Weather Workshop 2001
Maximum Normalized Wave Height for Storm Speed vs Wind Speed50 nm Fetch Area
0
0.5
1
1.5
2
2.5
3
1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49
Storm Speed (kt)
Max
imu
m N
orm
aliz
ed W
ave
Hei
gh
t
Wind 20
Wind 30
Wind 40
Wind 50
Wind 60
Wind 70
Wind 80
Wind 90
Wind 100
EnhancementEnhancement
ReductionReduction
COMET Winter Weather Workshop 2001
Fetch EnhancementsWind Speed vs. System Speed for 50 nmi Fetch Length
0
5
10
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20
25
30
35
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45
20
26
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50
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116
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128
134
140
146
Wind Speed (kt)
Syste
m S
peed
(kt)
Optimum Enhancement
Optimum Enhancement
COMET Winter Weather Workshop 2001
Fetch EnhancementsWind Speed vs. System Speed for 250 nmi Fetch Length
0
5
10
15
20
25
30
35
40
45
50
20
27
34
41
48
55
62
69
76
83
90
97
104
111
118
125
132
139
146
Wind Speed (kt)
Syste
m S
peed
(kt)
Optimum Enhancement
Optimum Enhancement
COMET Winter Weather Workshop 2001
Fetch EnhancementsWind Speed vs. System Speed for 250 nmi Fetch Length
0
5
10
15
20
25
30
35
40
45
50
20
27
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83
90
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104
111
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125
132
139
146
Wind Speed (kt)
Syste
m S
peed
(kt)
Fetch EnhancementsWind Speed vs. System Speed for 50 nmi Fetch Length
0
5
10
15
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25
30
35
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4520
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146
Wind Speed (kt)
Syste
m S
peed
(kt)
COMET Winter Weather Workshop 2001
Maximum Normalized Wave Height vs Wind Speedat Optimum Storm Speed for 50 nm Fetch Area
y = - 9/x + 1.7841x0.0873
R2 = 0.9576
0
0.5
1
1.5
2
2.5
3
20 24 28 32 36 40 44 48 52 56 60 64 68 72 76 80 84 88 92 96 10 0
Wind Speed (kt)
No
rmal
ized
Wav
e H
eig
ht
COMET Winter Weather Workshop 2001
Observation:Observation:
1. The greater the wind speed,1. The greater the wind speed, the greater the enhancementthe greater the enhancement
COMET Winter Weather Workshop 2001
Maximum Possible Significant Wave HeightsMaximum Possible Significant Wave Heights35-knot winds35-knot winds
COMET Winter Weather Workshop 2001
Maximum Possible Significant Wave HeightsMaximum Possible Significant Wave Heights50-knot winds50-knot winds
COMET Winter Weather Workshop 2001
Maximum Possible Significant Wave HeightsMaximum Possible Significant Wave Heights65-knot winds65-knot winds
COMET Winter Weather Workshop 2001
Maximum Possible Significant Wave HeightsMaximum Possible Significant Wave Heights80-knot winds80-knot winds
COMET Winter Weather Workshop 2001
Maximum Possible Significant Wave HeightsMaximum Possible Significant Wave Heights95-knot winds95-knot winds
COMET Winter Weather Workshop 2001
Observations:Observations:
2. The smaller the fetch, the2. The smaller the fetch, the greater the enhancementgreater the enhancement
3. The greater the wind speed,3. The greater the wind speed, the greater the optimumthe greater the optimum storm speedstorm speed
COMET Winter Weather Workshop 2001
Maximum Duration of Wave Growth for Storm Speed vs Wind Speed50 nm Fetch Area
0
10
20
30
40
50
60
70
80
90
1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49
Storm Speed (kt)
Ho
urs
of
Wav
e G
row
th
Wind 20
Wind 30
Wind 40
Wind 50
Wind 60
Wind 70
Wind 80
Wind 90
Wind 100
COMET Winter Weather Workshop 2001
Maximum Duration of Wave Growth vs Wind Speedat Optimum Storm Speed for 50 nm Fetch Area
0
10
20
30
40
50
60
70
80
90
20 24 28 32 36 40 44 48 52 56 60 64 68 72 76 80 84 88 92 96 10 0
Wind Speed (kt)
Wav
e G
row
th (
Ho
urs
)
Unlikely durationsUnlikely durations
COMET Winter Weather Workshop 2001
Maximum Possible Hours of Wave Growth
0
50
100
150
200
25020
28
36
44
52
60
68
76
84
92
10 0
Wind Speed (kt)
Maxim
um
Du
rati
on
of
Wave
Gro
wth
50-SSDur
100-SSDur
COMET Winter Weather Workshop 2001
Observation:Observation:
4. Optimum fetch-enhancement is 4. Optimum fetch-enhancement is more probable for high wind / smallmore probable for high wind / small fetch events than low wind / highfetch events than low wind / high fetch events . . . because thefetch events . . . because the required durations are on the orderrequired durations are on the order of 1-day of 1-day (ie: these events can(ie: these events can actually occur)actually occur)
COMET Winter Weather Workshop 2001
Conclusion 1Conclusion 1Observations 1-4 select sub-synoptic Observations 1-4 select sub-synoptic scale storm systems for the greatest scale storm systems for the greatest potential for optimum resonancepotential for optimum resonance(tropical cyclones and polar lows*)(tropical cyclones and polar lows*)
* * - as we understood them before Tuesday- as we understood them before Tuesday
COMET Winter Weather Workshop 2001
Wind Speed vs Storm Speed for Maximum Fetch Enhancement50 nm Fetch Area
y = -0.001x2 + 0.3131x + 3.65
R2 = 0.9986
0
5
10
15
20
25
20 24 28 32 36 40 44 48 52 56 60 64 68 72 76 80 84 88 92 96 10 0
Wind Speed (kt)
Op
tim
um
Sto
rm S
pee
d (
kt)
COMET Winter Weather Workshop 2001
Optimum Storm Speeds (kt) for Maximum Wave Enhancement
0
5
10
15
20
25
30
20
29
38
47
56
65
74
83
92
Wind Speed (kt)
Sto
rm S
peed
(kt)
50-StormSpeed
100-StormSpeed
Average speed of TCs Average speed of TCs south of 30south of 30ooNN
Average speed of TCs Average speed of TCs north of 40north of 40ooNN
50 nm Fetch
100 nm Fetch
COMET Winter Weather Workshop 2001
Observation:Observation:
5. Fetch enhancement for tropical 5. Fetch enhancement for tropical cyclones of TS or Hurricane strength cyclones of TS or Hurricane strength is greater in mid latitudes than in the is greater in mid latitudes than in the tropics.tropics.
COMET Winter Weather Workshop 2001
Conclusion 2Conclusion 2
The highest waves with tropical The highest waves with tropical storms or hurricanes should be storms or hurricanes should be expected in mid latitudes . . .expected in mid latitudes . . .
. . . a unique problem with ETs. . . a unique problem with ETs
COMET Winter Weather Workshop 2001
As tropical cyclones become ET,As tropical cyclones become ET,they are typically increasing in speedthey are typically increasing in speed
under the influence of aunder the influence of amid-latitude stream.mid-latitude stream.
The seas associated with theseThe seas associated with thesesystems (and even minimal hurricanessystems (and even minimal hurricanesthat move “quickly”) can be greaterthat move “quickly”) can be greater
than those associated withthan those associated withmajor hurricanes.major hurricanes.
COMET Winter Weather Workshop 2001
For example:For example:
A Hurricane in the TropicsA Hurricane in the Tropics Moving 5 kts . . . area of 65-kt windsMoving 5 kts . . . area of 65-kt windsover a fetch length of 100 nm . . . canover a fetch length of 100 nm . . . cangenerate Hgenerate Hsigsig of almost 11 m. of almost 11 m.
A Tropical Storm in Mid-LatitudesA Tropical Storm in Mid-LatitudesMoving 19Moving 1911//22 kts . . . area of 50-kt winds kts . . . area of 50-kt winds
over a fetch length of 100 nm . . . canover a fetch length of 100 nm . . . cangenerate Hgenerate Hsigsig of almost 15 m. of almost 15 m.
-27
COMET Winter Weather Workshop 2001
Accelerating FetchesAccelerating Fetches
If the storm system accelerates with a speedIf the storm system accelerates with a speedmatching that of the waves it generates, thematching that of the waves it generates, theconditions for conditions for perfectperfect resonance exists and resonance exists andwave growth is more easily maximized.wave growth is more easily maximized.
COMET Winter Weather Workshop 2001
Wave Speed vs Hours of Growth for Different Wind Speeds
0
10
20
30
40
50
60
1 8 15 22 29 36 43 50 57 64 71 78 85 92 99 106
113
120
Hours of Wave Growth
Wav
e G
rou
p S
pee
d (
kts)
20-Kt
40-Kt
60-Kt
80-Kt
100-Kt
Log. (100-Kt)
Log. (80-Kt)
Log. (60-Kt)
Log. (40-Kt)
Log. (20-Kt)
COMET Winter Weather Workshop 2001
Storms moving in a straight line, atStorms moving in a straight line, atthe optimum speed,the optimum speed,
can result in the potential forcan result in the potential forphenomenally large waves tophenomenally large waves to
developdevelop
COMET Winter Weather Workshop 2001
Luis (95)Luis (95) Felix (95)Felix (95)
Bonnie (98)Bonnie (98)Danielle (98)Danielle (98)
Luis (95)Luis (95) Felix (95)Felix (95)
Bonnie (98)Bonnie (98)Danielle (98)Danielle (98)
COMET Winter Weather Workshop 2001
HURRICANELUIS
Sept. 10-11, 1995
85 knots
10 / 06Z
2585 knots
10 / 12Z
10 / 18Z
85 knots
95 knots
11 / 00Z
11 / 06Z
105 knots
32
38
39
COMET Winter Weather Workshop 2001
Max ReportedMax ReportedSig. WavesSig. Waves17+ metres17+ metres
66
55
44
33
22
77 88
99
1010
HURRICANELUIS
Sept. 10-11, 1995
85 knots
10 / 06Z
2585 knots
10 / 12Z
10 / 18Z
85 knots
95 knots
11 / 00Z
11 / 06Z
105 knots
32
38
39
Wave Field atWave Field atSept.11 - 01ZSept.11 - 01Z
**
For 17 metres,For 17 metres,85 kts is required85 kts is requiredthroughout thisthroughout thisbox for aboutbox for about
14 hours14 hours
QEIIQEII
COMET Winter Weather Workshop 2001
Significant & Maximum Wave Heights at Buoy 44141During Hurricane LuisSeptember 10-11, 1995
0
5
10
15
20
25
30
35
14
16
18
20
22 0 2 4 6 8 10
12
14
Time (UTC)
Wave H
eig
hts
(m
etr
es)
Sig.Wave
Max.Wave
Nearest pointNearest pointto storm to storm
Storm speedStorm speed40+ knots40+ knots
andandincreasing increasing
COMET Winter Weather Workshop 2001
Since Luis was quickly outstripping Since Luis was quickly outstripping the waves generated by its wind-field,the waves generated by its wind-field,
the waves were not as large as theythe waves were not as large as theymight of been, had Luis movedmight of been, had Luis moved
considerably slower.considerably slower.
Since Luis was quickly outstripping Since Luis was quickly outstripping the waves generated by its wind-field,the waves generated by its wind-field,
the waves were not as large as theythe waves were not as large as theymight of been, had Luis movedmight of been, had Luis moved
considerably slower.considerably slower.
COMET Winter Weather Workshop 2001
60 knots
55 knots
50 knots
50 knots
50 knots
50 knots
50 knots
21 / 00Z
21 / 06Z
21 / 12Z
21 / 18Z
22 / 00Z
22 / 06Z
22 / 12Z
43
35
31
28
TS FELIXAug. 21-22, 1995
COMET Winter Weather Workshop 2001
60 knots
55 knots
50 knots
50 knots
50 knots
50 knots
50 knots
21 / 00Z
21 / 06Z
21 / 12Z
21 / 18Z
22 / 00Z
22 / 06Z
22 / 12Z
43
35
31
28
TS FELIXAug. 21-22, 1995
2
3
4
5
6
Max ReportedMax ReportedSig. WavesSig. Waves13+ metres13+ metres
**
Wave Field atWave Field atAug.22 - 00ZAug.22 - 00Z
For 13 metres,For 13 metres,50 kts is required50 kts is requiredthroughout thisthroughout thisbox for aboutbox for about
36 hours36 hours
7
COMET Winter Weather Workshop 2001
Significant & Maximum Wave Heights at 44137During Tropical Storm Felix
August 21-22, 1995
0
5
10
15
20
25
30
14
15
16
17
18
19
20
21
22
23 0 1 2 11 12
13
14
Time (UTC)
Wave H
eig
hts
(m
etr
es)
Sig.Wave
Max.Wave
Nearest pointNearest pointto storm to storm
Storm speedStorm speed30+ knots30+ knots
andandincreasingincreasing
COMET Winter Weather Workshop 2001
The waves in Felix were quiteThe waves in Felix were quitelarge, considering the wind field.large, considering the wind field.However, like Luis, Felix beganHowever, like Luis, Felix began
outstripping the waves . . . whichoutstripping the waves . . . whichmight have eventually grown larger,might have eventually grown larger,
had Felix’s translation remainedhad Felix’s translation remainedbelow 30 knots.below 30 knots.
The waves in Felix were quiteThe waves in Felix were quitelarge, considering the wind field.large, considering the wind field.However, like Luis, Felix beganHowever, like Luis, Felix began
outstripping the waves . . . whichoutstripping the waves . . . whichmight have eventually grown larger,might have eventually grown larger,
had Felix’s translation remainedhad Felix’s translation remainedbelow 30 knots.below 30 knots.
COMET Winter Weather Workshop 2001
TS BONNIEAug. 29-30, 1998
45 knots
29 / 00Z 45 knots
29 / 06Z 45 knots
29 / 12Z45 knots
29 / 18Z
45 knots
30 / 00Z
45 knots
30 / 06Z
45 knots
30 / 12Z
45 knots
30 / 18Z
18
18
26
28
34
25 26
COMET Winter Weather Workshop 2001
TS BONNIEAug. 29-30, 1998
45 knots
29 / 00Z 45 knots
29 / 06Z 45 knots
29 / 12Z45 knots
29 / 18Z
45 knots
30 / 00Z
45 knots
30 / 06Z
45 knots
30 / 12Z
45 knots
30 / 18Z
18
18
26
28
34
25 26
Max ReportedMax ReportedSig. WavesSig. Waves11 metres11 metres
**
2
For 11 metres,For 11 metres,45 kts is required45 kts is requiredthroughout thisthroughout thisbox for aboutbox for about
42 hours42 hours
Wave Field atWave Field atAug.30 - 00ZAug.30 - 00Z
34
5
67
COMET Winter Weather Workshop 2001
Significant & Maximum Wave Heights at Buoy 44137During Tropical Storm Bonnie
August 29-30, 1998
0
2
4
6
8
10
12
14
16
12
14
16
18
20
22 0 2 4 6 8 10
12
Time (UTC)
Wave H
eig
hts
(m
etr
es)
Sig.Wave
Max.Wave
Nearest pointNearest pointto storm to storm
Storm speedStorm speed25+ knots25+ knots
andandincreasing increasing
COMET Winter Weather Workshop 2001
The waves with Bonnie were closeThe waves with Bonnie were closeto being fully-developed for the windto being fully-developed for the wind
field associated with the storm.field associated with the storm.The proximity of the wave max withThe proximity of the wave max with
the storm centre shows that thethe storm centre shows that thetwo moved in reasonable harmony.two moved in reasonable harmony.A slightly slower translation speedA slightly slower translation speedfor the storm might have resultedfor the storm might have resulted
in slighly larger waves.in slighly larger waves.
The waves with Bonnie were closeThe waves with Bonnie were closeto being fully-developed for the windto being fully-developed for the wind
field associated with the storm.field associated with the storm.The proximity of the wave max withThe proximity of the wave max with
the storm centre shows that thethe storm centre shows that thetwo moved in reasonable harmony.two moved in reasonable harmony.A slightly slower translation speedA slightly slower translation speedfor the storm might have resultedfor the storm might have resulted
in slighly larger waves.in slighly larger waves.
COMET Winter Weather Workshop 2001
HURRICANEDANIELLE
Sept. 2-3, 1998
32
30
24
23
23
70 knots
02 / 18Z
70 knots
03 / 00Z
70 knots
03 / 06Z
70 knots
03 / 12Z
65 knots
03 / 18Z 65 knots
04 / 00Z
**
COMET Winter Weather Workshop 2001
HURRICANEDANIELLE
Sept. 2-3, 1998
32
30
24
23
23
70 knots
02 / 18Z
70 knots
03 / 00Z
70 knots
03 / 06Z
70 knots
03 / 12Z
65 knots
03 / 18Z 65 knots
04 / 00Z
2
Max ReportedMax ReportedSig. WavesSig. Waves16 metres16 metres
**
Wave Field atWave Field atSept.3 - 08ZSept.3 - 08Z
34 5
67
89
For 16 metres,For 16 metres,70 kts is required70 kts is requiredthroughout thisthroughout thisbox for aboutbox for about
16 hours16 hours
COMET Winter Weather Workshop 2001
Significant & Maximum Wave Heights at Buoy 44141During Hurricane Danielle
September 2-3, 1998
0
5
10
15
20
25
3021
23 1 3 5 7 9 11 13
15
17
19
Time (UTC)
Wave H
eig
hts
(m
etr
es)
Sig.Wave
Max.Wave
Nearest pointNearest pointto storm to storm
Storm speedStorm speed25 knots25 knots
andandslowing slowing
COMET Winter Weather Workshop 2001
Like Bonnie, the max in the wave-field Like Bonnie, the max in the wave-field with Danielle was very close to the with Danielle was very close to the storm centre . . . showing that thestorm centre . . . showing that the
two were moving in reasonabletwo were moving in reasonableharmony. harmony.
Danielle actually began slowing,Danielle actually began slowing,allowing the wave-field to catch upallowing the wave-field to catch up
and grow larger what might beand grow larger what might beexpected.expected.
Like Bonnie, the max in the wave-field Like Bonnie, the max in the wave-field with Danielle was very close to the with Danielle was very close to the storm centre . . . showing that thestorm centre . . . showing that the
two were moving in reasonabletwo were moving in reasonableharmony. harmony.
Danielle actually began slowing,Danielle actually began slowing,allowing the wave-field to catch upallowing the wave-field to catch up
and grow larger what might beand grow larger what might beexpected.expected.
COMET Winter Weather Workshop 2001
The Worst-Case Scenario is, therefore,The Worst-Case Scenario is, therefore,a storm centre . . . a storm centre . . .
- moving in a straight line, - moving in a straight line, - covering a large distance over open - covering a large distance over open ocean, ocean, - increasing in speed, continually - increasing in speed, continually matching the speed of the waves that matching the speed of the waves that corresponds closely with the peak in the corresponds closely with the peak in the energy spectrum energy spectrum
The Worst-Case Scenario is, therefore,The Worst-Case Scenario is, therefore,a storm centre . . . a storm centre . . .
- moving in a straight line, - moving in a straight line, - covering a large distance over open - covering a large distance over open ocean, ocean, - increasing in speed, continually - increasing in speed, continually matching the speed of the waves that matching the speed of the waves that corresponds closely with the peak in the corresponds closely with the peak in the energy spectrum energy spectrum
COMET Winter Weather Workshop 2001
The Pattern . . . The Pattern . . .
- area of maximum waves to the right of- area of maximum waves to the right of track track- very tight gradient in the wave field at- very tight gradient in the wave field at the leading edge . . . as the trapped-fetch the leading edge . . . as the trapped-fetch arrives, it brings with it a “wall of water” arrives, it brings with it a “wall of water” (no forerunners to warn of storm) (no forerunners to warn of storm)- waves - waves cancan subside rather quickly in the subside rather quickly in the wake of these storms, however, the wake of these storms, however, the trailing gradient is usually much weaker trailing gradient is usually much weaker
The Pattern . . . The Pattern . . .
- area of maximum waves to the right of- area of maximum waves to the right of track track- very tight gradient in the wave field at- very tight gradient in the wave field at the leading edge . . . as the trapped-fetch the leading edge . . . as the trapped-fetch arrives, it brings with it a “wall of water” arrives, it brings with it a “wall of water” (no forerunners to warn of storm) (no forerunners to warn of storm)- waves - waves cancan subside rather quickly in the subside rather quickly in the wake of these storms, however, the wake of these storms, however, the trailing gradient is usually much weaker trailing gradient is usually much weaker
COMET Winter Weather Workshop 2001
Modelling the ProblemModelling the ProblemSpecifically for TCsSpecifically for TCs
• Resonance is, uniquely, a unidirectional problem, so Resonance is, uniquely, a unidirectional problem, so the spectral issues simplify considerablythe spectral issues simplify considerably
• Since wind is, by far, the most critical issue, even a Since wind is, by far, the most critical issue, even a simple first generation parametric approach will give simple first generation parametric approach will give superior results, if the wind field is treated accurately.superior results, if the wind field is treated accurately.
COMET Winter Weather Workshop 2001
Currently, we are tacklingCurrently, we are tacklingthis problem by coupling the this problem by coupling the CHC’s hurricane wind modelCHC’s hurricane wind model
with a single-purpose wavewith a single-purpose wavemodel . . .model . . .
. . . that looks only at the . . . that looks only at the maximum possible Hmaximum possible Hsigsig
with a given storm with a given storm
Currently, we are tacklingCurrently, we are tacklingthis problem by coupling the this problem by coupling the CHC’s hurricane wind modelCHC’s hurricane wind model
with a single-purpose wavewith a single-purpose wavemodel . . .model . . .
. . . that looks only at the . . . that looks only at the maximum possible Hmaximum possible Hsigsig
with a given storm with a given storm
COMET Winter Weather Workshop 2001
COMET Winter Weather Workshop 2001
COMET Winter Weather Workshop 2001
The output of theThe output of the“trapped-fetch” model shows“trapped-fetch” model shows
trajectories, maximum Htrajectories, maximum Hsigsig, and, and
duration of wave growth fromduration of wave growth fromindependent fetch areas withinindependent fetch areas within
the tropical cyclonethe tropical cyclone
The output of theThe output of the“trapped-fetch” model shows“trapped-fetch” model shows
trajectories, maximum Htrajectories, maximum Hsigsig, and, and
duration of wave growth fromduration of wave growth fromindependent fetch areas withinindependent fetch areas within
the tropical cyclonethe tropical cyclone
COMET Winter Weather Workshop 2001
..
.
Point of initialwave development
Waves stopgrowing
Waves nolonger
sustained
9.237
54
Max.Sig. Wave
9.2 m
37 hoursof growth
54 hoursto end of
9.2 mmaintenance
COMET Winter Weather Workshop 2001
For Bonnie, theFor Bonnie, theCHC model predictsCHC model predictsa maximum Ha maximum Hsigsig
passing throughpassing throughsouthern Maritimesouthern Maritimewaters of 10.3m.waters of 10.3m.
Compare this to theCompare this to themaximum Hmaximum Hsig sig of of
10.8m reported by a10.8m reported by aweather buoy.weather buoy.
COMET Winter Weather Workshop 2001
For Luis, theFor Luis, theCHC model predictsCHC model predictsa maximum Ha maximum Hsigsig
of 18.9 m to theof 18.9 m to theright-of-track.right-of-track.
A weather buoyA weather buoyreported a maximumreported a maximumHHsigsig of 17.1 m. of 17.1 m.
COMET Winter Weather Workshop 2001
For Danielle, theFor Danielle, theCHC model predictsCHC model predictsa maximum Ha maximum Hsigsig
of 15.5 m passingof 15.5 m passingthrough southern through southern Maritime waters.Maritime waters.
A weather buoyA weather buoyreported 15.8 m.reported 15.8 m.
COMET Winter Weather Workshop 2001
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