Vermelding onderdeel organisatie February 1, 2012 1 Chapter 6: Data collection ct5308 Breakwaters and Closure Dams H.J. Verhagen Faculty of Civil Engineering and Geosciences Section Hydraulic Engineering
Chapter 6: Data Collection
Jun 19, 2015
6. Data Collection
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Vermelding onderdeel organisatie
February 1 2012
1
Chapter 6 Data collection
ct5308 Breakwaters and Closure Dams
HJ Verhagen
Faculty of Civil Engineering and Geosciences Section Hydraulic Engineering
February 1 2012 2
Type of data to be collected
bull Hydrographic data
bull bathymetry
bull tides
bull storm surges
bull waves
bull meteorological data
bull geotechnical data
bull data needed for the construction
bull construction materials
bull equipment
bull labour
February 1 2012 3
Bathymetry
bull Nautical Charts
bull reference level
bull list of symbols
bull date of production
bull Topographical maps
bull Satellite images
bull Custom made maps
bull lead and sextant
bull echosounder and GPS
February 1 2012 4
tides
bullvertical tide
bullhorizontal tide
tide tables (British admiralty)
internet (httptbonebiolscedutidesiteselhtml)
(httpeasytideukhogovuk)
(httpwwwshomfr)
(wwwgetijnl)
For horizontal tides
see hydrographic atlases
or make Delft3D computation
February 1 2012 5
storm surges
httpwwwhurricanecom
February 1 2012 6
waves measurements
February 1 2012 7
Global Wave Statistics (1)
February 1 2012 8
Global wave statistics (2)
February 1 2012 9
processed data
Atlas of the Oceans
Wind and Wave data
February 1 2012 10
ERA-40 wave atlas
httpwwwknminl
onderzkoceano
wavesera40
February 1 2012 11
wave data for North Sea
February 1 2012 12
example from Argoss (wwwwaveclimatecom)
standard histogram
February 1 2012 13
exceedance table
February 1 2012 14
exceedance graph
February 1 2012 15
comparison buoys and ship data
February 1 2012 16
Data from wwwhydrobasenet
February 1 2012 17
Sample output of Hydrobase
February 1 2012 18
Data from Hydrobase
February 1 2012 19
data from Meetpost Noordwijk
wwwgolfklimaatnl
0
50
100
150
200
250
300
350
400
450
0 200 400 600 800
time (hrs)
Hm
o (
cm
)
January 1979
February 1 2012 20
basic data
date time Hm0 accur H13 TTE3 Tm02 TH13 wave wind wind level setup
dir dir speed
cm cm cm 1 s 1 s 1 s degr degr 1 ms cm cm
19980101 0100 70 4 64 6 39 49 261 210 60 -27 27 222224000
19980101 0400 72 4 65 8 36 45 264 210 70 91 24 222224000
19980101 0700 62 4 56 8 36 46 258 200 80 58 11 222224000
19980101 1000 93 5 85 11 40 48 234 190 90 -31 6 222224000
19980101 1300 110 5 102 14 44 51 230 200 90 -83 -5 222224000
19980101 1600 162 7 148 17 42 52 230 200 120 43 -12 222224000
19980101 1900 132 6 121 11 40 48 224 190 130 40 -37 222224000
19980101 2200 205 8 190 18 51 61 220 190 170 -39 -33 222224000
19980102 0100 247 10 230 37 56 68 229 190 170 -114 -57 222224000
19980102 0400 275 11 255 40 55 68 236 210 160 -1 -1 222224000
19980102 0700 208 8 193 20 50 63 234 200 140 -2 -72 222224000
19980102 1000 142 6 132 14 47 59 227 190 120 -59 -13 222224000
19980102 1300 130 6 120 14 50 64 223 160 110 -97 -22 222224000
19980102 1600 117 5 108 13 43 53 213 170 100 73 87 222224000
19980102 1900 91 5 84 10 39 49 232 210 100 152 58 222224000
19980102 2200 243 10 226 22 52 62 267 280 150 119 118 222224000
19980103 0100 287 12 269 32 59 70 269 260 110 25 73 222224000
19980103 0400 240 10 224 21 55 66 265 230 90 28 60 222224000
19980103 0700 177 7 163 13 46 56 245 200 130 122 37 222224000
19980103 1000 179 7 165 16 47 56 223 180 170 -30 3 222224000
19980103 1300 285 12 266 35 58 70 230 210 190 -43 16 222224000
19980103 1600 341 15 318 56 61 73 242 250 130 -36 14 222224000
19980103 1900 342 15 319 53 60 73 246 260 170 133 20 222224000
19980103 2200 414 21 388 85 65 77 249 260 190 72 46 222224000
19980104 0100 465 21 435 228 72 88 254 260 190 40 68 222224000
19980104 0400 358 16 334 92 64 78 259 240 90 -22 18 222224000
19980104 0700 324 14 302 52 60 73 256 250 120 129 43 222224000
19980104 1000 247 10 229 33 55 69 252 220 100 34 33 222224000
February 1 2012 21
sort data in classes
Waveheight class Hs (cm)
Number of observations
P Q -ln(Q)
0 25 35 35 0000599 0999401 0000599
25 50 8260 8295 0141940 0858060 0153082 50 75 11424 19719 0337423 0662577 0411618
75 100 10004 29723 0508607 0491393 0710511
100 125 7649 37372 0639493 0360507 1020245
125 150 5563 42935 0734685 0265315 1326838
150 175 4389 47324 0809788 0190212 1659615
175 200 3167 50491 0863980 0136020 1994954
200 225 2360 52851 0904363 0095637 2347200
225 250 1671 54522 0932957 0067043 2702419
250 275 1234 55756 0954073 0045927 3080692
275 300 851 56607 0968634 0031366 3462047
300 325 556 57163 0978149 0021851 3823487
325 350 392 57555 0984856 0015144 4190168
350 375 276 57831 0989579 0010421 4563938
375 400 206 58037 0993104 0006896 4976819
400 425 136 58173 0995431 0004569 5388507
425 450 82 58255 0996834 0003166 5755400
450 475 66 58321 0997964 0002036 6196632
475 500 38 58359 0998614 0001386 6581307
500 525 30 58389 0999127 0000873 7043930
525 550 20 58409 0999470 0000530 7541769
550 575 22 58431 0999846 0000154 8778531
575 600 9 58440 1000000 0000000
58440
( )s sP P H H
( ) 1s sQ Q H H P
all data Noordwijk
y = 00151x - 05001
R2 = 09881
0
1
2
3
4
5
6
7
8
9
10
0 200 400 600Hs-l
nQ
February 1 2012 22
exceedance graph for Noordwijk
indivudual observations
0
200
400
600
800
1000
000001000001000001000001000001000001000000
exceedance
wave h
eig
ht
But what means that in a year during 01
of the time the Hs is larger than 5 m
February 1 2012 23
Peak over Threshold method
A storm is defined as a time that the wave is higher than a
certain value the height of the storm Hss is equal to the
highest observed Hs during that storm
Threshold = 15
In this period 9
storms observed
nr Hss
1 180 m
2 294 m
3 225 m
4 176 m
5 261 m
6 389 m
7 172 m
8 240 m
9 194 m
February 1 2012 24
Table with Hss classes
= 124 Wave height class
150 cumul P Q Qs W
150 175 384 384 021993 078007 6810 032522 175 200 381 765 043814 056186 4905 064136 200 225 266 1031 059049 040951 3575 091261 225 250 157 1188 068041 031959 2790 111202 250 275 148 1336 076518 023482 2050 134858 275 300 111 1447 082875 017125 1495 158094 300 325 81 1528 087514 012486 1090 180552 325 350 63 1591 091123 008877 775 204065 350 375 31 1622 092898 007102 620 219099 375 400 32 1654 094731 005269 460 238832 400 425 23 1677 096048 003952 345 257486 425 450 11 1688 096678 003322 290 268590 450 475 20 1708 097824 002176 190 295184 475 500 9 1717 098339 001661 145 311883 500 525 7 1724 098740 001260 110 328731 525 550 9 1733 099255 000745 065 360263 550 575 8 1741 099714 000286 025 415922 575 600 5 1746 1 0 000 DIV0 1746 20 year 873 Slope 085586 Intercept -104906 correlation 099524 beta 116842 gamma 122575
Hss for condition 1 10 668997
( )ss ssP P H H
1ss ssQ Q H H P
threshold 15 m
y = -07849Ln(x) + 16329
R2 = 09854
0
2
4
6
8
000010000100001000010000100000probability of exceedence
sto
rm h
eig
ht
Hss
February 1 2012 25
How to get storm exceedance
Q = probability of exceedance of a wave
Qs = probability of exceedance of a storm
s sQ N Qthreshold 15 m
y = -07849Ln(x) + 5141
R2 = 09854
0
2
4
6
8
10
001010100100010000
storm exceedence probability per year
sto
rm h
eig
ht
Hss
Statistically
nonsense
February 1 2012 26
The ldquoonce in 500 years stormrdquo
0785ln( )
10785ln 5141
500
100
ss sH Q
m
threshold 15 m
y = -07849Ln(x) + 5141
R2 = 09854
0
2
4
6
8
10
001010100100010000
storm exceedence probability per year
sto
rm h
eig
ht
Hss
February 1 2012 27
Using the Gumbel distribution
exp exp ssHP
February 1 2012 28
determination of and
ln exp
1ln ln
ss
ss
ssss
GAH B
HP
HP H
1ln lnG
P
Perform linear regression
for G = A Hss - B
February 1 2012 29
data for calculation of Gumbel 150 cumul P Q ln(Qs) -ln(H) Qs G
150 175 384 384 021993 078007 422098 -056 6810 -0415046
175 200 381 765 043814 056186 389284 -069 4905 0192121
200 225 266 1031 059049 040951 357655 -081 3575 0640938
225 250 157 1188 068041 031959 332863 -092 2790 0954366
250 275 148 1336 076518 023482 302042 -101 2050 1318085
275 300 111 1447 082875 017125 270471 -11 1495 1672191
300 325 81 1528 087514 012486 238876 -118 1090 2014645
325 350 63 1591 091123 008877 204769 -125 775 2375535
350 375 31 1622 092898 007102 182455 -132 620 2608194
375 400 32 1654 094731 005269 152606 -139 460 2916351
400 425 23 1677 096048 003952 123837 -145 345 3210883
425 450 11 1688 096678 003322 106471 -15 290 3387796
450 475 20 1708 097824 002176 064185 -156 190 3816515
475 500 9 1717 098339 001661 037156 -161 145 4089424
500 525 7 1724 098740 001260 009531 -166 110 4367707
525 550 9 1733 099255 000745 -043078 -17 065 4896399
550 575 8 1741 099714 000286 -138629 -175 025 5854211
575 600 5 1746 1 0 NUM -179 000 NUM
February 1 2012 30
Gumbel exceedance graph
Gumbel distribution
y = 07234x + 1882
R2 = 09871
0
2
4
6
8
10
0 2 4 6 8 10Gumbel Reduced variable
Sto
rm h
eig
ht
Hs
s
ssG AH B
= 1A = 0723
= B =1882
February 1 2012 31
calculation of a value
1ln ln
1ln ln
1
1ln ln
1
ln ln
ss
s
s
s
s s
HP
Q
QN
N
N Q
1500
873188 073ln ln 967
1873500
sH
= 1A = 073
= B =188
February 1 2012 32
transformation of the axis
Gumbel distribution
y = 07234x + 1882
R2 = 09871
0
2
4
6
8
10
0 2 4 6 8 10Gumbel Reduced variable
Sto
rm h
eig
ht
Hs
s
ln ln s
s s
NG
N Q
Ns = 873 storms per year
Qs G
110
1100
11000
110000
677
907
1138
1368
Figure Error No text of specified style in document-1 Storm exceedance on basis of Gumbel
10 100
February 1 2012 33
Weibull distribution
exp ssHQ
February 1 2012 34
determination of the reduced variable
1
1
ln
ln
1ln
ss
ss
ss
ss
WAH B
HQ
HQ
Q H
1
lnW Q
Three variables
and
So iteration is needed
February 1 2012 35
calculation for Weibull
alfa= 124
150 cumul P Q ln(Qs) -ln(H) Qs W
150 175 384 384 021993 078007 422098 -056 6810 032522
175 200 381 765 043814 056186 389284 -069 4905 064136
200 225 266 1031 059049 040951 357655 -081 3575 091261
225 250 157 1188 068041 031959 332863 -092 2790 111202
250 275 148 1336 076518 023482 302042 -101 2050 134858
275 300 111 1447 082875 017125 270471 -11 1495 158094
300 325 81 1528 087514 012486 238876 -118 1090 180552
325 350 63 1591 091123 008877 204769 -125 775 204065
350 375 31 1622 092898 007102 182455 -132 620 219099
375 400 32 1654 094731 005269 152606 -139 460 238832
400 425 23 1677 096048 003952 123837 -145 345 257486
425 450 11 1688 096678 003322 106471 -15 290 268590
450 475 20 1708 097824 002176 064185 -156 190 295184
475 500 9 1717 098339 001661 037156 -161 145 311883
500 525 7 1724 098740 001260 009531 -166 110 328731
525 550 9 1733 099255 000745 -043078 -17 065 360263
550 575 8 1741 099714 000286 -138629 -175 025 415922
575 600 5 1746 1 0 NUM -179 000 DIV0
1746
20 year 873 085586
-104906
099524
-07849
541 beta 116842
gamma 122575
Hs for condition 1 500 1028785 911838
1
lnssH Q
1
ln sss
s
QH
N
1124
1500
1500122 117 ln
873
122 117 675
912
sH
m
February 1 2012 36
Weibull exceedance graph
Weibull distribution
y = 11573x + 12497
R2 = 09905
0
2
4
6
8
10
0 2 4 6 8 10
Weibull Reduced variable
Str
om
heig
ht
Hss
10 100 1000 10000
February 1 2012 37
Summary
HT threshold value
Exponential
Gumbel
Weibull
150 m 163 m 136 m 122 m
HT 150 200 250 300 350 400
Ns 873 596 389 194 108 53
Hs 1500 Exponential Hs 1500 Gumbel Hs 1500 Weibull
1000 969 912
1009 950 990
948 917 963
939 893 948
908 886 917
876 818 890
February 1 2012 38
What to do if only random data are available
storm exceedance
0
200
400
600
800
01110100100010000
probability per year
Hs
s
February 1 2012 39
Example of long term data
This are
Hs-classes
February 1 2012 40
Long term (continuation)
So from this last column we can conclude
100 of time H gt 0 m s
23 of time H gt 1 m s
12 of time H gt 2 m s
001 of time H gt 9 m s
0
2
4
6
8
10
12
14
1E-071E-061E-051E-041E-031E-021E-011E+00
exceedance per year
wave
he
igh
t H
s (
m)
February 1 2012 41
From probability of waves to probability of storms
Suppose a ldquostormrdquo lasts for 12 hrs
===gt 730 stormsyear
once per year storm = 100730 = 013 =gt 67 m
once per 10 year storm = 0013 =gt 94 m
once per 100 year storm = 00013 =gt 119 m
0
5
10
15
20
1 10 100 1000 10000
return period in years
Hs o
f th
e g
ive
n s
torm
February 1 2012 42
Meteorological data
bull Not of direct importance for design
bull Can be important for hindcast of wave data and storm surge
bull Extremely important for the execution of the works (workability)
February 1 2012 43
Waves from Wind (Brettschneider)
February 1 2012 44
required soil data
February 1 2012 45
in situ test methods
February 1 2012 46
During construction
bull Quarry stone
bull Concrete
bull Local Equipment
bull Labour
bull skilled
bull cost
bull availability
bull expatriates
February 1 2012 2
Type of data to be collected
bull Hydrographic data
bull bathymetry
bull tides
bull storm surges
bull waves
bull meteorological data
bull geotechnical data
bull data needed for the construction
bull construction materials
bull equipment
bull labour
February 1 2012 3
Bathymetry
bull Nautical Charts
bull reference level
bull list of symbols
bull date of production
bull Topographical maps
bull Satellite images
bull Custom made maps
bull lead and sextant
bull echosounder and GPS
February 1 2012 4
tides
bullvertical tide
bullhorizontal tide
tide tables (British admiralty)
internet (httptbonebiolscedutidesiteselhtml)
(httpeasytideukhogovuk)
(httpwwwshomfr)
(wwwgetijnl)
For horizontal tides
see hydrographic atlases
or make Delft3D computation
February 1 2012 5
storm surges
httpwwwhurricanecom
February 1 2012 6
waves measurements
February 1 2012 7
Global Wave Statistics (1)
February 1 2012 8
Global wave statistics (2)
February 1 2012 9
processed data
Atlas of the Oceans
Wind and Wave data
February 1 2012 10
ERA-40 wave atlas
httpwwwknminl
onderzkoceano
wavesera40
February 1 2012 11
wave data for North Sea
February 1 2012 12
example from Argoss (wwwwaveclimatecom)
standard histogram
February 1 2012 13
exceedance table
February 1 2012 14
exceedance graph
February 1 2012 15
comparison buoys and ship data
February 1 2012 16
Data from wwwhydrobasenet
February 1 2012 17
Sample output of Hydrobase
February 1 2012 18
Data from Hydrobase
February 1 2012 19
data from Meetpost Noordwijk
wwwgolfklimaatnl
0
50
100
150
200
250
300
350
400
450
0 200 400 600 800
time (hrs)
Hm
o (
cm
)
January 1979
February 1 2012 20
basic data
date time Hm0 accur H13 TTE3 Tm02 TH13 wave wind wind level setup
dir dir speed
cm cm cm 1 s 1 s 1 s degr degr 1 ms cm cm
19980101 0100 70 4 64 6 39 49 261 210 60 -27 27 222224000
19980101 0400 72 4 65 8 36 45 264 210 70 91 24 222224000
19980101 0700 62 4 56 8 36 46 258 200 80 58 11 222224000
19980101 1000 93 5 85 11 40 48 234 190 90 -31 6 222224000
19980101 1300 110 5 102 14 44 51 230 200 90 -83 -5 222224000
19980101 1600 162 7 148 17 42 52 230 200 120 43 -12 222224000
19980101 1900 132 6 121 11 40 48 224 190 130 40 -37 222224000
19980101 2200 205 8 190 18 51 61 220 190 170 -39 -33 222224000
19980102 0100 247 10 230 37 56 68 229 190 170 -114 -57 222224000
19980102 0400 275 11 255 40 55 68 236 210 160 -1 -1 222224000
19980102 0700 208 8 193 20 50 63 234 200 140 -2 -72 222224000
19980102 1000 142 6 132 14 47 59 227 190 120 -59 -13 222224000
19980102 1300 130 6 120 14 50 64 223 160 110 -97 -22 222224000
19980102 1600 117 5 108 13 43 53 213 170 100 73 87 222224000
19980102 1900 91 5 84 10 39 49 232 210 100 152 58 222224000
19980102 2200 243 10 226 22 52 62 267 280 150 119 118 222224000
19980103 0100 287 12 269 32 59 70 269 260 110 25 73 222224000
19980103 0400 240 10 224 21 55 66 265 230 90 28 60 222224000
19980103 0700 177 7 163 13 46 56 245 200 130 122 37 222224000
19980103 1000 179 7 165 16 47 56 223 180 170 -30 3 222224000
19980103 1300 285 12 266 35 58 70 230 210 190 -43 16 222224000
19980103 1600 341 15 318 56 61 73 242 250 130 -36 14 222224000
19980103 1900 342 15 319 53 60 73 246 260 170 133 20 222224000
19980103 2200 414 21 388 85 65 77 249 260 190 72 46 222224000
19980104 0100 465 21 435 228 72 88 254 260 190 40 68 222224000
19980104 0400 358 16 334 92 64 78 259 240 90 -22 18 222224000
19980104 0700 324 14 302 52 60 73 256 250 120 129 43 222224000
19980104 1000 247 10 229 33 55 69 252 220 100 34 33 222224000
February 1 2012 21
sort data in classes
Waveheight class Hs (cm)
Number of observations
P Q -ln(Q)
0 25 35 35 0000599 0999401 0000599
25 50 8260 8295 0141940 0858060 0153082 50 75 11424 19719 0337423 0662577 0411618
75 100 10004 29723 0508607 0491393 0710511
100 125 7649 37372 0639493 0360507 1020245
125 150 5563 42935 0734685 0265315 1326838
150 175 4389 47324 0809788 0190212 1659615
175 200 3167 50491 0863980 0136020 1994954
200 225 2360 52851 0904363 0095637 2347200
225 250 1671 54522 0932957 0067043 2702419
250 275 1234 55756 0954073 0045927 3080692
275 300 851 56607 0968634 0031366 3462047
300 325 556 57163 0978149 0021851 3823487
325 350 392 57555 0984856 0015144 4190168
350 375 276 57831 0989579 0010421 4563938
375 400 206 58037 0993104 0006896 4976819
400 425 136 58173 0995431 0004569 5388507
425 450 82 58255 0996834 0003166 5755400
450 475 66 58321 0997964 0002036 6196632
475 500 38 58359 0998614 0001386 6581307
500 525 30 58389 0999127 0000873 7043930
525 550 20 58409 0999470 0000530 7541769
550 575 22 58431 0999846 0000154 8778531
575 600 9 58440 1000000 0000000
58440
( )s sP P H H
( ) 1s sQ Q H H P
all data Noordwijk
y = 00151x - 05001
R2 = 09881
0
1
2
3
4
5
6
7
8
9
10
0 200 400 600Hs-l
nQ
February 1 2012 22
exceedance graph for Noordwijk
indivudual observations
0
200
400
600
800
1000
000001000001000001000001000001000001000000
exceedance
wave h
eig
ht
But what means that in a year during 01
of the time the Hs is larger than 5 m
February 1 2012 23
Peak over Threshold method
A storm is defined as a time that the wave is higher than a
certain value the height of the storm Hss is equal to the
highest observed Hs during that storm
Threshold = 15
In this period 9
storms observed
nr Hss
1 180 m
2 294 m
3 225 m
4 176 m
5 261 m
6 389 m
7 172 m
8 240 m
9 194 m
February 1 2012 24
Table with Hss classes
= 124 Wave height class
150 cumul P Q Qs W
150 175 384 384 021993 078007 6810 032522 175 200 381 765 043814 056186 4905 064136 200 225 266 1031 059049 040951 3575 091261 225 250 157 1188 068041 031959 2790 111202 250 275 148 1336 076518 023482 2050 134858 275 300 111 1447 082875 017125 1495 158094 300 325 81 1528 087514 012486 1090 180552 325 350 63 1591 091123 008877 775 204065 350 375 31 1622 092898 007102 620 219099 375 400 32 1654 094731 005269 460 238832 400 425 23 1677 096048 003952 345 257486 425 450 11 1688 096678 003322 290 268590 450 475 20 1708 097824 002176 190 295184 475 500 9 1717 098339 001661 145 311883 500 525 7 1724 098740 001260 110 328731 525 550 9 1733 099255 000745 065 360263 550 575 8 1741 099714 000286 025 415922 575 600 5 1746 1 0 000 DIV0 1746 20 year 873 Slope 085586 Intercept -104906 correlation 099524 beta 116842 gamma 122575
Hss for condition 1 10 668997
( )ss ssP P H H
1ss ssQ Q H H P
threshold 15 m
y = -07849Ln(x) + 16329
R2 = 09854
0
2
4
6
8
000010000100001000010000100000probability of exceedence
sto
rm h
eig
ht
Hss
February 1 2012 25
How to get storm exceedance
Q = probability of exceedance of a wave
Qs = probability of exceedance of a storm
s sQ N Qthreshold 15 m
y = -07849Ln(x) + 5141
R2 = 09854
0
2
4
6
8
10
001010100100010000
storm exceedence probability per year
sto
rm h
eig
ht
Hss
Statistically
nonsense
February 1 2012 26
The ldquoonce in 500 years stormrdquo
0785ln( )
10785ln 5141
500
100
ss sH Q
m
threshold 15 m
y = -07849Ln(x) + 5141
R2 = 09854
0
2
4
6
8
10
001010100100010000
storm exceedence probability per year
sto
rm h
eig
ht
Hss
February 1 2012 27
Using the Gumbel distribution
exp exp ssHP
February 1 2012 28
determination of and
ln exp
1ln ln
ss
ss
ssss
GAH B
HP
HP H
1ln lnG
P
Perform linear regression
for G = A Hss - B
February 1 2012 29
data for calculation of Gumbel 150 cumul P Q ln(Qs) -ln(H) Qs G
150 175 384 384 021993 078007 422098 -056 6810 -0415046
175 200 381 765 043814 056186 389284 -069 4905 0192121
200 225 266 1031 059049 040951 357655 -081 3575 0640938
225 250 157 1188 068041 031959 332863 -092 2790 0954366
250 275 148 1336 076518 023482 302042 -101 2050 1318085
275 300 111 1447 082875 017125 270471 -11 1495 1672191
300 325 81 1528 087514 012486 238876 -118 1090 2014645
325 350 63 1591 091123 008877 204769 -125 775 2375535
350 375 31 1622 092898 007102 182455 -132 620 2608194
375 400 32 1654 094731 005269 152606 -139 460 2916351
400 425 23 1677 096048 003952 123837 -145 345 3210883
425 450 11 1688 096678 003322 106471 -15 290 3387796
450 475 20 1708 097824 002176 064185 -156 190 3816515
475 500 9 1717 098339 001661 037156 -161 145 4089424
500 525 7 1724 098740 001260 009531 -166 110 4367707
525 550 9 1733 099255 000745 -043078 -17 065 4896399
550 575 8 1741 099714 000286 -138629 -175 025 5854211
575 600 5 1746 1 0 NUM -179 000 NUM
February 1 2012 30
Gumbel exceedance graph
Gumbel distribution
y = 07234x + 1882
R2 = 09871
0
2
4
6
8
10
0 2 4 6 8 10Gumbel Reduced variable
Sto
rm h
eig
ht
Hs
s
ssG AH B
= 1A = 0723
= B =1882
February 1 2012 31
calculation of a value
1ln ln
1ln ln
1
1ln ln
1
ln ln
ss
s
s
s
s s
HP
Q
QN
N
N Q
1500
873188 073ln ln 967
1873500
sH
= 1A = 073
= B =188
February 1 2012 32
transformation of the axis
Gumbel distribution
y = 07234x + 1882
R2 = 09871
0
2
4
6
8
10
0 2 4 6 8 10Gumbel Reduced variable
Sto
rm h
eig
ht
Hs
s
ln ln s
s s
NG
N Q
Ns = 873 storms per year
Qs G
110
1100
11000
110000
677
907
1138
1368
Figure Error No text of specified style in document-1 Storm exceedance on basis of Gumbel
10 100
February 1 2012 33
Weibull distribution
exp ssHQ
February 1 2012 34
determination of the reduced variable
1
1
ln
ln
1ln
ss
ss
ss
ss
WAH B
HQ
HQ
Q H
1
lnW Q
Three variables
and
So iteration is needed
February 1 2012 35
calculation for Weibull
alfa= 124
150 cumul P Q ln(Qs) -ln(H) Qs W
150 175 384 384 021993 078007 422098 -056 6810 032522
175 200 381 765 043814 056186 389284 -069 4905 064136
200 225 266 1031 059049 040951 357655 -081 3575 091261
225 250 157 1188 068041 031959 332863 -092 2790 111202
250 275 148 1336 076518 023482 302042 -101 2050 134858
275 300 111 1447 082875 017125 270471 -11 1495 158094
300 325 81 1528 087514 012486 238876 -118 1090 180552
325 350 63 1591 091123 008877 204769 -125 775 204065
350 375 31 1622 092898 007102 182455 -132 620 219099
375 400 32 1654 094731 005269 152606 -139 460 238832
400 425 23 1677 096048 003952 123837 -145 345 257486
425 450 11 1688 096678 003322 106471 -15 290 268590
450 475 20 1708 097824 002176 064185 -156 190 295184
475 500 9 1717 098339 001661 037156 -161 145 311883
500 525 7 1724 098740 001260 009531 -166 110 328731
525 550 9 1733 099255 000745 -043078 -17 065 360263
550 575 8 1741 099714 000286 -138629 -175 025 415922
575 600 5 1746 1 0 NUM -179 000 DIV0
1746
20 year 873 085586
-104906
099524
-07849
541 beta 116842
gamma 122575
Hs for condition 1 500 1028785 911838
1
lnssH Q
1
ln sss
s
QH
N
1124
1500
1500122 117 ln
873
122 117 675
912
sH
m
February 1 2012 36
Weibull exceedance graph
Weibull distribution
y = 11573x + 12497
R2 = 09905
0
2
4
6
8
10
0 2 4 6 8 10
Weibull Reduced variable
Str
om
heig
ht
Hss
10 100 1000 10000
February 1 2012 37
Summary
HT threshold value
Exponential
Gumbel
Weibull
150 m 163 m 136 m 122 m
HT 150 200 250 300 350 400
Ns 873 596 389 194 108 53
Hs 1500 Exponential Hs 1500 Gumbel Hs 1500 Weibull
1000 969 912
1009 950 990
948 917 963
939 893 948
908 886 917
876 818 890
February 1 2012 38
What to do if only random data are available
storm exceedance
0
200
400
600
800
01110100100010000
probability per year
Hs
s
February 1 2012 39
Example of long term data
This are
Hs-classes
February 1 2012 40
Long term (continuation)
So from this last column we can conclude
100 of time H gt 0 m s
23 of time H gt 1 m s
12 of time H gt 2 m s
001 of time H gt 9 m s
0
2
4
6
8
10
12
14
1E-071E-061E-051E-041E-031E-021E-011E+00
exceedance per year
wave
he
igh
t H
s (
m)
February 1 2012 41
From probability of waves to probability of storms
Suppose a ldquostormrdquo lasts for 12 hrs
===gt 730 stormsyear
once per year storm = 100730 = 013 =gt 67 m
once per 10 year storm = 0013 =gt 94 m
once per 100 year storm = 00013 =gt 119 m
0
5
10
15
20
1 10 100 1000 10000
return period in years
Hs o
f th
e g
ive
n s
torm
February 1 2012 42
Meteorological data
bull Not of direct importance for design
bull Can be important for hindcast of wave data and storm surge
bull Extremely important for the execution of the works (workability)
February 1 2012 43
Waves from Wind (Brettschneider)
February 1 2012 44
required soil data
February 1 2012 45
in situ test methods
February 1 2012 46
During construction
bull Quarry stone
bull Concrete
bull Local Equipment
bull Labour
bull skilled
bull cost
bull availability
bull expatriates
February 1 2012 3
Bathymetry
bull Nautical Charts
bull reference level
bull list of symbols
bull date of production
bull Topographical maps
bull Satellite images
bull Custom made maps
bull lead and sextant
bull echosounder and GPS
February 1 2012 4
tides
bullvertical tide
bullhorizontal tide
tide tables (British admiralty)
internet (httptbonebiolscedutidesiteselhtml)
(httpeasytideukhogovuk)
(httpwwwshomfr)
(wwwgetijnl)
For horizontal tides
see hydrographic atlases
or make Delft3D computation
February 1 2012 5
storm surges
httpwwwhurricanecom
February 1 2012 6
waves measurements
February 1 2012 7
Global Wave Statistics (1)
February 1 2012 8
Global wave statistics (2)
February 1 2012 9
processed data
Atlas of the Oceans
Wind and Wave data
February 1 2012 10
ERA-40 wave atlas
httpwwwknminl
onderzkoceano
wavesera40
February 1 2012 11
wave data for North Sea
February 1 2012 12
example from Argoss (wwwwaveclimatecom)
standard histogram
February 1 2012 13
exceedance table
February 1 2012 14
exceedance graph
February 1 2012 15
comparison buoys and ship data
February 1 2012 16
Data from wwwhydrobasenet
February 1 2012 17
Sample output of Hydrobase
February 1 2012 18
Data from Hydrobase
February 1 2012 19
data from Meetpost Noordwijk
wwwgolfklimaatnl
0
50
100
150
200
250
300
350
400
450
0 200 400 600 800
time (hrs)
Hm
o (
cm
)
January 1979
February 1 2012 20
basic data
date time Hm0 accur H13 TTE3 Tm02 TH13 wave wind wind level setup
dir dir speed
cm cm cm 1 s 1 s 1 s degr degr 1 ms cm cm
19980101 0100 70 4 64 6 39 49 261 210 60 -27 27 222224000
19980101 0400 72 4 65 8 36 45 264 210 70 91 24 222224000
19980101 0700 62 4 56 8 36 46 258 200 80 58 11 222224000
19980101 1000 93 5 85 11 40 48 234 190 90 -31 6 222224000
19980101 1300 110 5 102 14 44 51 230 200 90 -83 -5 222224000
19980101 1600 162 7 148 17 42 52 230 200 120 43 -12 222224000
19980101 1900 132 6 121 11 40 48 224 190 130 40 -37 222224000
19980101 2200 205 8 190 18 51 61 220 190 170 -39 -33 222224000
19980102 0100 247 10 230 37 56 68 229 190 170 -114 -57 222224000
19980102 0400 275 11 255 40 55 68 236 210 160 -1 -1 222224000
19980102 0700 208 8 193 20 50 63 234 200 140 -2 -72 222224000
19980102 1000 142 6 132 14 47 59 227 190 120 -59 -13 222224000
19980102 1300 130 6 120 14 50 64 223 160 110 -97 -22 222224000
19980102 1600 117 5 108 13 43 53 213 170 100 73 87 222224000
19980102 1900 91 5 84 10 39 49 232 210 100 152 58 222224000
19980102 2200 243 10 226 22 52 62 267 280 150 119 118 222224000
19980103 0100 287 12 269 32 59 70 269 260 110 25 73 222224000
19980103 0400 240 10 224 21 55 66 265 230 90 28 60 222224000
19980103 0700 177 7 163 13 46 56 245 200 130 122 37 222224000
19980103 1000 179 7 165 16 47 56 223 180 170 -30 3 222224000
19980103 1300 285 12 266 35 58 70 230 210 190 -43 16 222224000
19980103 1600 341 15 318 56 61 73 242 250 130 -36 14 222224000
19980103 1900 342 15 319 53 60 73 246 260 170 133 20 222224000
19980103 2200 414 21 388 85 65 77 249 260 190 72 46 222224000
19980104 0100 465 21 435 228 72 88 254 260 190 40 68 222224000
19980104 0400 358 16 334 92 64 78 259 240 90 -22 18 222224000
19980104 0700 324 14 302 52 60 73 256 250 120 129 43 222224000
19980104 1000 247 10 229 33 55 69 252 220 100 34 33 222224000
February 1 2012 21
sort data in classes
Waveheight class Hs (cm)
Number of observations
P Q -ln(Q)
0 25 35 35 0000599 0999401 0000599
25 50 8260 8295 0141940 0858060 0153082 50 75 11424 19719 0337423 0662577 0411618
75 100 10004 29723 0508607 0491393 0710511
100 125 7649 37372 0639493 0360507 1020245
125 150 5563 42935 0734685 0265315 1326838
150 175 4389 47324 0809788 0190212 1659615
175 200 3167 50491 0863980 0136020 1994954
200 225 2360 52851 0904363 0095637 2347200
225 250 1671 54522 0932957 0067043 2702419
250 275 1234 55756 0954073 0045927 3080692
275 300 851 56607 0968634 0031366 3462047
300 325 556 57163 0978149 0021851 3823487
325 350 392 57555 0984856 0015144 4190168
350 375 276 57831 0989579 0010421 4563938
375 400 206 58037 0993104 0006896 4976819
400 425 136 58173 0995431 0004569 5388507
425 450 82 58255 0996834 0003166 5755400
450 475 66 58321 0997964 0002036 6196632
475 500 38 58359 0998614 0001386 6581307
500 525 30 58389 0999127 0000873 7043930
525 550 20 58409 0999470 0000530 7541769
550 575 22 58431 0999846 0000154 8778531
575 600 9 58440 1000000 0000000
58440
( )s sP P H H
( ) 1s sQ Q H H P
all data Noordwijk
y = 00151x - 05001
R2 = 09881
0
1
2
3
4
5
6
7
8
9
10
0 200 400 600Hs-l
nQ
February 1 2012 22
exceedance graph for Noordwijk
indivudual observations
0
200
400
600
800
1000
000001000001000001000001000001000001000000
exceedance
wave h
eig
ht
But what means that in a year during 01
of the time the Hs is larger than 5 m
February 1 2012 23
Peak over Threshold method
A storm is defined as a time that the wave is higher than a
certain value the height of the storm Hss is equal to the
highest observed Hs during that storm
Threshold = 15
In this period 9
storms observed
nr Hss
1 180 m
2 294 m
3 225 m
4 176 m
5 261 m
6 389 m
7 172 m
8 240 m
9 194 m
February 1 2012 24
Table with Hss classes
= 124 Wave height class
150 cumul P Q Qs W
150 175 384 384 021993 078007 6810 032522 175 200 381 765 043814 056186 4905 064136 200 225 266 1031 059049 040951 3575 091261 225 250 157 1188 068041 031959 2790 111202 250 275 148 1336 076518 023482 2050 134858 275 300 111 1447 082875 017125 1495 158094 300 325 81 1528 087514 012486 1090 180552 325 350 63 1591 091123 008877 775 204065 350 375 31 1622 092898 007102 620 219099 375 400 32 1654 094731 005269 460 238832 400 425 23 1677 096048 003952 345 257486 425 450 11 1688 096678 003322 290 268590 450 475 20 1708 097824 002176 190 295184 475 500 9 1717 098339 001661 145 311883 500 525 7 1724 098740 001260 110 328731 525 550 9 1733 099255 000745 065 360263 550 575 8 1741 099714 000286 025 415922 575 600 5 1746 1 0 000 DIV0 1746 20 year 873 Slope 085586 Intercept -104906 correlation 099524 beta 116842 gamma 122575
Hss for condition 1 10 668997
( )ss ssP P H H
1ss ssQ Q H H P
threshold 15 m
y = -07849Ln(x) + 16329
R2 = 09854
0
2
4
6
8
000010000100001000010000100000probability of exceedence
sto
rm h
eig
ht
Hss
February 1 2012 25
How to get storm exceedance
Q = probability of exceedance of a wave
Qs = probability of exceedance of a storm
s sQ N Qthreshold 15 m
y = -07849Ln(x) + 5141
R2 = 09854
0
2
4
6
8
10
001010100100010000
storm exceedence probability per year
sto
rm h
eig
ht
Hss
Statistically
nonsense
February 1 2012 26
The ldquoonce in 500 years stormrdquo
0785ln( )
10785ln 5141
500
100
ss sH Q
m
threshold 15 m
y = -07849Ln(x) + 5141
R2 = 09854
0
2
4
6
8
10
001010100100010000
storm exceedence probability per year
sto
rm h
eig
ht
Hss
February 1 2012 27
Using the Gumbel distribution
exp exp ssHP
February 1 2012 28
determination of and
ln exp
1ln ln
ss
ss
ssss
GAH B
HP
HP H
1ln lnG
P
Perform linear regression
for G = A Hss - B
February 1 2012 29
data for calculation of Gumbel 150 cumul P Q ln(Qs) -ln(H) Qs G
150 175 384 384 021993 078007 422098 -056 6810 -0415046
175 200 381 765 043814 056186 389284 -069 4905 0192121
200 225 266 1031 059049 040951 357655 -081 3575 0640938
225 250 157 1188 068041 031959 332863 -092 2790 0954366
250 275 148 1336 076518 023482 302042 -101 2050 1318085
275 300 111 1447 082875 017125 270471 -11 1495 1672191
300 325 81 1528 087514 012486 238876 -118 1090 2014645
325 350 63 1591 091123 008877 204769 -125 775 2375535
350 375 31 1622 092898 007102 182455 -132 620 2608194
375 400 32 1654 094731 005269 152606 -139 460 2916351
400 425 23 1677 096048 003952 123837 -145 345 3210883
425 450 11 1688 096678 003322 106471 -15 290 3387796
450 475 20 1708 097824 002176 064185 -156 190 3816515
475 500 9 1717 098339 001661 037156 -161 145 4089424
500 525 7 1724 098740 001260 009531 -166 110 4367707
525 550 9 1733 099255 000745 -043078 -17 065 4896399
550 575 8 1741 099714 000286 -138629 -175 025 5854211
575 600 5 1746 1 0 NUM -179 000 NUM
February 1 2012 30
Gumbel exceedance graph
Gumbel distribution
y = 07234x + 1882
R2 = 09871
0
2
4
6
8
10
0 2 4 6 8 10Gumbel Reduced variable
Sto
rm h
eig
ht
Hs
s
ssG AH B
= 1A = 0723
= B =1882
February 1 2012 31
calculation of a value
1ln ln
1ln ln
1
1ln ln
1
ln ln
ss
s
s
s
s s
HP
Q
QN
N
N Q
1500
873188 073ln ln 967
1873500
sH
= 1A = 073
= B =188
February 1 2012 32
transformation of the axis
Gumbel distribution
y = 07234x + 1882
R2 = 09871
0
2
4
6
8
10
0 2 4 6 8 10Gumbel Reduced variable
Sto
rm h
eig
ht
Hs
s
ln ln s
s s
NG
N Q
Ns = 873 storms per year
Qs G
110
1100
11000
110000
677
907
1138
1368
Figure Error No text of specified style in document-1 Storm exceedance on basis of Gumbel
10 100
February 1 2012 33
Weibull distribution
exp ssHQ
February 1 2012 34
determination of the reduced variable
1
1
ln
ln
1ln
ss
ss
ss
ss
WAH B
HQ
HQ
Q H
1
lnW Q
Three variables
and
So iteration is needed
February 1 2012 35
calculation for Weibull
alfa= 124
150 cumul P Q ln(Qs) -ln(H) Qs W
150 175 384 384 021993 078007 422098 -056 6810 032522
175 200 381 765 043814 056186 389284 -069 4905 064136
200 225 266 1031 059049 040951 357655 -081 3575 091261
225 250 157 1188 068041 031959 332863 -092 2790 111202
250 275 148 1336 076518 023482 302042 -101 2050 134858
275 300 111 1447 082875 017125 270471 -11 1495 158094
300 325 81 1528 087514 012486 238876 -118 1090 180552
325 350 63 1591 091123 008877 204769 -125 775 204065
350 375 31 1622 092898 007102 182455 -132 620 219099
375 400 32 1654 094731 005269 152606 -139 460 238832
400 425 23 1677 096048 003952 123837 -145 345 257486
425 450 11 1688 096678 003322 106471 -15 290 268590
450 475 20 1708 097824 002176 064185 -156 190 295184
475 500 9 1717 098339 001661 037156 -161 145 311883
500 525 7 1724 098740 001260 009531 -166 110 328731
525 550 9 1733 099255 000745 -043078 -17 065 360263
550 575 8 1741 099714 000286 -138629 -175 025 415922
575 600 5 1746 1 0 NUM -179 000 DIV0
1746
20 year 873 085586
-104906
099524
-07849
541 beta 116842
gamma 122575
Hs for condition 1 500 1028785 911838
1
lnssH Q
1
ln sss
s
QH
N
1124
1500
1500122 117 ln
873
122 117 675
912
sH
m
February 1 2012 36
Weibull exceedance graph
Weibull distribution
y = 11573x + 12497
R2 = 09905
0
2
4
6
8
10
0 2 4 6 8 10
Weibull Reduced variable
Str
om
heig
ht
Hss
10 100 1000 10000
February 1 2012 37
Summary
HT threshold value
Exponential
Gumbel
Weibull
150 m 163 m 136 m 122 m
HT 150 200 250 300 350 400
Ns 873 596 389 194 108 53
Hs 1500 Exponential Hs 1500 Gumbel Hs 1500 Weibull
1000 969 912
1009 950 990
948 917 963
939 893 948
908 886 917
876 818 890
February 1 2012 38
What to do if only random data are available
storm exceedance
0
200
400
600
800
01110100100010000
probability per year
Hs
s
February 1 2012 39
Example of long term data
This are
Hs-classes
February 1 2012 40
Long term (continuation)
So from this last column we can conclude
100 of time H gt 0 m s
23 of time H gt 1 m s
12 of time H gt 2 m s
001 of time H gt 9 m s
0
2
4
6
8
10
12
14
1E-071E-061E-051E-041E-031E-021E-011E+00
exceedance per year
wave
he
igh
t H
s (
m)
February 1 2012 41
From probability of waves to probability of storms
Suppose a ldquostormrdquo lasts for 12 hrs
===gt 730 stormsyear
once per year storm = 100730 = 013 =gt 67 m
once per 10 year storm = 0013 =gt 94 m
once per 100 year storm = 00013 =gt 119 m
0
5
10
15
20
1 10 100 1000 10000
return period in years
Hs o
f th
e g
ive
n s
torm
February 1 2012 42
Meteorological data
bull Not of direct importance for design
bull Can be important for hindcast of wave data and storm surge
bull Extremely important for the execution of the works (workability)
February 1 2012 43
Waves from Wind (Brettschneider)
February 1 2012 44
required soil data
February 1 2012 45
in situ test methods
February 1 2012 46
During construction
bull Quarry stone
bull Concrete
bull Local Equipment
bull Labour
bull skilled
bull cost
bull availability
bull expatriates
February 1 2012 4
tides
bullvertical tide
bullhorizontal tide
tide tables (British admiralty)
internet (httptbonebiolscedutidesiteselhtml)
(httpeasytideukhogovuk)
(httpwwwshomfr)
(wwwgetijnl)
For horizontal tides
see hydrographic atlases
or make Delft3D computation
February 1 2012 5
storm surges
httpwwwhurricanecom
February 1 2012 6
waves measurements
February 1 2012 7
Global Wave Statistics (1)
February 1 2012 8
Global wave statistics (2)
February 1 2012 9
processed data
Atlas of the Oceans
Wind and Wave data
February 1 2012 10
ERA-40 wave atlas
httpwwwknminl
onderzkoceano
wavesera40
February 1 2012 11
wave data for North Sea
February 1 2012 12
example from Argoss (wwwwaveclimatecom)
standard histogram
February 1 2012 13
exceedance table
February 1 2012 14
exceedance graph
February 1 2012 15
comparison buoys and ship data
February 1 2012 16
Data from wwwhydrobasenet
February 1 2012 17
Sample output of Hydrobase
February 1 2012 18
Data from Hydrobase
February 1 2012 19
data from Meetpost Noordwijk
wwwgolfklimaatnl
0
50
100
150
200
250
300
350
400
450
0 200 400 600 800
time (hrs)
Hm
o (
cm
)
January 1979
February 1 2012 20
basic data
date time Hm0 accur H13 TTE3 Tm02 TH13 wave wind wind level setup
dir dir speed
cm cm cm 1 s 1 s 1 s degr degr 1 ms cm cm
19980101 0100 70 4 64 6 39 49 261 210 60 -27 27 222224000
19980101 0400 72 4 65 8 36 45 264 210 70 91 24 222224000
19980101 0700 62 4 56 8 36 46 258 200 80 58 11 222224000
19980101 1000 93 5 85 11 40 48 234 190 90 -31 6 222224000
19980101 1300 110 5 102 14 44 51 230 200 90 -83 -5 222224000
19980101 1600 162 7 148 17 42 52 230 200 120 43 -12 222224000
19980101 1900 132 6 121 11 40 48 224 190 130 40 -37 222224000
19980101 2200 205 8 190 18 51 61 220 190 170 -39 -33 222224000
19980102 0100 247 10 230 37 56 68 229 190 170 -114 -57 222224000
19980102 0400 275 11 255 40 55 68 236 210 160 -1 -1 222224000
19980102 0700 208 8 193 20 50 63 234 200 140 -2 -72 222224000
19980102 1000 142 6 132 14 47 59 227 190 120 -59 -13 222224000
19980102 1300 130 6 120 14 50 64 223 160 110 -97 -22 222224000
19980102 1600 117 5 108 13 43 53 213 170 100 73 87 222224000
19980102 1900 91 5 84 10 39 49 232 210 100 152 58 222224000
19980102 2200 243 10 226 22 52 62 267 280 150 119 118 222224000
19980103 0100 287 12 269 32 59 70 269 260 110 25 73 222224000
19980103 0400 240 10 224 21 55 66 265 230 90 28 60 222224000
19980103 0700 177 7 163 13 46 56 245 200 130 122 37 222224000
19980103 1000 179 7 165 16 47 56 223 180 170 -30 3 222224000
19980103 1300 285 12 266 35 58 70 230 210 190 -43 16 222224000
19980103 1600 341 15 318 56 61 73 242 250 130 -36 14 222224000
19980103 1900 342 15 319 53 60 73 246 260 170 133 20 222224000
19980103 2200 414 21 388 85 65 77 249 260 190 72 46 222224000
19980104 0100 465 21 435 228 72 88 254 260 190 40 68 222224000
19980104 0400 358 16 334 92 64 78 259 240 90 -22 18 222224000
19980104 0700 324 14 302 52 60 73 256 250 120 129 43 222224000
19980104 1000 247 10 229 33 55 69 252 220 100 34 33 222224000
February 1 2012 21
sort data in classes
Waveheight class Hs (cm)
Number of observations
P Q -ln(Q)
0 25 35 35 0000599 0999401 0000599
25 50 8260 8295 0141940 0858060 0153082 50 75 11424 19719 0337423 0662577 0411618
75 100 10004 29723 0508607 0491393 0710511
100 125 7649 37372 0639493 0360507 1020245
125 150 5563 42935 0734685 0265315 1326838
150 175 4389 47324 0809788 0190212 1659615
175 200 3167 50491 0863980 0136020 1994954
200 225 2360 52851 0904363 0095637 2347200
225 250 1671 54522 0932957 0067043 2702419
250 275 1234 55756 0954073 0045927 3080692
275 300 851 56607 0968634 0031366 3462047
300 325 556 57163 0978149 0021851 3823487
325 350 392 57555 0984856 0015144 4190168
350 375 276 57831 0989579 0010421 4563938
375 400 206 58037 0993104 0006896 4976819
400 425 136 58173 0995431 0004569 5388507
425 450 82 58255 0996834 0003166 5755400
450 475 66 58321 0997964 0002036 6196632
475 500 38 58359 0998614 0001386 6581307
500 525 30 58389 0999127 0000873 7043930
525 550 20 58409 0999470 0000530 7541769
550 575 22 58431 0999846 0000154 8778531
575 600 9 58440 1000000 0000000
58440
( )s sP P H H
( ) 1s sQ Q H H P
all data Noordwijk
y = 00151x - 05001
R2 = 09881
0
1
2
3
4
5
6
7
8
9
10
0 200 400 600Hs-l
nQ
February 1 2012 22
exceedance graph for Noordwijk
indivudual observations
0
200
400
600
800
1000
000001000001000001000001000001000001000000
exceedance
wave h
eig
ht
But what means that in a year during 01
of the time the Hs is larger than 5 m
February 1 2012 23
Peak over Threshold method
A storm is defined as a time that the wave is higher than a
certain value the height of the storm Hss is equal to the
highest observed Hs during that storm
Threshold = 15
In this period 9
storms observed
nr Hss
1 180 m
2 294 m
3 225 m
4 176 m
5 261 m
6 389 m
7 172 m
8 240 m
9 194 m
February 1 2012 24
Table with Hss classes
= 124 Wave height class
150 cumul P Q Qs W
150 175 384 384 021993 078007 6810 032522 175 200 381 765 043814 056186 4905 064136 200 225 266 1031 059049 040951 3575 091261 225 250 157 1188 068041 031959 2790 111202 250 275 148 1336 076518 023482 2050 134858 275 300 111 1447 082875 017125 1495 158094 300 325 81 1528 087514 012486 1090 180552 325 350 63 1591 091123 008877 775 204065 350 375 31 1622 092898 007102 620 219099 375 400 32 1654 094731 005269 460 238832 400 425 23 1677 096048 003952 345 257486 425 450 11 1688 096678 003322 290 268590 450 475 20 1708 097824 002176 190 295184 475 500 9 1717 098339 001661 145 311883 500 525 7 1724 098740 001260 110 328731 525 550 9 1733 099255 000745 065 360263 550 575 8 1741 099714 000286 025 415922 575 600 5 1746 1 0 000 DIV0 1746 20 year 873 Slope 085586 Intercept -104906 correlation 099524 beta 116842 gamma 122575
Hss for condition 1 10 668997
( )ss ssP P H H
1ss ssQ Q H H P
threshold 15 m
y = -07849Ln(x) + 16329
R2 = 09854
0
2
4
6
8
000010000100001000010000100000probability of exceedence
sto
rm h
eig
ht
Hss
February 1 2012 25
How to get storm exceedance
Q = probability of exceedance of a wave
Qs = probability of exceedance of a storm
s sQ N Qthreshold 15 m
y = -07849Ln(x) + 5141
R2 = 09854
0
2
4
6
8
10
001010100100010000
storm exceedence probability per year
sto
rm h
eig
ht
Hss
Statistically
nonsense
February 1 2012 26
The ldquoonce in 500 years stormrdquo
0785ln( )
10785ln 5141
500
100
ss sH Q
m
threshold 15 m
y = -07849Ln(x) + 5141
R2 = 09854
0
2
4
6
8
10
001010100100010000
storm exceedence probability per year
sto
rm h
eig
ht
Hss
February 1 2012 27
Using the Gumbel distribution
exp exp ssHP
February 1 2012 28
determination of and
ln exp
1ln ln
ss
ss
ssss
GAH B
HP
HP H
1ln lnG
P
Perform linear regression
for G = A Hss - B
February 1 2012 29
data for calculation of Gumbel 150 cumul P Q ln(Qs) -ln(H) Qs G
150 175 384 384 021993 078007 422098 -056 6810 -0415046
175 200 381 765 043814 056186 389284 -069 4905 0192121
200 225 266 1031 059049 040951 357655 -081 3575 0640938
225 250 157 1188 068041 031959 332863 -092 2790 0954366
250 275 148 1336 076518 023482 302042 -101 2050 1318085
275 300 111 1447 082875 017125 270471 -11 1495 1672191
300 325 81 1528 087514 012486 238876 -118 1090 2014645
325 350 63 1591 091123 008877 204769 -125 775 2375535
350 375 31 1622 092898 007102 182455 -132 620 2608194
375 400 32 1654 094731 005269 152606 -139 460 2916351
400 425 23 1677 096048 003952 123837 -145 345 3210883
425 450 11 1688 096678 003322 106471 -15 290 3387796
450 475 20 1708 097824 002176 064185 -156 190 3816515
475 500 9 1717 098339 001661 037156 -161 145 4089424
500 525 7 1724 098740 001260 009531 -166 110 4367707
525 550 9 1733 099255 000745 -043078 -17 065 4896399
550 575 8 1741 099714 000286 -138629 -175 025 5854211
575 600 5 1746 1 0 NUM -179 000 NUM
February 1 2012 30
Gumbel exceedance graph
Gumbel distribution
y = 07234x + 1882
R2 = 09871
0
2
4
6
8
10
0 2 4 6 8 10Gumbel Reduced variable
Sto
rm h
eig
ht
Hs
s
ssG AH B
= 1A = 0723
= B =1882
February 1 2012 31
calculation of a value
1ln ln
1ln ln
1
1ln ln
1
ln ln
ss
s
s
s
s s
HP
Q
QN
N
N Q
1500
873188 073ln ln 967
1873500
sH
= 1A = 073
= B =188
February 1 2012 32
transformation of the axis
Gumbel distribution
y = 07234x + 1882
R2 = 09871
0
2
4
6
8
10
0 2 4 6 8 10Gumbel Reduced variable
Sto
rm h
eig
ht
Hs
s
ln ln s
s s
NG
N Q
Ns = 873 storms per year
Qs G
110
1100
11000
110000
677
907
1138
1368
Figure Error No text of specified style in document-1 Storm exceedance on basis of Gumbel
10 100
February 1 2012 33
Weibull distribution
exp ssHQ
February 1 2012 34
determination of the reduced variable
1
1
ln
ln
1ln
ss
ss
ss
ss
WAH B
HQ
HQ
Q H
1
lnW Q
Three variables
and
So iteration is needed
February 1 2012 35
calculation for Weibull
alfa= 124
150 cumul P Q ln(Qs) -ln(H) Qs W
150 175 384 384 021993 078007 422098 -056 6810 032522
175 200 381 765 043814 056186 389284 -069 4905 064136
200 225 266 1031 059049 040951 357655 -081 3575 091261
225 250 157 1188 068041 031959 332863 -092 2790 111202
250 275 148 1336 076518 023482 302042 -101 2050 134858
275 300 111 1447 082875 017125 270471 -11 1495 158094
300 325 81 1528 087514 012486 238876 -118 1090 180552
325 350 63 1591 091123 008877 204769 -125 775 204065
350 375 31 1622 092898 007102 182455 -132 620 219099
375 400 32 1654 094731 005269 152606 -139 460 238832
400 425 23 1677 096048 003952 123837 -145 345 257486
425 450 11 1688 096678 003322 106471 -15 290 268590
450 475 20 1708 097824 002176 064185 -156 190 295184
475 500 9 1717 098339 001661 037156 -161 145 311883
500 525 7 1724 098740 001260 009531 -166 110 328731
525 550 9 1733 099255 000745 -043078 -17 065 360263
550 575 8 1741 099714 000286 -138629 -175 025 415922
575 600 5 1746 1 0 NUM -179 000 DIV0
1746
20 year 873 085586
-104906
099524
-07849
541 beta 116842
gamma 122575
Hs for condition 1 500 1028785 911838
1
lnssH Q
1
ln sss
s
QH
N
1124
1500
1500122 117 ln
873
122 117 675
912
sH
m
February 1 2012 36
Weibull exceedance graph
Weibull distribution
y = 11573x + 12497
R2 = 09905
0
2
4
6
8
10
0 2 4 6 8 10
Weibull Reduced variable
Str
om
heig
ht
Hss
10 100 1000 10000
February 1 2012 37
Summary
HT threshold value
Exponential
Gumbel
Weibull
150 m 163 m 136 m 122 m
HT 150 200 250 300 350 400
Ns 873 596 389 194 108 53
Hs 1500 Exponential Hs 1500 Gumbel Hs 1500 Weibull
1000 969 912
1009 950 990
948 917 963
939 893 948
908 886 917
876 818 890
February 1 2012 38
What to do if only random data are available
storm exceedance
0
200
400
600
800
01110100100010000
probability per year
Hs
s
February 1 2012 39
Example of long term data
This are
Hs-classes
February 1 2012 40
Long term (continuation)
So from this last column we can conclude
100 of time H gt 0 m s
23 of time H gt 1 m s
12 of time H gt 2 m s
001 of time H gt 9 m s
0
2
4
6
8
10
12
14
1E-071E-061E-051E-041E-031E-021E-011E+00
exceedance per year
wave
he
igh
t H
s (
m)
February 1 2012 41
From probability of waves to probability of storms
Suppose a ldquostormrdquo lasts for 12 hrs
===gt 730 stormsyear
once per year storm = 100730 = 013 =gt 67 m
once per 10 year storm = 0013 =gt 94 m
once per 100 year storm = 00013 =gt 119 m
0
5
10
15
20
1 10 100 1000 10000
return period in years
Hs o
f th
e g
ive
n s
torm
February 1 2012 42
Meteorological data
bull Not of direct importance for design
bull Can be important for hindcast of wave data and storm surge
bull Extremely important for the execution of the works (workability)
February 1 2012 43
Waves from Wind (Brettschneider)
February 1 2012 44
required soil data
February 1 2012 45
in situ test methods
February 1 2012 46
During construction
bull Quarry stone
bull Concrete
bull Local Equipment
bull Labour
bull skilled
bull cost
bull availability
bull expatriates
February 1 2012 5
storm surges
httpwwwhurricanecom
February 1 2012 6
waves measurements
February 1 2012 7
Global Wave Statistics (1)
February 1 2012 8
Global wave statistics (2)
February 1 2012 9
processed data
Atlas of the Oceans
Wind and Wave data
February 1 2012 10
ERA-40 wave atlas
httpwwwknminl
onderzkoceano
wavesera40
February 1 2012 11
wave data for North Sea
February 1 2012 12
example from Argoss (wwwwaveclimatecom)
standard histogram
February 1 2012 13
exceedance table
February 1 2012 14
exceedance graph
February 1 2012 15
comparison buoys and ship data
February 1 2012 16
Data from wwwhydrobasenet
February 1 2012 17
Sample output of Hydrobase
February 1 2012 18
Data from Hydrobase
February 1 2012 19
data from Meetpost Noordwijk
wwwgolfklimaatnl
0
50
100
150
200
250
300
350
400
450
0 200 400 600 800
time (hrs)
Hm
o (
cm
)
January 1979
February 1 2012 20
basic data
date time Hm0 accur H13 TTE3 Tm02 TH13 wave wind wind level setup
dir dir speed
cm cm cm 1 s 1 s 1 s degr degr 1 ms cm cm
19980101 0100 70 4 64 6 39 49 261 210 60 -27 27 222224000
19980101 0400 72 4 65 8 36 45 264 210 70 91 24 222224000
19980101 0700 62 4 56 8 36 46 258 200 80 58 11 222224000
19980101 1000 93 5 85 11 40 48 234 190 90 -31 6 222224000
19980101 1300 110 5 102 14 44 51 230 200 90 -83 -5 222224000
19980101 1600 162 7 148 17 42 52 230 200 120 43 -12 222224000
19980101 1900 132 6 121 11 40 48 224 190 130 40 -37 222224000
19980101 2200 205 8 190 18 51 61 220 190 170 -39 -33 222224000
19980102 0100 247 10 230 37 56 68 229 190 170 -114 -57 222224000
19980102 0400 275 11 255 40 55 68 236 210 160 -1 -1 222224000
19980102 0700 208 8 193 20 50 63 234 200 140 -2 -72 222224000
19980102 1000 142 6 132 14 47 59 227 190 120 -59 -13 222224000
19980102 1300 130 6 120 14 50 64 223 160 110 -97 -22 222224000
19980102 1600 117 5 108 13 43 53 213 170 100 73 87 222224000
19980102 1900 91 5 84 10 39 49 232 210 100 152 58 222224000
19980102 2200 243 10 226 22 52 62 267 280 150 119 118 222224000
19980103 0100 287 12 269 32 59 70 269 260 110 25 73 222224000
19980103 0400 240 10 224 21 55 66 265 230 90 28 60 222224000
19980103 0700 177 7 163 13 46 56 245 200 130 122 37 222224000
19980103 1000 179 7 165 16 47 56 223 180 170 -30 3 222224000
19980103 1300 285 12 266 35 58 70 230 210 190 -43 16 222224000
19980103 1600 341 15 318 56 61 73 242 250 130 -36 14 222224000
19980103 1900 342 15 319 53 60 73 246 260 170 133 20 222224000
19980103 2200 414 21 388 85 65 77 249 260 190 72 46 222224000
19980104 0100 465 21 435 228 72 88 254 260 190 40 68 222224000
19980104 0400 358 16 334 92 64 78 259 240 90 -22 18 222224000
19980104 0700 324 14 302 52 60 73 256 250 120 129 43 222224000
19980104 1000 247 10 229 33 55 69 252 220 100 34 33 222224000
February 1 2012 21
sort data in classes
Waveheight class Hs (cm)
Number of observations
P Q -ln(Q)
0 25 35 35 0000599 0999401 0000599
25 50 8260 8295 0141940 0858060 0153082 50 75 11424 19719 0337423 0662577 0411618
75 100 10004 29723 0508607 0491393 0710511
100 125 7649 37372 0639493 0360507 1020245
125 150 5563 42935 0734685 0265315 1326838
150 175 4389 47324 0809788 0190212 1659615
175 200 3167 50491 0863980 0136020 1994954
200 225 2360 52851 0904363 0095637 2347200
225 250 1671 54522 0932957 0067043 2702419
250 275 1234 55756 0954073 0045927 3080692
275 300 851 56607 0968634 0031366 3462047
300 325 556 57163 0978149 0021851 3823487
325 350 392 57555 0984856 0015144 4190168
350 375 276 57831 0989579 0010421 4563938
375 400 206 58037 0993104 0006896 4976819
400 425 136 58173 0995431 0004569 5388507
425 450 82 58255 0996834 0003166 5755400
450 475 66 58321 0997964 0002036 6196632
475 500 38 58359 0998614 0001386 6581307
500 525 30 58389 0999127 0000873 7043930
525 550 20 58409 0999470 0000530 7541769
550 575 22 58431 0999846 0000154 8778531
575 600 9 58440 1000000 0000000
58440
( )s sP P H H
( ) 1s sQ Q H H P
all data Noordwijk
y = 00151x - 05001
R2 = 09881
0
1
2
3
4
5
6
7
8
9
10
0 200 400 600Hs-l
nQ
February 1 2012 22
exceedance graph for Noordwijk
indivudual observations
0
200
400
600
800
1000
000001000001000001000001000001000001000000
exceedance
wave h
eig
ht
But what means that in a year during 01
of the time the Hs is larger than 5 m
February 1 2012 23
Peak over Threshold method
A storm is defined as a time that the wave is higher than a
certain value the height of the storm Hss is equal to the
highest observed Hs during that storm
Threshold = 15
In this period 9
storms observed
nr Hss
1 180 m
2 294 m
3 225 m
4 176 m
5 261 m
6 389 m
7 172 m
8 240 m
9 194 m
February 1 2012 24
Table with Hss classes
= 124 Wave height class
150 cumul P Q Qs W
150 175 384 384 021993 078007 6810 032522 175 200 381 765 043814 056186 4905 064136 200 225 266 1031 059049 040951 3575 091261 225 250 157 1188 068041 031959 2790 111202 250 275 148 1336 076518 023482 2050 134858 275 300 111 1447 082875 017125 1495 158094 300 325 81 1528 087514 012486 1090 180552 325 350 63 1591 091123 008877 775 204065 350 375 31 1622 092898 007102 620 219099 375 400 32 1654 094731 005269 460 238832 400 425 23 1677 096048 003952 345 257486 425 450 11 1688 096678 003322 290 268590 450 475 20 1708 097824 002176 190 295184 475 500 9 1717 098339 001661 145 311883 500 525 7 1724 098740 001260 110 328731 525 550 9 1733 099255 000745 065 360263 550 575 8 1741 099714 000286 025 415922 575 600 5 1746 1 0 000 DIV0 1746 20 year 873 Slope 085586 Intercept -104906 correlation 099524 beta 116842 gamma 122575
Hss for condition 1 10 668997
( )ss ssP P H H
1ss ssQ Q H H P
threshold 15 m
y = -07849Ln(x) + 16329
R2 = 09854
0
2
4
6
8
000010000100001000010000100000probability of exceedence
sto
rm h
eig
ht
Hss
February 1 2012 25
How to get storm exceedance
Q = probability of exceedance of a wave
Qs = probability of exceedance of a storm
s sQ N Qthreshold 15 m
y = -07849Ln(x) + 5141
R2 = 09854
0
2
4
6
8
10
001010100100010000
storm exceedence probability per year
sto
rm h
eig
ht
Hss
Statistically
nonsense
February 1 2012 26
The ldquoonce in 500 years stormrdquo
0785ln( )
10785ln 5141
500
100
ss sH Q
m
threshold 15 m
y = -07849Ln(x) + 5141
R2 = 09854
0
2
4
6
8
10
001010100100010000
storm exceedence probability per year
sto
rm h
eig
ht
Hss
February 1 2012 27
Using the Gumbel distribution
exp exp ssHP
February 1 2012 28
determination of and
ln exp
1ln ln
ss
ss
ssss
GAH B
HP
HP H
1ln lnG
P
Perform linear regression
for G = A Hss - B
February 1 2012 29
data for calculation of Gumbel 150 cumul P Q ln(Qs) -ln(H) Qs G
150 175 384 384 021993 078007 422098 -056 6810 -0415046
175 200 381 765 043814 056186 389284 -069 4905 0192121
200 225 266 1031 059049 040951 357655 -081 3575 0640938
225 250 157 1188 068041 031959 332863 -092 2790 0954366
250 275 148 1336 076518 023482 302042 -101 2050 1318085
275 300 111 1447 082875 017125 270471 -11 1495 1672191
300 325 81 1528 087514 012486 238876 -118 1090 2014645
325 350 63 1591 091123 008877 204769 -125 775 2375535
350 375 31 1622 092898 007102 182455 -132 620 2608194
375 400 32 1654 094731 005269 152606 -139 460 2916351
400 425 23 1677 096048 003952 123837 -145 345 3210883
425 450 11 1688 096678 003322 106471 -15 290 3387796
450 475 20 1708 097824 002176 064185 -156 190 3816515
475 500 9 1717 098339 001661 037156 -161 145 4089424
500 525 7 1724 098740 001260 009531 -166 110 4367707
525 550 9 1733 099255 000745 -043078 -17 065 4896399
550 575 8 1741 099714 000286 -138629 -175 025 5854211
575 600 5 1746 1 0 NUM -179 000 NUM
February 1 2012 30
Gumbel exceedance graph
Gumbel distribution
y = 07234x + 1882
R2 = 09871
0
2
4
6
8
10
0 2 4 6 8 10Gumbel Reduced variable
Sto
rm h
eig
ht
Hs
s
ssG AH B
= 1A = 0723
= B =1882
February 1 2012 31
calculation of a value
1ln ln
1ln ln
1
1ln ln
1
ln ln
ss
s
s
s
s s
HP
Q
QN
N
N Q
1500
873188 073ln ln 967
1873500
sH
= 1A = 073
= B =188
February 1 2012 32
transformation of the axis
Gumbel distribution
y = 07234x + 1882
R2 = 09871
0
2
4
6
8
10
0 2 4 6 8 10Gumbel Reduced variable
Sto
rm h
eig
ht
Hs
s
ln ln s
s s
NG
N Q
Ns = 873 storms per year
Qs G
110
1100
11000
110000
677
907
1138
1368
Figure Error No text of specified style in document-1 Storm exceedance on basis of Gumbel
10 100
February 1 2012 33
Weibull distribution
exp ssHQ
February 1 2012 34
determination of the reduced variable
1
1
ln
ln
1ln
ss
ss
ss
ss
WAH B
HQ
HQ
Q H
1
lnW Q
Three variables
and
So iteration is needed
February 1 2012 35
calculation for Weibull
alfa= 124
150 cumul P Q ln(Qs) -ln(H) Qs W
150 175 384 384 021993 078007 422098 -056 6810 032522
175 200 381 765 043814 056186 389284 -069 4905 064136
200 225 266 1031 059049 040951 357655 -081 3575 091261
225 250 157 1188 068041 031959 332863 -092 2790 111202
250 275 148 1336 076518 023482 302042 -101 2050 134858
275 300 111 1447 082875 017125 270471 -11 1495 158094
300 325 81 1528 087514 012486 238876 -118 1090 180552
325 350 63 1591 091123 008877 204769 -125 775 204065
350 375 31 1622 092898 007102 182455 -132 620 219099
375 400 32 1654 094731 005269 152606 -139 460 238832
400 425 23 1677 096048 003952 123837 -145 345 257486
425 450 11 1688 096678 003322 106471 -15 290 268590
450 475 20 1708 097824 002176 064185 -156 190 295184
475 500 9 1717 098339 001661 037156 -161 145 311883
500 525 7 1724 098740 001260 009531 -166 110 328731
525 550 9 1733 099255 000745 -043078 -17 065 360263
550 575 8 1741 099714 000286 -138629 -175 025 415922
575 600 5 1746 1 0 NUM -179 000 DIV0
1746
20 year 873 085586
-104906
099524
-07849
541 beta 116842
gamma 122575
Hs for condition 1 500 1028785 911838
1
lnssH Q
1
ln sss
s
QH
N
1124
1500
1500122 117 ln
873
122 117 675
912
sH
m
February 1 2012 36
Weibull exceedance graph
Weibull distribution
y = 11573x + 12497
R2 = 09905
0
2
4
6
8
10
0 2 4 6 8 10
Weibull Reduced variable
Str
om
heig
ht
Hss
10 100 1000 10000
February 1 2012 37
Summary
HT threshold value
Exponential
Gumbel
Weibull
150 m 163 m 136 m 122 m
HT 150 200 250 300 350 400
Ns 873 596 389 194 108 53
Hs 1500 Exponential Hs 1500 Gumbel Hs 1500 Weibull
1000 969 912
1009 950 990
948 917 963
939 893 948
908 886 917
876 818 890
February 1 2012 38
What to do if only random data are available
storm exceedance
0
200
400
600
800
01110100100010000
probability per year
Hs
s
February 1 2012 39
Example of long term data
This are
Hs-classes
February 1 2012 40
Long term (continuation)
So from this last column we can conclude
100 of time H gt 0 m s
23 of time H gt 1 m s
12 of time H gt 2 m s
001 of time H gt 9 m s
0
2
4
6
8
10
12
14
1E-071E-061E-051E-041E-031E-021E-011E+00
exceedance per year
wave
he
igh
t H
s (
m)
February 1 2012 41
From probability of waves to probability of storms
Suppose a ldquostormrdquo lasts for 12 hrs
===gt 730 stormsyear
once per year storm = 100730 = 013 =gt 67 m
once per 10 year storm = 0013 =gt 94 m
once per 100 year storm = 00013 =gt 119 m
0
5
10
15
20
1 10 100 1000 10000
return period in years
Hs o
f th
e g
ive
n s
torm
February 1 2012 42
Meteorological data
bull Not of direct importance for design
bull Can be important for hindcast of wave data and storm surge
bull Extremely important for the execution of the works (workability)
February 1 2012 43
Waves from Wind (Brettschneider)
February 1 2012 44
required soil data
February 1 2012 45
in situ test methods
February 1 2012 46
During construction
bull Quarry stone
bull Concrete
bull Local Equipment
bull Labour
bull skilled
bull cost
bull availability
bull expatriates
February 1 2012 6
waves measurements
February 1 2012 7
Global Wave Statistics (1)
February 1 2012 8
Global wave statistics (2)
February 1 2012 9
processed data
Atlas of the Oceans
Wind and Wave data
February 1 2012 10
ERA-40 wave atlas
httpwwwknminl
onderzkoceano
wavesera40
February 1 2012 11
wave data for North Sea
February 1 2012 12
example from Argoss (wwwwaveclimatecom)
standard histogram
February 1 2012 13
exceedance table
February 1 2012 14
exceedance graph
February 1 2012 15
comparison buoys and ship data
February 1 2012 16
Data from wwwhydrobasenet
February 1 2012 17
Sample output of Hydrobase
February 1 2012 18
Data from Hydrobase
February 1 2012 19
data from Meetpost Noordwijk
wwwgolfklimaatnl
0
50
100
150
200
250
300
350
400
450
0 200 400 600 800
time (hrs)
Hm
o (
cm
)
January 1979
February 1 2012 20
basic data
date time Hm0 accur H13 TTE3 Tm02 TH13 wave wind wind level setup
dir dir speed
cm cm cm 1 s 1 s 1 s degr degr 1 ms cm cm
19980101 0100 70 4 64 6 39 49 261 210 60 -27 27 222224000
19980101 0400 72 4 65 8 36 45 264 210 70 91 24 222224000
19980101 0700 62 4 56 8 36 46 258 200 80 58 11 222224000
19980101 1000 93 5 85 11 40 48 234 190 90 -31 6 222224000
19980101 1300 110 5 102 14 44 51 230 200 90 -83 -5 222224000
19980101 1600 162 7 148 17 42 52 230 200 120 43 -12 222224000
19980101 1900 132 6 121 11 40 48 224 190 130 40 -37 222224000
19980101 2200 205 8 190 18 51 61 220 190 170 -39 -33 222224000
19980102 0100 247 10 230 37 56 68 229 190 170 -114 -57 222224000
19980102 0400 275 11 255 40 55 68 236 210 160 -1 -1 222224000
19980102 0700 208 8 193 20 50 63 234 200 140 -2 -72 222224000
19980102 1000 142 6 132 14 47 59 227 190 120 -59 -13 222224000
19980102 1300 130 6 120 14 50 64 223 160 110 -97 -22 222224000
19980102 1600 117 5 108 13 43 53 213 170 100 73 87 222224000
19980102 1900 91 5 84 10 39 49 232 210 100 152 58 222224000
19980102 2200 243 10 226 22 52 62 267 280 150 119 118 222224000
19980103 0100 287 12 269 32 59 70 269 260 110 25 73 222224000
19980103 0400 240 10 224 21 55 66 265 230 90 28 60 222224000
19980103 0700 177 7 163 13 46 56 245 200 130 122 37 222224000
19980103 1000 179 7 165 16 47 56 223 180 170 -30 3 222224000
19980103 1300 285 12 266 35 58 70 230 210 190 -43 16 222224000
19980103 1600 341 15 318 56 61 73 242 250 130 -36 14 222224000
19980103 1900 342 15 319 53 60 73 246 260 170 133 20 222224000
19980103 2200 414 21 388 85 65 77 249 260 190 72 46 222224000
19980104 0100 465 21 435 228 72 88 254 260 190 40 68 222224000
19980104 0400 358 16 334 92 64 78 259 240 90 -22 18 222224000
19980104 0700 324 14 302 52 60 73 256 250 120 129 43 222224000
19980104 1000 247 10 229 33 55 69 252 220 100 34 33 222224000
February 1 2012 21
sort data in classes
Waveheight class Hs (cm)
Number of observations
P Q -ln(Q)
0 25 35 35 0000599 0999401 0000599
25 50 8260 8295 0141940 0858060 0153082 50 75 11424 19719 0337423 0662577 0411618
75 100 10004 29723 0508607 0491393 0710511
100 125 7649 37372 0639493 0360507 1020245
125 150 5563 42935 0734685 0265315 1326838
150 175 4389 47324 0809788 0190212 1659615
175 200 3167 50491 0863980 0136020 1994954
200 225 2360 52851 0904363 0095637 2347200
225 250 1671 54522 0932957 0067043 2702419
250 275 1234 55756 0954073 0045927 3080692
275 300 851 56607 0968634 0031366 3462047
300 325 556 57163 0978149 0021851 3823487
325 350 392 57555 0984856 0015144 4190168
350 375 276 57831 0989579 0010421 4563938
375 400 206 58037 0993104 0006896 4976819
400 425 136 58173 0995431 0004569 5388507
425 450 82 58255 0996834 0003166 5755400
450 475 66 58321 0997964 0002036 6196632
475 500 38 58359 0998614 0001386 6581307
500 525 30 58389 0999127 0000873 7043930
525 550 20 58409 0999470 0000530 7541769
550 575 22 58431 0999846 0000154 8778531
575 600 9 58440 1000000 0000000
58440
( )s sP P H H
( ) 1s sQ Q H H P
all data Noordwijk
y = 00151x - 05001
R2 = 09881
0
1
2
3
4
5
6
7
8
9
10
0 200 400 600Hs-l
nQ
February 1 2012 22
exceedance graph for Noordwijk
indivudual observations
0
200
400
600
800
1000
000001000001000001000001000001000001000000
exceedance
wave h
eig
ht
But what means that in a year during 01
of the time the Hs is larger than 5 m
February 1 2012 23
Peak over Threshold method
A storm is defined as a time that the wave is higher than a
certain value the height of the storm Hss is equal to the
highest observed Hs during that storm
Threshold = 15
In this period 9
storms observed
nr Hss
1 180 m
2 294 m
3 225 m
4 176 m
5 261 m
6 389 m
7 172 m
8 240 m
9 194 m
February 1 2012 24
Table with Hss classes
= 124 Wave height class
150 cumul P Q Qs W
150 175 384 384 021993 078007 6810 032522 175 200 381 765 043814 056186 4905 064136 200 225 266 1031 059049 040951 3575 091261 225 250 157 1188 068041 031959 2790 111202 250 275 148 1336 076518 023482 2050 134858 275 300 111 1447 082875 017125 1495 158094 300 325 81 1528 087514 012486 1090 180552 325 350 63 1591 091123 008877 775 204065 350 375 31 1622 092898 007102 620 219099 375 400 32 1654 094731 005269 460 238832 400 425 23 1677 096048 003952 345 257486 425 450 11 1688 096678 003322 290 268590 450 475 20 1708 097824 002176 190 295184 475 500 9 1717 098339 001661 145 311883 500 525 7 1724 098740 001260 110 328731 525 550 9 1733 099255 000745 065 360263 550 575 8 1741 099714 000286 025 415922 575 600 5 1746 1 0 000 DIV0 1746 20 year 873 Slope 085586 Intercept -104906 correlation 099524 beta 116842 gamma 122575
Hss for condition 1 10 668997
( )ss ssP P H H
1ss ssQ Q H H P
threshold 15 m
y = -07849Ln(x) + 16329
R2 = 09854
0
2
4
6
8
000010000100001000010000100000probability of exceedence
sto
rm h
eig
ht
Hss
February 1 2012 25
How to get storm exceedance
Q = probability of exceedance of a wave
Qs = probability of exceedance of a storm
s sQ N Qthreshold 15 m
y = -07849Ln(x) + 5141
R2 = 09854
0
2
4
6
8
10
001010100100010000
storm exceedence probability per year
sto
rm h
eig
ht
Hss
Statistically
nonsense
February 1 2012 26
The ldquoonce in 500 years stormrdquo
0785ln( )
10785ln 5141
500
100
ss sH Q
m
threshold 15 m
y = -07849Ln(x) + 5141
R2 = 09854
0
2
4
6
8
10
001010100100010000
storm exceedence probability per year
sto
rm h
eig
ht
Hss
February 1 2012 27
Using the Gumbel distribution
exp exp ssHP
February 1 2012 28
determination of and
ln exp
1ln ln
ss
ss
ssss
GAH B
HP
HP H
1ln lnG
P
Perform linear regression
for G = A Hss - B
February 1 2012 29
data for calculation of Gumbel 150 cumul P Q ln(Qs) -ln(H) Qs G
150 175 384 384 021993 078007 422098 -056 6810 -0415046
175 200 381 765 043814 056186 389284 -069 4905 0192121
200 225 266 1031 059049 040951 357655 -081 3575 0640938
225 250 157 1188 068041 031959 332863 -092 2790 0954366
250 275 148 1336 076518 023482 302042 -101 2050 1318085
275 300 111 1447 082875 017125 270471 -11 1495 1672191
300 325 81 1528 087514 012486 238876 -118 1090 2014645
325 350 63 1591 091123 008877 204769 -125 775 2375535
350 375 31 1622 092898 007102 182455 -132 620 2608194
375 400 32 1654 094731 005269 152606 -139 460 2916351
400 425 23 1677 096048 003952 123837 -145 345 3210883
425 450 11 1688 096678 003322 106471 -15 290 3387796
450 475 20 1708 097824 002176 064185 -156 190 3816515
475 500 9 1717 098339 001661 037156 -161 145 4089424
500 525 7 1724 098740 001260 009531 -166 110 4367707
525 550 9 1733 099255 000745 -043078 -17 065 4896399
550 575 8 1741 099714 000286 -138629 -175 025 5854211
575 600 5 1746 1 0 NUM -179 000 NUM
February 1 2012 30
Gumbel exceedance graph
Gumbel distribution
y = 07234x + 1882
R2 = 09871
0
2
4
6
8
10
0 2 4 6 8 10Gumbel Reduced variable
Sto
rm h
eig
ht
Hs
s
ssG AH B
= 1A = 0723
= B =1882
February 1 2012 31
calculation of a value
1ln ln
1ln ln
1
1ln ln
1
ln ln
ss
s
s
s
s s
HP
Q
QN
N
N Q
1500
873188 073ln ln 967
1873500
sH
= 1A = 073
= B =188
February 1 2012 32
transformation of the axis
Gumbel distribution
y = 07234x + 1882
R2 = 09871
0
2
4
6
8
10
0 2 4 6 8 10Gumbel Reduced variable
Sto
rm h
eig
ht
Hs
s
ln ln s
s s
NG
N Q
Ns = 873 storms per year
Qs G
110
1100
11000
110000
677
907
1138
1368
Figure Error No text of specified style in document-1 Storm exceedance on basis of Gumbel
10 100
February 1 2012 33
Weibull distribution
exp ssHQ
February 1 2012 34
determination of the reduced variable
1
1
ln
ln
1ln
ss
ss
ss
ss
WAH B
HQ
HQ
Q H
1
lnW Q
Three variables
and
So iteration is needed
February 1 2012 35
calculation for Weibull
alfa= 124
150 cumul P Q ln(Qs) -ln(H) Qs W
150 175 384 384 021993 078007 422098 -056 6810 032522
175 200 381 765 043814 056186 389284 -069 4905 064136
200 225 266 1031 059049 040951 357655 -081 3575 091261
225 250 157 1188 068041 031959 332863 -092 2790 111202
250 275 148 1336 076518 023482 302042 -101 2050 134858
275 300 111 1447 082875 017125 270471 -11 1495 158094
300 325 81 1528 087514 012486 238876 -118 1090 180552
325 350 63 1591 091123 008877 204769 -125 775 204065
350 375 31 1622 092898 007102 182455 -132 620 219099
375 400 32 1654 094731 005269 152606 -139 460 238832
400 425 23 1677 096048 003952 123837 -145 345 257486
425 450 11 1688 096678 003322 106471 -15 290 268590
450 475 20 1708 097824 002176 064185 -156 190 295184
475 500 9 1717 098339 001661 037156 -161 145 311883
500 525 7 1724 098740 001260 009531 -166 110 328731
525 550 9 1733 099255 000745 -043078 -17 065 360263
550 575 8 1741 099714 000286 -138629 -175 025 415922
575 600 5 1746 1 0 NUM -179 000 DIV0
1746
20 year 873 085586
-104906
099524
-07849
541 beta 116842
gamma 122575
Hs for condition 1 500 1028785 911838
1
lnssH Q
1
ln sss
s
QH
N
1124
1500
1500122 117 ln
873
122 117 675
912
sH
m
February 1 2012 36
Weibull exceedance graph
Weibull distribution
y = 11573x + 12497
R2 = 09905
0
2
4
6
8
10
0 2 4 6 8 10
Weibull Reduced variable
Str
om
heig
ht
Hss
10 100 1000 10000
February 1 2012 37
Summary
HT threshold value
Exponential
Gumbel
Weibull
150 m 163 m 136 m 122 m
HT 150 200 250 300 350 400
Ns 873 596 389 194 108 53
Hs 1500 Exponential Hs 1500 Gumbel Hs 1500 Weibull
1000 969 912
1009 950 990
948 917 963
939 893 948
908 886 917
876 818 890
February 1 2012 38
What to do if only random data are available
storm exceedance
0
200
400
600
800
01110100100010000
probability per year
Hs
s
February 1 2012 39
Example of long term data
This are
Hs-classes
February 1 2012 40
Long term (continuation)
So from this last column we can conclude
100 of time H gt 0 m s
23 of time H gt 1 m s
12 of time H gt 2 m s
001 of time H gt 9 m s
0
2
4
6
8
10
12
14
1E-071E-061E-051E-041E-031E-021E-011E+00
exceedance per year
wave
he
igh
t H
s (
m)
February 1 2012 41
From probability of waves to probability of storms
Suppose a ldquostormrdquo lasts for 12 hrs
===gt 730 stormsyear
once per year storm = 100730 = 013 =gt 67 m
once per 10 year storm = 0013 =gt 94 m
once per 100 year storm = 00013 =gt 119 m
0
5
10
15
20
1 10 100 1000 10000
return period in years
Hs o
f th
e g
ive
n s
torm
February 1 2012 42
Meteorological data
bull Not of direct importance for design
bull Can be important for hindcast of wave data and storm surge
bull Extremely important for the execution of the works (workability)
February 1 2012 43
Waves from Wind (Brettschneider)
February 1 2012 44
required soil data
February 1 2012 45
in situ test methods
February 1 2012 46
During construction
bull Quarry stone
bull Concrete
bull Local Equipment
bull Labour
bull skilled
bull cost
bull availability
bull expatriates
February 1 2012 7
Global Wave Statistics (1)
February 1 2012 8
Global wave statistics (2)
February 1 2012 9
processed data
Atlas of the Oceans
Wind and Wave data
February 1 2012 10
ERA-40 wave atlas
httpwwwknminl
onderzkoceano
wavesera40
February 1 2012 11
wave data for North Sea
February 1 2012 12
example from Argoss (wwwwaveclimatecom)
standard histogram
February 1 2012 13
exceedance table
February 1 2012 14
exceedance graph
February 1 2012 15
comparison buoys and ship data
February 1 2012 16
Data from wwwhydrobasenet
February 1 2012 17
Sample output of Hydrobase
February 1 2012 18
Data from Hydrobase
February 1 2012 19
data from Meetpost Noordwijk
wwwgolfklimaatnl
0
50
100
150
200
250
300
350
400
450
0 200 400 600 800
time (hrs)
Hm
o (
cm
)
January 1979
February 1 2012 20
basic data
date time Hm0 accur H13 TTE3 Tm02 TH13 wave wind wind level setup
dir dir speed
cm cm cm 1 s 1 s 1 s degr degr 1 ms cm cm
19980101 0100 70 4 64 6 39 49 261 210 60 -27 27 222224000
19980101 0400 72 4 65 8 36 45 264 210 70 91 24 222224000
19980101 0700 62 4 56 8 36 46 258 200 80 58 11 222224000
19980101 1000 93 5 85 11 40 48 234 190 90 -31 6 222224000
19980101 1300 110 5 102 14 44 51 230 200 90 -83 -5 222224000
19980101 1600 162 7 148 17 42 52 230 200 120 43 -12 222224000
19980101 1900 132 6 121 11 40 48 224 190 130 40 -37 222224000
19980101 2200 205 8 190 18 51 61 220 190 170 -39 -33 222224000
19980102 0100 247 10 230 37 56 68 229 190 170 -114 -57 222224000
19980102 0400 275 11 255 40 55 68 236 210 160 -1 -1 222224000
19980102 0700 208 8 193 20 50 63 234 200 140 -2 -72 222224000
19980102 1000 142 6 132 14 47 59 227 190 120 -59 -13 222224000
19980102 1300 130 6 120 14 50 64 223 160 110 -97 -22 222224000
19980102 1600 117 5 108 13 43 53 213 170 100 73 87 222224000
19980102 1900 91 5 84 10 39 49 232 210 100 152 58 222224000
19980102 2200 243 10 226 22 52 62 267 280 150 119 118 222224000
19980103 0100 287 12 269 32 59 70 269 260 110 25 73 222224000
19980103 0400 240 10 224 21 55 66 265 230 90 28 60 222224000
19980103 0700 177 7 163 13 46 56 245 200 130 122 37 222224000
19980103 1000 179 7 165 16 47 56 223 180 170 -30 3 222224000
19980103 1300 285 12 266 35 58 70 230 210 190 -43 16 222224000
19980103 1600 341 15 318 56 61 73 242 250 130 -36 14 222224000
19980103 1900 342 15 319 53 60 73 246 260 170 133 20 222224000
19980103 2200 414 21 388 85 65 77 249 260 190 72 46 222224000
19980104 0100 465 21 435 228 72 88 254 260 190 40 68 222224000
19980104 0400 358 16 334 92 64 78 259 240 90 -22 18 222224000
19980104 0700 324 14 302 52 60 73 256 250 120 129 43 222224000
19980104 1000 247 10 229 33 55 69 252 220 100 34 33 222224000
February 1 2012 21
sort data in classes
Waveheight class Hs (cm)
Number of observations
P Q -ln(Q)
0 25 35 35 0000599 0999401 0000599
25 50 8260 8295 0141940 0858060 0153082 50 75 11424 19719 0337423 0662577 0411618
75 100 10004 29723 0508607 0491393 0710511
100 125 7649 37372 0639493 0360507 1020245
125 150 5563 42935 0734685 0265315 1326838
150 175 4389 47324 0809788 0190212 1659615
175 200 3167 50491 0863980 0136020 1994954
200 225 2360 52851 0904363 0095637 2347200
225 250 1671 54522 0932957 0067043 2702419
250 275 1234 55756 0954073 0045927 3080692
275 300 851 56607 0968634 0031366 3462047
300 325 556 57163 0978149 0021851 3823487
325 350 392 57555 0984856 0015144 4190168
350 375 276 57831 0989579 0010421 4563938
375 400 206 58037 0993104 0006896 4976819
400 425 136 58173 0995431 0004569 5388507
425 450 82 58255 0996834 0003166 5755400
450 475 66 58321 0997964 0002036 6196632
475 500 38 58359 0998614 0001386 6581307
500 525 30 58389 0999127 0000873 7043930
525 550 20 58409 0999470 0000530 7541769
550 575 22 58431 0999846 0000154 8778531
575 600 9 58440 1000000 0000000
58440
( )s sP P H H
( ) 1s sQ Q H H P
all data Noordwijk
y = 00151x - 05001
R2 = 09881
0
1
2
3
4
5
6
7
8
9
10
0 200 400 600Hs-l
nQ
February 1 2012 22
exceedance graph for Noordwijk
indivudual observations
0
200
400
600
800
1000
000001000001000001000001000001000001000000
exceedance
wave h
eig
ht
But what means that in a year during 01
of the time the Hs is larger than 5 m
February 1 2012 23
Peak over Threshold method
A storm is defined as a time that the wave is higher than a
certain value the height of the storm Hss is equal to the
highest observed Hs during that storm
Threshold = 15
In this period 9
storms observed
nr Hss
1 180 m
2 294 m
3 225 m
4 176 m
5 261 m
6 389 m
7 172 m
8 240 m
9 194 m
February 1 2012 24
Table with Hss classes
= 124 Wave height class
150 cumul P Q Qs W
150 175 384 384 021993 078007 6810 032522 175 200 381 765 043814 056186 4905 064136 200 225 266 1031 059049 040951 3575 091261 225 250 157 1188 068041 031959 2790 111202 250 275 148 1336 076518 023482 2050 134858 275 300 111 1447 082875 017125 1495 158094 300 325 81 1528 087514 012486 1090 180552 325 350 63 1591 091123 008877 775 204065 350 375 31 1622 092898 007102 620 219099 375 400 32 1654 094731 005269 460 238832 400 425 23 1677 096048 003952 345 257486 425 450 11 1688 096678 003322 290 268590 450 475 20 1708 097824 002176 190 295184 475 500 9 1717 098339 001661 145 311883 500 525 7 1724 098740 001260 110 328731 525 550 9 1733 099255 000745 065 360263 550 575 8 1741 099714 000286 025 415922 575 600 5 1746 1 0 000 DIV0 1746 20 year 873 Slope 085586 Intercept -104906 correlation 099524 beta 116842 gamma 122575
Hss for condition 1 10 668997
( )ss ssP P H H
1ss ssQ Q H H P
threshold 15 m
y = -07849Ln(x) + 16329
R2 = 09854
0
2
4
6
8
000010000100001000010000100000probability of exceedence
sto
rm h
eig
ht
Hss
February 1 2012 25
How to get storm exceedance
Q = probability of exceedance of a wave
Qs = probability of exceedance of a storm
s sQ N Qthreshold 15 m
y = -07849Ln(x) + 5141
R2 = 09854
0
2
4
6
8
10
001010100100010000
storm exceedence probability per year
sto
rm h
eig
ht
Hss
Statistically
nonsense
February 1 2012 26
The ldquoonce in 500 years stormrdquo
0785ln( )
10785ln 5141
500
100
ss sH Q
m
threshold 15 m
y = -07849Ln(x) + 5141
R2 = 09854
0
2
4
6
8
10
001010100100010000
storm exceedence probability per year
sto
rm h
eig
ht
Hss
February 1 2012 27
Using the Gumbel distribution
exp exp ssHP
February 1 2012 28
determination of and
ln exp
1ln ln
ss
ss
ssss
GAH B
HP
HP H
1ln lnG
P
Perform linear regression
for G = A Hss - B
February 1 2012 29
data for calculation of Gumbel 150 cumul P Q ln(Qs) -ln(H) Qs G
150 175 384 384 021993 078007 422098 -056 6810 -0415046
175 200 381 765 043814 056186 389284 -069 4905 0192121
200 225 266 1031 059049 040951 357655 -081 3575 0640938
225 250 157 1188 068041 031959 332863 -092 2790 0954366
250 275 148 1336 076518 023482 302042 -101 2050 1318085
275 300 111 1447 082875 017125 270471 -11 1495 1672191
300 325 81 1528 087514 012486 238876 -118 1090 2014645
325 350 63 1591 091123 008877 204769 -125 775 2375535
350 375 31 1622 092898 007102 182455 -132 620 2608194
375 400 32 1654 094731 005269 152606 -139 460 2916351
400 425 23 1677 096048 003952 123837 -145 345 3210883
425 450 11 1688 096678 003322 106471 -15 290 3387796
450 475 20 1708 097824 002176 064185 -156 190 3816515
475 500 9 1717 098339 001661 037156 -161 145 4089424
500 525 7 1724 098740 001260 009531 -166 110 4367707
525 550 9 1733 099255 000745 -043078 -17 065 4896399
550 575 8 1741 099714 000286 -138629 -175 025 5854211
575 600 5 1746 1 0 NUM -179 000 NUM
February 1 2012 30
Gumbel exceedance graph
Gumbel distribution
y = 07234x + 1882
R2 = 09871
0
2
4
6
8
10
0 2 4 6 8 10Gumbel Reduced variable
Sto
rm h
eig
ht
Hs
s
ssG AH B
= 1A = 0723
= B =1882
February 1 2012 31
calculation of a value
1ln ln
1ln ln
1
1ln ln
1
ln ln
ss
s
s
s
s s
HP
Q
QN
N
N Q
1500
873188 073ln ln 967
1873500
sH
= 1A = 073
= B =188
February 1 2012 32
transformation of the axis
Gumbel distribution
y = 07234x + 1882
R2 = 09871
0
2
4
6
8
10
0 2 4 6 8 10Gumbel Reduced variable
Sto
rm h
eig
ht
Hs
s
ln ln s
s s
NG
N Q
Ns = 873 storms per year
Qs G
110
1100
11000
110000
677
907
1138
1368
Figure Error No text of specified style in document-1 Storm exceedance on basis of Gumbel
10 100
February 1 2012 33
Weibull distribution
exp ssHQ
February 1 2012 34
determination of the reduced variable
1
1
ln
ln
1ln
ss
ss
ss
ss
WAH B
HQ
HQ
Q H
1
lnW Q
Three variables
and
So iteration is needed
February 1 2012 35
calculation for Weibull
alfa= 124
150 cumul P Q ln(Qs) -ln(H) Qs W
150 175 384 384 021993 078007 422098 -056 6810 032522
175 200 381 765 043814 056186 389284 -069 4905 064136
200 225 266 1031 059049 040951 357655 -081 3575 091261
225 250 157 1188 068041 031959 332863 -092 2790 111202
250 275 148 1336 076518 023482 302042 -101 2050 134858
275 300 111 1447 082875 017125 270471 -11 1495 158094
300 325 81 1528 087514 012486 238876 -118 1090 180552
325 350 63 1591 091123 008877 204769 -125 775 204065
350 375 31 1622 092898 007102 182455 -132 620 219099
375 400 32 1654 094731 005269 152606 -139 460 238832
400 425 23 1677 096048 003952 123837 -145 345 257486
425 450 11 1688 096678 003322 106471 -15 290 268590
450 475 20 1708 097824 002176 064185 -156 190 295184
475 500 9 1717 098339 001661 037156 -161 145 311883
500 525 7 1724 098740 001260 009531 -166 110 328731
525 550 9 1733 099255 000745 -043078 -17 065 360263
550 575 8 1741 099714 000286 -138629 -175 025 415922
575 600 5 1746 1 0 NUM -179 000 DIV0
1746
20 year 873 085586
-104906
099524
-07849
541 beta 116842
gamma 122575
Hs for condition 1 500 1028785 911838
1
lnssH Q
1
ln sss
s
QH
N
1124
1500
1500122 117 ln
873
122 117 675
912
sH
m
February 1 2012 36
Weibull exceedance graph
Weibull distribution
y = 11573x + 12497
R2 = 09905
0
2
4
6
8
10
0 2 4 6 8 10
Weibull Reduced variable
Str
om
heig
ht
Hss
10 100 1000 10000
February 1 2012 37
Summary
HT threshold value
Exponential
Gumbel
Weibull
150 m 163 m 136 m 122 m
HT 150 200 250 300 350 400
Ns 873 596 389 194 108 53
Hs 1500 Exponential Hs 1500 Gumbel Hs 1500 Weibull
1000 969 912
1009 950 990
948 917 963
939 893 948
908 886 917
876 818 890
February 1 2012 38
What to do if only random data are available
storm exceedance
0
200
400
600
800
01110100100010000
probability per year
Hs
s
February 1 2012 39
Example of long term data
This are
Hs-classes
February 1 2012 40
Long term (continuation)
So from this last column we can conclude
100 of time H gt 0 m s
23 of time H gt 1 m s
12 of time H gt 2 m s
001 of time H gt 9 m s
0
2
4
6
8
10
12
14
1E-071E-061E-051E-041E-031E-021E-011E+00
exceedance per year
wave
he
igh
t H
s (
m)
February 1 2012 41
From probability of waves to probability of storms
Suppose a ldquostormrdquo lasts for 12 hrs
===gt 730 stormsyear
once per year storm = 100730 = 013 =gt 67 m
once per 10 year storm = 0013 =gt 94 m
once per 100 year storm = 00013 =gt 119 m
0
5
10
15
20
1 10 100 1000 10000
return period in years
Hs o
f th
e g
ive
n s
torm
February 1 2012 42
Meteorological data
bull Not of direct importance for design
bull Can be important for hindcast of wave data and storm surge
bull Extremely important for the execution of the works (workability)
February 1 2012 43
Waves from Wind (Brettschneider)
February 1 2012 44
required soil data
February 1 2012 45
in situ test methods
February 1 2012 46
During construction
bull Quarry stone
bull Concrete
bull Local Equipment
bull Labour
bull skilled
bull cost
bull availability
bull expatriates
February 1 2012 8
Global wave statistics (2)
February 1 2012 9
processed data
Atlas of the Oceans
Wind and Wave data
February 1 2012 10
ERA-40 wave atlas
httpwwwknminl
onderzkoceano
wavesera40
February 1 2012 11
wave data for North Sea
February 1 2012 12
example from Argoss (wwwwaveclimatecom)
standard histogram
February 1 2012 13
exceedance table
February 1 2012 14
exceedance graph
February 1 2012 15
comparison buoys and ship data
February 1 2012 16
Data from wwwhydrobasenet
February 1 2012 17
Sample output of Hydrobase
February 1 2012 18
Data from Hydrobase
February 1 2012 19
data from Meetpost Noordwijk
wwwgolfklimaatnl
0
50
100
150
200
250
300
350
400
450
0 200 400 600 800
time (hrs)
Hm
o (
cm
)
January 1979
February 1 2012 20
basic data
date time Hm0 accur H13 TTE3 Tm02 TH13 wave wind wind level setup
dir dir speed
cm cm cm 1 s 1 s 1 s degr degr 1 ms cm cm
19980101 0100 70 4 64 6 39 49 261 210 60 -27 27 222224000
19980101 0400 72 4 65 8 36 45 264 210 70 91 24 222224000
19980101 0700 62 4 56 8 36 46 258 200 80 58 11 222224000
19980101 1000 93 5 85 11 40 48 234 190 90 -31 6 222224000
19980101 1300 110 5 102 14 44 51 230 200 90 -83 -5 222224000
19980101 1600 162 7 148 17 42 52 230 200 120 43 -12 222224000
19980101 1900 132 6 121 11 40 48 224 190 130 40 -37 222224000
19980101 2200 205 8 190 18 51 61 220 190 170 -39 -33 222224000
19980102 0100 247 10 230 37 56 68 229 190 170 -114 -57 222224000
19980102 0400 275 11 255 40 55 68 236 210 160 -1 -1 222224000
19980102 0700 208 8 193 20 50 63 234 200 140 -2 -72 222224000
19980102 1000 142 6 132 14 47 59 227 190 120 -59 -13 222224000
19980102 1300 130 6 120 14 50 64 223 160 110 -97 -22 222224000
19980102 1600 117 5 108 13 43 53 213 170 100 73 87 222224000
19980102 1900 91 5 84 10 39 49 232 210 100 152 58 222224000
19980102 2200 243 10 226 22 52 62 267 280 150 119 118 222224000
19980103 0100 287 12 269 32 59 70 269 260 110 25 73 222224000
19980103 0400 240 10 224 21 55 66 265 230 90 28 60 222224000
19980103 0700 177 7 163 13 46 56 245 200 130 122 37 222224000
19980103 1000 179 7 165 16 47 56 223 180 170 -30 3 222224000
19980103 1300 285 12 266 35 58 70 230 210 190 -43 16 222224000
19980103 1600 341 15 318 56 61 73 242 250 130 -36 14 222224000
19980103 1900 342 15 319 53 60 73 246 260 170 133 20 222224000
19980103 2200 414 21 388 85 65 77 249 260 190 72 46 222224000
19980104 0100 465 21 435 228 72 88 254 260 190 40 68 222224000
19980104 0400 358 16 334 92 64 78 259 240 90 -22 18 222224000
19980104 0700 324 14 302 52 60 73 256 250 120 129 43 222224000
19980104 1000 247 10 229 33 55 69 252 220 100 34 33 222224000
February 1 2012 21
sort data in classes
Waveheight class Hs (cm)
Number of observations
P Q -ln(Q)
0 25 35 35 0000599 0999401 0000599
25 50 8260 8295 0141940 0858060 0153082 50 75 11424 19719 0337423 0662577 0411618
75 100 10004 29723 0508607 0491393 0710511
100 125 7649 37372 0639493 0360507 1020245
125 150 5563 42935 0734685 0265315 1326838
150 175 4389 47324 0809788 0190212 1659615
175 200 3167 50491 0863980 0136020 1994954
200 225 2360 52851 0904363 0095637 2347200
225 250 1671 54522 0932957 0067043 2702419
250 275 1234 55756 0954073 0045927 3080692
275 300 851 56607 0968634 0031366 3462047
300 325 556 57163 0978149 0021851 3823487
325 350 392 57555 0984856 0015144 4190168
350 375 276 57831 0989579 0010421 4563938
375 400 206 58037 0993104 0006896 4976819
400 425 136 58173 0995431 0004569 5388507
425 450 82 58255 0996834 0003166 5755400
450 475 66 58321 0997964 0002036 6196632
475 500 38 58359 0998614 0001386 6581307
500 525 30 58389 0999127 0000873 7043930
525 550 20 58409 0999470 0000530 7541769
550 575 22 58431 0999846 0000154 8778531
575 600 9 58440 1000000 0000000
58440
( )s sP P H H
( ) 1s sQ Q H H P
all data Noordwijk
y = 00151x - 05001
R2 = 09881
0
1
2
3
4
5
6
7
8
9
10
0 200 400 600Hs-l
nQ
February 1 2012 22
exceedance graph for Noordwijk
indivudual observations
0
200
400
600
800
1000
000001000001000001000001000001000001000000
exceedance
wave h
eig
ht
But what means that in a year during 01
of the time the Hs is larger than 5 m
February 1 2012 23
Peak over Threshold method
A storm is defined as a time that the wave is higher than a
certain value the height of the storm Hss is equal to the
highest observed Hs during that storm
Threshold = 15
In this period 9
storms observed
nr Hss
1 180 m
2 294 m
3 225 m
4 176 m
5 261 m
6 389 m
7 172 m
8 240 m
9 194 m
February 1 2012 24
Table with Hss classes
= 124 Wave height class
150 cumul P Q Qs W
150 175 384 384 021993 078007 6810 032522 175 200 381 765 043814 056186 4905 064136 200 225 266 1031 059049 040951 3575 091261 225 250 157 1188 068041 031959 2790 111202 250 275 148 1336 076518 023482 2050 134858 275 300 111 1447 082875 017125 1495 158094 300 325 81 1528 087514 012486 1090 180552 325 350 63 1591 091123 008877 775 204065 350 375 31 1622 092898 007102 620 219099 375 400 32 1654 094731 005269 460 238832 400 425 23 1677 096048 003952 345 257486 425 450 11 1688 096678 003322 290 268590 450 475 20 1708 097824 002176 190 295184 475 500 9 1717 098339 001661 145 311883 500 525 7 1724 098740 001260 110 328731 525 550 9 1733 099255 000745 065 360263 550 575 8 1741 099714 000286 025 415922 575 600 5 1746 1 0 000 DIV0 1746 20 year 873 Slope 085586 Intercept -104906 correlation 099524 beta 116842 gamma 122575
Hss for condition 1 10 668997
( )ss ssP P H H
1ss ssQ Q H H P
threshold 15 m
y = -07849Ln(x) + 16329
R2 = 09854
0
2
4
6
8
000010000100001000010000100000probability of exceedence
sto
rm h
eig
ht
Hss
February 1 2012 25
How to get storm exceedance
Q = probability of exceedance of a wave
Qs = probability of exceedance of a storm
s sQ N Qthreshold 15 m
y = -07849Ln(x) + 5141
R2 = 09854
0
2
4
6
8
10
001010100100010000
storm exceedence probability per year
sto
rm h
eig
ht
Hss
Statistically
nonsense
February 1 2012 26
The ldquoonce in 500 years stormrdquo
0785ln( )
10785ln 5141
500
100
ss sH Q
m
threshold 15 m
y = -07849Ln(x) + 5141
R2 = 09854
0
2
4
6
8
10
001010100100010000
storm exceedence probability per year
sto
rm h
eig
ht
Hss
February 1 2012 27
Using the Gumbel distribution
exp exp ssHP
February 1 2012 28
determination of and
ln exp
1ln ln
ss
ss
ssss
GAH B
HP
HP H
1ln lnG
P
Perform linear regression
for G = A Hss - B
February 1 2012 29
data for calculation of Gumbel 150 cumul P Q ln(Qs) -ln(H) Qs G
150 175 384 384 021993 078007 422098 -056 6810 -0415046
175 200 381 765 043814 056186 389284 -069 4905 0192121
200 225 266 1031 059049 040951 357655 -081 3575 0640938
225 250 157 1188 068041 031959 332863 -092 2790 0954366
250 275 148 1336 076518 023482 302042 -101 2050 1318085
275 300 111 1447 082875 017125 270471 -11 1495 1672191
300 325 81 1528 087514 012486 238876 -118 1090 2014645
325 350 63 1591 091123 008877 204769 -125 775 2375535
350 375 31 1622 092898 007102 182455 -132 620 2608194
375 400 32 1654 094731 005269 152606 -139 460 2916351
400 425 23 1677 096048 003952 123837 -145 345 3210883
425 450 11 1688 096678 003322 106471 -15 290 3387796
450 475 20 1708 097824 002176 064185 -156 190 3816515
475 500 9 1717 098339 001661 037156 -161 145 4089424
500 525 7 1724 098740 001260 009531 -166 110 4367707
525 550 9 1733 099255 000745 -043078 -17 065 4896399
550 575 8 1741 099714 000286 -138629 -175 025 5854211
575 600 5 1746 1 0 NUM -179 000 NUM
February 1 2012 30
Gumbel exceedance graph
Gumbel distribution
y = 07234x + 1882
R2 = 09871
0
2
4
6
8
10
0 2 4 6 8 10Gumbel Reduced variable
Sto
rm h
eig
ht
Hs
s
ssG AH B
= 1A = 0723
= B =1882
February 1 2012 31
calculation of a value
1ln ln
1ln ln
1
1ln ln
1
ln ln
ss
s
s
s
s s
HP
Q
QN
N
N Q
1500
873188 073ln ln 967
1873500
sH
= 1A = 073
= B =188
February 1 2012 32
transformation of the axis
Gumbel distribution
y = 07234x + 1882
R2 = 09871
0
2
4
6
8
10
0 2 4 6 8 10Gumbel Reduced variable
Sto
rm h
eig
ht
Hs
s
ln ln s
s s
NG
N Q
Ns = 873 storms per year
Qs G
110
1100
11000
110000
677
907
1138
1368
Figure Error No text of specified style in document-1 Storm exceedance on basis of Gumbel
10 100
February 1 2012 33
Weibull distribution
exp ssHQ
February 1 2012 34
determination of the reduced variable
1
1
ln
ln
1ln
ss
ss
ss
ss
WAH B
HQ
HQ
Q H
1
lnW Q
Three variables
and
So iteration is needed
February 1 2012 35
calculation for Weibull
alfa= 124
150 cumul P Q ln(Qs) -ln(H) Qs W
150 175 384 384 021993 078007 422098 -056 6810 032522
175 200 381 765 043814 056186 389284 -069 4905 064136
200 225 266 1031 059049 040951 357655 -081 3575 091261
225 250 157 1188 068041 031959 332863 -092 2790 111202
250 275 148 1336 076518 023482 302042 -101 2050 134858
275 300 111 1447 082875 017125 270471 -11 1495 158094
300 325 81 1528 087514 012486 238876 -118 1090 180552
325 350 63 1591 091123 008877 204769 -125 775 204065
350 375 31 1622 092898 007102 182455 -132 620 219099
375 400 32 1654 094731 005269 152606 -139 460 238832
400 425 23 1677 096048 003952 123837 -145 345 257486
425 450 11 1688 096678 003322 106471 -15 290 268590
450 475 20 1708 097824 002176 064185 -156 190 295184
475 500 9 1717 098339 001661 037156 -161 145 311883
500 525 7 1724 098740 001260 009531 -166 110 328731
525 550 9 1733 099255 000745 -043078 -17 065 360263
550 575 8 1741 099714 000286 -138629 -175 025 415922
575 600 5 1746 1 0 NUM -179 000 DIV0
1746
20 year 873 085586
-104906
099524
-07849
541 beta 116842
gamma 122575
Hs for condition 1 500 1028785 911838
1
lnssH Q
1
ln sss
s
QH
N
1124
1500
1500122 117 ln
873
122 117 675
912
sH
m
February 1 2012 36
Weibull exceedance graph
Weibull distribution
y = 11573x + 12497
R2 = 09905
0
2
4
6
8
10
0 2 4 6 8 10
Weibull Reduced variable
Str
om
heig
ht
Hss
10 100 1000 10000
February 1 2012 37
Summary
HT threshold value
Exponential
Gumbel
Weibull
150 m 163 m 136 m 122 m
HT 150 200 250 300 350 400
Ns 873 596 389 194 108 53
Hs 1500 Exponential Hs 1500 Gumbel Hs 1500 Weibull
1000 969 912
1009 950 990
948 917 963
939 893 948
908 886 917
876 818 890
February 1 2012 38
What to do if only random data are available
storm exceedance
0
200
400
600
800
01110100100010000
probability per year
Hs
s
February 1 2012 39
Example of long term data
This are
Hs-classes
February 1 2012 40
Long term (continuation)
So from this last column we can conclude
100 of time H gt 0 m s
23 of time H gt 1 m s
12 of time H gt 2 m s
001 of time H gt 9 m s
0
2
4
6
8
10
12
14
1E-071E-061E-051E-041E-031E-021E-011E+00
exceedance per year
wave
he
igh
t H
s (
m)
February 1 2012 41
From probability of waves to probability of storms
Suppose a ldquostormrdquo lasts for 12 hrs
===gt 730 stormsyear
once per year storm = 100730 = 013 =gt 67 m
once per 10 year storm = 0013 =gt 94 m
once per 100 year storm = 00013 =gt 119 m
0
5
10
15
20
1 10 100 1000 10000
return period in years
Hs o
f th
e g
ive
n s
torm
February 1 2012 42
Meteorological data
bull Not of direct importance for design
bull Can be important for hindcast of wave data and storm surge
bull Extremely important for the execution of the works (workability)
February 1 2012 43
Waves from Wind (Brettschneider)
February 1 2012 44
required soil data
February 1 2012 45
in situ test methods
February 1 2012 46
During construction
bull Quarry stone
bull Concrete
bull Local Equipment
bull Labour
bull skilled
bull cost
bull availability
bull expatriates
February 1 2012 9
processed data
Atlas of the Oceans
Wind and Wave data
February 1 2012 10
ERA-40 wave atlas
httpwwwknminl
onderzkoceano
wavesera40
February 1 2012 11
wave data for North Sea
February 1 2012 12
example from Argoss (wwwwaveclimatecom)
standard histogram
February 1 2012 13
exceedance table
February 1 2012 14
exceedance graph
February 1 2012 15
comparison buoys and ship data
February 1 2012 16
Data from wwwhydrobasenet
February 1 2012 17
Sample output of Hydrobase
February 1 2012 18
Data from Hydrobase
February 1 2012 19
data from Meetpost Noordwijk
wwwgolfklimaatnl
0
50
100
150
200
250
300
350
400
450
0 200 400 600 800
time (hrs)
Hm
o (
cm
)
January 1979
February 1 2012 20
basic data
date time Hm0 accur H13 TTE3 Tm02 TH13 wave wind wind level setup
dir dir speed
cm cm cm 1 s 1 s 1 s degr degr 1 ms cm cm
19980101 0100 70 4 64 6 39 49 261 210 60 -27 27 222224000
19980101 0400 72 4 65 8 36 45 264 210 70 91 24 222224000
19980101 0700 62 4 56 8 36 46 258 200 80 58 11 222224000
19980101 1000 93 5 85 11 40 48 234 190 90 -31 6 222224000
19980101 1300 110 5 102 14 44 51 230 200 90 -83 -5 222224000
19980101 1600 162 7 148 17 42 52 230 200 120 43 -12 222224000
19980101 1900 132 6 121 11 40 48 224 190 130 40 -37 222224000
19980101 2200 205 8 190 18 51 61 220 190 170 -39 -33 222224000
19980102 0100 247 10 230 37 56 68 229 190 170 -114 -57 222224000
19980102 0400 275 11 255 40 55 68 236 210 160 -1 -1 222224000
19980102 0700 208 8 193 20 50 63 234 200 140 -2 -72 222224000
19980102 1000 142 6 132 14 47 59 227 190 120 -59 -13 222224000
19980102 1300 130 6 120 14 50 64 223 160 110 -97 -22 222224000
19980102 1600 117 5 108 13 43 53 213 170 100 73 87 222224000
19980102 1900 91 5 84 10 39 49 232 210 100 152 58 222224000
19980102 2200 243 10 226 22 52 62 267 280 150 119 118 222224000
19980103 0100 287 12 269 32 59 70 269 260 110 25 73 222224000
19980103 0400 240 10 224 21 55 66 265 230 90 28 60 222224000
19980103 0700 177 7 163 13 46 56 245 200 130 122 37 222224000
19980103 1000 179 7 165 16 47 56 223 180 170 -30 3 222224000
19980103 1300 285 12 266 35 58 70 230 210 190 -43 16 222224000
19980103 1600 341 15 318 56 61 73 242 250 130 -36 14 222224000
19980103 1900 342 15 319 53 60 73 246 260 170 133 20 222224000
19980103 2200 414 21 388 85 65 77 249 260 190 72 46 222224000
19980104 0100 465 21 435 228 72 88 254 260 190 40 68 222224000
19980104 0400 358 16 334 92 64 78 259 240 90 -22 18 222224000
19980104 0700 324 14 302 52 60 73 256 250 120 129 43 222224000
19980104 1000 247 10 229 33 55 69 252 220 100 34 33 222224000
February 1 2012 21
sort data in classes
Waveheight class Hs (cm)
Number of observations
P Q -ln(Q)
0 25 35 35 0000599 0999401 0000599
25 50 8260 8295 0141940 0858060 0153082 50 75 11424 19719 0337423 0662577 0411618
75 100 10004 29723 0508607 0491393 0710511
100 125 7649 37372 0639493 0360507 1020245
125 150 5563 42935 0734685 0265315 1326838
150 175 4389 47324 0809788 0190212 1659615
175 200 3167 50491 0863980 0136020 1994954
200 225 2360 52851 0904363 0095637 2347200
225 250 1671 54522 0932957 0067043 2702419
250 275 1234 55756 0954073 0045927 3080692
275 300 851 56607 0968634 0031366 3462047
300 325 556 57163 0978149 0021851 3823487
325 350 392 57555 0984856 0015144 4190168
350 375 276 57831 0989579 0010421 4563938
375 400 206 58037 0993104 0006896 4976819
400 425 136 58173 0995431 0004569 5388507
425 450 82 58255 0996834 0003166 5755400
450 475 66 58321 0997964 0002036 6196632
475 500 38 58359 0998614 0001386 6581307
500 525 30 58389 0999127 0000873 7043930
525 550 20 58409 0999470 0000530 7541769
550 575 22 58431 0999846 0000154 8778531
575 600 9 58440 1000000 0000000
58440
( )s sP P H H
( ) 1s sQ Q H H P
all data Noordwijk
y = 00151x - 05001
R2 = 09881
0
1
2
3
4
5
6
7
8
9
10
0 200 400 600Hs-l
nQ
February 1 2012 22
exceedance graph for Noordwijk
indivudual observations
0
200
400
600
800
1000
000001000001000001000001000001000001000000
exceedance
wave h
eig
ht
But what means that in a year during 01
of the time the Hs is larger than 5 m
February 1 2012 23
Peak over Threshold method
A storm is defined as a time that the wave is higher than a
certain value the height of the storm Hss is equal to the
highest observed Hs during that storm
Threshold = 15
In this period 9
storms observed
nr Hss
1 180 m
2 294 m
3 225 m
4 176 m
5 261 m
6 389 m
7 172 m
8 240 m
9 194 m
February 1 2012 24
Table with Hss classes
= 124 Wave height class
150 cumul P Q Qs W
150 175 384 384 021993 078007 6810 032522 175 200 381 765 043814 056186 4905 064136 200 225 266 1031 059049 040951 3575 091261 225 250 157 1188 068041 031959 2790 111202 250 275 148 1336 076518 023482 2050 134858 275 300 111 1447 082875 017125 1495 158094 300 325 81 1528 087514 012486 1090 180552 325 350 63 1591 091123 008877 775 204065 350 375 31 1622 092898 007102 620 219099 375 400 32 1654 094731 005269 460 238832 400 425 23 1677 096048 003952 345 257486 425 450 11 1688 096678 003322 290 268590 450 475 20 1708 097824 002176 190 295184 475 500 9 1717 098339 001661 145 311883 500 525 7 1724 098740 001260 110 328731 525 550 9 1733 099255 000745 065 360263 550 575 8 1741 099714 000286 025 415922 575 600 5 1746 1 0 000 DIV0 1746 20 year 873 Slope 085586 Intercept -104906 correlation 099524 beta 116842 gamma 122575
Hss for condition 1 10 668997
( )ss ssP P H H
1ss ssQ Q H H P
threshold 15 m
y = -07849Ln(x) + 16329
R2 = 09854
0
2
4
6
8
000010000100001000010000100000probability of exceedence
sto
rm h
eig
ht
Hss
February 1 2012 25
How to get storm exceedance
Q = probability of exceedance of a wave
Qs = probability of exceedance of a storm
s sQ N Qthreshold 15 m
y = -07849Ln(x) + 5141
R2 = 09854
0
2
4
6
8
10
001010100100010000
storm exceedence probability per year
sto
rm h
eig
ht
Hss
Statistically
nonsense
February 1 2012 26
The ldquoonce in 500 years stormrdquo
0785ln( )
10785ln 5141
500
100
ss sH Q
m
threshold 15 m
y = -07849Ln(x) + 5141
R2 = 09854
0
2
4
6
8
10
001010100100010000
storm exceedence probability per year
sto
rm h
eig
ht
Hss
February 1 2012 27
Using the Gumbel distribution
exp exp ssHP
February 1 2012 28
determination of and
ln exp
1ln ln
ss
ss
ssss
GAH B
HP
HP H
1ln lnG
P
Perform linear regression
for G = A Hss - B
February 1 2012 29
data for calculation of Gumbel 150 cumul P Q ln(Qs) -ln(H) Qs G
150 175 384 384 021993 078007 422098 -056 6810 -0415046
175 200 381 765 043814 056186 389284 -069 4905 0192121
200 225 266 1031 059049 040951 357655 -081 3575 0640938
225 250 157 1188 068041 031959 332863 -092 2790 0954366
250 275 148 1336 076518 023482 302042 -101 2050 1318085
275 300 111 1447 082875 017125 270471 -11 1495 1672191
300 325 81 1528 087514 012486 238876 -118 1090 2014645
325 350 63 1591 091123 008877 204769 -125 775 2375535
350 375 31 1622 092898 007102 182455 -132 620 2608194
375 400 32 1654 094731 005269 152606 -139 460 2916351
400 425 23 1677 096048 003952 123837 -145 345 3210883
425 450 11 1688 096678 003322 106471 -15 290 3387796
450 475 20 1708 097824 002176 064185 -156 190 3816515
475 500 9 1717 098339 001661 037156 -161 145 4089424
500 525 7 1724 098740 001260 009531 -166 110 4367707
525 550 9 1733 099255 000745 -043078 -17 065 4896399
550 575 8 1741 099714 000286 -138629 -175 025 5854211
575 600 5 1746 1 0 NUM -179 000 NUM
February 1 2012 30
Gumbel exceedance graph
Gumbel distribution
y = 07234x + 1882
R2 = 09871
0
2
4
6
8
10
0 2 4 6 8 10Gumbel Reduced variable
Sto
rm h
eig
ht
Hs
s
ssG AH B
= 1A = 0723
= B =1882
February 1 2012 31
calculation of a value
1ln ln
1ln ln
1
1ln ln
1
ln ln
ss
s
s
s
s s
HP
Q
QN
N
N Q
1500
873188 073ln ln 967
1873500
sH
= 1A = 073
= B =188
February 1 2012 32
transformation of the axis
Gumbel distribution
y = 07234x + 1882
R2 = 09871
0
2
4
6
8
10
0 2 4 6 8 10Gumbel Reduced variable
Sto
rm h
eig
ht
Hs
s
ln ln s
s s
NG
N Q
Ns = 873 storms per year
Qs G
110
1100
11000
110000
677
907
1138
1368
Figure Error No text of specified style in document-1 Storm exceedance on basis of Gumbel
10 100
February 1 2012 33
Weibull distribution
exp ssHQ
February 1 2012 34
determination of the reduced variable
1
1
ln
ln
1ln
ss
ss
ss
ss
WAH B
HQ
HQ
Q H
1
lnW Q
Three variables
and
So iteration is needed
February 1 2012 35
calculation for Weibull
alfa= 124
150 cumul P Q ln(Qs) -ln(H) Qs W
150 175 384 384 021993 078007 422098 -056 6810 032522
175 200 381 765 043814 056186 389284 -069 4905 064136
200 225 266 1031 059049 040951 357655 -081 3575 091261
225 250 157 1188 068041 031959 332863 -092 2790 111202
250 275 148 1336 076518 023482 302042 -101 2050 134858
275 300 111 1447 082875 017125 270471 -11 1495 158094
300 325 81 1528 087514 012486 238876 -118 1090 180552
325 350 63 1591 091123 008877 204769 -125 775 204065
350 375 31 1622 092898 007102 182455 -132 620 219099
375 400 32 1654 094731 005269 152606 -139 460 238832
400 425 23 1677 096048 003952 123837 -145 345 257486
425 450 11 1688 096678 003322 106471 -15 290 268590
450 475 20 1708 097824 002176 064185 -156 190 295184
475 500 9 1717 098339 001661 037156 -161 145 311883
500 525 7 1724 098740 001260 009531 -166 110 328731
525 550 9 1733 099255 000745 -043078 -17 065 360263
550 575 8 1741 099714 000286 -138629 -175 025 415922
575 600 5 1746 1 0 NUM -179 000 DIV0
1746
20 year 873 085586
-104906
099524
-07849
541 beta 116842
gamma 122575
Hs for condition 1 500 1028785 911838
1
lnssH Q
1
ln sss
s
QH
N
1124
1500
1500122 117 ln
873
122 117 675
912
sH
m
February 1 2012 36
Weibull exceedance graph
Weibull distribution
y = 11573x + 12497
R2 = 09905
0
2
4
6
8
10
0 2 4 6 8 10
Weibull Reduced variable
Str
om
heig
ht
Hss
10 100 1000 10000
February 1 2012 37
Summary
HT threshold value
Exponential
Gumbel
Weibull
150 m 163 m 136 m 122 m
HT 150 200 250 300 350 400
Ns 873 596 389 194 108 53
Hs 1500 Exponential Hs 1500 Gumbel Hs 1500 Weibull
1000 969 912
1009 950 990
948 917 963
939 893 948
908 886 917
876 818 890
February 1 2012 38
What to do if only random data are available
storm exceedance
0
200
400
600
800
01110100100010000
probability per year
Hs
s
February 1 2012 39
Example of long term data
This are
Hs-classes
February 1 2012 40
Long term (continuation)
So from this last column we can conclude
100 of time H gt 0 m s
23 of time H gt 1 m s
12 of time H gt 2 m s
001 of time H gt 9 m s
0
2
4
6
8
10
12
14
1E-071E-061E-051E-041E-031E-021E-011E+00
exceedance per year
wave
he
igh
t H
s (
m)
February 1 2012 41
From probability of waves to probability of storms
Suppose a ldquostormrdquo lasts for 12 hrs
===gt 730 stormsyear
once per year storm = 100730 = 013 =gt 67 m
once per 10 year storm = 0013 =gt 94 m
once per 100 year storm = 00013 =gt 119 m
0
5
10
15
20
1 10 100 1000 10000
return period in years
Hs o
f th
e g
ive
n s
torm
February 1 2012 42
Meteorological data
bull Not of direct importance for design
bull Can be important for hindcast of wave data and storm surge
bull Extremely important for the execution of the works (workability)
February 1 2012 43
Waves from Wind (Brettschneider)
February 1 2012 44
required soil data
February 1 2012 45
in situ test methods
February 1 2012 46
During construction
bull Quarry stone
bull Concrete
bull Local Equipment
bull Labour
bull skilled
bull cost
bull availability
bull expatriates
February 1 2012 10
ERA-40 wave atlas
httpwwwknminl
onderzkoceano
wavesera40
February 1 2012 11
wave data for North Sea
February 1 2012 12
example from Argoss (wwwwaveclimatecom)
standard histogram
February 1 2012 13
exceedance table
February 1 2012 14
exceedance graph
February 1 2012 15
comparison buoys and ship data
February 1 2012 16
Data from wwwhydrobasenet
February 1 2012 17
Sample output of Hydrobase
February 1 2012 18
Data from Hydrobase
February 1 2012 19
data from Meetpost Noordwijk
wwwgolfklimaatnl
0
50
100
150
200
250
300
350
400
450
0 200 400 600 800
time (hrs)
Hm
o (
cm
)
January 1979
February 1 2012 20
basic data
date time Hm0 accur H13 TTE3 Tm02 TH13 wave wind wind level setup
dir dir speed
cm cm cm 1 s 1 s 1 s degr degr 1 ms cm cm
19980101 0100 70 4 64 6 39 49 261 210 60 -27 27 222224000
19980101 0400 72 4 65 8 36 45 264 210 70 91 24 222224000
19980101 0700 62 4 56 8 36 46 258 200 80 58 11 222224000
19980101 1000 93 5 85 11 40 48 234 190 90 -31 6 222224000
19980101 1300 110 5 102 14 44 51 230 200 90 -83 -5 222224000
19980101 1600 162 7 148 17 42 52 230 200 120 43 -12 222224000
19980101 1900 132 6 121 11 40 48 224 190 130 40 -37 222224000
19980101 2200 205 8 190 18 51 61 220 190 170 -39 -33 222224000
19980102 0100 247 10 230 37 56 68 229 190 170 -114 -57 222224000
19980102 0400 275 11 255 40 55 68 236 210 160 -1 -1 222224000
19980102 0700 208 8 193 20 50 63 234 200 140 -2 -72 222224000
19980102 1000 142 6 132 14 47 59 227 190 120 -59 -13 222224000
19980102 1300 130 6 120 14 50 64 223 160 110 -97 -22 222224000
19980102 1600 117 5 108 13 43 53 213 170 100 73 87 222224000
19980102 1900 91 5 84 10 39 49 232 210 100 152 58 222224000
19980102 2200 243 10 226 22 52 62 267 280 150 119 118 222224000
19980103 0100 287 12 269 32 59 70 269 260 110 25 73 222224000
19980103 0400 240 10 224 21 55 66 265 230 90 28 60 222224000
19980103 0700 177 7 163 13 46 56 245 200 130 122 37 222224000
19980103 1000 179 7 165 16 47 56 223 180 170 -30 3 222224000
19980103 1300 285 12 266 35 58 70 230 210 190 -43 16 222224000
19980103 1600 341 15 318 56 61 73 242 250 130 -36 14 222224000
19980103 1900 342 15 319 53 60 73 246 260 170 133 20 222224000
19980103 2200 414 21 388 85 65 77 249 260 190 72 46 222224000
19980104 0100 465 21 435 228 72 88 254 260 190 40 68 222224000
19980104 0400 358 16 334 92 64 78 259 240 90 -22 18 222224000
19980104 0700 324 14 302 52 60 73 256 250 120 129 43 222224000
19980104 1000 247 10 229 33 55 69 252 220 100 34 33 222224000
February 1 2012 21
sort data in classes
Waveheight class Hs (cm)
Number of observations
P Q -ln(Q)
0 25 35 35 0000599 0999401 0000599
25 50 8260 8295 0141940 0858060 0153082 50 75 11424 19719 0337423 0662577 0411618
75 100 10004 29723 0508607 0491393 0710511
100 125 7649 37372 0639493 0360507 1020245
125 150 5563 42935 0734685 0265315 1326838
150 175 4389 47324 0809788 0190212 1659615
175 200 3167 50491 0863980 0136020 1994954
200 225 2360 52851 0904363 0095637 2347200
225 250 1671 54522 0932957 0067043 2702419
250 275 1234 55756 0954073 0045927 3080692
275 300 851 56607 0968634 0031366 3462047
300 325 556 57163 0978149 0021851 3823487
325 350 392 57555 0984856 0015144 4190168
350 375 276 57831 0989579 0010421 4563938
375 400 206 58037 0993104 0006896 4976819
400 425 136 58173 0995431 0004569 5388507
425 450 82 58255 0996834 0003166 5755400
450 475 66 58321 0997964 0002036 6196632
475 500 38 58359 0998614 0001386 6581307
500 525 30 58389 0999127 0000873 7043930
525 550 20 58409 0999470 0000530 7541769
550 575 22 58431 0999846 0000154 8778531
575 600 9 58440 1000000 0000000
58440
( )s sP P H H
( ) 1s sQ Q H H P
all data Noordwijk
y = 00151x - 05001
R2 = 09881
0
1
2
3
4
5
6
7
8
9
10
0 200 400 600Hs-l
nQ
February 1 2012 22
exceedance graph for Noordwijk
indivudual observations
0
200
400
600
800
1000
000001000001000001000001000001000001000000
exceedance
wave h
eig
ht
But what means that in a year during 01
of the time the Hs is larger than 5 m
February 1 2012 23
Peak over Threshold method
A storm is defined as a time that the wave is higher than a
certain value the height of the storm Hss is equal to the
highest observed Hs during that storm
Threshold = 15
In this period 9
storms observed
nr Hss
1 180 m
2 294 m
3 225 m
4 176 m
5 261 m
6 389 m
7 172 m
8 240 m
9 194 m
February 1 2012 24
Table with Hss classes
= 124 Wave height class
150 cumul P Q Qs W
150 175 384 384 021993 078007 6810 032522 175 200 381 765 043814 056186 4905 064136 200 225 266 1031 059049 040951 3575 091261 225 250 157 1188 068041 031959 2790 111202 250 275 148 1336 076518 023482 2050 134858 275 300 111 1447 082875 017125 1495 158094 300 325 81 1528 087514 012486 1090 180552 325 350 63 1591 091123 008877 775 204065 350 375 31 1622 092898 007102 620 219099 375 400 32 1654 094731 005269 460 238832 400 425 23 1677 096048 003952 345 257486 425 450 11 1688 096678 003322 290 268590 450 475 20 1708 097824 002176 190 295184 475 500 9 1717 098339 001661 145 311883 500 525 7 1724 098740 001260 110 328731 525 550 9 1733 099255 000745 065 360263 550 575 8 1741 099714 000286 025 415922 575 600 5 1746 1 0 000 DIV0 1746 20 year 873 Slope 085586 Intercept -104906 correlation 099524 beta 116842 gamma 122575
Hss for condition 1 10 668997
( )ss ssP P H H
1ss ssQ Q H H P
threshold 15 m
y = -07849Ln(x) + 16329
R2 = 09854
0
2
4
6
8
000010000100001000010000100000probability of exceedence
sto
rm h
eig
ht
Hss
February 1 2012 25
How to get storm exceedance
Q = probability of exceedance of a wave
Qs = probability of exceedance of a storm
s sQ N Qthreshold 15 m
y = -07849Ln(x) + 5141
R2 = 09854
0
2
4
6
8
10
001010100100010000
storm exceedence probability per year
sto
rm h
eig
ht
Hss
Statistically
nonsense
February 1 2012 26
The ldquoonce in 500 years stormrdquo
0785ln( )
10785ln 5141
500
100
ss sH Q
m
threshold 15 m
y = -07849Ln(x) + 5141
R2 = 09854
0
2
4
6
8
10
001010100100010000
storm exceedence probability per year
sto
rm h
eig
ht
Hss
February 1 2012 27
Using the Gumbel distribution
exp exp ssHP
February 1 2012 28
determination of and
ln exp
1ln ln
ss
ss
ssss
GAH B
HP
HP H
1ln lnG
P
Perform linear regression
for G = A Hss - B
February 1 2012 29
data for calculation of Gumbel 150 cumul P Q ln(Qs) -ln(H) Qs G
150 175 384 384 021993 078007 422098 -056 6810 -0415046
175 200 381 765 043814 056186 389284 -069 4905 0192121
200 225 266 1031 059049 040951 357655 -081 3575 0640938
225 250 157 1188 068041 031959 332863 -092 2790 0954366
250 275 148 1336 076518 023482 302042 -101 2050 1318085
275 300 111 1447 082875 017125 270471 -11 1495 1672191
300 325 81 1528 087514 012486 238876 -118 1090 2014645
325 350 63 1591 091123 008877 204769 -125 775 2375535
350 375 31 1622 092898 007102 182455 -132 620 2608194
375 400 32 1654 094731 005269 152606 -139 460 2916351
400 425 23 1677 096048 003952 123837 -145 345 3210883
425 450 11 1688 096678 003322 106471 -15 290 3387796
450 475 20 1708 097824 002176 064185 -156 190 3816515
475 500 9 1717 098339 001661 037156 -161 145 4089424
500 525 7 1724 098740 001260 009531 -166 110 4367707
525 550 9 1733 099255 000745 -043078 -17 065 4896399
550 575 8 1741 099714 000286 -138629 -175 025 5854211
575 600 5 1746 1 0 NUM -179 000 NUM
February 1 2012 30
Gumbel exceedance graph
Gumbel distribution
y = 07234x + 1882
R2 = 09871
0
2
4
6
8
10
0 2 4 6 8 10Gumbel Reduced variable
Sto
rm h
eig
ht
Hs
s
ssG AH B
= 1A = 0723
= B =1882
February 1 2012 31
calculation of a value
1ln ln
1ln ln
1
1ln ln
1
ln ln
ss
s
s
s
s s
HP
Q
QN
N
N Q
1500
873188 073ln ln 967
1873500
sH
= 1A = 073
= B =188
February 1 2012 32
transformation of the axis
Gumbel distribution
y = 07234x + 1882
R2 = 09871
0
2
4
6
8
10
0 2 4 6 8 10Gumbel Reduced variable
Sto
rm h
eig
ht
Hs
s
ln ln s
s s
NG
N Q
Ns = 873 storms per year
Qs G
110
1100
11000
110000
677
907
1138
1368
Figure Error No text of specified style in document-1 Storm exceedance on basis of Gumbel
10 100
February 1 2012 33
Weibull distribution
exp ssHQ
February 1 2012 34
determination of the reduced variable
1
1
ln
ln
1ln
ss
ss
ss
ss
WAH B
HQ
HQ
Q H
1
lnW Q
Three variables
and
So iteration is needed
February 1 2012 35
calculation for Weibull
alfa= 124
150 cumul P Q ln(Qs) -ln(H) Qs W
150 175 384 384 021993 078007 422098 -056 6810 032522
175 200 381 765 043814 056186 389284 -069 4905 064136
200 225 266 1031 059049 040951 357655 -081 3575 091261
225 250 157 1188 068041 031959 332863 -092 2790 111202
250 275 148 1336 076518 023482 302042 -101 2050 134858
275 300 111 1447 082875 017125 270471 -11 1495 158094
300 325 81 1528 087514 012486 238876 -118 1090 180552
325 350 63 1591 091123 008877 204769 -125 775 204065
350 375 31 1622 092898 007102 182455 -132 620 219099
375 400 32 1654 094731 005269 152606 -139 460 238832
400 425 23 1677 096048 003952 123837 -145 345 257486
425 450 11 1688 096678 003322 106471 -15 290 268590
450 475 20 1708 097824 002176 064185 -156 190 295184
475 500 9 1717 098339 001661 037156 -161 145 311883
500 525 7 1724 098740 001260 009531 -166 110 328731
525 550 9 1733 099255 000745 -043078 -17 065 360263
550 575 8 1741 099714 000286 -138629 -175 025 415922
575 600 5 1746 1 0 NUM -179 000 DIV0
1746
20 year 873 085586
-104906
099524
-07849
541 beta 116842
gamma 122575
Hs for condition 1 500 1028785 911838
1
lnssH Q
1
ln sss
s
QH
N
1124
1500
1500122 117 ln
873
122 117 675
912
sH
m
February 1 2012 36
Weibull exceedance graph
Weibull distribution
y = 11573x + 12497
R2 = 09905
0
2
4
6
8
10
0 2 4 6 8 10
Weibull Reduced variable
Str
om
heig
ht
Hss
10 100 1000 10000
February 1 2012 37
Summary
HT threshold value
Exponential
Gumbel
Weibull
150 m 163 m 136 m 122 m
HT 150 200 250 300 350 400
Ns 873 596 389 194 108 53
Hs 1500 Exponential Hs 1500 Gumbel Hs 1500 Weibull
1000 969 912
1009 950 990
948 917 963
939 893 948
908 886 917
876 818 890
February 1 2012 38
What to do if only random data are available
storm exceedance
0
200
400
600
800
01110100100010000
probability per year
Hs
s
February 1 2012 39
Example of long term data
This are
Hs-classes
February 1 2012 40
Long term (continuation)
So from this last column we can conclude
100 of time H gt 0 m s
23 of time H gt 1 m s
12 of time H gt 2 m s
001 of time H gt 9 m s
0
2
4
6
8
10
12
14
1E-071E-061E-051E-041E-031E-021E-011E+00
exceedance per year
wave
he
igh
t H
s (
m)
February 1 2012 41
From probability of waves to probability of storms
Suppose a ldquostormrdquo lasts for 12 hrs
===gt 730 stormsyear
once per year storm = 100730 = 013 =gt 67 m
once per 10 year storm = 0013 =gt 94 m
once per 100 year storm = 00013 =gt 119 m
0
5
10
15
20
1 10 100 1000 10000
return period in years
Hs o
f th
e g
ive
n s
torm
February 1 2012 42
Meteorological data
bull Not of direct importance for design
bull Can be important for hindcast of wave data and storm surge
bull Extremely important for the execution of the works (workability)
February 1 2012 43
Waves from Wind (Brettschneider)
February 1 2012 44
required soil data
February 1 2012 45
in situ test methods
February 1 2012 46
During construction
bull Quarry stone
bull Concrete
bull Local Equipment
bull Labour
bull skilled
bull cost
bull availability
bull expatriates
February 1 2012 11
wave data for North Sea
February 1 2012 12
example from Argoss (wwwwaveclimatecom)
standard histogram
February 1 2012 13
exceedance table
February 1 2012 14
exceedance graph
February 1 2012 15
comparison buoys and ship data
February 1 2012 16
Data from wwwhydrobasenet
February 1 2012 17
Sample output of Hydrobase
February 1 2012 18
Data from Hydrobase
February 1 2012 19
data from Meetpost Noordwijk
wwwgolfklimaatnl
0
50
100
150
200
250
300
350
400
450
0 200 400 600 800
time (hrs)
Hm
o (
cm
)
January 1979
February 1 2012 20
basic data
date time Hm0 accur H13 TTE3 Tm02 TH13 wave wind wind level setup
dir dir speed
cm cm cm 1 s 1 s 1 s degr degr 1 ms cm cm
19980101 0100 70 4 64 6 39 49 261 210 60 -27 27 222224000
19980101 0400 72 4 65 8 36 45 264 210 70 91 24 222224000
19980101 0700 62 4 56 8 36 46 258 200 80 58 11 222224000
19980101 1000 93 5 85 11 40 48 234 190 90 -31 6 222224000
19980101 1300 110 5 102 14 44 51 230 200 90 -83 -5 222224000
19980101 1600 162 7 148 17 42 52 230 200 120 43 -12 222224000
19980101 1900 132 6 121 11 40 48 224 190 130 40 -37 222224000
19980101 2200 205 8 190 18 51 61 220 190 170 -39 -33 222224000
19980102 0100 247 10 230 37 56 68 229 190 170 -114 -57 222224000
19980102 0400 275 11 255 40 55 68 236 210 160 -1 -1 222224000
19980102 0700 208 8 193 20 50 63 234 200 140 -2 -72 222224000
19980102 1000 142 6 132 14 47 59 227 190 120 -59 -13 222224000
19980102 1300 130 6 120 14 50 64 223 160 110 -97 -22 222224000
19980102 1600 117 5 108 13 43 53 213 170 100 73 87 222224000
19980102 1900 91 5 84 10 39 49 232 210 100 152 58 222224000
19980102 2200 243 10 226 22 52 62 267 280 150 119 118 222224000
19980103 0100 287 12 269 32 59 70 269 260 110 25 73 222224000
19980103 0400 240 10 224 21 55 66 265 230 90 28 60 222224000
19980103 0700 177 7 163 13 46 56 245 200 130 122 37 222224000
19980103 1000 179 7 165 16 47 56 223 180 170 -30 3 222224000
19980103 1300 285 12 266 35 58 70 230 210 190 -43 16 222224000
19980103 1600 341 15 318 56 61 73 242 250 130 -36 14 222224000
19980103 1900 342 15 319 53 60 73 246 260 170 133 20 222224000
19980103 2200 414 21 388 85 65 77 249 260 190 72 46 222224000
19980104 0100 465 21 435 228 72 88 254 260 190 40 68 222224000
19980104 0400 358 16 334 92 64 78 259 240 90 -22 18 222224000
19980104 0700 324 14 302 52 60 73 256 250 120 129 43 222224000
19980104 1000 247 10 229 33 55 69 252 220 100 34 33 222224000
February 1 2012 21
sort data in classes
Waveheight class Hs (cm)
Number of observations
P Q -ln(Q)
0 25 35 35 0000599 0999401 0000599
25 50 8260 8295 0141940 0858060 0153082 50 75 11424 19719 0337423 0662577 0411618
75 100 10004 29723 0508607 0491393 0710511
100 125 7649 37372 0639493 0360507 1020245
125 150 5563 42935 0734685 0265315 1326838
150 175 4389 47324 0809788 0190212 1659615
175 200 3167 50491 0863980 0136020 1994954
200 225 2360 52851 0904363 0095637 2347200
225 250 1671 54522 0932957 0067043 2702419
250 275 1234 55756 0954073 0045927 3080692
275 300 851 56607 0968634 0031366 3462047
300 325 556 57163 0978149 0021851 3823487
325 350 392 57555 0984856 0015144 4190168
350 375 276 57831 0989579 0010421 4563938
375 400 206 58037 0993104 0006896 4976819
400 425 136 58173 0995431 0004569 5388507
425 450 82 58255 0996834 0003166 5755400
450 475 66 58321 0997964 0002036 6196632
475 500 38 58359 0998614 0001386 6581307
500 525 30 58389 0999127 0000873 7043930
525 550 20 58409 0999470 0000530 7541769
550 575 22 58431 0999846 0000154 8778531
575 600 9 58440 1000000 0000000
58440
( )s sP P H H
( ) 1s sQ Q H H P
all data Noordwijk
y = 00151x - 05001
R2 = 09881
0
1
2
3
4
5
6
7
8
9
10
0 200 400 600Hs-l
nQ
February 1 2012 22
exceedance graph for Noordwijk
indivudual observations
0
200
400
600
800
1000
000001000001000001000001000001000001000000
exceedance
wave h
eig
ht
But what means that in a year during 01
of the time the Hs is larger than 5 m
February 1 2012 23
Peak over Threshold method
A storm is defined as a time that the wave is higher than a
certain value the height of the storm Hss is equal to the
highest observed Hs during that storm
Threshold = 15
In this period 9
storms observed
nr Hss
1 180 m
2 294 m
3 225 m
4 176 m
5 261 m
6 389 m
7 172 m
8 240 m
9 194 m
February 1 2012 24
Table with Hss classes
= 124 Wave height class
150 cumul P Q Qs W
150 175 384 384 021993 078007 6810 032522 175 200 381 765 043814 056186 4905 064136 200 225 266 1031 059049 040951 3575 091261 225 250 157 1188 068041 031959 2790 111202 250 275 148 1336 076518 023482 2050 134858 275 300 111 1447 082875 017125 1495 158094 300 325 81 1528 087514 012486 1090 180552 325 350 63 1591 091123 008877 775 204065 350 375 31 1622 092898 007102 620 219099 375 400 32 1654 094731 005269 460 238832 400 425 23 1677 096048 003952 345 257486 425 450 11 1688 096678 003322 290 268590 450 475 20 1708 097824 002176 190 295184 475 500 9 1717 098339 001661 145 311883 500 525 7 1724 098740 001260 110 328731 525 550 9 1733 099255 000745 065 360263 550 575 8 1741 099714 000286 025 415922 575 600 5 1746 1 0 000 DIV0 1746 20 year 873 Slope 085586 Intercept -104906 correlation 099524 beta 116842 gamma 122575
Hss for condition 1 10 668997
( )ss ssP P H H
1ss ssQ Q H H P
threshold 15 m
y = -07849Ln(x) + 16329
R2 = 09854
0
2
4
6
8
000010000100001000010000100000probability of exceedence
sto
rm h
eig
ht
Hss
February 1 2012 25
How to get storm exceedance
Q = probability of exceedance of a wave
Qs = probability of exceedance of a storm
s sQ N Qthreshold 15 m
y = -07849Ln(x) + 5141
R2 = 09854
0
2
4
6
8
10
001010100100010000
storm exceedence probability per year
sto
rm h
eig
ht
Hss
Statistically
nonsense
February 1 2012 26
The ldquoonce in 500 years stormrdquo
0785ln( )
10785ln 5141
500
100
ss sH Q
m
threshold 15 m
y = -07849Ln(x) + 5141
R2 = 09854
0
2
4
6
8
10
001010100100010000
storm exceedence probability per year
sto
rm h
eig
ht
Hss
February 1 2012 27
Using the Gumbel distribution
exp exp ssHP
February 1 2012 28
determination of and
ln exp
1ln ln
ss
ss
ssss
GAH B
HP
HP H
1ln lnG
P
Perform linear regression
for G = A Hss - B
February 1 2012 29
data for calculation of Gumbel 150 cumul P Q ln(Qs) -ln(H) Qs G
150 175 384 384 021993 078007 422098 -056 6810 -0415046
175 200 381 765 043814 056186 389284 -069 4905 0192121
200 225 266 1031 059049 040951 357655 -081 3575 0640938
225 250 157 1188 068041 031959 332863 -092 2790 0954366
250 275 148 1336 076518 023482 302042 -101 2050 1318085
275 300 111 1447 082875 017125 270471 -11 1495 1672191
300 325 81 1528 087514 012486 238876 -118 1090 2014645
325 350 63 1591 091123 008877 204769 -125 775 2375535
350 375 31 1622 092898 007102 182455 -132 620 2608194
375 400 32 1654 094731 005269 152606 -139 460 2916351
400 425 23 1677 096048 003952 123837 -145 345 3210883
425 450 11 1688 096678 003322 106471 -15 290 3387796
450 475 20 1708 097824 002176 064185 -156 190 3816515
475 500 9 1717 098339 001661 037156 -161 145 4089424
500 525 7 1724 098740 001260 009531 -166 110 4367707
525 550 9 1733 099255 000745 -043078 -17 065 4896399
550 575 8 1741 099714 000286 -138629 -175 025 5854211
575 600 5 1746 1 0 NUM -179 000 NUM
February 1 2012 30
Gumbel exceedance graph
Gumbel distribution
y = 07234x + 1882
R2 = 09871
0
2
4
6
8
10
0 2 4 6 8 10Gumbel Reduced variable
Sto
rm h
eig
ht
Hs
s
ssG AH B
= 1A = 0723
= B =1882
February 1 2012 31
calculation of a value
1ln ln
1ln ln
1
1ln ln
1
ln ln
ss
s
s
s
s s
HP
Q
QN
N
N Q
1500
873188 073ln ln 967
1873500
sH
= 1A = 073
= B =188
February 1 2012 32
transformation of the axis
Gumbel distribution
y = 07234x + 1882
R2 = 09871
0
2
4
6
8
10
0 2 4 6 8 10Gumbel Reduced variable
Sto
rm h
eig
ht
Hs
s
ln ln s
s s
NG
N Q
Ns = 873 storms per year
Qs G
110
1100
11000
110000
677
907
1138
1368
Figure Error No text of specified style in document-1 Storm exceedance on basis of Gumbel
10 100
February 1 2012 33
Weibull distribution
exp ssHQ
February 1 2012 34
determination of the reduced variable
1
1
ln
ln
1ln
ss
ss
ss
ss
WAH B
HQ
HQ
Q H
1
lnW Q
Three variables
and
So iteration is needed
February 1 2012 35
calculation for Weibull
alfa= 124
150 cumul P Q ln(Qs) -ln(H) Qs W
150 175 384 384 021993 078007 422098 -056 6810 032522
175 200 381 765 043814 056186 389284 -069 4905 064136
200 225 266 1031 059049 040951 357655 -081 3575 091261
225 250 157 1188 068041 031959 332863 -092 2790 111202
250 275 148 1336 076518 023482 302042 -101 2050 134858
275 300 111 1447 082875 017125 270471 -11 1495 158094
300 325 81 1528 087514 012486 238876 -118 1090 180552
325 350 63 1591 091123 008877 204769 -125 775 204065
350 375 31 1622 092898 007102 182455 -132 620 219099
375 400 32 1654 094731 005269 152606 -139 460 238832
400 425 23 1677 096048 003952 123837 -145 345 257486
425 450 11 1688 096678 003322 106471 -15 290 268590
450 475 20 1708 097824 002176 064185 -156 190 295184
475 500 9 1717 098339 001661 037156 -161 145 311883
500 525 7 1724 098740 001260 009531 -166 110 328731
525 550 9 1733 099255 000745 -043078 -17 065 360263
550 575 8 1741 099714 000286 -138629 -175 025 415922
575 600 5 1746 1 0 NUM -179 000 DIV0
1746
20 year 873 085586
-104906
099524
-07849
541 beta 116842
gamma 122575
Hs for condition 1 500 1028785 911838
1
lnssH Q
1
ln sss
s
QH
N
1124
1500
1500122 117 ln
873
122 117 675
912
sH
m
February 1 2012 36
Weibull exceedance graph
Weibull distribution
y = 11573x + 12497
R2 = 09905
0
2
4
6
8
10
0 2 4 6 8 10
Weibull Reduced variable
Str
om
heig
ht
Hss
10 100 1000 10000
February 1 2012 37
Summary
HT threshold value
Exponential
Gumbel
Weibull
150 m 163 m 136 m 122 m
HT 150 200 250 300 350 400
Ns 873 596 389 194 108 53
Hs 1500 Exponential Hs 1500 Gumbel Hs 1500 Weibull
1000 969 912
1009 950 990
948 917 963
939 893 948
908 886 917
876 818 890
February 1 2012 38
What to do if only random data are available
storm exceedance
0
200
400
600
800
01110100100010000
probability per year
Hs
s
February 1 2012 39
Example of long term data
This are
Hs-classes
February 1 2012 40
Long term (continuation)
So from this last column we can conclude
100 of time H gt 0 m s
23 of time H gt 1 m s
12 of time H gt 2 m s
001 of time H gt 9 m s
0
2
4
6
8
10
12
14
1E-071E-061E-051E-041E-031E-021E-011E+00
exceedance per year
wave
he
igh
t H
s (
m)
February 1 2012 41
From probability of waves to probability of storms
Suppose a ldquostormrdquo lasts for 12 hrs
===gt 730 stormsyear
once per year storm = 100730 = 013 =gt 67 m
once per 10 year storm = 0013 =gt 94 m
once per 100 year storm = 00013 =gt 119 m
0
5
10
15
20
1 10 100 1000 10000
return period in years
Hs o
f th
e g
ive
n s
torm
February 1 2012 42
Meteorological data
bull Not of direct importance for design
bull Can be important for hindcast of wave data and storm surge
bull Extremely important for the execution of the works (workability)
February 1 2012 43
Waves from Wind (Brettschneider)
February 1 2012 44
required soil data
February 1 2012 45
in situ test methods
February 1 2012 46
During construction
bull Quarry stone
bull Concrete
bull Local Equipment
bull Labour
bull skilled
bull cost
bull availability
bull expatriates
February 1 2012 12
example from Argoss (wwwwaveclimatecom)
standard histogram
February 1 2012 13
exceedance table
February 1 2012 14
exceedance graph
February 1 2012 15
comparison buoys and ship data
February 1 2012 16
Data from wwwhydrobasenet
February 1 2012 17
Sample output of Hydrobase
February 1 2012 18
Data from Hydrobase
February 1 2012 19
data from Meetpost Noordwijk
wwwgolfklimaatnl
0
50
100
150
200
250
300
350
400
450
0 200 400 600 800
time (hrs)
Hm
o (
cm
)
January 1979
February 1 2012 20
basic data
date time Hm0 accur H13 TTE3 Tm02 TH13 wave wind wind level setup
dir dir speed
cm cm cm 1 s 1 s 1 s degr degr 1 ms cm cm
19980101 0100 70 4 64 6 39 49 261 210 60 -27 27 222224000
19980101 0400 72 4 65 8 36 45 264 210 70 91 24 222224000
19980101 0700 62 4 56 8 36 46 258 200 80 58 11 222224000
19980101 1000 93 5 85 11 40 48 234 190 90 -31 6 222224000
19980101 1300 110 5 102 14 44 51 230 200 90 -83 -5 222224000
19980101 1600 162 7 148 17 42 52 230 200 120 43 -12 222224000
19980101 1900 132 6 121 11 40 48 224 190 130 40 -37 222224000
19980101 2200 205 8 190 18 51 61 220 190 170 -39 -33 222224000
19980102 0100 247 10 230 37 56 68 229 190 170 -114 -57 222224000
19980102 0400 275 11 255 40 55 68 236 210 160 -1 -1 222224000
19980102 0700 208 8 193 20 50 63 234 200 140 -2 -72 222224000
19980102 1000 142 6 132 14 47 59 227 190 120 -59 -13 222224000
19980102 1300 130 6 120 14 50 64 223 160 110 -97 -22 222224000
19980102 1600 117 5 108 13 43 53 213 170 100 73 87 222224000
19980102 1900 91 5 84 10 39 49 232 210 100 152 58 222224000
19980102 2200 243 10 226 22 52 62 267 280 150 119 118 222224000
19980103 0100 287 12 269 32 59 70 269 260 110 25 73 222224000
19980103 0400 240 10 224 21 55 66 265 230 90 28 60 222224000
19980103 0700 177 7 163 13 46 56 245 200 130 122 37 222224000
19980103 1000 179 7 165 16 47 56 223 180 170 -30 3 222224000
19980103 1300 285 12 266 35 58 70 230 210 190 -43 16 222224000
19980103 1600 341 15 318 56 61 73 242 250 130 -36 14 222224000
19980103 1900 342 15 319 53 60 73 246 260 170 133 20 222224000
19980103 2200 414 21 388 85 65 77 249 260 190 72 46 222224000
19980104 0100 465 21 435 228 72 88 254 260 190 40 68 222224000
19980104 0400 358 16 334 92 64 78 259 240 90 -22 18 222224000
19980104 0700 324 14 302 52 60 73 256 250 120 129 43 222224000
19980104 1000 247 10 229 33 55 69 252 220 100 34 33 222224000
February 1 2012 21
sort data in classes
Waveheight class Hs (cm)
Number of observations
P Q -ln(Q)
0 25 35 35 0000599 0999401 0000599
25 50 8260 8295 0141940 0858060 0153082 50 75 11424 19719 0337423 0662577 0411618
75 100 10004 29723 0508607 0491393 0710511
100 125 7649 37372 0639493 0360507 1020245
125 150 5563 42935 0734685 0265315 1326838
150 175 4389 47324 0809788 0190212 1659615
175 200 3167 50491 0863980 0136020 1994954
200 225 2360 52851 0904363 0095637 2347200
225 250 1671 54522 0932957 0067043 2702419
250 275 1234 55756 0954073 0045927 3080692
275 300 851 56607 0968634 0031366 3462047
300 325 556 57163 0978149 0021851 3823487
325 350 392 57555 0984856 0015144 4190168
350 375 276 57831 0989579 0010421 4563938
375 400 206 58037 0993104 0006896 4976819
400 425 136 58173 0995431 0004569 5388507
425 450 82 58255 0996834 0003166 5755400
450 475 66 58321 0997964 0002036 6196632
475 500 38 58359 0998614 0001386 6581307
500 525 30 58389 0999127 0000873 7043930
525 550 20 58409 0999470 0000530 7541769
550 575 22 58431 0999846 0000154 8778531
575 600 9 58440 1000000 0000000
58440
( )s sP P H H
( ) 1s sQ Q H H P
all data Noordwijk
y = 00151x - 05001
R2 = 09881
0
1
2
3
4
5
6
7
8
9
10
0 200 400 600Hs-l
nQ
February 1 2012 22
exceedance graph for Noordwijk
indivudual observations
0
200
400
600
800
1000
000001000001000001000001000001000001000000
exceedance
wave h
eig
ht
But what means that in a year during 01
of the time the Hs is larger than 5 m
February 1 2012 23
Peak over Threshold method
A storm is defined as a time that the wave is higher than a
certain value the height of the storm Hss is equal to the
highest observed Hs during that storm
Threshold = 15
In this period 9
storms observed
nr Hss
1 180 m
2 294 m
3 225 m
4 176 m
5 261 m
6 389 m
7 172 m
8 240 m
9 194 m
February 1 2012 24
Table with Hss classes
= 124 Wave height class
150 cumul P Q Qs W
150 175 384 384 021993 078007 6810 032522 175 200 381 765 043814 056186 4905 064136 200 225 266 1031 059049 040951 3575 091261 225 250 157 1188 068041 031959 2790 111202 250 275 148 1336 076518 023482 2050 134858 275 300 111 1447 082875 017125 1495 158094 300 325 81 1528 087514 012486 1090 180552 325 350 63 1591 091123 008877 775 204065 350 375 31 1622 092898 007102 620 219099 375 400 32 1654 094731 005269 460 238832 400 425 23 1677 096048 003952 345 257486 425 450 11 1688 096678 003322 290 268590 450 475 20 1708 097824 002176 190 295184 475 500 9 1717 098339 001661 145 311883 500 525 7 1724 098740 001260 110 328731 525 550 9 1733 099255 000745 065 360263 550 575 8 1741 099714 000286 025 415922 575 600 5 1746 1 0 000 DIV0 1746 20 year 873 Slope 085586 Intercept -104906 correlation 099524 beta 116842 gamma 122575
Hss for condition 1 10 668997
( )ss ssP P H H
1ss ssQ Q H H P
threshold 15 m
y = -07849Ln(x) + 16329
R2 = 09854
0
2
4
6
8
000010000100001000010000100000probability of exceedence
sto
rm h
eig
ht
Hss
February 1 2012 25
How to get storm exceedance
Q = probability of exceedance of a wave
Qs = probability of exceedance of a storm
s sQ N Qthreshold 15 m
y = -07849Ln(x) + 5141
R2 = 09854
0
2
4
6
8
10
001010100100010000
storm exceedence probability per year
sto
rm h
eig
ht
Hss
Statistically
nonsense
February 1 2012 26
The ldquoonce in 500 years stormrdquo
0785ln( )
10785ln 5141
500
100
ss sH Q
m
threshold 15 m
y = -07849Ln(x) + 5141
R2 = 09854
0
2
4
6
8
10
001010100100010000
storm exceedence probability per year
sto
rm h
eig
ht
Hss
February 1 2012 27
Using the Gumbel distribution
exp exp ssHP
February 1 2012 28
determination of and
ln exp
1ln ln
ss
ss
ssss
GAH B
HP
HP H
1ln lnG
P
Perform linear regression
for G = A Hss - B
February 1 2012 29
data for calculation of Gumbel 150 cumul P Q ln(Qs) -ln(H) Qs G
150 175 384 384 021993 078007 422098 -056 6810 -0415046
175 200 381 765 043814 056186 389284 -069 4905 0192121
200 225 266 1031 059049 040951 357655 -081 3575 0640938
225 250 157 1188 068041 031959 332863 -092 2790 0954366
250 275 148 1336 076518 023482 302042 -101 2050 1318085
275 300 111 1447 082875 017125 270471 -11 1495 1672191
300 325 81 1528 087514 012486 238876 -118 1090 2014645
325 350 63 1591 091123 008877 204769 -125 775 2375535
350 375 31 1622 092898 007102 182455 -132 620 2608194
375 400 32 1654 094731 005269 152606 -139 460 2916351
400 425 23 1677 096048 003952 123837 -145 345 3210883
425 450 11 1688 096678 003322 106471 -15 290 3387796
450 475 20 1708 097824 002176 064185 -156 190 3816515
475 500 9 1717 098339 001661 037156 -161 145 4089424
500 525 7 1724 098740 001260 009531 -166 110 4367707
525 550 9 1733 099255 000745 -043078 -17 065 4896399
550 575 8 1741 099714 000286 -138629 -175 025 5854211
575 600 5 1746 1 0 NUM -179 000 NUM
February 1 2012 30
Gumbel exceedance graph
Gumbel distribution
y = 07234x + 1882
R2 = 09871
0
2
4
6
8
10
0 2 4 6 8 10Gumbel Reduced variable
Sto
rm h
eig
ht
Hs
s
ssG AH B
= 1A = 0723
= B =1882
February 1 2012 31
calculation of a value
1ln ln
1ln ln
1
1ln ln
1
ln ln
ss
s
s
s
s s
HP
Q
QN
N
N Q
1500
873188 073ln ln 967
1873500
sH
= 1A = 073
= B =188
February 1 2012 32
transformation of the axis
Gumbel distribution
y = 07234x + 1882
R2 = 09871
0
2
4
6
8
10
0 2 4 6 8 10Gumbel Reduced variable
Sto
rm h
eig
ht
Hs
s
ln ln s
s s
NG
N Q
Ns = 873 storms per year
Qs G
110
1100
11000
110000
677
907
1138
1368
Figure Error No text of specified style in document-1 Storm exceedance on basis of Gumbel
10 100
February 1 2012 33
Weibull distribution
exp ssHQ
February 1 2012 34
determination of the reduced variable
1
1
ln
ln
1ln
ss
ss
ss
ss
WAH B
HQ
HQ
Q H
1
lnW Q
Three variables
and
So iteration is needed
February 1 2012 35
calculation for Weibull
alfa= 124
150 cumul P Q ln(Qs) -ln(H) Qs W
150 175 384 384 021993 078007 422098 -056 6810 032522
175 200 381 765 043814 056186 389284 -069 4905 064136
200 225 266 1031 059049 040951 357655 -081 3575 091261
225 250 157 1188 068041 031959 332863 -092 2790 111202
250 275 148 1336 076518 023482 302042 -101 2050 134858
275 300 111 1447 082875 017125 270471 -11 1495 158094
300 325 81 1528 087514 012486 238876 -118 1090 180552
325 350 63 1591 091123 008877 204769 -125 775 204065
350 375 31 1622 092898 007102 182455 -132 620 219099
375 400 32 1654 094731 005269 152606 -139 460 238832
400 425 23 1677 096048 003952 123837 -145 345 257486
425 450 11 1688 096678 003322 106471 -15 290 268590
450 475 20 1708 097824 002176 064185 -156 190 295184
475 500 9 1717 098339 001661 037156 -161 145 311883
500 525 7 1724 098740 001260 009531 -166 110 328731
525 550 9 1733 099255 000745 -043078 -17 065 360263
550 575 8 1741 099714 000286 -138629 -175 025 415922
575 600 5 1746 1 0 NUM -179 000 DIV0
1746
20 year 873 085586
-104906
099524
-07849
541 beta 116842
gamma 122575
Hs for condition 1 500 1028785 911838
1
lnssH Q
1
ln sss
s
QH
N
1124
1500
1500122 117 ln
873
122 117 675
912
sH
m
February 1 2012 36
Weibull exceedance graph
Weibull distribution
y = 11573x + 12497
R2 = 09905
0
2
4
6
8
10
0 2 4 6 8 10
Weibull Reduced variable
Str
om
heig
ht
Hss
10 100 1000 10000
February 1 2012 37
Summary
HT threshold value
Exponential
Gumbel
Weibull
150 m 163 m 136 m 122 m
HT 150 200 250 300 350 400
Ns 873 596 389 194 108 53
Hs 1500 Exponential Hs 1500 Gumbel Hs 1500 Weibull
1000 969 912
1009 950 990
948 917 963
939 893 948
908 886 917
876 818 890
February 1 2012 38
What to do if only random data are available
storm exceedance
0
200
400
600
800
01110100100010000
probability per year
Hs
s
February 1 2012 39
Example of long term data
This are
Hs-classes
February 1 2012 40
Long term (continuation)
So from this last column we can conclude
100 of time H gt 0 m s
23 of time H gt 1 m s
12 of time H gt 2 m s
001 of time H gt 9 m s
0
2
4
6
8
10
12
14
1E-071E-061E-051E-041E-031E-021E-011E+00
exceedance per year
wave
he
igh
t H
s (
m)
February 1 2012 41
From probability of waves to probability of storms
Suppose a ldquostormrdquo lasts for 12 hrs
===gt 730 stormsyear
once per year storm = 100730 = 013 =gt 67 m
once per 10 year storm = 0013 =gt 94 m
once per 100 year storm = 00013 =gt 119 m
0
5
10
15
20
1 10 100 1000 10000
return period in years
Hs o
f th
e g
ive
n s
torm
February 1 2012 42
Meteorological data
bull Not of direct importance for design
bull Can be important for hindcast of wave data and storm surge
bull Extremely important for the execution of the works (workability)
February 1 2012 43
Waves from Wind (Brettschneider)
February 1 2012 44
required soil data
February 1 2012 45
in situ test methods
February 1 2012 46
During construction
bull Quarry stone
bull Concrete
bull Local Equipment
bull Labour
bull skilled
bull cost
bull availability
bull expatriates
February 1 2012 13
exceedance table
February 1 2012 14
exceedance graph
February 1 2012 15
comparison buoys and ship data
February 1 2012 16
Data from wwwhydrobasenet
February 1 2012 17
Sample output of Hydrobase
February 1 2012 18
Data from Hydrobase
February 1 2012 19
data from Meetpost Noordwijk
wwwgolfklimaatnl
0
50
100
150
200
250
300
350
400
450
0 200 400 600 800
time (hrs)
Hm
o (
cm
)
January 1979
February 1 2012 20
basic data
date time Hm0 accur H13 TTE3 Tm02 TH13 wave wind wind level setup
dir dir speed
cm cm cm 1 s 1 s 1 s degr degr 1 ms cm cm
19980101 0100 70 4 64 6 39 49 261 210 60 -27 27 222224000
19980101 0400 72 4 65 8 36 45 264 210 70 91 24 222224000
19980101 0700 62 4 56 8 36 46 258 200 80 58 11 222224000
19980101 1000 93 5 85 11 40 48 234 190 90 -31 6 222224000
19980101 1300 110 5 102 14 44 51 230 200 90 -83 -5 222224000
19980101 1600 162 7 148 17 42 52 230 200 120 43 -12 222224000
19980101 1900 132 6 121 11 40 48 224 190 130 40 -37 222224000
19980101 2200 205 8 190 18 51 61 220 190 170 -39 -33 222224000
19980102 0100 247 10 230 37 56 68 229 190 170 -114 -57 222224000
19980102 0400 275 11 255 40 55 68 236 210 160 -1 -1 222224000
19980102 0700 208 8 193 20 50 63 234 200 140 -2 -72 222224000
19980102 1000 142 6 132 14 47 59 227 190 120 -59 -13 222224000
19980102 1300 130 6 120 14 50 64 223 160 110 -97 -22 222224000
19980102 1600 117 5 108 13 43 53 213 170 100 73 87 222224000
19980102 1900 91 5 84 10 39 49 232 210 100 152 58 222224000
19980102 2200 243 10 226 22 52 62 267 280 150 119 118 222224000
19980103 0100 287 12 269 32 59 70 269 260 110 25 73 222224000
19980103 0400 240 10 224 21 55 66 265 230 90 28 60 222224000
19980103 0700 177 7 163 13 46 56 245 200 130 122 37 222224000
19980103 1000 179 7 165 16 47 56 223 180 170 -30 3 222224000
19980103 1300 285 12 266 35 58 70 230 210 190 -43 16 222224000
19980103 1600 341 15 318 56 61 73 242 250 130 -36 14 222224000
19980103 1900 342 15 319 53 60 73 246 260 170 133 20 222224000
19980103 2200 414 21 388 85 65 77 249 260 190 72 46 222224000
19980104 0100 465 21 435 228 72 88 254 260 190 40 68 222224000
19980104 0400 358 16 334 92 64 78 259 240 90 -22 18 222224000
19980104 0700 324 14 302 52 60 73 256 250 120 129 43 222224000
19980104 1000 247 10 229 33 55 69 252 220 100 34 33 222224000
February 1 2012 21
sort data in classes
Waveheight class Hs (cm)
Number of observations
P Q -ln(Q)
0 25 35 35 0000599 0999401 0000599
25 50 8260 8295 0141940 0858060 0153082 50 75 11424 19719 0337423 0662577 0411618
75 100 10004 29723 0508607 0491393 0710511
100 125 7649 37372 0639493 0360507 1020245
125 150 5563 42935 0734685 0265315 1326838
150 175 4389 47324 0809788 0190212 1659615
175 200 3167 50491 0863980 0136020 1994954
200 225 2360 52851 0904363 0095637 2347200
225 250 1671 54522 0932957 0067043 2702419
250 275 1234 55756 0954073 0045927 3080692
275 300 851 56607 0968634 0031366 3462047
300 325 556 57163 0978149 0021851 3823487
325 350 392 57555 0984856 0015144 4190168
350 375 276 57831 0989579 0010421 4563938
375 400 206 58037 0993104 0006896 4976819
400 425 136 58173 0995431 0004569 5388507
425 450 82 58255 0996834 0003166 5755400
450 475 66 58321 0997964 0002036 6196632
475 500 38 58359 0998614 0001386 6581307
500 525 30 58389 0999127 0000873 7043930
525 550 20 58409 0999470 0000530 7541769
550 575 22 58431 0999846 0000154 8778531
575 600 9 58440 1000000 0000000
58440
( )s sP P H H
( ) 1s sQ Q H H P
all data Noordwijk
y = 00151x - 05001
R2 = 09881
0
1
2
3
4
5
6
7
8
9
10
0 200 400 600Hs-l
nQ
February 1 2012 22
exceedance graph for Noordwijk
indivudual observations
0
200
400
600
800
1000
000001000001000001000001000001000001000000
exceedance
wave h
eig
ht
But what means that in a year during 01
of the time the Hs is larger than 5 m
February 1 2012 23
Peak over Threshold method
A storm is defined as a time that the wave is higher than a
certain value the height of the storm Hss is equal to the
highest observed Hs during that storm
Threshold = 15
In this period 9
storms observed
nr Hss
1 180 m
2 294 m
3 225 m
4 176 m
5 261 m
6 389 m
7 172 m
8 240 m
9 194 m
February 1 2012 24
Table with Hss classes
= 124 Wave height class
150 cumul P Q Qs W
150 175 384 384 021993 078007 6810 032522 175 200 381 765 043814 056186 4905 064136 200 225 266 1031 059049 040951 3575 091261 225 250 157 1188 068041 031959 2790 111202 250 275 148 1336 076518 023482 2050 134858 275 300 111 1447 082875 017125 1495 158094 300 325 81 1528 087514 012486 1090 180552 325 350 63 1591 091123 008877 775 204065 350 375 31 1622 092898 007102 620 219099 375 400 32 1654 094731 005269 460 238832 400 425 23 1677 096048 003952 345 257486 425 450 11 1688 096678 003322 290 268590 450 475 20 1708 097824 002176 190 295184 475 500 9 1717 098339 001661 145 311883 500 525 7 1724 098740 001260 110 328731 525 550 9 1733 099255 000745 065 360263 550 575 8 1741 099714 000286 025 415922 575 600 5 1746 1 0 000 DIV0 1746 20 year 873 Slope 085586 Intercept -104906 correlation 099524 beta 116842 gamma 122575
Hss for condition 1 10 668997
( )ss ssP P H H
1ss ssQ Q H H P
threshold 15 m
y = -07849Ln(x) + 16329
R2 = 09854
0
2
4
6
8
000010000100001000010000100000probability of exceedence
sto
rm h
eig
ht
Hss
February 1 2012 25
How to get storm exceedance
Q = probability of exceedance of a wave
Qs = probability of exceedance of a storm
s sQ N Qthreshold 15 m
y = -07849Ln(x) + 5141
R2 = 09854
0
2
4
6
8
10
001010100100010000
storm exceedence probability per year
sto
rm h
eig
ht
Hss
Statistically
nonsense
February 1 2012 26
The ldquoonce in 500 years stormrdquo
0785ln( )
10785ln 5141
500
100
ss sH Q
m
threshold 15 m
y = -07849Ln(x) + 5141
R2 = 09854
0
2
4
6
8
10
001010100100010000
storm exceedence probability per year
sto
rm h
eig
ht
Hss
February 1 2012 27
Using the Gumbel distribution
exp exp ssHP
February 1 2012 28
determination of and
ln exp
1ln ln
ss
ss
ssss
GAH B
HP
HP H
1ln lnG
P
Perform linear regression
for G = A Hss - B
February 1 2012 29
data for calculation of Gumbel 150 cumul P Q ln(Qs) -ln(H) Qs G
150 175 384 384 021993 078007 422098 -056 6810 -0415046
175 200 381 765 043814 056186 389284 -069 4905 0192121
200 225 266 1031 059049 040951 357655 -081 3575 0640938
225 250 157 1188 068041 031959 332863 -092 2790 0954366
250 275 148 1336 076518 023482 302042 -101 2050 1318085
275 300 111 1447 082875 017125 270471 -11 1495 1672191
300 325 81 1528 087514 012486 238876 -118 1090 2014645
325 350 63 1591 091123 008877 204769 -125 775 2375535
350 375 31 1622 092898 007102 182455 -132 620 2608194
375 400 32 1654 094731 005269 152606 -139 460 2916351
400 425 23 1677 096048 003952 123837 -145 345 3210883
425 450 11 1688 096678 003322 106471 -15 290 3387796
450 475 20 1708 097824 002176 064185 -156 190 3816515
475 500 9 1717 098339 001661 037156 -161 145 4089424
500 525 7 1724 098740 001260 009531 -166 110 4367707
525 550 9 1733 099255 000745 -043078 -17 065 4896399
550 575 8 1741 099714 000286 -138629 -175 025 5854211
575 600 5 1746 1 0 NUM -179 000 NUM
February 1 2012 30
Gumbel exceedance graph
Gumbel distribution
y = 07234x + 1882
R2 = 09871
0
2
4
6
8
10
0 2 4 6 8 10Gumbel Reduced variable
Sto
rm h
eig
ht
Hs
s
ssG AH B
= 1A = 0723
= B =1882
February 1 2012 31
calculation of a value
1ln ln
1ln ln
1
1ln ln
1
ln ln
ss
s
s
s
s s
HP
Q
QN
N
N Q
1500
873188 073ln ln 967
1873500
sH
= 1A = 073
= B =188
February 1 2012 32
transformation of the axis
Gumbel distribution
y = 07234x + 1882
R2 = 09871
0
2
4
6
8
10
0 2 4 6 8 10Gumbel Reduced variable
Sto
rm h
eig
ht
Hs
s
ln ln s
s s
NG
N Q
Ns = 873 storms per year
Qs G
110
1100
11000
110000
677
907
1138
1368
Figure Error No text of specified style in document-1 Storm exceedance on basis of Gumbel
10 100
February 1 2012 33
Weibull distribution
exp ssHQ
February 1 2012 34
determination of the reduced variable
1
1
ln
ln
1ln
ss
ss
ss
ss
WAH B
HQ
HQ
Q H
1
lnW Q
Three variables
and
So iteration is needed
February 1 2012 35
calculation for Weibull
alfa= 124
150 cumul P Q ln(Qs) -ln(H) Qs W
150 175 384 384 021993 078007 422098 -056 6810 032522
175 200 381 765 043814 056186 389284 -069 4905 064136
200 225 266 1031 059049 040951 357655 -081 3575 091261
225 250 157 1188 068041 031959 332863 -092 2790 111202
250 275 148 1336 076518 023482 302042 -101 2050 134858
275 300 111 1447 082875 017125 270471 -11 1495 158094
300 325 81 1528 087514 012486 238876 -118 1090 180552
325 350 63 1591 091123 008877 204769 -125 775 204065
350 375 31 1622 092898 007102 182455 -132 620 219099
375 400 32 1654 094731 005269 152606 -139 460 238832
400 425 23 1677 096048 003952 123837 -145 345 257486
425 450 11 1688 096678 003322 106471 -15 290 268590
450 475 20 1708 097824 002176 064185 -156 190 295184
475 500 9 1717 098339 001661 037156 -161 145 311883
500 525 7 1724 098740 001260 009531 -166 110 328731
525 550 9 1733 099255 000745 -043078 -17 065 360263
550 575 8 1741 099714 000286 -138629 -175 025 415922
575 600 5 1746 1 0 NUM -179 000 DIV0
1746
20 year 873 085586
-104906
099524
-07849
541 beta 116842
gamma 122575
Hs for condition 1 500 1028785 911838
1
lnssH Q
1
ln sss
s
QH
N
1124
1500
1500122 117 ln
873
122 117 675
912
sH
m
February 1 2012 36
Weibull exceedance graph
Weibull distribution
y = 11573x + 12497
R2 = 09905
0
2
4
6
8
10
0 2 4 6 8 10
Weibull Reduced variable
Str
om
heig
ht
Hss
10 100 1000 10000
February 1 2012 37
Summary
HT threshold value
Exponential
Gumbel
Weibull
150 m 163 m 136 m 122 m
HT 150 200 250 300 350 400
Ns 873 596 389 194 108 53
Hs 1500 Exponential Hs 1500 Gumbel Hs 1500 Weibull
1000 969 912
1009 950 990
948 917 963
939 893 948
908 886 917
876 818 890
February 1 2012 38
What to do if only random data are available
storm exceedance
0
200
400
600
800
01110100100010000
probability per year
Hs
s
February 1 2012 39
Example of long term data
This are
Hs-classes
February 1 2012 40
Long term (continuation)
So from this last column we can conclude
100 of time H gt 0 m s
23 of time H gt 1 m s
12 of time H gt 2 m s
001 of time H gt 9 m s
0
2
4
6
8
10
12
14
1E-071E-061E-051E-041E-031E-021E-011E+00
exceedance per year
wave
he
igh
t H
s (
m)
February 1 2012 41
From probability of waves to probability of storms
Suppose a ldquostormrdquo lasts for 12 hrs
===gt 730 stormsyear
once per year storm = 100730 = 013 =gt 67 m
once per 10 year storm = 0013 =gt 94 m
once per 100 year storm = 00013 =gt 119 m
0
5
10
15
20
1 10 100 1000 10000
return period in years
Hs o
f th
e g
ive
n s
torm
February 1 2012 42
Meteorological data
bull Not of direct importance for design
bull Can be important for hindcast of wave data and storm surge
bull Extremely important for the execution of the works (workability)
February 1 2012 43
Waves from Wind (Brettschneider)
February 1 2012 44
required soil data
February 1 2012 45
in situ test methods
February 1 2012 46
During construction
bull Quarry stone
bull Concrete
bull Local Equipment
bull Labour
bull skilled
bull cost
bull availability
bull expatriates
February 1 2012 14
exceedance graph
February 1 2012 15
comparison buoys and ship data
February 1 2012 16
Data from wwwhydrobasenet
February 1 2012 17
Sample output of Hydrobase
February 1 2012 18
Data from Hydrobase
February 1 2012 19
data from Meetpost Noordwijk
wwwgolfklimaatnl
0
50
100
150
200
250
300
350
400
450
0 200 400 600 800
time (hrs)
Hm
o (
cm
)
January 1979
February 1 2012 20
basic data
date time Hm0 accur H13 TTE3 Tm02 TH13 wave wind wind level setup
dir dir speed
cm cm cm 1 s 1 s 1 s degr degr 1 ms cm cm
19980101 0100 70 4 64 6 39 49 261 210 60 -27 27 222224000
19980101 0400 72 4 65 8 36 45 264 210 70 91 24 222224000
19980101 0700 62 4 56 8 36 46 258 200 80 58 11 222224000
19980101 1000 93 5 85 11 40 48 234 190 90 -31 6 222224000
19980101 1300 110 5 102 14 44 51 230 200 90 -83 -5 222224000
19980101 1600 162 7 148 17 42 52 230 200 120 43 -12 222224000
19980101 1900 132 6 121 11 40 48 224 190 130 40 -37 222224000
19980101 2200 205 8 190 18 51 61 220 190 170 -39 -33 222224000
19980102 0100 247 10 230 37 56 68 229 190 170 -114 -57 222224000
19980102 0400 275 11 255 40 55 68 236 210 160 -1 -1 222224000
19980102 0700 208 8 193 20 50 63 234 200 140 -2 -72 222224000
19980102 1000 142 6 132 14 47 59 227 190 120 -59 -13 222224000
19980102 1300 130 6 120 14 50 64 223 160 110 -97 -22 222224000
19980102 1600 117 5 108 13 43 53 213 170 100 73 87 222224000
19980102 1900 91 5 84 10 39 49 232 210 100 152 58 222224000
19980102 2200 243 10 226 22 52 62 267 280 150 119 118 222224000
19980103 0100 287 12 269 32 59 70 269 260 110 25 73 222224000
19980103 0400 240 10 224 21 55 66 265 230 90 28 60 222224000
19980103 0700 177 7 163 13 46 56 245 200 130 122 37 222224000
19980103 1000 179 7 165 16 47 56 223 180 170 -30 3 222224000
19980103 1300 285 12 266 35 58 70 230 210 190 -43 16 222224000
19980103 1600 341 15 318 56 61 73 242 250 130 -36 14 222224000
19980103 1900 342 15 319 53 60 73 246 260 170 133 20 222224000
19980103 2200 414 21 388 85 65 77 249 260 190 72 46 222224000
19980104 0100 465 21 435 228 72 88 254 260 190 40 68 222224000
19980104 0400 358 16 334 92 64 78 259 240 90 -22 18 222224000
19980104 0700 324 14 302 52 60 73 256 250 120 129 43 222224000
19980104 1000 247 10 229 33 55 69 252 220 100 34 33 222224000
February 1 2012 21
sort data in classes
Waveheight class Hs (cm)
Number of observations
P Q -ln(Q)
0 25 35 35 0000599 0999401 0000599
25 50 8260 8295 0141940 0858060 0153082 50 75 11424 19719 0337423 0662577 0411618
75 100 10004 29723 0508607 0491393 0710511
100 125 7649 37372 0639493 0360507 1020245
125 150 5563 42935 0734685 0265315 1326838
150 175 4389 47324 0809788 0190212 1659615
175 200 3167 50491 0863980 0136020 1994954
200 225 2360 52851 0904363 0095637 2347200
225 250 1671 54522 0932957 0067043 2702419
250 275 1234 55756 0954073 0045927 3080692
275 300 851 56607 0968634 0031366 3462047
300 325 556 57163 0978149 0021851 3823487
325 350 392 57555 0984856 0015144 4190168
350 375 276 57831 0989579 0010421 4563938
375 400 206 58037 0993104 0006896 4976819
400 425 136 58173 0995431 0004569 5388507
425 450 82 58255 0996834 0003166 5755400
450 475 66 58321 0997964 0002036 6196632
475 500 38 58359 0998614 0001386 6581307
500 525 30 58389 0999127 0000873 7043930
525 550 20 58409 0999470 0000530 7541769
550 575 22 58431 0999846 0000154 8778531
575 600 9 58440 1000000 0000000
58440
( )s sP P H H
( ) 1s sQ Q H H P
all data Noordwijk
y = 00151x - 05001
R2 = 09881
0
1
2
3
4
5
6
7
8
9
10
0 200 400 600Hs-l
nQ
February 1 2012 22
exceedance graph for Noordwijk
indivudual observations
0
200
400
600
800
1000
000001000001000001000001000001000001000000
exceedance
wave h
eig
ht
But what means that in a year during 01
of the time the Hs is larger than 5 m
February 1 2012 23
Peak over Threshold method
A storm is defined as a time that the wave is higher than a
certain value the height of the storm Hss is equal to the
highest observed Hs during that storm
Threshold = 15
In this period 9
storms observed
nr Hss
1 180 m
2 294 m
3 225 m
4 176 m
5 261 m
6 389 m
7 172 m
8 240 m
9 194 m
February 1 2012 24
Table with Hss classes
= 124 Wave height class
150 cumul P Q Qs W
150 175 384 384 021993 078007 6810 032522 175 200 381 765 043814 056186 4905 064136 200 225 266 1031 059049 040951 3575 091261 225 250 157 1188 068041 031959 2790 111202 250 275 148 1336 076518 023482 2050 134858 275 300 111 1447 082875 017125 1495 158094 300 325 81 1528 087514 012486 1090 180552 325 350 63 1591 091123 008877 775 204065 350 375 31 1622 092898 007102 620 219099 375 400 32 1654 094731 005269 460 238832 400 425 23 1677 096048 003952 345 257486 425 450 11 1688 096678 003322 290 268590 450 475 20 1708 097824 002176 190 295184 475 500 9 1717 098339 001661 145 311883 500 525 7 1724 098740 001260 110 328731 525 550 9 1733 099255 000745 065 360263 550 575 8 1741 099714 000286 025 415922 575 600 5 1746 1 0 000 DIV0 1746 20 year 873 Slope 085586 Intercept -104906 correlation 099524 beta 116842 gamma 122575
Hss for condition 1 10 668997
( )ss ssP P H H
1ss ssQ Q H H P
threshold 15 m
y = -07849Ln(x) + 16329
R2 = 09854
0
2
4
6
8
000010000100001000010000100000probability of exceedence
sto
rm h
eig
ht
Hss
February 1 2012 25
How to get storm exceedance
Q = probability of exceedance of a wave
Qs = probability of exceedance of a storm
s sQ N Qthreshold 15 m
y = -07849Ln(x) + 5141
R2 = 09854
0
2
4
6
8
10
001010100100010000
storm exceedence probability per year
sto
rm h
eig
ht
Hss
Statistically
nonsense
February 1 2012 26
The ldquoonce in 500 years stormrdquo
0785ln( )
10785ln 5141
500
100
ss sH Q
m
threshold 15 m
y = -07849Ln(x) + 5141
R2 = 09854
0
2
4
6
8
10
001010100100010000
storm exceedence probability per year
sto
rm h
eig
ht
Hss
February 1 2012 27
Using the Gumbel distribution
exp exp ssHP
February 1 2012 28
determination of and
ln exp
1ln ln
ss
ss
ssss
GAH B
HP
HP H
1ln lnG
P
Perform linear regression
for G = A Hss - B
February 1 2012 29
data for calculation of Gumbel 150 cumul P Q ln(Qs) -ln(H) Qs G
150 175 384 384 021993 078007 422098 -056 6810 -0415046
175 200 381 765 043814 056186 389284 -069 4905 0192121
200 225 266 1031 059049 040951 357655 -081 3575 0640938
225 250 157 1188 068041 031959 332863 -092 2790 0954366
250 275 148 1336 076518 023482 302042 -101 2050 1318085
275 300 111 1447 082875 017125 270471 -11 1495 1672191
300 325 81 1528 087514 012486 238876 -118 1090 2014645
325 350 63 1591 091123 008877 204769 -125 775 2375535
350 375 31 1622 092898 007102 182455 -132 620 2608194
375 400 32 1654 094731 005269 152606 -139 460 2916351
400 425 23 1677 096048 003952 123837 -145 345 3210883
425 450 11 1688 096678 003322 106471 -15 290 3387796
450 475 20 1708 097824 002176 064185 -156 190 3816515
475 500 9 1717 098339 001661 037156 -161 145 4089424
500 525 7 1724 098740 001260 009531 -166 110 4367707
525 550 9 1733 099255 000745 -043078 -17 065 4896399
550 575 8 1741 099714 000286 -138629 -175 025 5854211
575 600 5 1746 1 0 NUM -179 000 NUM
February 1 2012 30
Gumbel exceedance graph
Gumbel distribution
y = 07234x + 1882
R2 = 09871
0
2
4
6
8
10
0 2 4 6 8 10Gumbel Reduced variable
Sto
rm h
eig
ht
Hs
s
ssG AH B
= 1A = 0723
= B =1882
February 1 2012 31
calculation of a value
1ln ln
1ln ln
1
1ln ln
1
ln ln
ss
s
s
s
s s
HP
Q
QN
N
N Q
1500
873188 073ln ln 967
1873500
sH
= 1A = 073
= B =188
February 1 2012 32
transformation of the axis
Gumbel distribution
y = 07234x + 1882
R2 = 09871
0
2
4
6
8
10
0 2 4 6 8 10Gumbel Reduced variable
Sto
rm h
eig
ht
Hs
s
ln ln s
s s
NG
N Q
Ns = 873 storms per year
Qs G
110
1100
11000
110000
677
907
1138
1368
Figure Error No text of specified style in document-1 Storm exceedance on basis of Gumbel
10 100
February 1 2012 33
Weibull distribution
exp ssHQ
February 1 2012 34
determination of the reduced variable
1
1
ln
ln
1ln
ss
ss
ss
ss
WAH B
HQ
HQ
Q H
1
lnW Q
Three variables
and
So iteration is needed
February 1 2012 35
calculation for Weibull
alfa= 124
150 cumul P Q ln(Qs) -ln(H) Qs W
150 175 384 384 021993 078007 422098 -056 6810 032522
175 200 381 765 043814 056186 389284 -069 4905 064136
200 225 266 1031 059049 040951 357655 -081 3575 091261
225 250 157 1188 068041 031959 332863 -092 2790 111202
250 275 148 1336 076518 023482 302042 -101 2050 134858
275 300 111 1447 082875 017125 270471 -11 1495 158094
300 325 81 1528 087514 012486 238876 -118 1090 180552
325 350 63 1591 091123 008877 204769 -125 775 204065
350 375 31 1622 092898 007102 182455 -132 620 219099
375 400 32 1654 094731 005269 152606 -139 460 238832
400 425 23 1677 096048 003952 123837 -145 345 257486
425 450 11 1688 096678 003322 106471 -15 290 268590
450 475 20 1708 097824 002176 064185 -156 190 295184
475 500 9 1717 098339 001661 037156 -161 145 311883
500 525 7 1724 098740 001260 009531 -166 110 328731
525 550 9 1733 099255 000745 -043078 -17 065 360263
550 575 8 1741 099714 000286 -138629 -175 025 415922
575 600 5 1746 1 0 NUM -179 000 DIV0
1746
20 year 873 085586
-104906
099524
-07849
541 beta 116842
gamma 122575
Hs for condition 1 500 1028785 911838
1
lnssH Q
1
ln sss
s
QH
N
1124
1500
1500122 117 ln
873
122 117 675
912
sH
m
February 1 2012 36
Weibull exceedance graph
Weibull distribution
y = 11573x + 12497
R2 = 09905
0
2
4
6
8
10
0 2 4 6 8 10
Weibull Reduced variable
Str
om
heig
ht
Hss
10 100 1000 10000
February 1 2012 37
Summary
HT threshold value
Exponential
Gumbel
Weibull
150 m 163 m 136 m 122 m
HT 150 200 250 300 350 400
Ns 873 596 389 194 108 53
Hs 1500 Exponential Hs 1500 Gumbel Hs 1500 Weibull
1000 969 912
1009 950 990
948 917 963
939 893 948
908 886 917
876 818 890
February 1 2012 38
What to do if only random data are available
storm exceedance
0
200
400
600
800
01110100100010000
probability per year
Hs
s
February 1 2012 39
Example of long term data
This are
Hs-classes
February 1 2012 40
Long term (continuation)
So from this last column we can conclude
100 of time H gt 0 m s
23 of time H gt 1 m s
12 of time H gt 2 m s
001 of time H gt 9 m s
0
2
4
6
8
10
12
14
1E-071E-061E-051E-041E-031E-021E-011E+00
exceedance per year
wave
he
igh
t H
s (
m)
February 1 2012 41
From probability of waves to probability of storms
Suppose a ldquostormrdquo lasts for 12 hrs
===gt 730 stormsyear
once per year storm = 100730 = 013 =gt 67 m
once per 10 year storm = 0013 =gt 94 m
once per 100 year storm = 00013 =gt 119 m
0
5
10
15
20
1 10 100 1000 10000
return period in years
Hs o
f th
e g
ive
n s
torm
February 1 2012 42
Meteorological data
bull Not of direct importance for design
bull Can be important for hindcast of wave data and storm surge
bull Extremely important for the execution of the works (workability)
February 1 2012 43
Waves from Wind (Brettschneider)
February 1 2012 44
required soil data
February 1 2012 45
in situ test methods
February 1 2012 46
During construction
bull Quarry stone
bull Concrete
bull Local Equipment
bull Labour
bull skilled
bull cost
bull availability
bull expatriates
February 1 2012 15
comparison buoys and ship data
February 1 2012 16
Data from wwwhydrobasenet
February 1 2012 17
Sample output of Hydrobase
February 1 2012 18
Data from Hydrobase
February 1 2012 19
data from Meetpost Noordwijk
wwwgolfklimaatnl
0
50
100
150
200
250
300
350
400
450
0 200 400 600 800
time (hrs)
Hm
o (
cm
)
January 1979
February 1 2012 20
basic data
date time Hm0 accur H13 TTE3 Tm02 TH13 wave wind wind level setup
dir dir speed
cm cm cm 1 s 1 s 1 s degr degr 1 ms cm cm
19980101 0100 70 4 64 6 39 49 261 210 60 -27 27 222224000
19980101 0400 72 4 65 8 36 45 264 210 70 91 24 222224000
19980101 0700 62 4 56 8 36 46 258 200 80 58 11 222224000
19980101 1000 93 5 85 11 40 48 234 190 90 -31 6 222224000
19980101 1300 110 5 102 14 44 51 230 200 90 -83 -5 222224000
19980101 1600 162 7 148 17 42 52 230 200 120 43 -12 222224000
19980101 1900 132 6 121 11 40 48 224 190 130 40 -37 222224000
19980101 2200 205 8 190 18 51 61 220 190 170 -39 -33 222224000
19980102 0100 247 10 230 37 56 68 229 190 170 -114 -57 222224000
19980102 0400 275 11 255 40 55 68 236 210 160 -1 -1 222224000
19980102 0700 208 8 193 20 50 63 234 200 140 -2 -72 222224000
19980102 1000 142 6 132 14 47 59 227 190 120 -59 -13 222224000
19980102 1300 130 6 120 14 50 64 223 160 110 -97 -22 222224000
19980102 1600 117 5 108 13 43 53 213 170 100 73 87 222224000
19980102 1900 91 5 84 10 39 49 232 210 100 152 58 222224000
19980102 2200 243 10 226 22 52 62 267 280 150 119 118 222224000
19980103 0100 287 12 269 32 59 70 269 260 110 25 73 222224000
19980103 0400 240 10 224 21 55 66 265 230 90 28 60 222224000
19980103 0700 177 7 163 13 46 56 245 200 130 122 37 222224000
19980103 1000 179 7 165 16 47 56 223 180 170 -30 3 222224000
19980103 1300 285 12 266 35 58 70 230 210 190 -43 16 222224000
19980103 1600 341 15 318 56 61 73 242 250 130 -36 14 222224000
19980103 1900 342 15 319 53 60 73 246 260 170 133 20 222224000
19980103 2200 414 21 388 85 65 77 249 260 190 72 46 222224000
19980104 0100 465 21 435 228 72 88 254 260 190 40 68 222224000
19980104 0400 358 16 334 92 64 78 259 240 90 -22 18 222224000
19980104 0700 324 14 302 52 60 73 256 250 120 129 43 222224000
19980104 1000 247 10 229 33 55 69 252 220 100 34 33 222224000
February 1 2012 21
sort data in classes
Waveheight class Hs (cm)
Number of observations
P Q -ln(Q)
0 25 35 35 0000599 0999401 0000599
25 50 8260 8295 0141940 0858060 0153082 50 75 11424 19719 0337423 0662577 0411618
75 100 10004 29723 0508607 0491393 0710511
100 125 7649 37372 0639493 0360507 1020245
125 150 5563 42935 0734685 0265315 1326838
150 175 4389 47324 0809788 0190212 1659615
175 200 3167 50491 0863980 0136020 1994954
200 225 2360 52851 0904363 0095637 2347200
225 250 1671 54522 0932957 0067043 2702419
250 275 1234 55756 0954073 0045927 3080692
275 300 851 56607 0968634 0031366 3462047
300 325 556 57163 0978149 0021851 3823487
325 350 392 57555 0984856 0015144 4190168
350 375 276 57831 0989579 0010421 4563938
375 400 206 58037 0993104 0006896 4976819
400 425 136 58173 0995431 0004569 5388507
425 450 82 58255 0996834 0003166 5755400
450 475 66 58321 0997964 0002036 6196632
475 500 38 58359 0998614 0001386 6581307
500 525 30 58389 0999127 0000873 7043930
525 550 20 58409 0999470 0000530 7541769
550 575 22 58431 0999846 0000154 8778531
575 600 9 58440 1000000 0000000
58440
( )s sP P H H
( ) 1s sQ Q H H P
all data Noordwijk
y = 00151x - 05001
R2 = 09881
0
1
2
3
4
5
6
7
8
9
10
0 200 400 600Hs-l
nQ
February 1 2012 22
exceedance graph for Noordwijk
indivudual observations
0
200
400
600
800
1000
000001000001000001000001000001000001000000
exceedance
wave h
eig
ht
But what means that in a year during 01
of the time the Hs is larger than 5 m
February 1 2012 23
Peak over Threshold method
A storm is defined as a time that the wave is higher than a
certain value the height of the storm Hss is equal to the
highest observed Hs during that storm
Threshold = 15
In this period 9
storms observed
nr Hss
1 180 m
2 294 m
3 225 m
4 176 m
5 261 m
6 389 m
7 172 m
8 240 m
9 194 m
February 1 2012 24
Table with Hss classes
= 124 Wave height class
150 cumul P Q Qs W
150 175 384 384 021993 078007 6810 032522 175 200 381 765 043814 056186 4905 064136 200 225 266 1031 059049 040951 3575 091261 225 250 157 1188 068041 031959 2790 111202 250 275 148 1336 076518 023482 2050 134858 275 300 111 1447 082875 017125 1495 158094 300 325 81 1528 087514 012486 1090 180552 325 350 63 1591 091123 008877 775 204065 350 375 31 1622 092898 007102 620 219099 375 400 32 1654 094731 005269 460 238832 400 425 23 1677 096048 003952 345 257486 425 450 11 1688 096678 003322 290 268590 450 475 20 1708 097824 002176 190 295184 475 500 9 1717 098339 001661 145 311883 500 525 7 1724 098740 001260 110 328731 525 550 9 1733 099255 000745 065 360263 550 575 8 1741 099714 000286 025 415922 575 600 5 1746 1 0 000 DIV0 1746 20 year 873 Slope 085586 Intercept -104906 correlation 099524 beta 116842 gamma 122575
Hss for condition 1 10 668997
( )ss ssP P H H
1ss ssQ Q H H P
threshold 15 m
y = -07849Ln(x) + 16329
R2 = 09854
0
2
4
6
8
000010000100001000010000100000probability of exceedence
sto
rm h
eig
ht
Hss
February 1 2012 25
How to get storm exceedance
Q = probability of exceedance of a wave
Qs = probability of exceedance of a storm
s sQ N Qthreshold 15 m
y = -07849Ln(x) + 5141
R2 = 09854
0
2
4
6
8
10
001010100100010000
storm exceedence probability per year
sto
rm h
eig
ht
Hss
Statistically
nonsense
February 1 2012 26
The ldquoonce in 500 years stormrdquo
0785ln( )
10785ln 5141
500
100
ss sH Q
m
threshold 15 m
y = -07849Ln(x) + 5141
R2 = 09854
0
2
4
6
8
10
001010100100010000
storm exceedence probability per year
sto
rm h
eig
ht
Hss
February 1 2012 27
Using the Gumbel distribution
exp exp ssHP
February 1 2012 28
determination of and
ln exp
1ln ln
ss
ss
ssss
GAH B
HP
HP H
1ln lnG
P
Perform linear regression
for G = A Hss - B
February 1 2012 29
data for calculation of Gumbel 150 cumul P Q ln(Qs) -ln(H) Qs G
150 175 384 384 021993 078007 422098 -056 6810 -0415046
175 200 381 765 043814 056186 389284 -069 4905 0192121
200 225 266 1031 059049 040951 357655 -081 3575 0640938
225 250 157 1188 068041 031959 332863 -092 2790 0954366
250 275 148 1336 076518 023482 302042 -101 2050 1318085
275 300 111 1447 082875 017125 270471 -11 1495 1672191
300 325 81 1528 087514 012486 238876 -118 1090 2014645
325 350 63 1591 091123 008877 204769 -125 775 2375535
350 375 31 1622 092898 007102 182455 -132 620 2608194
375 400 32 1654 094731 005269 152606 -139 460 2916351
400 425 23 1677 096048 003952 123837 -145 345 3210883
425 450 11 1688 096678 003322 106471 -15 290 3387796
450 475 20 1708 097824 002176 064185 -156 190 3816515
475 500 9 1717 098339 001661 037156 -161 145 4089424
500 525 7 1724 098740 001260 009531 -166 110 4367707
525 550 9 1733 099255 000745 -043078 -17 065 4896399
550 575 8 1741 099714 000286 -138629 -175 025 5854211
575 600 5 1746 1 0 NUM -179 000 NUM
February 1 2012 30
Gumbel exceedance graph
Gumbel distribution
y = 07234x + 1882
R2 = 09871
0
2
4
6
8
10
0 2 4 6 8 10Gumbel Reduced variable
Sto
rm h
eig
ht
Hs
s
ssG AH B
= 1A = 0723
= B =1882
February 1 2012 31
calculation of a value
1ln ln
1ln ln
1
1ln ln
1
ln ln
ss
s
s
s
s s
HP
Q
QN
N
N Q
1500
873188 073ln ln 967
1873500
sH
= 1A = 073
= B =188
February 1 2012 32
transformation of the axis
Gumbel distribution
y = 07234x + 1882
R2 = 09871
0
2
4
6
8
10
0 2 4 6 8 10Gumbel Reduced variable
Sto
rm h
eig
ht
Hs
s
ln ln s
s s
NG
N Q
Ns = 873 storms per year
Qs G
110
1100
11000
110000
677
907
1138
1368
Figure Error No text of specified style in document-1 Storm exceedance on basis of Gumbel
10 100
February 1 2012 33
Weibull distribution
exp ssHQ
February 1 2012 34
determination of the reduced variable
1
1
ln
ln
1ln
ss
ss
ss
ss
WAH B
HQ
HQ
Q H
1
lnW Q
Three variables
and
So iteration is needed
February 1 2012 35
calculation for Weibull
alfa= 124
150 cumul P Q ln(Qs) -ln(H) Qs W
150 175 384 384 021993 078007 422098 -056 6810 032522
175 200 381 765 043814 056186 389284 -069 4905 064136
200 225 266 1031 059049 040951 357655 -081 3575 091261
225 250 157 1188 068041 031959 332863 -092 2790 111202
250 275 148 1336 076518 023482 302042 -101 2050 134858
275 300 111 1447 082875 017125 270471 -11 1495 158094
300 325 81 1528 087514 012486 238876 -118 1090 180552
325 350 63 1591 091123 008877 204769 -125 775 204065
350 375 31 1622 092898 007102 182455 -132 620 219099
375 400 32 1654 094731 005269 152606 -139 460 238832
400 425 23 1677 096048 003952 123837 -145 345 257486
425 450 11 1688 096678 003322 106471 -15 290 268590
450 475 20 1708 097824 002176 064185 -156 190 295184
475 500 9 1717 098339 001661 037156 -161 145 311883
500 525 7 1724 098740 001260 009531 -166 110 328731
525 550 9 1733 099255 000745 -043078 -17 065 360263
550 575 8 1741 099714 000286 -138629 -175 025 415922
575 600 5 1746 1 0 NUM -179 000 DIV0
1746
20 year 873 085586
-104906
099524
-07849
541 beta 116842
gamma 122575
Hs for condition 1 500 1028785 911838
1
lnssH Q
1
ln sss
s
QH
N
1124
1500
1500122 117 ln
873
122 117 675
912
sH
m
February 1 2012 36
Weibull exceedance graph
Weibull distribution
y = 11573x + 12497
R2 = 09905
0
2
4
6
8
10
0 2 4 6 8 10
Weibull Reduced variable
Str
om
heig
ht
Hss
10 100 1000 10000
February 1 2012 37
Summary
HT threshold value
Exponential
Gumbel
Weibull
150 m 163 m 136 m 122 m
HT 150 200 250 300 350 400
Ns 873 596 389 194 108 53
Hs 1500 Exponential Hs 1500 Gumbel Hs 1500 Weibull
1000 969 912
1009 950 990
948 917 963
939 893 948
908 886 917
876 818 890
February 1 2012 38
What to do if only random data are available
storm exceedance
0
200
400
600
800
01110100100010000
probability per year
Hs
s
February 1 2012 39
Example of long term data
This are
Hs-classes
February 1 2012 40
Long term (continuation)
So from this last column we can conclude
100 of time H gt 0 m s
23 of time H gt 1 m s
12 of time H gt 2 m s
001 of time H gt 9 m s
0
2
4
6
8
10
12
14
1E-071E-061E-051E-041E-031E-021E-011E+00
exceedance per year
wave
he
igh
t H
s (
m)
February 1 2012 41
From probability of waves to probability of storms
Suppose a ldquostormrdquo lasts for 12 hrs
===gt 730 stormsyear
once per year storm = 100730 = 013 =gt 67 m
once per 10 year storm = 0013 =gt 94 m
once per 100 year storm = 00013 =gt 119 m
0
5
10
15
20
1 10 100 1000 10000
return period in years
Hs o
f th
e g
ive
n s
torm
February 1 2012 42
Meteorological data
bull Not of direct importance for design
bull Can be important for hindcast of wave data and storm surge
bull Extremely important for the execution of the works (workability)
February 1 2012 43
Waves from Wind (Brettschneider)
February 1 2012 44
required soil data
February 1 2012 45
in situ test methods
February 1 2012 46
During construction
bull Quarry stone
bull Concrete
bull Local Equipment
bull Labour
bull skilled
bull cost
bull availability
bull expatriates
February 1 2012 16
Data from wwwhydrobasenet
February 1 2012 17
Sample output of Hydrobase
February 1 2012 18
Data from Hydrobase
February 1 2012 19
data from Meetpost Noordwijk
wwwgolfklimaatnl
0
50
100
150
200
250
300
350
400
450
0 200 400 600 800
time (hrs)
Hm
o (
cm
)
January 1979
February 1 2012 20
basic data
date time Hm0 accur H13 TTE3 Tm02 TH13 wave wind wind level setup
dir dir speed
cm cm cm 1 s 1 s 1 s degr degr 1 ms cm cm
19980101 0100 70 4 64 6 39 49 261 210 60 -27 27 222224000
19980101 0400 72 4 65 8 36 45 264 210 70 91 24 222224000
19980101 0700 62 4 56 8 36 46 258 200 80 58 11 222224000
19980101 1000 93 5 85 11 40 48 234 190 90 -31 6 222224000
19980101 1300 110 5 102 14 44 51 230 200 90 -83 -5 222224000
19980101 1600 162 7 148 17 42 52 230 200 120 43 -12 222224000
19980101 1900 132 6 121 11 40 48 224 190 130 40 -37 222224000
19980101 2200 205 8 190 18 51 61 220 190 170 -39 -33 222224000
19980102 0100 247 10 230 37 56 68 229 190 170 -114 -57 222224000
19980102 0400 275 11 255 40 55 68 236 210 160 -1 -1 222224000
19980102 0700 208 8 193 20 50 63 234 200 140 -2 -72 222224000
19980102 1000 142 6 132 14 47 59 227 190 120 -59 -13 222224000
19980102 1300 130 6 120 14 50 64 223 160 110 -97 -22 222224000
19980102 1600 117 5 108 13 43 53 213 170 100 73 87 222224000
19980102 1900 91 5 84 10 39 49 232 210 100 152 58 222224000
19980102 2200 243 10 226 22 52 62 267 280 150 119 118 222224000
19980103 0100 287 12 269 32 59 70 269 260 110 25 73 222224000
19980103 0400 240 10 224 21 55 66 265 230 90 28 60 222224000
19980103 0700 177 7 163 13 46 56 245 200 130 122 37 222224000
19980103 1000 179 7 165 16 47 56 223 180 170 -30 3 222224000
19980103 1300 285 12 266 35 58 70 230 210 190 -43 16 222224000
19980103 1600 341 15 318 56 61 73 242 250 130 -36 14 222224000
19980103 1900 342 15 319 53 60 73 246 260 170 133 20 222224000
19980103 2200 414 21 388 85 65 77 249 260 190 72 46 222224000
19980104 0100 465 21 435 228 72 88 254 260 190 40 68 222224000
19980104 0400 358 16 334 92 64 78 259 240 90 -22 18 222224000
19980104 0700 324 14 302 52 60 73 256 250 120 129 43 222224000
19980104 1000 247 10 229 33 55 69 252 220 100 34 33 222224000
February 1 2012 21
sort data in classes
Waveheight class Hs (cm)
Number of observations
P Q -ln(Q)
0 25 35 35 0000599 0999401 0000599
25 50 8260 8295 0141940 0858060 0153082 50 75 11424 19719 0337423 0662577 0411618
75 100 10004 29723 0508607 0491393 0710511
100 125 7649 37372 0639493 0360507 1020245
125 150 5563 42935 0734685 0265315 1326838
150 175 4389 47324 0809788 0190212 1659615
175 200 3167 50491 0863980 0136020 1994954
200 225 2360 52851 0904363 0095637 2347200
225 250 1671 54522 0932957 0067043 2702419
250 275 1234 55756 0954073 0045927 3080692
275 300 851 56607 0968634 0031366 3462047
300 325 556 57163 0978149 0021851 3823487
325 350 392 57555 0984856 0015144 4190168
350 375 276 57831 0989579 0010421 4563938
375 400 206 58037 0993104 0006896 4976819
400 425 136 58173 0995431 0004569 5388507
425 450 82 58255 0996834 0003166 5755400
450 475 66 58321 0997964 0002036 6196632
475 500 38 58359 0998614 0001386 6581307
500 525 30 58389 0999127 0000873 7043930
525 550 20 58409 0999470 0000530 7541769
550 575 22 58431 0999846 0000154 8778531
575 600 9 58440 1000000 0000000
58440
( )s sP P H H
( ) 1s sQ Q H H P
all data Noordwijk
y = 00151x - 05001
R2 = 09881
0
1
2
3
4
5
6
7
8
9
10
0 200 400 600Hs-l
nQ
February 1 2012 22
exceedance graph for Noordwijk
indivudual observations
0
200
400
600
800
1000
000001000001000001000001000001000001000000
exceedance
wave h
eig
ht
But what means that in a year during 01
of the time the Hs is larger than 5 m
February 1 2012 23
Peak over Threshold method
A storm is defined as a time that the wave is higher than a
certain value the height of the storm Hss is equal to the
highest observed Hs during that storm
Threshold = 15
In this period 9
storms observed
nr Hss
1 180 m
2 294 m
3 225 m
4 176 m
5 261 m
6 389 m
7 172 m
8 240 m
9 194 m
February 1 2012 24
Table with Hss classes
= 124 Wave height class
150 cumul P Q Qs W
150 175 384 384 021993 078007 6810 032522 175 200 381 765 043814 056186 4905 064136 200 225 266 1031 059049 040951 3575 091261 225 250 157 1188 068041 031959 2790 111202 250 275 148 1336 076518 023482 2050 134858 275 300 111 1447 082875 017125 1495 158094 300 325 81 1528 087514 012486 1090 180552 325 350 63 1591 091123 008877 775 204065 350 375 31 1622 092898 007102 620 219099 375 400 32 1654 094731 005269 460 238832 400 425 23 1677 096048 003952 345 257486 425 450 11 1688 096678 003322 290 268590 450 475 20 1708 097824 002176 190 295184 475 500 9 1717 098339 001661 145 311883 500 525 7 1724 098740 001260 110 328731 525 550 9 1733 099255 000745 065 360263 550 575 8 1741 099714 000286 025 415922 575 600 5 1746 1 0 000 DIV0 1746 20 year 873 Slope 085586 Intercept -104906 correlation 099524 beta 116842 gamma 122575
Hss for condition 1 10 668997
( )ss ssP P H H
1ss ssQ Q H H P
threshold 15 m
y = -07849Ln(x) + 16329
R2 = 09854
0
2
4
6
8
000010000100001000010000100000probability of exceedence
sto
rm h
eig
ht
Hss
February 1 2012 25
How to get storm exceedance
Q = probability of exceedance of a wave
Qs = probability of exceedance of a storm
s sQ N Qthreshold 15 m
y = -07849Ln(x) + 5141
R2 = 09854
0
2
4
6
8
10
001010100100010000
storm exceedence probability per year
sto
rm h
eig
ht
Hss
Statistically
nonsense
February 1 2012 26
The ldquoonce in 500 years stormrdquo
0785ln( )
10785ln 5141
500
100
ss sH Q
m
threshold 15 m
y = -07849Ln(x) + 5141
R2 = 09854
0
2
4
6
8
10
001010100100010000
storm exceedence probability per year
sto
rm h
eig
ht
Hss
February 1 2012 27
Using the Gumbel distribution
exp exp ssHP
February 1 2012 28
determination of and
ln exp
1ln ln
ss
ss
ssss
GAH B
HP
HP H
1ln lnG
P
Perform linear regression
for G = A Hss - B
February 1 2012 29
data for calculation of Gumbel 150 cumul P Q ln(Qs) -ln(H) Qs G
150 175 384 384 021993 078007 422098 -056 6810 -0415046
175 200 381 765 043814 056186 389284 -069 4905 0192121
200 225 266 1031 059049 040951 357655 -081 3575 0640938
225 250 157 1188 068041 031959 332863 -092 2790 0954366
250 275 148 1336 076518 023482 302042 -101 2050 1318085
275 300 111 1447 082875 017125 270471 -11 1495 1672191
300 325 81 1528 087514 012486 238876 -118 1090 2014645
325 350 63 1591 091123 008877 204769 -125 775 2375535
350 375 31 1622 092898 007102 182455 -132 620 2608194
375 400 32 1654 094731 005269 152606 -139 460 2916351
400 425 23 1677 096048 003952 123837 -145 345 3210883
425 450 11 1688 096678 003322 106471 -15 290 3387796
450 475 20 1708 097824 002176 064185 -156 190 3816515
475 500 9 1717 098339 001661 037156 -161 145 4089424
500 525 7 1724 098740 001260 009531 -166 110 4367707
525 550 9 1733 099255 000745 -043078 -17 065 4896399
550 575 8 1741 099714 000286 -138629 -175 025 5854211
575 600 5 1746 1 0 NUM -179 000 NUM
February 1 2012 30
Gumbel exceedance graph
Gumbel distribution
y = 07234x + 1882
R2 = 09871
0
2
4
6
8
10
0 2 4 6 8 10Gumbel Reduced variable
Sto
rm h
eig
ht
Hs
s
ssG AH B
= 1A = 0723
= B =1882
February 1 2012 31
calculation of a value
1ln ln
1ln ln
1
1ln ln
1
ln ln
ss
s
s
s
s s
HP
Q
QN
N
N Q
1500
873188 073ln ln 967
1873500
sH
= 1A = 073
= B =188
February 1 2012 32
transformation of the axis
Gumbel distribution
y = 07234x + 1882
R2 = 09871
0
2
4
6
8
10
0 2 4 6 8 10Gumbel Reduced variable
Sto
rm h
eig
ht
Hs
s
ln ln s
s s
NG
N Q
Ns = 873 storms per year
Qs G
110
1100
11000
110000
677
907
1138
1368
Figure Error No text of specified style in document-1 Storm exceedance on basis of Gumbel
10 100
February 1 2012 33
Weibull distribution
exp ssHQ
February 1 2012 34
determination of the reduced variable
1
1
ln
ln
1ln
ss
ss
ss
ss
WAH B
HQ
HQ
Q H
1
lnW Q
Three variables
and
So iteration is needed
February 1 2012 35
calculation for Weibull
alfa= 124
150 cumul P Q ln(Qs) -ln(H) Qs W
150 175 384 384 021993 078007 422098 -056 6810 032522
175 200 381 765 043814 056186 389284 -069 4905 064136
200 225 266 1031 059049 040951 357655 -081 3575 091261
225 250 157 1188 068041 031959 332863 -092 2790 111202
250 275 148 1336 076518 023482 302042 -101 2050 134858
275 300 111 1447 082875 017125 270471 -11 1495 158094
300 325 81 1528 087514 012486 238876 -118 1090 180552
325 350 63 1591 091123 008877 204769 -125 775 204065
350 375 31 1622 092898 007102 182455 -132 620 219099
375 400 32 1654 094731 005269 152606 -139 460 238832
400 425 23 1677 096048 003952 123837 -145 345 257486
425 450 11 1688 096678 003322 106471 -15 290 268590
450 475 20 1708 097824 002176 064185 -156 190 295184
475 500 9 1717 098339 001661 037156 -161 145 311883
500 525 7 1724 098740 001260 009531 -166 110 328731
525 550 9 1733 099255 000745 -043078 -17 065 360263
550 575 8 1741 099714 000286 -138629 -175 025 415922
575 600 5 1746 1 0 NUM -179 000 DIV0
1746
20 year 873 085586
-104906
099524
-07849
541 beta 116842
gamma 122575
Hs for condition 1 500 1028785 911838
1
lnssH Q
1
ln sss
s
QH
N
1124
1500
1500122 117 ln
873
122 117 675
912
sH
m
February 1 2012 36
Weibull exceedance graph
Weibull distribution
y = 11573x + 12497
R2 = 09905
0
2
4
6
8
10
0 2 4 6 8 10
Weibull Reduced variable
Str
om
heig
ht
Hss
10 100 1000 10000
February 1 2012 37
Summary
HT threshold value
Exponential
Gumbel
Weibull
150 m 163 m 136 m 122 m
HT 150 200 250 300 350 400
Ns 873 596 389 194 108 53
Hs 1500 Exponential Hs 1500 Gumbel Hs 1500 Weibull
1000 969 912
1009 950 990
948 917 963
939 893 948
908 886 917
876 818 890
February 1 2012 38
What to do if only random data are available
storm exceedance
0
200
400
600
800
01110100100010000
probability per year
Hs
s
February 1 2012 39
Example of long term data
This are
Hs-classes
February 1 2012 40
Long term (continuation)
So from this last column we can conclude
100 of time H gt 0 m s
23 of time H gt 1 m s
12 of time H gt 2 m s
001 of time H gt 9 m s
0
2
4
6
8
10
12
14
1E-071E-061E-051E-041E-031E-021E-011E+00
exceedance per year
wave
he
igh
t H
s (
m)
February 1 2012 41
From probability of waves to probability of storms
Suppose a ldquostormrdquo lasts for 12 hrs
===gt 730 stormsyear
once per year storm = 100730 = 013 =gt 67 m
once per 10 year storm = 0013 =gt 94 m
once per 100 year storm = 00013 =gt 119 m
0
5
10
15
20
1 10 100 1000 10000
return period in years
Hs o
f th
e g
ive
n s
torm
February 1 2012 42
Meteorological data
bull Not of direct importance for design
bull Can be important for hindcast of wave data and storm surge
bull Extremely important for the execution of the works (workability)
February 1 2012 43
Waves from Wind (Brettschneider)
February 1 2012 44
required soil data
February 1 2012 45
in situ test methods
February 1 2012 46
During construction
bull Quarry stone
bull Concrete
bull Local Equipment
bull Labour
bull skilled
bull cost
bull availability
bull expatriates
February 1 2012 17
Sample output of Hydrobase
February 1 2012 18
Data from Hydrobase
February 1 2012 19
data from Meetpost Noordwijk
wwwgolfklimaatnl
0
50
100
150
200
250
300
350
400
450
0 200 400 600 800
time (hrs)
Hm
o (
cm
)
January 1979
February 1 2012 20
basic data
date time Hm0 accur H13 TTE3 Tm02 TH13 wave wind wind level setup
dir dir speed
cm cm cm 1 s 1 s 1 s degr degr 1 ms cm cm
19980101 0100 70 4 64 6 39 49 261 210 60 -27 27 222224000
19980101 0400 72 4 65 8 36 45 264 210 70 91 24 222224000
19980101 0700 62 4 56 8 36 46 258 200 80 58 11 222224000
19980101 1000 93 5 85 11 40 48 234 190 90 -31 6 222224000
19980101 1300 110 5 102 14 44 51 230 200 90 -83 -5 222224000
19980101 1600 162 7 148 17 42 52 230 200 120 43 -12 222224000
19980101 1900 132 6 121 11 40 48 224 190 130 40 -37 222224000
19980101 2200 205 8 190 18 51 61 220 190 170 -39 -33 222224000
19980102 0100 247 10 230 37 56 68 229 190 170 -114 -57 222224000
19980102 0400 275 11 255 40 55 68 236 210 160 -1 -1 222224000
19980102 0700 208 8 193 20 50 63 234 200 140 -2 -72 222224000
19980102 1000 142 6 132 14 47 59 227 190 120 -59 -13 222224000
19980102 1300 130 6 120 14 50 64 223 160 110 -97 -22 222224000
19980102 1600 117 5 108 13 43 53 213 170 100 73 87 222224000
19980102 1900 91 5 84 10 39 49 232 210 100 152 58 222224000
19980102 2200 243 10 226 22 52 62 267 280 150 119 118 222224000
19980103 0100 287 12 269 32 59 70 269 260 110 25 73 222224000
19980103 0400 240 10 224 21 55 66 265 230 90 28 60 222224000
19980103 0700 177 7 163 13 46 56 245 200 130 122 37 222224000
19980103 1000 179 7 165 16 47 56 223 180 170 -30 3 222224000
19980103 1300 285 12 266 35 58 70 230 210 190 -43 16 222224000
19980103 1600 341 15 318 56 61 73 242 250 130 -36 14 222224000
19980103 1900 342 15 319 53 60 73 246 260 170 133 20 222224000
19980103 2200 414 21 388 85 65 77 249 260 190 72 46 222224000
19980104 0100 465 21 435 228 72 88 254 260 190 40 68 222224000
19980104 0400 358 16 334 92 64 78 259 240 90 -22 18 222224000
19980104 0700 324 14 302 52 60 73 256 250 120 129 43 222224000
19980104 1000 247 10 229 33 55 69 252 220 100 34 33 222224000
February 1 2012 21
sort data in classes
Waveheight class Hs (cm)
Number of observations
P Q -ln(Q)
0 25 35 35 0000599 0999401 0000599
25 50 8260 8295 0141940 0858060 0153082 50 75 11424 19719 0337423 0662577 0411618
75 100 10004 29723 0508607 0491393 0710511
100 125 7649 37372 0639493 0360507 1020245
125 150 5563 42935 0734685 0265315 1326838
150 175 4389 47324 0809788 0190212 1659615
175 200 3167 50491 0863980 0136020 1994954
200 225 2360 52851 0904363 0095637 2347200
225 250 1671 54522 0932957 0067043 2702419
250 275 1234 55756 0954073 0045927 3080692
275 300 851 56607 0968634 0031366 3462047
300 325 556 57163 0978149 0021851 3823487
325 350 392 57555 0984856 0015144 4190168
350 375 276 57831 0989579 0010421 4563938
375 400 206 58037 0993104 0006896 4976819
400 425 136 58173 0995431 0004569 5388507
425 450 82 58255 0996834 0003166 5755400
450 475 66 58321 0997964 0002036 6196632
475 500 38 58359 0998614 0001386 6581307
500 525 30 58389 0999127 0000873 7043930
525 550 20 58409 0999470 0000530 7541769
550 575 22 58431 0999846 0000154 8778531
575 600 9 58440 1000000 0000000
58440
( )s sP P H H
( ) 1s sQ Q H H P
all data Noordwijk
y = 00151x - 05001
R2 = 09881
0
1
2
3
4
5
6
7
8
9
10
0 200 400 600Hs-l
nQ
February 1 2012 22
exceedance graph for Noordwijk
indivudual observations
0
200
400
600
800
1000
000001000001000001000001000001000001000000
exceedance
wave h
eig
ht
But what means that in a year during 01
of the time the Hs is larger than 5 m
February 1 2012 23
Peak over Threshold method
A storm is defined as a time that the wave is higher than a
certain value the height of the storm Hss is equal to the
highest observed Hs during that storm
Threshold = 15
In this period 9
storms observed
nr Hss
1 180 m
2 294 m
3 225 m
4 176 m
5 261 m
6 389 m
7 172 m
8 240 m
9 194 m
February 1 2012 24
Table with Hss classes
= 124 Wave height class
150 cumul P Q Qs W
150 175 384 384 021993 078007 6810 032522 175 200 381 765 043814 056186 4905 064136 200 225 266 1031 059049 040951 3575 091261 225 250 157 1188 068041 031959 2790 111202 250 275 148 1336 076518 023482 2050 134858 275 300 111 1447 082875 017125 1495 158094 300 325 81 1528 087514 012486 1090 180552 325 350 63 1591 091123 008877 775 204065 350 375 31 1622 092898 007102 620 219099 375 400 32 1654 094731 005269 460 238832 400 425 23 1677 096048 003952 345 257486 425 450 11 1688 096678 003322 290 268590 450 475 20 1708 097824 002176 190 295184 475 500 9 1717 098339 001661 145 311883 500 525 7 1724 098740 001260 110 328731 525 550 9 1733 099255 000745 065 360263 550 575 8 1741 099714 000286 025 415922 575 600 5 1746 1 0 000 DIV0 1746 20 year 873 Slope 085586 Intercept -104906 correlation 099524 beta 116842 gamma 122575
Hss for condition 1 10 668997
( )ss ssP P H H
1ss ssQ Q H H P
threshold 15 m
y = -07849Ln(x) + 16329
R2 = 09854
0
2
4
6
8
000010000100001000010000100000probability of exceedence
sto
rm h
eig
ht
Hss
February 1 2012 25
How to get storm exceedance
Q = probability of exceedance of a wave
Qs = probability of exceedance of a storm
s sQ N Qthreshold 15 m
y = -07849Ln(x) + 5141
R2 = 09854
0
2
4
6
8
10
001010100100010000
storm exceedence probability per year
sto
rm h
eig
ht
Hss
Statistically
nonsense
February 1 2012 26
The ldquoonce in 500 years stormrdquo
0785ln( )
10785ln 5141
500
100
ss sH Q
m
threshold 15 m
y = -07849Ln(x) + 5141
R2 = 09854
0
2
4
6
8
10
001010100100010000
storm exceedence probability per year
sto
rm h
eig
ht
Hss
February 1 2012 27
Using the Gumbel distribution
exp exp ssHP
February 1 2012 28
determination of and
ln exp
1ln ln
ss
ss
ssss
GAH B
HP
HP H
1ln lnG
P
Perform linear regression
for G = A Hss - B
February 1 2012 29
data for calculation of Gumbel 150 cumul P Q ln(Qs) -ln(H) Qs G
150 175 384 384 021993 078007 422098 -056 6810 -0415046
175 200 381 765 043814 056186 389284 -069 4905 0192121
200 225 266 1031 059049 040951 357655 -081 3575 0640938
225 250 157 1188 068041 031959 332863 -092 2790 0954366
250 275 148 1336 076518 023482 302042 -101 2050 1318085
275 300 111 1447 082875 017125 270471 -11 1495 1672191
300 325 81 1528 087514 012486 238876 -118 1090 2014645
325 350 63 1591 091123 008877 204769 -125 775 2375535
350 375 31 1622 092898 007102 182455 -132 620 2608194
375 400 32 1654 094731 005269 152606 -139 460 2916351
400 425 23 1677 096048 003952 123837 -145 345 3210883
425 450 11 1688 096678 003322 106471 -15 290 3387796
450 475 20 1708 097824 002176 064185 -156 190 3816515
475 500 9 1717 098339 001661 037156 -161 145 4089424
500 525 7 1724 098740 001260 009531 -166 110 4367707
525 550 9 1733 099255 000745 -043078 -17 065 4896399
550 575 8 1741 099714 000286 -138629 -175 025 5854211
575 600 5 1746 1 0 NUM -179 000 NUM
February 1 2012 30
Gumbel exceedance graph
Gumbel distribution
y = 07234x + 1882
R2 = 09871
0
2
4
6
8
10
0 2 4 6 8 10Gumbel Reduced variable
Sto
rm h
eig
ht
Hs
s
ssG AH B
= 1A = 0723
= B =1882
February 1 2012 31
calculation of a value
1ln ln
1ln ln
1
1ln ln
1
ln ln
ss
s
s
s
s s
HP
Q
QN
N
N Q
1500
873188 073ln ln 967
1873500
sH
= 1A = 073
= B =188
February 1 2012 32
transformation of the axis
Gumbel distribution
y = 07234x + 1882
R2 = 09871
0
2
4
6
8
10
0 2 4 6 8 10Gumbel Reduced variable
Sto
rm h
eig
ht
Hs
s
ln ln s
s s
NG
N Q
Ns = 873 storms per year
Qs G
110
1100
11000
110000
677
907
1138
1368
Figure Error No text of specified style in document-1 Storm exceedance on basis of Gumbel
10 100
February 1 2012 33
Weibull distribution
exp ssHQ
February 1 2012 34
determination of the reduced variable
1
1
ln
ln
1ln
ss
ss
ss
ss
WAH B
HQ
HQ
Q H
1
lnW Q
Three variables
and
So iteration is needed
February 1 2012 35
calculation for Weibull
alfa= 124
150 cumul P Q ln(Qs) -ln(H) Qs W
150 175 384 384 021993 078007 422098 -056 6810 032522
175 200 381 765 043814 056186 389284 -069 4905 064136
200 225 266 1031 059049 040951 357655 -081 3575 091261
225 250 157 1188 068041 031959 332863 -092 2790 111202
250 275 148 1336 076518 023482 302042 -101 2050 134858
275 300 111 1447 082875 017125 270471 -11 1495 158094
300 325 81 1528 087514 012486 238876 -118 1090 180552
325 350 63 1591 091123 008877 204769 -125 775 204065
350 375 31 1622 092898 007102 182455 -132 620 219099
375 400 32 1654 094731 005269 152606 -139 460 238832
400 425 23 1677 096048 003952 123837 -145 345 257486
425 450 11 1688 096678 003322 106471 -15 290 268590
450 475 20 1708 097824 002176 064185 -156 190 295184
475 500 9 1717 098339 001661 037156 -161 145 311883
500 525 7 1724 098740 001260 009531 -166 110 328731
525 550 9 1733 099255 000745 -043078 -17 065 360263
550 575 8 1741 099714 000286 -138629 -175 025 415922
575 600 5 1746 1 0 NUM -179 000 DIV0
1746
20 year 873 085586
-104906
099524
-07849
541 beta 116842
gamma 122575
Hs for condition 1 500 1028785 911838
1
lnssH Q
1
ln sss
s
QH
N
1124
1500
1500122 117 ln
873
122 117 675
912
sH
m
February 1 2012 36
Weibull exceedance graph
Weibull distribution
y = 11573x + 12497
R2 = 09905
0
2
4
6
8
10
0 2 4 6 8 10
Weibull Reduced variable
Str
om
heig
ht
Hss
10 100 1000 10000
February 1 2012 37
Summary
HT threshold value
Exponential
Gumbel
Weibull
150 m 163 m 136 m 122 m
HT 150 200 250 300 350 400
Ns 873 596 389 194 108 53
Hs 1500 Exponential Hs 1500 Gumbel Hs 1500 Weibull
1000 969 912
1009 950 990
948 917 963
939 893 948
908 886 917
876 818 890
February 1 2012 38
What to do if only random data are available
storm exceedance
0
200
400
600
800
01110100100010000
probability per year
Hs
s
February 1 2012 39
Example of long term data
This are
Hs-classes
February 1 2012 40
Long term (continuation)
So from this last column we can conclude
100 of time H gt 0 m s
23 of time H gt 1 m s
12 of time H gt 2 m s
001 of time H gt 9 m s
0
2
4
6
8
10
12
14
1E-071E-061E-051E-041E-031E-021E-011E+00
exceedance per year
wave
he
igh
t H
s (
m)
February 1 2012 41
From probability of waves to probability of storms
Suppose a ldquostormrdquo lasts for 12 hrs
===gt 730 stormsyear
once per year storm = 100730 = 013 =gt 67 m
once per 10 year storm = 0013 =gt 94 m
once per 100 year storm = 00013 =gt 119 m
0
5
10
15
20
1 10 100 1000 10000
return period in years
Hs o
f th
e g
ive
n s
torm
February 1 2012 42
Meteorological data
bull Not of direct importance for design
bull Can be important for hindcast of wave data and storm surge
bull Extremely important for the execution of the works (workability)
February 1 2012 43
Waves from Wind (Brettschneider)
February 1 2012 44
required soil data
February 1 2012 45
in situ test methods
February 1 2012 46
During construction
bull Quarry stone
bull Concrete
bull Local Equipment
bull Labour
bull skilled
bull cost
bull availability
bull expatriates
February 1 2012 18
Data from Hydrobase
February 1 2012 19
data from Meetpost Noordwijk
wwwgolfklimaatnl
0
50
100
150
200
250
300
350
400
450
0 200 400 600 800
time (hrs)
Hm
o (
cm
)
January 1979
February 1 2012 20
basic data
date time Hm0 accur H13 TTE3 Tm02 TH13 wave wind wind level setup
dir dir speed
cm cm cm 1 s 1 s 1 s degr degr 1 ms cm cm
19980101 0100 70 4 64 6 39 49 261 210 60 -27 27 222224000
19980101 0400 72 4 65 8 36 45 264 210 70 91 24 222224000
19980101 0700 62 4 56 8 36 46 258 200 80 58 11 222224000
19980101 1000 93 5 85 11 40 48 234 190 90 -31 6 222224000
19980101 1300 110 5 102 14 44 51 230 200 90 -83 -5 222224000
19980101 1600 162 7 148 17 42 52 230 200 120 43 -12 222224000
19980101 1900 132 6 121 11 40 48 224 190 130 40 -37 222224000
19980101 2200 205 8 190 18 51 61 220 190 170 -39 -33 222224000
19980102 0100 247 10 230 37 56 68 229 190 170 -114 -57 222224000
19980102 0400 275 11 255 40 55 68 236 210 160 -1 -1 222224000
19980102 0700 208 8 193 20 50 63 234 200 140 -2 -72 222224000
19980102 1000 142 6 132 14 47 59 227 190 120 -59 -13 222224000
19980102 1300 130 6 120 14 50 64 223 160 110 -97 -22 222224000
19980102 1600 117 5 108 13 43 53 213 170 100 73 87 222224000
19980102 1900 91 5 84 10 39 49 232 210 100 152 58 222224000
19980102 2200 243 10 226 22 52 62 267 280 150 119 118 222224000
19980103 0100 287 12 269 32 59 70 269 260 110 25 73 222224000
19980103 0400 240 10 224 21 55 66 265 230 90 28 60 222224000
19980103 0700 177 7 163 13 46 56 245 200 130 122 37 222224000
19980103 1000 179 7 165 16 47 56 223 180 170 -30 3 222224000
19980103 1300 285 12 266 35 58 70 230 210 190 -43 16 222224000
19980103 1600 341 15 318 56 61 73 242 250 130 -36 14 222224000
19980103 1900 342 15 319 53 60 73 246 260 170 133 20 222224000
19980103 2200 414 21 388 85 65 77 249 260 190 72 46 222224000
19980104 0100 465 21 435 228 72 88 254 260 190 40 68 222224000
19980104 0400 358 16 334 92 64 78 259 240 90 -22 18 222224000
19980104 0700 324 14 302 52 60 73 256 250 120 129 43 222224000
19980104 1000 247 10 229 33 55 69 252 220 100 34 33 222224000
February 1 2012 21
sort data in classes
Waveheight class Hs (cm)
Number of observations
P Q -ln(Q)
0 25 35 35 0000599 0999401 0000599
25 50 8260 8295 0141940 0858060 0153082 50 75 11424 19719 0337423 0662577 0411618
75 100 10004 29723 0508607 0491393 0710511
100 125 7649 37372 0639493 0360507 1020245
125 150 5563 42935 0734685 0265315 1326838
150 175 4389 47324 0809788 0190212 1659615
175 200 3167 50491 0863980 0136020 1994954
200 225 2360 52851 0904363 0095637 2347200
225 250 1671 54522 0932957 0067043 2702419
250 275 1234 55756 0954073 0045927 3080692
275 300 851 56607 0968634 0031366 3462047
300 325 556 57163 0978149 0021851 3823487
325 350 392 57555 0984856 0015144 4190168
350 375 276 57831 0989579 0010421 4563938
375 400 206 58037 0993104 0006896 4976819
400 425 136 58173 0995431 0004569 5388507
425 450 82 58255 0996834 0003166 5755400
450 475 66 58321 0997964 0002036 6196632
475 500 38 58359 0998614 0001386 6581307
500 525 30 58389 0999127 0000873 7043930
525 550 20 58409 0999470 0000530 7541769
550 575 22 58431 0999846 0000154 8778531
575 600 9 58440 1000000 0000000
58440
( )s sP P H H
( ) 1s sQ Q H H P
all data Noordwijk
y = 00151x - 05001
R2 = 09881
0
1
2
3
4
5
6
7
8
9
10
0 200 400 600Hs-l
nQ
February 1 2012 22
exceedance graph for Noordwijk
indivudual observations
0
200
400
600
800
1000
000001000001000001000001000001000001000000
exceedance
wave h
eig
ht
But what means that in a year during 01
of the time the Hs is larger than 5 m
February 1 2012 23
Peak over Threshold method
A storm is defined as a time that the wave is higher than a
certain value the height of the storm Hss is equal to the
highest observed Hs during that storm
Threshold = 15
In this period 9
storms observed
nr Hss
1 180 m
2 294 m
3 225 m
4 176 m
5 261 m
6 389 m
7 172 m
8 240 m
9 194 m
February 1 2012 24
Table with Hss classes
= 124 Wave height class
150 cumul P Q Qs W
150 175 384 384 021993 078007 6810 032522 175 200 381 765 043814 056186 4905 064136 200 225 266 1031 059049 040951 3575 091261 225 250 157 1188 068041 031959 2790 111202 250 275 148 1336 076518 023482 2050 134858 275 300 111 1447 082875 017125 1495 158094 300 325 81 1528 087514 012486 1090 180552 325 350 63 1591 091123 008877 775 204065 350 375 31 1622 092898 007102 620 219099 375 400 32 1654 094731 005269 460 238832 400 425 23 1677 096048 003952 345 257486 425 450 11 1688 096678 003322 290 268590 450 475 20 1708 097824 002176 190 295184 475 500 9 1717 098339 001661 145 311883 500 525 7 1724 098740 001260 110 328731 525 550 9 1733 099255 000745 065 360263 550 575 8 1741 099714 000286 025 415922 575 600 5 1746 1 0 000 DIV0 1746 20 year 873 Slope 085586 Intercept -104906 correlation 099524 beta 116842 gamma 122575
Hss for condition 1 10 668997
( )ss ssP P H H
1ss ssQ Q H H P
threshold 15 m
y = -07849Ln(x) + 16329
R2 = 09854
0
2
4
6
8
000010000100001000010000100000probability of exceedence
sto
rm h
eig
ht
Hss
February 1 2012 25
How to get storm exceedance
Q = probability of exceedance of a wave
Qs = probability of exceedance of a storm
s sQ N Qthreshold 15 m
y = -07849Ln(x) + 5141
R2 = 09854
0
2
4
6
8
10
001010100100010000
storm exceedence probability per year
sto
rm h
eig
ht
Hss
Statistically
nonsense
February 1 2012 26
The ldquoonce in 500 years stormrdquo
0785ln( )
10785ln 5141
500
100
ss sH Q
m
threshold 15 m
y = -07849Ln(x) + 5141
R2 = 09854
0
2
4
6
8
10
001010100100010000
storm exceedence probability per year
sto
rm h
eig
ht
Hss
February 1 2012 27
Using the Gumbel distribution
exp exp ssHP
February 1 2012 28
determination of and
ln exp
1ln ln
ss
ss
ssss
GAH B
HP
HP H
1ln lnG
P
Perform linear regression
for G = A Hss - B
February 1 2012 29
data for calculation of Gumbel 150 cumul P Q ln(Qs) -ln(H) Qs G
150 175 384 384 021993 078007 422098 -056 6810 -0415046
175 200 381 765 043814 056186 389284 -069 4905 0192121
200 225 266 1031 059049 040951 357655 -081 3575 0640938
225 250 157 1188 068041 031959 332863 -092 2790 0954366
250 275 148 1336 076518 023482 302042 -101 2050 1318085
275 300 111 1447 082875 017125 270471 -11 1495 1672191
300 325 81 1528 087514 012486 238876 -118 1090 2014645
325 350 63 1591 091123 008877 204769 -125 775 2375535
350 375 31 1622 092898 007102 182455 -132 620 2608194
375 400 32 1654 094731 005269 152606 -139 460 2916351
400 425 23 1677 096048 003952 123837 -145 345 3210883
425 450 11 1688 096678 003322 106471 -15 290 3387796
450 475 20 1708 097824 002176 064185 -156 190 3816515
475 500 9 1717 098339 001661 037156 -161 145 4089424
500 525 7 1724 098740 001260 009531 -166 110 4367707
525 550 9 1733 099255 000745 -043078 -17 065 4896399
550 575 8 1741 099714 000286 -138629 -175 025 5854211
575 600 5 1746 1 0 NUM -179 000 NUM
February 1 2012 30
Gumbel exceedance graph
Gumbel distribution
y = 07234x + 1882
R2 = 09871
0
2
4
6
8
10
0 2 4 6 8 10Gumbel Reduced variable
Sto
rm h
eig
ht
Hs
s
ssG AH B
= 1A = 0723
= B =1882
February 1 2012 31
calculation of a value
1ln ln
1ln ln
1
1ln ln
1
ln ln
ss
s
s
s
s s
HP
Q
QN
N
N Q
1500
873188 073ln ln 967
1873500
sH
= 1A = 073
= B =188
February 1 2012 32
transformation of the axis
Gumbel distribution
y = 07234x + 1882
R2 = 09871
0
2
4
6
8
10
0 2 4 6 8 10Gumbel Reduced variable
Sto
rm h
eig
ht
Hs
s
ln ln s
s s
NG
N Q
Ns = 873 storms per year
Qs G
110
1100
11000
110000
677
907
1138
1368
Figure Error No text of specified style in document-1 Storm exceedance on basis of Gumbel
10 100
February 1 2012 33
Weibull distribution
exp ssHQ
February 1 2012 34
determination of the reduced variable
1
1
ln
ln
1ln
ss
ss
ss
ss
WAH B
HQ
HQ
Q H
1
lnW Q
Three variables
and
So iteration is needed
February 1 2012 35
calculation for Weibull
alfa= 124
150 cumul P Q ln(Qs) -ln(H) Qs W
150 175 384 384 021993 078007 422098 -056 6810 032522
175 200 381 765 043814 056186 389284 -069 4905 064136
200 225 266 1031 059049 040951 357655 -081 3575 091261
225 250 157 1188 068041 031959 332863 -092 2790 111202
250 275 148 1336 076518 023482 302042 -101 2050 134858
275 300 111 1447 082875 017125 270471 -11 1495 158094
300 325 81 1528 087514 012486 238876 -118 1090 180552
325 350 63 1591 091123 008877 204769 -125 775 204065
350 375 31 1622 092898 007102 182455 -132 620 219099
375 400 32 1654 094731 005269 152606 -139 460 238832
400 425 23 1677 096048 003952 123837 -145 345 257486
425 450 11 1688 096678 003322 106471 -15 290 268590
450 475 20 1708 097824 002176 064185 -156 190 295184
475 500 9 1717 098339 001661 037156 -161 145 311883
500 525 7 1724 098740 001260 009531 -166 110 328731
525 550 9 1733 099255 000745 -043078 -17 065 360263
550 575 8 1741 099714 000286 -138629 -175 025 415922
575 600 5 1746 1 0 NUM -179 000 DIV0
1746
20 year 873 085586
-104906
099524
-07849
541 beta 116842
gamma 122575
Hs for condition 1 500 1028785 911838
1
lnssH Q
1
ln sss
s
QH
N
1124
1500
1500122 117 ln
873
122 117 675
912
sH
m
February 1 2012 36
Weibull exceedance graph
Weibull distribution
y = 11573x + 12497
R2 = 09905
0
2
4
6
8
10
0 2 4 6 8 10
Weibull Reduced variable
Str
om
heig
ht
Hss
10 100 1000 10000
February 1 2012 37
Summary
HT threshold value
Exponential
Gumbel
Weibull
150 m 163 m 136 m 122 m
HT 150 200 250 300 350 400
Ns 873 596 389 194 108 53
Hs 1500 Exponential Hs 1500 Gumbel Hs 1500 Weibull
1000 969 912
1009 950 990
948 917 963
939 893 948
908 886 917
876 818 890
February 1 2012 38
What to do if only random data are available
storm exceedance
0
200
400
600
800
01110100100010000
probability per year
Hs
s
February 1 2012 39
Example of long term data
This are
Hs-classes
February 1 2012 40
Long term (continuation)
So from this last column we can conclude
100 of time H gt 0 m s
23 of time H gt 1 m s
12 of time H gt 2 m s
001 of time H gt 9 m s
0
2
4
6
8
10
12
14
1E-071E-061E-051E-041E-031E-021E-011E+00
exceedance per year
wave
he
igh
t H
s (
m)
February 1 2012 41
From probability of waves to probability of storms
Suppose a ldquostormrdquo lasts for 12 hrs
===gt 730 stormsyear
once per year storm = 100730 = 013 =gt 67 m
once per 10 year storm = 0013 =gt 94 m
once per 100 year storm = 00013 =gt 119 m
0
5
10
15
20
1 10 100 1000 10000
return period in years
Hs o
f th
e g
ive
n s
torm
February 1 2012 42
Meteorological data
bull Not of direct importance for design
bull Can be important for hindcast of wave data and storm surge
bull Extremely important for the execution of the works (workability)
February 1 2012 43
Waves from Wind (Brettschneider)
February 1 2012 44
required soil data
February 1 2012 45
in situ test methods
February 1 2012 46
During construction
bull Quarry stone
bull Concrete
bull Local Equipment
bull Labour
bull skilled
bull cost
bull availability
bull expatriates
February 1 2012 19
data from Meetpost Noordwijk
wwwgolfklimaatnl
0
50
100
150
200
250
300
350
400
450
0 200 400 600 800
time (hrs)
Hm
o (
cm
)
January 1979
February 1 2012 20
basic data
date time Hm0 accur H13 TTE3 Tm02 TH13 wave wind wind level setup
dir dir speed
cm cm cm 1 s 1 s 1 s degr degr 1 ms cm cm
19980101 0100 70 4 64 6 39 49 261 210 60 -27 27 222224000
19980101 0400 72 4 65 8 36 45 264 210 70 91 24 222224000
19980101 0700 62 4 56 8 36 46 258 200 80 58 11 222224000
19980101 1000 93 5 85 11 40 48 234 190 90 -31 6 222224000
19980101 1300 110 5 102 14 44 51 230 200 90 -83 -5 222224000
19980101 1600 162 7 148 17 42 52 230 200 120 43 -12 222224000
19980101 1900 132 6 121 11 40 48 224 190 130 40 -37 222224000
19980101 2200 205 8 190 18 51 61 220 190 170 -39 -33 222224000
19980102 0100 247 10 230 37 56 68 229 190 170 -114 -57 222224000
19980102 0400 275 11 255 40 55 68 236 210 160 -1 -1 222224000
19980102 0700 208 8 193 20 50 63 234 200 140 -2 -72 222224000
19980102 1000 142 6 132 14 47 59 227 190 120 -59 -13 222224000
19980102 1300 130 6 120 14 50 64 223 160 110 -97 -22 222224000
19980102 1600 117 5 108 13 43 53 213 170 100 73 87 222224000
19980102 1900 91 5 84 10 39 49 232 210 100 152 58 222224000
19980102 2200 243 10 226 22 52 62 267 280 150 119 118 222224000
19980103 0100 287 12 269 32 59 70 269 260 110 25 73 222224000
19980103 0400 240 10 224 21 55 66 265 230 90 28 60 222224000
19980103 0700 177 7 163 13 46 56 245 200 130 122 37 222224000
19980103 1000 179 7 165 16 47 56 223 180 170 -30 3 222224000
19980103 1300 285 12 266 35 58 70 230 210 190 -43 16 222224000
19980103 1600 341 15 318 56 61 73 242 250 130 -36 14 222224000
19980103 1900 342 15 319 53 60 73 246 260 170 133 20 222224000
19980103 2200 414 21 388 85 65 77 249 260 190 72 46 222224000
19980104 0100 465 21 435 228 72 88 254 260 190 40 68 222224000
19980104 0400 358 16 334 92 64 78 259 240 90 -22 18 222224000
19980104 0700 324 14 302 52 60 73 256 250 120 129 43 222224000
19980104 1000 247 10 229 33 55 69 252 220 100 34 33 222224000
February 1 2012 21
sort data in classes
Waveheight class Hs (cm)
Number of observations
P Q -ln(Q)
0 25 35 35 0000599 0999401 0000599
25 50 8260 8295 0141940 0858060 0153082 50 75 11424 19719 0337423 0662577 0411618
75 100 10004 29723 0508607 0491393 0710511
100 125 7649 37372 0639493 0360507 1020245
125 150 5563 42935 0734685 0265315 1326838
150 175 4389 47324 0809788 0190212 1659615
175 200 3167 50491 0863980 0136020 1994954
200 225 2360 52851 0904363 0095637 2347200
225 250 1671 54522 0932957 0067043 2702419
250 275 1234 55756 0954073 0045927 3080692
275 300 851 56607 0968634 0031366 3462047
300 325 556 57163 0978149 0021851 3823487
325 350 392 57555 0984856 0015144 4190168
350 375 276 57831 0989579 0010421 4563938
375 400 206 58037 0993104 0006896 4976819
400 425 136 58173 0995431 0004569 5388507
425 450 82 58255 0996834 0003166 5755400
450 475 66 58321 0997964 0002036 6196632
475 500 38 58359 0998614 0001386 6581307
500 525 30 58389 0999127 0000873 7043930
525 550 20 58409 0999470 0000530 7541769
550 575 22 58431 0999846 0000154 8778531
575 600 9 58440 1000000 0000000
58440
( )s sP P H H
( ) 1s sQ Q H H P
all data Noordwijk
y = 00151x - 05001
R2 = 09881
0
1
2
3
4
5
6
7
8
9
10
0 200 400 600Hs-l
nQ
February 1 2012 22
exceedance graph for Noordwijk
indivudual observations
0
200
400
600
800
1000
000001000001000001000001000001000001000000
exceedance
wave h
eig
ht
But what means that in a year during 01
of the time the Hs is larger than 5 m
February 1 2012 23
Peak over Threshold method
A storm is defined as a time that the wave is higher than a
certain value the height of the storm Hss is equal to the
highest observed Hs during that storm
Threshold = 15
In this period 9
storms observed
nr Hss
1 180 m
2 294 m
3 225 m
4 176 m
5 261 m
6 389 m
7 172 m
8 240 m
9 194 m
February 1 2012 24
Table with Hss classes
= 124 Wave height class
150 cumul P Q Qs W
150 175 384 384 021993 078007 6810 032522 175 200 381 765 043814 056186 4905 064136 200 225 266 1031 059049 040951 3575 091261 225 250 157 1188 068041 031959 2790 111202 250 275 148 1336 076518 023482 2050 134858 275 300 111 1447 082875 017125 1495 158094 300 325 81 1528 087514 012486 1090 180552 325 350 63 1591 091123 008877 775 204065 350 375 31 1622 092898 007102 620 219099 375 400 32 1654 094731 005269 460 238832 400 425 23 1677 096048 003952 345 257486 425 450 11 1688 096678 003322 290 268590 450 475 20 1708 097824 002176 190 295184 475 500 9 1717 098339 001661 145 311883 500 525 7 1724 098740 001260 110 328731 525 550 9 1733 099255 000745 065 360263 550 575 8 1741 099714 000286 025 415922 575 600 5 1746 1 0 000 DIV0 1746 20 year 873 Slope 085586 Intercept -104906 correlation 099524 beta 116842 gamma 122575
Hss for condition 1 10 668997
( )ss ssP P H H
1ss ssQ Q H H P
threshold 15 m
y = -07849Ln(x) + 16329
R2 = 09854
0
2
4
6
8
000010000100001000010000100000probability of exceedence
sto
rm h
eig
ht
Hss
February 1 2012 25
How to get storm exceedance
Q = probability of exceedance of a wave
Qs = probability of exceedance of a storm
s sQ N Qthreshold 15 m
y = -07849Ln(x) + 5141
R2 = 09854
0
2
4
6
8
10
001010100100010000
storm exceedence probability per year
sto
rm h
eig
ht
Hss
Statistically
nonsense
February 1 2012 26
The ldquoonce in 500 years stormrdquo
0785ln( )
10785ln 5141
500
100
ss sH Q
m
threshold 15 m
y = -07849Ln(x) + 5141
R2 = 09854
0
2
4
6
8
10
001010100100010000
storm exceedence probability per year
sto
rm h
eig
ht
Hss
February 1 2012 27
Using the Gumbel distribution
exp exp ssHP
February 1 2012 28
determination of and
ln exp
1ln ln
ss
ss
ssss
GAH B
HP
HP H
1ln lnG
P
Perform linear regression
for G = A Hss - B
February 1 2012 29
data for calculation of Gumbel 150 cumul P Q ln(Qs) -ln(H) Qs G
150 175 384 384 021993 078007 422098 -056 6810 -0415046
175 200 381 765 043814 056186 389284 -069 4905 0192121
200 225 266 1031 059049 040951 357655 -081 3575 0640938
225 250 157 1188 068041 031959 332863 -092 2790 0954366
250 275 148 1336 076518 023482 302042 -101 2050 1318085
275 300 111 1447 082875 017125 270471 -11 1495 1672191
300 325 81 1528 087514 012486 238876 -118 1090 2014645
325 350 63 1591 091123 008877 204769 -125 775 2375535
350 375 31 1622 092898 007102 182455 -132 620 2608194
375 400 32 1654 094731 005269 152606 -139 460 2916351
400 425 23 1677 096048 003952 123837 -145 345 3210883
425 450 11 1688 096678 003322 106471 -15 290 3387796
450 475 20 1708 097824 002176 064185 -156 190 3816515
475 500 9 1717 098339 001661 037156 -161 145 4089424
500 525 7 1724 098740 001260 009531 -166 110 4367707
525 550 9 1733 099255 000745 -043078 -17 065 4896399
550 575 8 1741 099714 000286 -138629 -175 025 5854211
575 600 5 1746 1 0 NUM -179 000 NUM
February 1 2012 30
Gumbel exceedance graph
Gumbel distribution
y = 07234x + 1882
R2 = 09871
0
2
4
6
8
10
0 2 4 6 8 10Gumbel Reduced variable
Sto
rm h
eig
ht
Hs
s
ssG AH B
= 1A = 0723
= B =1882
February 1 2012 31
calculation of a value
1ln ln
1ln ln
1
1ln ln
1
ln ln
ss
s
s
s
s s
HP
Q
QN
N
N Q
1500
873188 073ln ln 967
1873500
sH
= 1A = 073
= B =188
February 1 2012 32
transformation of the axis
Gumbel distribution
y = 07234x + 1882
R2 = 09871
0
2
4
6
8
10
0 2 4 6 8 10Gumbel Reduced variable
Sto
rm h
eig
ht
Hs
s
ln ln s
s s
NG
N Q
Ns = 873 storms per year
Qs G
110
1100
11000
110000
677
907
1138
1368
Figure Error No text of specified style in document-1 Storm exceedance on basis of Gumbel
10 100
February 1 2012 33
Weibull distribution
exp ssHQ
February 1 2012 34
determination of the reduced variable
1
1
ln
ln
1ln
ss
ss
ss
ss
WAH B
HQ
HQ
Q H
1
lnW Q
Three variables
and
So iteration is needed
February 1 2012 35
calculation for Weibull
alfa= 124
150 cumul P Q ln(Qs) -ln(H) Qs W
150 175 384 384 021993 078007 422098 -056 6810 032522
175 200 381 765 043814 056186 389284 -069 4905 064136
200 225 266 1031 059049 040951 357655 -081 3575 091261
225 250 157 1188 068041 031959 332863 -092 2790 111202
250 275 148 1336 076518 023482 302042 -101 2050 134858
275 300 111 1447 082875 017125 270471 -11 1495 158094
300 325 81 1528 087514 012486 238876 -118 1090 180552
325 350 63 1591 091123 008877 204769 -125 775 204065
350 375 31 1622 092898 007102 182455 -132 620 219099
375 400 32 1654 094731 005269 152606 -139 460 238832
400 425 23 1677 096048 003952 123837 -145 345 257486
425 450 11 1688 096678 003322 106471 -15 290 268590
450 475 20 1708 097824 002176 064185 -156 190 295184
475 500 9 1717 098339 001661 037156 -161 145 311883
500 525 7 1724 098740 001260 009531 -166 110 328731
525 550 9 1733 099255 000745 -043078 -17 065 360263
550 575 8 1741 099714 000286 -138629 -175 025 415922
575 600 5 1746 1 0 NUM -179 000 DIV0
1746
20 year 873 085586
-104906
099524
-07849
541 beta 116842
gamma 122575
Hs for condition 1 500 1028785 911838
1
lnssH Q
1
ln sss
s
QH
N
1124
1500
1500122 117 ln
873
122 117 675
912
sH
m
February 1 2012 36
Weibull exceedance graph
Weibull distribution
y = 11573x + 12497
R2 = 09905
0
2
4
6
8
10
0 2 4 6 8 10
Weibull Reduced variable
Str
om
heig
ht
Hss
10 100 1000 10000
February 1 2012 37
Summary
HT threshold value
Exponential
Gumbel
Weibull
150 m 163 m 136 m 122 m
HT 150 200 250 300 350 400
Ns 873 596 389 194 108 53
Hs 1500 Exponential Hs 1500 Gumbel Hs 1500 Weibull
1000 969 912
1009 950 990
948 917 963
939 893 948
908 886 917
876 818 890
February 1 2012 38
What to do if only random data are available
storm exceedance
0
200
400
600
800
01110100100010000
probability per year
Hs
s
February 1 2012 39
Example of long term data
This are
Hs-classes
February 1 2012 40
Long term (continuation)
So from this last column we can conclude
100 of time H gt 0 m s
23 of time H gt 1 m s
12 of time H gt 2 m s
001 of time H gt 9 m s
0
2
4
6
8
10
12
14
1E-071E-061E-051E-041E-031E-021E-011E+00
exceedance per year
wave
he
igh
t H
s (
m)
February 1 2012 41
From probability of waves to probability of storms
Suppose a ldquostormrdquo lasts for 12 hrs
===gt 730 stormsyear
once per year storm = 100730 = 013 =gt 67 m
once per 10 year storm = 0013 =gt 94 m
once per 100 year storm = 00013 =gt 119 m
0
5
10
15
20
1 10 100 1000 10000
return period in years
Hs o
f th
e g
ive
n s
torm
February 1 2012 42
Meteorological data
bull Not of direct importance for design
bull Can be important for hindcast of wave data and storm surge
bull Extremely important for the execution of the works (workability)
February 1 2012 43
Waves from Wind (Brettschneider)
February 1 2012 44
required soil data
February 1 2012 45
in situ test methods
February 1 2012 46
During construction
bull Quarry stone
bull Concrete
bull Local Equipment
bull Labour
bull skilled
bull cost
bull availability
bull expatriates
February 1 2012 20
basic data
date time Hm0 accur H13 TTE3 Tm02 TH13 wave wind wind level setup
dir dir speed
cm cm cm 1 s 1 s 1 s degr degr 1 ms cm cm
19980101 0100 70 4 64 6 39 49 261 210 60 -27 27 222224000
19980101 0400 72 4 65 8 36 45 264 210 70 91 24 222224000
19980101 0700 62 4 56 8 36 46 258 200 80 58 11 222224000
19980101 1000 93 5 85 11 40 48 234 190 90 -31 6 222224000
19980101 1300 110 5 102 14 44 51 230 200 90 -83 -5 222224000
19980101 1600 162 7 148 17 42 52 230 200 120 43 -12 222224000
19980101 1900 132 6 121 11 40 48 224 190 130 40 -37 222224000
19980101 2200 205 8 190 18 51 61 220 190 170 -39 -33 222224000
19980102 0100 247 10 230 37 56 68 229 190 170 -114 -57 222224000
19980102 0400 275 11 255 40 55 68 236 210 160 -1 -1 222224000
19980102 0700 208 8 193 20 50 63 234 200 140 -2 -72 222224000
19980102 1000 142 6 132 14 47 59 227 190 120 -59 -13 222224000
19980102 1300 130 6 120 14 50 64 223 160 110 -97 -22 222224000
19980102 1600 117 5 108 13 43 53 213 170 100 73 87 222224000
19980102 1900 91 5 84 10 39 49 232 210 100 152 58 222224000
19980102 2200 243 10 226 22 52 62 267 280 150 119 118 222224000
19980103 0100 287 12 269 32 59 70 269 260 110 25 73 222224000
19980103 0400 240 10 224 21 55 66 265 230 90 28 60 222224000
19980103 0700 177 7 163 13 46 56 245 200 130 122 37 222224000
19980103 1000 179 7 165 16 47 56 223 180 170 -30 3 222224000
19980103 1300 285 12 266 35 58 70 230 210 190 -43 16 222224000
19980103 1600 341 15 318 56 61 73 242 250 130 -36 14 222224000
19980103 1900 342 15 319 53 60 73 246 260 170 133 20 222224000
19980103 2200 414 21 388 85 65 77 249 260 190 72 46 222224000
19980104 0100 465 21 435 228 72 88 254 260 190 40 68 222224000
19980104 0400 358 16 334 92 64 78 259 240 90 -22 18 222224000
19980104 0700 324 14 302 52 60 73 256 250 120 129 43 222224000
19980104 1000 247 10 229 33 55 69 252 220 100 34 33 222224000
February 1 2012 21
sort data in classes
Waveheight class Hs (cm)
Number of observations
P Q -ln(Q)
0 25 35 35 0000599 0999401 0000599
25 50 8260 8295 0141940 0858060 0153082 50 75 11424 19719 0337423 0662577 0411618
75 100 10004 29723 0508607 0491393 0710511
100 125 7649 37372 0639493 0360507 1020245
125 150 5563 42935 0734685 0265315 1326838
150 175 4389 47324 0809788 0190212 1659615
175 200 3167 50491 0863980 0136020 1994954
200 225 2360 52851 0904363 0095637 2347200
225 250 1671 54522 0932957 0067043 2702419
250 275 1234 55756 0954073 0045927 3080692
275 300 851 56607 0968634 0031366 3462047
300 325 556 57163 0978149 0021851 3823487
325 350 392 57555 0984856 0015144 4190168
350 375 276 57831 0989579 0010421 4563938
375 400 206 58037 0993104 0006896 4976819
400 425 136 58173 0995431 0004569 5388507
425 450 82 58255 0996834 0003166 5755400
450 475 66 58321 0997964 0002036 6196632
475 500 38 58359 0998614 0001386 6581307
500 525 30 58389 0999127 0000873 7043930
525 550 20 58409 0999470 0000530 7541769
550 575 22 58431 0999846 0000154 8778531
575 600 9 58440 1000000 0000000
58440
( )s sP P H H
( ) 1s sQ Q H H P
all data Noordwijk
y = 00151x - 05001
R2 = 09881
0
1
2
3
4
5
6
7
8
9
10
0 200 400 600Hs-l
nQ
February 1 2012 22
exceedance graph for Noordwijk
indivudual observations
0
200
400
600
800
1000
000001000001000001000001000001000001000000
exceedance
wave h
eig
ht
But what means that in a year during 01
of the time the Hs is larger than 5 m
February 1 2012 23
Peak over Threshold method
A storm is defined as a time that the wave is higher than a
certain value the height of the storm Hss is equal to the
highest observed Hs during that storm
Threshold = 15
In this period 9
storms observed
nr Hss
1 180 m
2 294 m
3 225 m
4 176 m
5 261 m
6 389 m
7 172 m
8 240 m
9 194 m
February 1 2012 24
Table with Hss classes
= 124 Wave height class
150 cumul P Q Qs W
150 175 384 384 021993 078007 6810 032522 175 200 381 765 043814 056186 4905 064136 200 225 266 1031 059049 040951 3575 091261 225 250 157 1188 068041 031959 2790 111202 250 275 148 1336 076518 023482 2050 134858 275 300 111 1447 082875 017125 1495 158094 300 325 81 1528 087514 012486 1090 180552 325 350 63 1591 091123 008877 775 204065 350 375 31 1622 092898 007102 620 219099 375 400 32 1654 094731 005269 460 238832 400 425 23 1677 096048 003952 345 257486 425 450 11 1688 096678 003322 290 268590 450 475 20 1708 097824 002176 190 295184 475 500 9 1717 098339 001661 145 311883 500 525 7 1724 098740 001260 110 328731 525 550 9 1733 099255 000745 065 360263 550 575 8 1741 099714 000286 025 415922 575 600 5 1746 1 0 000 DIV0 1746 20 year 873 Slope 085586 Intercept -104906 correlation 099524 beta 116842 gamma 122575
Hss for condition 1 10 668997
( )ss ssP P H H
1ss ssQ Q H H P
threshold 15 m
y = -07849Ln(x) + 16329
R2 = 09854
0
2
4
6
8
000010000100001000010000100000probability of exceedence
sto
rm h
eig
ht
Hss
February 1 2012 25
How to get storm exceedance
Q = probability of exceedance of a wave
Qs = probability of exceedance of a storm
s sQ N Qthreshold 15 m
y = -07849Ln(x) + 5141
R2 = 09854
0
2
4
6
8
10
001010100100010000
storm exceedence probability per year
sto
rm h
eig
ht
Hss
Statistically
nonsense
February 1 2012 26
The ldquoonce in 500 years stormrdquo
0785ln( )
10785ln 5141
500
100
ss sH Q
m
threshold 15 m
y = -07849Ln(x) + 5141
R2 = 09854
0
2
4
6
8
10
001010100100010000
storm exceedence probability per year
sto
rm h
eig
ht
Hss
February 1 2012 27
Using the Gumbel distribution
exp exp ssHP
February 1 2012 28
determination of and
ln exp
1ln ln
ss
ss
ssss
GAH B
HP
HP H
1ln lnG
P
Perform linear regression
for G = A Hss - B
February 1 2012 29
data for calculation of Gumbel 150 cumul P Q ln(Qs) -ln(H) Qs G
150 175 384 384 021993 078007 422098 -056 6810 -0415046
175 200 381 765 043814 056186 389284 -069 4905 0192121
200 225 266 1031 059049 040951 357655 -081 3575 0640938
225 250 157 1188 068041 031959 332863 -092 2790 0954366
250 275 148 1336 076518 023482 302042 -101 2050 1318085
275 300 111 1447 082875 017125 270471 -11 1495 1672191
300 325 81 1528 087514 012486 238876 -118 1090 2014645
325 350 63 1591 091123 008877 204769 -125 775 2375535
350 375 31 1622 092898 007102 182455 -132 620 2608194
375 400 32 1654 094731 005269 152606 -139 460 2916351
400 425 23 1677 096048 003952 123837 -145 345 3210883
425 450 11 1688 096678 003322 106471 -15 290 3387796
450 475 20 1708 097824 002176 064185 -156 190 3816515
475 500 9 1717 098339 001661 037156 -161 145 4089424
500 525 7 1724 098740 001260 009531 -166 110 4367707
525 550 9 1733 099255 000745 -043078 -17 065 4896399
550 575 8 1741 099714 000286 -138629 -175 025 5854211
575 600 5 1746 1 0 NUM -179 000 NUM
February 1 2012 30
Gumbel exceedance graph
Gumbel distribution
y = 07234x + 1882
R2 = 09871
0
2
4
6
8
10
0 2 4 6 8 10Gumbel Reduced variable
Sto
rm h
eig
ht
Hs
s
ssG AH B
= 1A = 0723
= B =1882
February 1 2012 31
calculation of a value
1ln ln
1ln ln
1
1ln ln
1
ln ln
ss
s
s
s
s s
HP
Q
QN
N
N Q
1500
873188 073ln ln 967
1873500
sH
= 1A = 073
= B =188
February 1 2012 32
transformation of the axis
Gumbel distribution
y = 07234x + 1882
R2 = 09871
0
2
4
6
8
10
0 2 4 6 8 10Gumbel Reduced variable
Sto
rm h
eig
ht
Hs
s
ln ln s
s s
NG
N Q
Ns = 873 storms per year
Qs G
110
1100
11000
110000
677
907
1138
1368
Figure Error No text of specified style in document-1 Storm exceedance on basis of Gumbel
10 100
February 1 2012 33
Weibull distribution
exp ssHQ
February 1 2012 34
determination of the reduced variable
1
1
ln
ln
1ln
ss
ss
ss
ss
WAH B
HQ
HQ
Q H
1
lnW Q
Three variables
and
So iteration is needed
February 1 2012 35
calculation for Weibull
alfa= 124
150 cumul P Q ln(Qs) -ln(H) Qs W
150 175 384 384 021993 078007 422098 -056 6810 032522
175 200 381 765 043814 056186 389284 -069 4905 064136
200 225 266 1031 059049 040951 357655 -081 3575 091261
225 250 157 1188 068041 031959 332863 -092 2790 111202
250 275 148 1336 076518 023482 302042 -101 2050 134858
275 300 111 1447 082875 017125 270471 -11 1495 158094
300 325 81 1528 087514 012486 238876 -118 1090 180552
325 350 63 1591 091123 008877 204769 -125 775 204065
350 375 31 1622 092898 007102 182455 -132 620 219099
375 400 32 1654 094731 005269 152606 -139 460 238832
400 425 23 1677 096048 003952 123837 -145 345 257486
425 450 11 1688 096678 003322 106471 -15 290 268590
450 475 20 1708 097824 002176 064185 -156 190 295184
475 500 9 1717 098339 001661 037156 -161 145 311883
500 525 7 1724 098740 001260 009531 -166 110 328731
525 550 9 1733 099255 000745 -043078 -17 065 360263
550 575 8 1741 099714 000286 -138629 -175 025 415922
575 600 5 1746 1 0 NUM -179 000 DIV0
1746
20 year 873 085586
-104906
099524
-07849
541 beta 116842
gamma 122575
Hs for condition 1 500 1028785 911838
1
lnssH Q
1
ln sss
s
QH
N
1124
1500
1500122 117 ln
873
122 117 675
912
sH
m
February 1 2012 36
Weibull exceedance graph
Weibull distribution
y = 11573x + 12497
R2 = 09905
0
2
4
6
8
10
0 2 4 6 8 10
Weibull Reduced variable
Str
om
heig
ht
Hss
10 100 1000 10000
February 1 2012 37
Summary
HT threshold value
Exponential
Gumbel
Weibull
150 m 163 m 136 m 122 m
HT 150 200 250 300 350 400
Ns 873 596 389 194 108 53
Hs 1500 Exponential Hs 1500 Gumbel Hs 1500 Weibull
1000 969 912
1009 950 990
948 917 963
939 893 948
908 886 917
876 818 890
February 1 2012 38
What to do if only random data are available
storm exceedance
0
200
400
600
800
01110100100010000
probability per year
Hs
s
February 1 2012 39
Example of long term data
This are
Hs-classes
February 1 2012 40
Long term (continuation)
So from this last column we can conclude
100 of time H gt 0 m s
23 of time H gt 1 m s
12 of time H gt 2 m s
001 of time H gt 9 m s
0
2
4
6
8
10
12
14
1E-071E-061E-051E-041E-031E-021E-011E+00
exceedance per year
wave
he
igh
t H
s (
m)
February 1 2012 41
From probability of waves to probability of storms
Suppose a ldquostormrdquo lasts for 12 hrs
===gt 730 stormsyear
once per year storm = 100730 = 013 =gt 67 m
once per 10 year storm = 0013 =gt 94 m
once per 100 year storm = 00013 =gt 119 m
0
5
10
15
20
1 10 100 1000 10000
return period in years
Hs o
f th
e g
ive
n s
torm
February 1 2012 42
Meteorological data
bull Not of direct importance for design
bull Can be important for hindcast of wave data and storm surge
bull Extremely important for the execution of the works (workability)
February 1 2012 43
Waves from Wind (Brettschneider)
February 1 2012 44
required soil data
February 1 2012 45
in situ test methods
February 1 2012 46
During construction
bull Quarry stone
bull Concrete
bull Local Equipment
bull Labour
bull skilled
bull cost
bull availability
bull expatriates
February 1 2012 21
sort data in classes
Waveheight class Hs (cm)
Number of observations
P Q -ln(Q)
0 25 35 35 0000599 0999401 0000599
25 50 8260 8295 0141940 0858060 0153082 50 75 11424 19719 0337423 0662577 0411618
75 100 10004 29723 0508607 0491393 0710511
100 125 7649 37372 0639493 0360507 1020245
125 150 5563 42935 0734685 0265315 1326838
150 175 4389 47324 0809788 0190212 1659615
175 200 3167 50491 0863980 0136020 1994954
200 225 2360 52851 0904363 0095637 2347200
225 250 1671 54522 0932957 0067043 2702419
250 275 1234 55756 0954073 0045927 3080692
275 300 851 56607 0968634 0031366 3462047
300 325 556 57163 0978149 0021851 3823487
325 350 392 57555 0984856 0015144 4190168
350 375 276 57831 0989579 0010421 4563938
375 400 206 58037 0993104 0006896 4976819
400 425 136 58173 0995431 0004569 5388507
425 450 82 58255 0996834 0003166 5755400
450 475 66 58321 0997964 0002036 6196632
475 500 38 58359 0998614 0001386 6581307
500 525 30 58389 0999127 0000873 7043930
525 550 20 58409 0999470 0000530 7541769
550 575 22 58431 0999846 0000154 8778531
575 600 9 58440 1000000 0000000
58440
( )s sP P H H
( ) 1s sQ Q H H P
all data Noordwijk
y = 00151x - 05001
R2 = 09881
0
1
2
3
4
5
6
7
8
9
10
0 200 400 600Hs-l
nQ
February 1 2012 22
exceedance graph for Noordwijk
indivudual observations
0
200
400
600
800
1000
000001000001000001000001000001000001000000
exceedance
wave h
eig
ht
But what means that in a year during 01
of the time the Hs is larger than 5 m
February 1 2012 23
Peak over Threshold method
A storm is defined as a time that the wave is higher than a
certain value the height of the storm Hss is equal to the
highest observed Hs during that storm
Threshold = 15
In this period 9
storms observed
nr Hss
1 180 m
2 294 m
3 225 m
4 176 m
5 261 m
6 389 m
7 172 m
8 240 m
9 194 m
February 1 2012 24
Table with Hss classes
= 124 Wave height class
150 cumul P Q Qs W
150 175 384 384 021993 078007 6810 032522 175 200 381 765 043814 056186 4905 064136 200 225 266 1031 059049 040951 3575 091261 225 250 157 1188 068041 031959 2790 111202 250 275 148 1336 076518 023482 2050 134858 275 300 111 1447 082875 017125 1495 158094 300 325 81 1528 087514 012486 1090 180552 325 350 63 1591 091123 008877 775 204065 350 375 31 1622 092898 007102 620 219099 375 400 32 1654 094731 005269 460 238832 400 425 23 1677 096048 003952 345 257486 425 450 11 1688 096678 003322 290 268590 450 475 20 1708 097824 002176 190 295184 475 500 9 1717 098339 001661 145 311883 500 525 7 1724 098740 001260 110 328731 525 550 9 1733 099255 000745 065 360263 550 575 8 1741 099714 000286 025 415922 575 600 5 1746 1 0 000 DIV0 1746 20 year 873 Slope 085586 Intercept -104906 correlation 099524 beta 116842 gamma 122575
Hss for condition 1 10 668997
( )ss ssP P H H
1ss ssQ Q H H P
threshold 15 m
y = -07849Ln(x) + 16329
R2 = 09854
0
2
4
6
8
000010000100001000010000100000probability of exceedence
sto
rm h
eig
ht
Hss
February 1 2012 25
How to get storm exceedance
Q = probability of exceedance of a wave
Qs = probability of exceedance of a storm
s sQ N Qthreshold 15 m
y = -07849Ln(x) + 5141
R2 = 09854
0
2
4
6
8
10
001010100100010000
storm exceedence probability per year
sto
rm h
eig
ht
Hss
Statistically
nonsense
February 1 2012 26
The ldquoonce in 500 years stormrdquo
0785ln( )
10785ln 5141
500
100
ss sH Q
m
threshold 15 m
y = -07849Ln(x) + 5141
R2 = 09854
0
2
4
6
8
10
001010100100010000
storm exceedence probability per year
sto
rm h
eig
ht
Hss
February 1 2012 27
Using the Gumbel distribution
exp exp ssHP
February 1 2012 28
determination of and
ln exp
1ln ln
ss
ss
ssss
GAH B
HP
HP H
1ln lnG
P
Perform linear regression
for G = A Hss - B
February 1 2012 29
data for calculation of Gumbel 150 cumul P Q ln(Qs) -ln(H) Qs G
150 175 384 384 021993 078007 422098 -056 6810 -0415046
175 200 381 765 043814 056186 389284 -069 4905 0192121
200 225 266 1031 059049 040951 357655 -081 3575 0640938
225 250 157 1188 068041 031959 332863 -092 2790 0954366
250 275 148 1336 076518 023482 302042 -101 2050 1318085
275 300 111 1447 082875 017125 270471 -11 1495 1672191
300 325 81 1528 087514 012486 238876 -118 1090 2014645
325 350 63 1591 091123 008877 204769 -125 775 2375535
350 375 31 1622 092898 007102 182455 -132 620 2608194
375 400 32 1654 094731 005269 152606 -139 460 2916351
400 425 23 1677 096048 003952 123837 -145 345 3210883
425 450 11 1688 096678 003322 106471 -15 290 3387796
450 475 20 1708 097824 002176 064185 -156 190 3816515
475 500 9 1717 098339 001661 037156 -161 145 4089424
500 525 7 1724 098740 001260 009531 -166 110 4367707
525 550 9 1733 099255 000745 -043078 -17 065 4896399
550 575 8 1741 099714 000286 -138629 -175 025 5854211
575 600 5 1746 1 0 NUM -179 000 NUM
February 1 2012 30
Gumbel exceedance graph
Gumbel distribution
y = 07234x + 1882
R2 = 09871
0
2
4
6
8
10
0 2 4 6 8 10Gumbel Reduced variable
Sto
rm h
eig
ht
Hs
s
ssG AH B
= 1A = 0723
= B =1882
February 1 2012 31
calculation of a value
1ln ln
1ln ln
1
1ln ln
1
ln ln
ss
s
s
s
s s
HP
Q
QN
N
N Q
1500
873188 073ln ln 967
1873500
sH
= 1A = 073
= B =188
February 1 2012 32
transformation of the axis
Gumbel distribution
y = 07234x + 1882
R2 = 09871
0
2
4
6
8
10
0 2 4 6 8 10Gumbel Reduced variable
Sto
rm h
eig
ht
Hs
s
ln ln s
s s
NG
N Q
Ns = 873 storms per year
Qs G
110
1100
11000
110000
677
907
1138
1368
Figure Error No text of specified style in document-1 Storm exceedance on basis of Gumbel
10 100
February 1 2012 33
Weibull distribution
exp ssHQ
February 1 2012 34
determination of the reduced variable
1
1
ln
ln
1ln
ss
ss
ss
ss
WAH B
HQ
HQ
Q H
1
lnW Q
Three variables
and
So iteration is needed
February 1 2012 35
calculation for Weibull
alfa= 124
150 cumul P Q ln(Qs) -ln(H) Qs W
150 175 384 384 021993 078007 422098 -056 6810 032522
175 200 381 765 043814 056186 389284 -069 4905 064136
200 225 266 1031 059049 040951 357655 -081 3575 091261
225 250 157 1188 068041 031959 332863 -092 2790 111202
250 275 148 1336 076518 023482 302042 -101 2050 134858
275 300 111 1447 082875 017125 270471 -11 1495 158094
300 325 81 1528 087514 012486 238876 -118 1090 180552
325 350 63 1591 091123 008877 204769 -125 775 204065
350 375 31 1622 092898 007102 182455 -132 620 219099
375 400 32 1654 094731 005269 152606 -139 460 238832
400 425 23 1677 096048 003952 123837 -145 345 257486
425 450 11 1688 096678 003322 106471 -15 290 268590
450 475 20 1708 097824 002176 064185 -156 190 295184
475 500 9 1717 098339 001661 037156 -161 145 311883
500 525 7 1724 098740 001260 009531 -166 110 328731
525 550 9 1733 099255 000745 -043078 -17 065 360263
550 575 8 1741 099714 000286 -138629 -175 025 415922
575 600 5 1746 1 0 NUM -179 000 DIV0
1746
20 year 873 085586
-104906
099524
-07849
541 beta 116842
gamma 122575
Hs for condition 1 500 1028785 911838
1
lnssH Q
1
ln sss
s
QH
N
1124
1500
1500122 117 ln
873
122 117 675
912
sH
m
February 1 2012 36
Weibull exceedance graph
Weibull distribution
y = 11573x + 12497
R2 = 09905
0
2
4
6
8
10
0 2 4 6 8 10
Weibull Reduced variable
Str
om
heig
ht
Hss
10 100 1000 10000
February 1 2012 37
Summary
HT threshold value
Exponential
Gumbel
Weibull
150 m 163 m 136 m 122 m
HT 150 200 250 300 350 400
Ns 873 596 389 194 108 53
Hs 1500 Exponential Hs 1500 Gumbel Hs 1500 Weibull
1000 969 912
1009 950 990
948 917 963
939 893 948
908 886 917
876 818 890
February 1 2012 38
What to do if only random data are available
storm exceedance
0
200
400
600
800
01110100100010000
probability per year
Hs
s
February 1 2012 39
Example of long term data
This are
Hs-classes
February 1 2012 40
Long term (continuation)
So from this last column we can conclude
100 of time H gt 0 m s
23 of time H gt 1 m s
12 of time H gt 2 m s
001 of time H gt 9 m s
0
2
4
6
8
10
12
14
1E-071E-061E-051E-041E-031E-021E-011E+00
exceedance per year
wave
he
igh
t H
s (
m)
February 1 2012 41
From probability of waves to probability of storms
Suppose a ldquostormrdquo lasts for 12 hrs
===gt 730 stormsyear
once per year storm = 100730 = 013 =gt 67 m
once per 10 year storm = 0013 =gt 94 m
once per 100 year storm = 00013 =gt 119 m
0
5
10
15
20
1 10 100 1000 10000
return period in years
Hs o
f th
e g
ive
n s
torm
February 1 2012 42
Meteorological data
bull Not of direct importance for design
bull Can be important for hindcast of wave data and storm surge
bull Extremely important for the execution of the works (workability)
February 1 2012 43
Waves from Wind (Brettschneider)
February 1 2012 44
required soil data
February 1 2012 45
in situ test methods
February 1 2012 46
During construction
bull Quarry stone
bull Concrete
bull Local Equipment
bull Labour
bull skilled
bull cost
bull availability
bull expatriates
February 1 2012 22
exceedance graph for Noordwijk
indivudual observations
0
200
400
600
800
1000
000001000001000001000001000001000001000000
exceedance
wave h
eig
ht
But what means that in a year during 01
of the time the Hs is larger than 5 m
February 1 2012 23
Peak over Threshold method
A storm is defined as a time that the wave is higher than a
certain value the height of the storm Hss is equal to the
highest observed Hs during that storm
Threshold = 15
In this period 9
storms observed
nr Hss
1 180 m
2 294 m
3 225 m
4 176 m
5 261 m
6 389 m
7 172 m
8 240 m
9 194 m
February 1 2012 24
Table with Hss classes
= 124 Wave height class
150 cumul P Q Qs W
150 175 384 384 021993 078007 6810 032522 175 200 381 765 043814 056186 4905 064136 200 225 266 1031 059049 040951 3575 091261 225 250 157 1188 068041 031959 2790 111202 250 275 148 1336 076518 023482 2050 134858 275 300 111 1447 082875 017125 1495 158094 300 325 81 1528 087514 012486 1090 180552 325 350 63 1591 091123 008877 775 204065 350 375 31 1622 092898 007102 620 219099 375 400 32 1654 094731 005269 460 238832 400 425 23 1677 096048 003952 345 257486 425 450 11 1688 096678 003322 290 268590 450 475 20 1708 097824 002176 190 295184 475 500 9 1717 098339 001661 145 311883 500 525 7 1724 098740 001260 110 328731 525 550 9 1733 099255 000745 065 360263 550 575 8 1741 099714 000286 025 415922 575 600 5 1746 1 0 000 DIV0 1746 20 year 873 Slope 085586 Intercept -104906 correlation 099524 beta 116842 gamma 122575
Hss for condition 1 10 668997
( )ss ssP P H H
1ss ssQ Q H H P
threshold 15 m
y = -07849Ln(x) + 16329
R2 = 09854
0
2
4
6
8
000010000100001000010000100000probability of exceedence
sto
rm h
eig
ht
Hss
February 1 2012 25
How to get storm exceedance
Q = probability of exceedance of a wave
Qs = probability of exceedance of a storm
s sQ N Qthreshold 15 m
y = -07849Ln(x) + 5141
R2 = 09854
0
2
4
6
8
10
001010100100010000
storm exceedence probability per year
sto
rm h
eig
ht
Hss
Statistically
nonsense
February 1 2012 26
The ldquoonce in 500 years stormrdquo
0785ln( )
10785ln 5141
500
100
ss sH Q
m
threshold 15 m
y = -07849Ln(x) + 5141
R2 = 09854
0
2
4
6
8
10
001010100100010000
storm exceedence probability per year
sto
rm h
eig
ht
Hss
February 1 2012 27
Using the Gumbel distribution
exp exp ssHP
February 1 2012 28
determination of and
ln exp
1ln ln
ss
ss
ssss
GAH B
HP
HP H
1ln lnG
P
Perform linear regression
for G = A Hss - B
February 1 2012 29
data for calculation of Gumbel 150 cumul P Q ln(Qs) -ln(H) Qs G
150 175 384 384 021993 078007 422098 -056 6810 -0415046
175 200 381 765 043814 056186 389284 -069 4905 0192121
200 225 266 1031 059049 040951 357655 -081 3575 0640938
225 250 157 1188 068041 031959 332863 -092 2790 0954366
250 275 148 1336 076518 023482 302042 -101 2050 1318085
275 300 111 1447 082875 017125 270471 -11 1495 1672191
300 325 81 1528 087514 012486 238876 -118 1090 2014645
325 350 63 1591 091123 008877 204769 -125 775 2375535
350 375 31 1622 092898 007102 182455 -132 620 2608194
375 400 32 1654 094731 005269 152606 -139 460 2916351
400 425 23 1677 096048 003952 123837 -145 345 3210883
425 450 11 1688 096678 003322 106471 -15 290 3387796
450 475 20 1708 097824 002176 064185 -156 190 3816515
475 500 9 1717 098339 001661 037156 -161 145 4089424
500 525 7 1724 098740 001260 009531 -166 110 4367707
525 550 9 1733 099255 000745 -043078 -17 065 4896399
550 575 8 1741 099714 000286 -138629 -175 025 5854211
575 600 5 1746 1 0 NUM -179 000 NUM
February 1 2012 30
Gumbel exceedance graph
Gumbel distribution
y = 07234x + 1882
R2 = 09871
0
2
4
6
8
10
0 2 4 6 8 10Gumbel Reduced variable
Sto
rm h
eig
ht
Hs
s
ssG AH B
= 1A = 0723
= B =1882
February 1 2012 31
calculation of a value
1ln ln
1ln ln
1
1ln ln
1
ln ln
ss
s
s
s
s s
HP
Q
QN
N
N Q
1500
873188 073ln ln 967
1873500
sH
= 1A = 073
= B =188
February 1 2012 32
transformation of the axis
Gumbel distribution
y = 07234x + 1882
R2 = 09871
0
2
4
6
8
10
0 2 4 6 8 10Gumbel Reduced variable
Sto
rm h
eig
ht
Hs
s
ln ln s
s s
NG
N Q
Ns = 873 storms per year
Qs G
110
1100
11000
110000
677
907
1138
1368
Figure Error No text of specified style in document-1 Storm exceedance on basis of Gumbel
10 100
February 1 2012 33
Weibull distribution
exp ssHQ
February 1 2012 34
determination of the reduced variable
1
1
ln
ln
1ln
ss
ss
ss
ss
WAH B
HQ
HQ
Q H
1
lnW Q
Three variables
and
So iteration is needed
February 1 2012 35
calculation for Weibull
alfa= 124
150 cumul P Q ln(Qs) -ln(H) Qs W
150 175 384 384 021993 078007 422098 -056 6810 032522
175 200 381 765 043814 056186 389284 -069 4905 064136
200 225 266 1031 059049 040951 357655 -081 3575 091261
225 250 157 1188 068041 031959 332863 -092 2790 111202
250 275 148 1336 076518 023482 302042 -101 2050 134858
275 300 111 1447 082875 017125 270471 -11 1495 158094
300 325 81 1528 087514 012486 238876 -118 1090 180552
325 350 63 1591 091123 008877 204769 -125 775 204065
350 375 31 1622 092898 007102 182455 -132 620 219099
375 400 32 1654 094731 005269 152606 -139 460 238832
400 425 23 1677 096048 003952 123837 -145 345 257486
425 450 11 1688 096678 003322 106471 -15 290 268590
450 475 20 1708 097824 002176 064185 -156 190 295184
475 500 9 1717 098339 001661 037156 -161 145 311883
500 525 7 1724 098740 001260 009531 -166 110 328731
525 550 9 1733 099255 000745 -043078 -17 065 360263
550 575 8 1741 099714 000286 -138629 -175 025 415922
575 600 5 1746 1 0 NUM -179 000 DIV0
1746
20 year 873 085586
-104906
099524
-07849
541 beta 116842
gamma 122575
Hs for condition 1 500 1028785 911838
1
lnssH Q
1
ln sss
s
QH
N
1124
1500
1500122 117 ln
873
122 117 675
912
sH
m
February 1 2012 36
Weibull exceedance graph
Weibull distribution
y = 11573x + 12497
R2 = 09905
0
2
4
6
8
10
0 2 4 6 8 10
Weibull Reduced variable
Str
om
heig
ht
Hss
10 100 1000 10000
February 1 2012 37
Summary
HT threshold value
Exponential
Gumbel
Weibull
150 m 163 m 136 m 122 m
HT 150 200 250 300 350 400
Ns 873 596 389 194 108 53
Hs 1500 Exponential Hs 1500 Gumbel Hs 1500 Weibull
1000 969 912
1009 950 990
948 917 963
939 893 948
908 886 917
876 818 890
February 1 2012 38
What to do if only random data are available
storm exceedance
0
200
400
600
800
01110100100010000
probability per year
Hs
s
February 1 2012 39
Example of long term data
This are
Hs-classes
February 1 2012 40
Long term (continuation)
So from this last column we can conclude
100 of time H gt 0 m s
23 of time H gt 1 m s
12 of time H gt 2 m s
001 of time H gt 9 m s
0
2
4
6
8
10
12
14
1E-071E-061E-051E-041E-031E-021E-011E+00
exceedance per year
wave
he
igh
t H
s (
m)
February 1 2012 41
From probability of waves to probability of storms
Suppose a ldquostormrdquo lasts for 12 hrs
===gt 730 stormsyear
once per year storm = 100730 = 013 =gt 67 m
once per 10 year storm = 0013 =gt 94 m
once per 100 year storm = 00013 =gt 119 m
0
5
10
15
20
1 10 100 1000 10000
return period in years
Hs o
f th
e g
ive
n s
torm
February 1 2012 42
Meteorological data
bull Not of direct importance for design
bull Can be important for hindcast of wave data and storm surge
bull Extremely important for the execution of the works (workability)
February 1 2012 43
Waves from Wind (Brettschneider)
February 1 2012 44
required soil data
February 1 2012 45
in situ test methods
February 1 2012 46
During construction
bull Quarry stone
bull Concrete
bull Local Equipment
bull Labour
bull skilled
bull cost
bull availability
bull expatriates
February 1 2012 23
Peak over Threshold method
A storm is defined as a time that the wave is higher than a
certain value the height of the storm Hss is equal to the
highest observed Hs during that storm
Threshold = 15
In this period 9
storms observed
nr Hss
1 180 m
2 294 m
3 225 m
4 176 m
5 261 m
6 389 m
7 172 m
8 240 m
9 194 m
February 1 2012 24
Table with Hss classes
= 124 Wave height class
150 cumul P Q Qs W
150 175 384 384 021993 078007 6810 032522 175 200 381 765 043814 056186 4905 064136 200 225 266 1031 059049 040951 3575 091261 225 250 157 1188 068041 031959 2790 111202 250 275 148 1336 076518 023482 2050 134858 275 300 111 1447 082875 017125 1495 158094 300 325 81 1528 087514 012486 1090 180552 325 350 63 1591 091123 008877 775 204065 350 375 31 1622 092898 007102 620 219099 375 400 32 1654 094731 005269 460 238832 400 425 23 1677 096048 003952 345 257486 425 450 11 1688 096678 003322 290 268590 450 475 20 1708 097824 002176 190 295184 475 500 9 1717 098339 001661 145 311883 500 525 7 1724 098740 001260 110 328731 525 550 9 1733 099255 000745 065 360263 550 575 8 1741 099714 000286 025 415922 575 600 5 1746 1 0 000 DIV0 1746 20 year 873 Slope 085586 Intercept -104906 correlation 099524 beta 116842 gamma 122575
Hss for condition 1 10 668997
( )ss ssP P H H
1ss ssQ Q H H P
threshold 15 m
y = -07849Ln(x) + 16329
R2 = 09854
0
2
4
6
8
000010000100001000010000100000probability of exceedence
sto
rm h
eig
ht
Hss
February 1 2012 25
How to get storm exceedance
Q = probability of exceedance of a wave
Qs = probability of exceedance of a storm
s sQ N Qthreshold 15 m
y = -07849Ln(x) + 5141
R2 = 09854
0
2
4
6
8
10
001010100100010000
storm exceedence probability per year
sto
rm h
eig
ht
Hss
Statistically
nonsense
February 1 2012 26
The ldquoonce in 500 years stormrdquo
0785ln( )
10785ln 5141
500
100
ss sH Q
m
threshold 15 m
y = -07849Ln(x) + 5141
R2 = 09854
0
2
4
6
8
10
001010100100010000
storm exceedence probability per year
sto
rm h
eig
ht
Hss
February 1 2012 27
Using the Gumbel distribution
exp exp ssHP
February 1 2012 28
determination of and
ln exp
1ln ln
ss
ss
ssss
GAH B
HP
HP H
1ln lnG
P
Perform linear regression
for G = A Hss - B
February 1 2012 29
data for calculation of Gumbel 150 cumul P Q ln(Qs) -ln(H) Qs G
150 175 384 384 021993 078007 422098 -056 6810 -0415046
175 200 381 765 043814 056186 389284 -069 4905 0192121
200 225 266 1031 059049 040951 357655 -081 3575 0640938
225 250 157 1188 068041 031959 332863 -092 2790 0954366
250 275 148 1336 076518 023482 302042 -101 2050 1318085
275 300 111 1447 082875 017125 270471 -11 1495 1672191
300 325 81 1528 087514 012486 238876 -118 1090 2014645
325 350 63 1591 091123 008877 204769 -125 775 2375535
350 375 31 1622 092898 007102 182455 -132 620 2608194
375 400 32 1654 094731 005269 152606 -139 460 2916351
400 425 23 1677 096048 003952 123837 -145 345 3210883
425 450 11 1688 096678 003322 106471 -15 290 3387796
450 475 20 1708 097824 002176 064185 -156 190 3816515
475 500 9 1717 098339 001661 037156 -161 145 4089424
500 525 7 1724 098740 001260 009531 -166 110 4367707
525 550 9 1733 099255 000745 -043078 -17 065 4896399
550 575 8 1741 099714 000286 -138629 -175 025 5854211
575 600 5 1746 1 0 NUM -179 000 NUM
February 1 2012 30
Gumbel exceedance graph
Gumbel distribution
y = 07234x + 1882
R2 = 09871
0
2
4
6
8
10
0 2 4 6 8 10Gumbel Reduced variable
Sto
rm h
eig
ht
Hs
s
ssG AH B
= 1A = 0723
= B =1882
February 1 2012 31
calculation of a value
1ln ln
1ln ln
1
1ln ln
1
ln ln
ss
s
s
s
s s
HP
Q
QN
N
N Q
1500
873188 073ln ln 967
1873500
sH
= 1A = 073
= B =188
February 1 2012 32
transformation of the axis
Gumbel distribution
y = 07234x + 1882
R2 = 09871
0
2
4
6
8
10
0 2 4 6 8 10Gumbel Reduced variable
Sto
rm h
eig
ht
Hs
s
ln ln s
s s
NG
N Q
Ns = 873 storms per year
Qs G
110
1100
11000
110000
677
907
1138
1368
Figure Error No text of specified style in document-1 Storm exceedance on basis of Gumbel
10 100
February 1 2012 33
Weibull distribution
exp ssHQ
February 1 2012 34
determination of the reduced variable
1
1
ln
ln
1ln
ss
ss
ss
ss
WAH B
HQ
HQ
Q H
1
lnW Q
Three variables
and
So iteration is needed
February 1 2012 35
calculation for Weibull
alfa= 124
150 cumul P Q ln(Qs) -ln(H) Qs W
150 175 384 384 021993 078007 422098 -056 6810 032522
175 200 381 765 043814 056186 389284 -069 4905 064136
200 225 266 1031 059049 040951 357655 -081 3575 091261
225 250 157 1188 068041 031959 332863 -092 2790 111202
250 275 148 1336 076518 023482 302042 -101 2050 134858
275 300 111 1447 082875 017125 270471 -11 1495 158094
300 325 81 1528 087514 012486 238876 -118 1090 180552
325 350 63 1591 091123 008877 204769 -125 775 204065
350 375 31 1622 092898 007102 182455 -132 620 219099
375 400 32 1654 094731 005269 152606 -139 460 238832
400 425 23 1677 096048 003952 123837 -145 345 257486
425 450 11 1688 096678 003322 106471 -15 290 268590
450 475 20 1708 097824 002176 064185 -156 190 295184
475 500 9 1717 098339 001661 037156 -161 145 311883
500 525 7 1724 098740 001260 009531 -166 110 328731
525 550 9 1733 099255 000745 -043078 -17 065 360263
550 575 8 1741 099714 000286 -138629 -175 025 415922
575 600 5 1746 1 0 NUM -179 000 DIV0
1746
20 year 873 085586
-104906
099524
-07849
541 beta 116842
gamma 122575
Hs for condition 1 500 1028785 911838
1
lnssH Q
1
ln sss
s
QH
N
1124
1500
1500122 117 ln
873
122 117 675
912
sH
m
February 1 2012 36
Weibull exceedance graph
Weibull distribution
y = 11573x + 12497
R2 = 09905
0
2
4
6
8
10
0 2 4 6 8 10
Weibull Reduced variable
Str
om
heig
ht
Hss
10 100 1000 10000
February 1 2012 37
Summary
HT threshold value
Exponential
Gumbel
Weibull
150 m 163 m 136 m 122 m
HT 150 200 250 300 350 400
Ns 873 596 389 194 108 53
Hs 1500 Exponential Hs 1500 Gumbel Hs 1500 Weibull
1000 969 912
1009 950 990
948 917 963
939 893 948
908 886 917
876 818 890
February 1 2012 38
What to do if only random data are available
storm exceedance
0
200
400
600
800
01110100100010000
probability per year
Hs
s
February 1 2012 39
Example of long term data
This are
Hs-classes
February 1 2012 40
Long term (continuation)
So from this last column we can conclude
100 of time H gt 0 m s
23 of time H gt 1 m s
12 of time H gt 2 m s
001 of time H gt 9 m s
0
2
4
6
8
10
12
14
1E-071E-061E-051E-041E-031E-021E-011E+00
exceedance per year
wave
he
igh
t H
s (
m)
February 1 2012 41
From probability of waves to probability of storms
Suppose a ldquostormrdquo lasts for 12 hrs
===gt 730 stormsyear
once per year storm = 100730 = 013 =gt 67 m
once per 10 year storm = 0013 =gt 94 m
once per 100 year storm = 00013 =gt 119 m
0
5
10
15
20
1 10 100 1000 10000
return period in years
Hs o
f th
e g
ive
n s
torm
February 1 2012 42
Meteorological data
bull Not of direct importance for design
bull Can be important for hindcast of wave data and storm surge
bull Extremely important for the execution of the works (workability)
February 1 2012 43
Waves from Wind (Brettschneider)
February 1 2012 44
required soil data
February 1 2012 45
in situ test methods
February 1 2012 46
During construction
bull Quarry stone
bull Concrete
bull Local Equipment
bull Labour
bull skilled
bull cost
bull availability
bull expatriates
February 1 2012 24
Table with Hss classes
= 124 Wave height class
150 cumul P Q Qs W
150 175 384 384 021993 078007 6810 032522 175 200 381 765 043814 056186 4905 064136 200 225 266 1031 059049 040951 3575 091261 225 250 157 1188 068041 031959 2790 111202 250 275 148 1336 076518 023482 2050 134858 275 300 111 1447 082875 017125 1495 158094 300 325 81 1528 087514 012486 1090 180552 325 350 63 1591 091123 008877 775 204065 350 375 31 1622 092898 007102 620 219099 375 400 32 1654 094731 005269 460 238832 400 425 23 1677 096048 003952 345 257486 425 450 11 1688 096678 003322 290 268590 450 475 20 1708 097824 002176 190 295184 475 500 9 1717 098339 001661 145 311883 500 525 7 1724 098740 001260 110 328731 525 550 9 1733 099255 000745 065 360263 550 575 8 1741 099714 000286 025 415922 575 600 5 1746 1 0 000 DIV0 1746 20 year 873 Slope 085586 Intercept -104906 correlation 099524 beta 116842 gamma 122575
Hss for condition 1 10 668997
( )ss ssP P H H
1ss ssQ Q H H P
threshold 15 m
y = -07849Ln(x) + 16329
R2 = 09854
0
2
4
6
8
000010000100001000010000100000probability of exceedence
sto
rm h
eig
ht
Hss
February 1 2012 25
How to get storm exceedance
Q = probability of exceedance of a wave
Qs = probability of exceedance of a storm
s sQ N Qthreshold 15 m
y = -07849Ln(x) + 5141
R2 = 09854
0
2
4
6
8
10
001010100100010000
storm exceedence probability per year
sto
rm h
eig
ht
Hss
Statistically
nonsense
February 1 2012 26
The ldquoonce in 500 years stormrdquo
0785ln( )
10785ln 5141
500
100
ss sH Q
m
threshold 15 m
y = -07849Ln(x) + 5141
R2 = 09854
0
2
4
6
8
10
001010100100010000
storm exceedence probability per year
sto
rm h
eig
ht
Hss
February 1 2012 27
Using the Gumbel distribution
exp exp ssHP
February 1 2012 28
determination of and
ln exp
1ln ln
ss
ss
ssss
GAH B
HP
HP H
1ln lnG
P
Perform linear regression
for G = A Hss - B
February 1 2012 29
data for calculation of Gumbel 150 cumul P Q ln(Qs) -ln(H) Qs G
150 175 384 384 021993 078007 422098 -056 6810 -0415046
175 200 381 765 043814 056186 389284 -069 4905 0192121
200 225 266 1031 059049 040951 357655 -081 3575 0640938
225 250 157 1188 068041 031959 332863 -092 2790 0954366
250 275 148 1336 076518 023482 302042 -101 2050 1318085
275 300 111 1447 082875 017125 270471 -11 1495 1672191
300 325 81 1528 087514 012486 238876 -118 1090 2014645
325 350 63 1591 091123 008877 204769 -125 775 2375535
350 375 31 1622 092898 007102 182455 -132 620 2608194
375 400 32 1654 094731 005269 152606 -139 460 2916351
400 425 23 1677 096048 003952 123837 -145 345 3210883
425 450 11 1688 096678 003322 106471 -15 290 3387796
450 475 20 1708 097824 002176 064185 -156 190 3816515
475 500 9 1717 098339 001661 037156 -161 145 4089424
500 525 7 1724 098740 001260 009531 -166 110 4367707
525 550 9 1733 099255 000745 -043078 -17 065 4896399
550 575 8 1741 099714 000286 -138629 -175 025 5854211
575 600 5 1746 1 0 NUM -179 000 NUM
February 1 2012 30
Gumbel exceedance graph
Gumbel distribution
y = 07234x + 1882
R2 = 09871
0
2
4
6
8
10
0 2 4 6 8 10Gumbel Reduced variable
Sto
rm h
eig
ht
Hs
s
ssG AH B
= 1A = 0723
= B =1882
February 1 2012 31
calculation of a value
1ln ln
1ln ln
1
1ln ln
1
ln ln
ss
s
s
s
s s
HP
Q
QN
N
N Q
1500
873188 073ln ln 967
1873500
sH
= 1A = 073
= B =188
February 1 2012 32
transformation of the axis
Gumbel distribution
y = 07234x + 1882
R2 = 09871
0
2
4
6
8
10
0 2 4 6 8 10Gumbel Reduced variable
Sto
rm h
eig
ht
Hs
s
ln ln s
s s
NG
N Q
Ns = 873 storms per year
Qs G
110
1100
11000
110000
677
907
1138
1368
Figure Error No text of specified style in document-1 Storm exceedance on basis of Gumbel
10 100
February 1 2012 33
Weibull distribution
exp ssHQ
February 1 2012 34
determination of the reduced variable
1
1
ln
ln
1ln
ss
ss
ss
ss
WAH B
HQ
HQ
Q H
1
lnW Q
Three variables
and
So iteration is needed
February 1 2012 35
calculation for Weibull
alfa= 124
150 cumul P Q ln(Qs) -ln(H) Qs W
150 175 384 384 021993 078007 422098 -056 6810 032522
175 200 381 765 043814 056186 389284 -069 4905 064136
200 225 266 1031 059049 040951 357655 -081 3575 091261
225 250 157 1188 068041 031959 332863 -092 2790 111202
250 275 148 1336 076518 023482 302042 -101 2050 134858
275 300 111 1447 082875 017125 270471 -11 1495 158094
300 325 81 1528 087514 012486 238876 -118 1090 180552
325 350 63 1591 091123 008877 204769 -125 775 204065
350 375 31 1622 092898 007102 182455 -132 620 219099
375 400 32 1654 094731 005269 152606 -139 460 238832
400 425 23 1677 096048 003952 123837 -145 345 257486
425 450 11 1688 096678 003322 106471 -15 290 268590
450 475 20 1708 097824 002176 064185 -156 190 295184
475 500 9 1717 098339 001661 037156 -161 145 311883
500 525 7 1724 098740 001260 009531 -166 110 328731
525 550 9 1733 099255 000745 -043078 -17 065 360263
550 575 8 1741 099714 000286 -138629 -175 025 415922
575 600 5 1746 1 0 NUM -179 000 DIV0
1746
20 year 873 085586
-104906
099524
-07849
541 beta 116842
gamma 122575
Hs for condition 1 500 1028785 911838
1
lnssH Q
1
ln sss
s
QH
N
1124
1500
1500122 117 ln
873
122 117 675
912
sH
m
February 1 2012 36
Weibull exceedance graph
Weibull distribution
y = 11573x + 12497
R2 = 09905
0
2
4
6
8
10
0 2 4 6 8 10
Weibull Reduced variable
Str
om
heig
ht
Hss
10 100 1000 10000
February 1 2012 37
Summary
HT threshold value
Exponential
Gumbel
Weibull
150 m 163 m 136 m 122 m
HT 150 200 250 300 350 400
Ns 873 596 389 194 108 53
Hs 1500 Exponential Hs 1500 Gumbel Hs 1500 Weibull
1000 969 912
1009 950 990
948 917 963
939 893 948
908 886 917
876 818 890
February 1 2012 38
What to do if only random data are available
storm exceedance
0
200
400
600
800
01110100100010000
probability per year
Hs
s
February 1 2012 39
Example of long term data
This are
Hs-classes
February 1 2012 40
Long term (continuation)
So from this last column we can conclude
100 of time H gt 0 m s
23 of time H gt 1 m s
12 of time H gt 2 m s
001 of time H gt 9 m s
0
2
4
6
8
10
12
14
1E-071E-061E-051E-041E-031E-021E-011E+00
exceedance per year
wave
he
igh
t H
s (
m)
February 1 2012 41
From probability of waves to probability of storms
Suppose a ldquostormrdquo lasts for 12 hrs
===gt 730 stormsyear
once per year storm = 100730 = 013 =gt 67 m
once per 10 year storm = 0013 =gt 94 m
once per 100 year storm = 00013 =gt 119 m
0
5
10
15
20
1 10 100 1000 10000
return period in years
Hs o
f th
e g
ive
n s
torm
February 1 2012 42
Meteorological data
bull Not of direct importance for design
bull Can be important for hindcast of wave data and storm surge
bull Extremely important for the execution of the works (workability)
February 1 2012 43
Waves from Wind (Brettschneider)
February 1 2012 44
required soil data
February 1 2012 45
in situ test methods
February 1 2012 46
During construction
bull Quarry stone
bull Concrete
bull Local Equipment
bull Labour
bull skilled
bull cost
bull availability
bull expatriates
February 1 2012 25
How to get storm exceedance
Q = probability of exceedance of a wave
Qs = probability of exceedance of a storm
s sQ N Qthreshold 15 m
y = -07849Ln(x) + 5141
R2 = 09854
0
2
4
6
8
10
001010100100010000
storm exceedence probability per year
sto
rm h
eig
ht
Hss
Statistically
nonsense
February 1 2012 26
The ldquoonce in 500 years stormrdquo
0785ln( )
10785ln 5141
500
100
ss sH Q
m
threshold 15 m
y = -07849Ln(x) + 5141
R2 = 09854
0
2
4
6
8
10
001010100100010000
storm exceedence probability per year
sto
rm h
eig
ht
Hss
February 1 2012 27
Using the Gumbel distribution
exp exp ssHP
February 1 2012 28
determination of and
ln exp
1ln ln
ss
ss
ssss
GAH B
HP
HP H
1ln lnG
P
Perform linear regression
for G = A Hss - B
February 1 2012 29
data for calculation of Gumbel 150 cumul P Q ln(Qs) -ln(H) Qs G
150 175 384 384 021993 078007 422098 -056 6810 -0415046
175 200 381 765 043814 056186 389284 -069 4905 0192121
200 225 266 1031 059049 040951 357655 -081 3575 0640938
225 250 157 1188 068041 031959 332863 -092 2790 0954366
250 275 148 1336 076518 023482 302042 -101 2050 1318085
275 300 111 1447 082875 017125 270471 -11 1495 1672191
300 325 81 1528 087514 012486 238876 -118 1090 2014645
325 350 63 1591 091123 008877 204769 -125 775 2375535
350 375 31 1622 092898 007102 182455 -132 620 2608194
375 400 32 1654 094731 005269 152606 -139 460 2916351
400 425 23 1677 096048 003952 123837 -145 345 3210883
425 450 11 1688 096678 003322 106471 -15 290 3387796
450 475 20 1708 097824 002176 064185 -156 190 3816515
475 500 9 1717 098339 001661 037156 -161 145 4089424
500 525 7 1724 098740 001260 009531 -166 110 4367707
525 550 9 1733 099255 000745 -043078 -17 065 4896399
550 575 8 1741 099714 000286 -138629 -175 025 5854211
575 600 5 1746 1 0 NUM -179 000 NUM
February 1 2012 30
Gumbel exceedance graph
Gumbel distribution
y = 07234x + 1882
R2 = 09871
0
2
4
6
8
10
0 2 4 6 8 10Gumbel Reduced variable
Sto
rm h
eig
ht
Hs
s
ssG AH B
= 1A = 0723
= B =1882
February 1 2012 31
calculation of a value
1ln ln
1ln ln
1
1ln ln
1
ln ln
ss
s
s
s
s s
HP
Q
QN
N
N Q
1500
873188 073ln ln 967
1873500
sH
= 1A = 073
= B =188
February 1 2012 32
transformation of the axis
Gumbel distribution
y = 07234x + 1882
R2 = 09871
0
2
4
6
8
10
0 2 4 6 8 10Gumbel Reduced variable
Sto
rm h
eig
ht
Hs
s
ln ln s
s s
NG
N Q
Ns = 873 storms per year
Qs G
110
1100
11000
110000
677
907
1138
1368
Figure Error No text of specified style in document-1 Storm exceedance on basis of Gumbel
10 100
February 1 2012 33
Weibull distribution
exp ssHQ
February 1 2012 34
determination of the reduced variable
1
1
ln
ln
1ln
ss
ss
ss
ss
WAH B
HQ
HQ
Q H
1
lnW Q
Three variables
and
So iteration is needed
February 1 2012 35
calculation for Weibull
alfa= 124
150 cumul P Q ln(Qs) -ln(H) Qs W
150 175 384 384 021993 078007 422098 -056 6810 032522
175 200 381 765 043814 056186 389284 -069 4905 064136
200 225 266 1031 059049 040951 357655 -081 3575 091261
225 250 157 1188 068041 031959 332863 -092 2790 111202
250 275 148 1336 076518 023482 302042 -101 2050 134858
275 300 111 1447 082875 017125 270471 -11 1495 158094
300 325 81 1528 087514 012486 238876 -118 1090 180552
325 350 63 1591 091123 008877 204769 -125 775 204065
350 375 31 1622 092898 007102 182455 -132 620 219099
375 400 32 1654 094731 005269 152606 -139 460 238832
400 425 23 1677 096048 003952 123837 -145 345 257486
425 450 11 1688 096678 003322 106471 -15 290 268590
450 475 20 1708 097824 002176 064185 -156 190 295184
475 500 9 1717 098339 001661 037156 -161 145 311883
500 525 7 1724 098740 001260 009531 -166 110 328731
525 550 9 1733 099255 000745 -043078 -17 065 360263
550 575 8 1741 099714 000286 -138629 -175 025 415922
575 600 5 1746 1 0 NUM -179 000 DIV0
1746
20 year 873 085586
-104906
099524
-07849
541 beta 116842
gamma 122575
Hs for condition 1 500 1028785 911838
1
lnssH Q
1
ln sss
s
QH
N
1124
1500
1500122 117 ln
873
122 117 675
912
sH
m
February 1 2012 36
Weibull exceedance graph
Weibull distribution
y = 11573x + 12497
R2 = 09905
0
2
4
6
8
10
0 2 4 6 8 10
Weibull Reduced variable
Str
om
heig
ht
Hss
10 100 1000 10000
February 1 2012 37
Summary
HT threshold value
Exponential
Gumbel
Weibull
150 m 163 m 136 m 122 m
HT 150 200 250 300 350 400
Ns 873 596 389 194 108 53
Hs 1500 Exponential Hs 1500 Gumbel Hs 1500 Weibull
1000 969 912
1009 950 990
948 917 963
939 893 948
908 886 917
876 818 890
February 1 2012 38
What to do if only random data are available
storm exceedance
0
200
400
600
800
01110100100010000
probability per year
Hs
s
February 1 2012 39
Example of long term data
This are
Hs-classes
February 1 2012 40
Long term (continuation)
So from this last column we can conclude
100 of time H gt 0 m s
23 of time H gt 1 m s
12 of time H gt 2 m s
001 of time H gt 9 m s
0
2
4
6
8
10
12
14
1E-071E-061E-051E-041E-031E-021E-011E+00
exceedance per year
wave
he
igh
t H
s (
m)
February 1 2012 41
From probability of waves to probability of storms
Suppose a ldquostormrdquo lasts for 12 hrs
===gt 730 stormsyear
once per year storm = 100730 = 013 =gt 67 m
once per 10 year storm = 0013 =gt 94 m
once per 100 year storm = 00013 =gt 119 m
0
5
10
15
20
1 10 100 1000 10000
return period in years
Hs o
f th
e g
ive
n s
torm
February 1 2012 42
Meteorological data
bull Not of direct importance for design
bull Can be important for hindcast of wave data and storm surge
bull Extremely important for the execution of the works (workability)
February 1 2012 43
Waves from Wind (Brettschneider)
February 1 2012 44
required soil data
February 1 2012 45
in situ test methods
February 1 2012 46
During construction
bull Quarry stone
bull Concrete
bull Local Equipment
bull Labour
bull skilled
bull cost
bull availability
bull expatriates
February 1 2012 26
The ldquoonce in 500 years stormrdquo
0785ln( )
10785ln 5141
500
100
ss sH Q
m
threshold 15 m
y = -07849Ln(x) + 5141
R2 = 09854
0
2
4
6
8
10
001010100100010000
storm exceedence probability per year
sto
rm h
eig
ht
Hss
February 1 2012 27
Using the Gumbel distribution
exp exp ssHP
February 1 2012 28
determination of and
ln exp
1ln ln
ss
ss
ssss
GAH B
HP
HP H
1ln lnG
P
Perform linear regression
for G = A Hss - B
February 1 2012 29
data for calculation of Gumbel 150 cumul P Q ln(Qs) -ln(H) Qs G
150 175 384 384 021993 078007 422098 -056 6810 -0415046
175 200 381 765 043814 056186 389284 -069 4905 0192121
200 225 266 1031 059049 040951 357655 -081 3575 0640938
225 250 157 1188 068041 031959 332863 -092 2790 0954366
250 275 148 1336 076518 023482 302042 -101 2050 1318085
275 300 111 1447 082875 017125 270471 -11 1495 1672191
300 325 81 1528 087514 012486 238876 -118 1090 2014645
325 350 63 1591 091123 008877 204769 -125 775 2375535
350 375 31 1622 092898 007102 182455 -132 620 2608194
375 400 32 1654 094731 005269 152606 -139 460 2916351
400 425 23 1677 096048 003952 123837 -145 345 3210883
425 450 11 1688 096678 003322 106471 -15 290 3387796
450 475 20 1708 097824 002176 064185 -156 190 3816515
475 500 9 1717 098339 001661 037156 -161 145 4089424
500 525 7 1724 098740 001260 009531 -166 110 4367707
525 550 9 1733 099255 000745 -043078 -17 065 4896399
550 575 8 1741 099714 000286 -138629 -175 025 5854211
575 600 5 1746 1 0 NUM -179 000 NUM
February 1 2012 30
Gumbel exceedance graph
Gumbel distribution
y = 07234x + 1882
R2 = 09871
0
2
4
6
8
10
0 2 4 6 8 10Gumbel Reduced variable
Sto
rm h
eig
ht
Hs
s
ssG AH B
= 1A = 0723
= B =1882
February 1 2012 31
calculation of a value
1ln ln
1ln ln
1
1ln ln
1
ln ln
ss
s
s
s
s s
HP
Q
QN
N
N Q
1500
873188 073ln ln 967
1873500
sH
= 1A = 073
= B =188
February 1 2012 32
transformation of the axis
Gumbel distribution
y = 07234x + 1882
R2 = 09871
0
2
4
6
8
10
0 2 4 6 8 10Gumbel Reduced variable
Sto
rm h
eig
ht
Hs
s
ln ln s
s s
NG
N Q
Ns = 873 storms per year
Qs G
110
1100
11000
110000
677
907
1138
1368
Figure Error No text of specified style in document-1 Storm exceedance on basis of Gumbel
10 100
February 1 2012 33
Weibull distribution
exp ssHQ
February 1 2012 34
determination of the reduced variable
1
1
ln
ln
1ln
ss
ss
ss
ss
WAH B
HQ
HQ
Q H
1
lnW Q
Three variables
and
So iteration is needed
February 1 2012 35
calculation for Weibull
alfa= 124
150 cumul P Q ln(Qs) -ln(H) Qs W
150 175 384 384 021993 078007 422098 -056 6810 032522
175 200 381 765 043814 056186 389284 -069 4905 064136
200 225 266 1031 059049 040951 357655 -081 3575 091261
225 250 157 1188 068041 031959 332863 -092 2790 111202
250 275 148 1336 076518 023482 302042 -101 2050 134858
275 300 111 1447 082875 017125 270471 -11 1495 158094
300 325 81 1528 087514 012486 238876 -118 1090 180552
325 350 63 1591 091123 008877 204769 -125 775 204065
350 375 31 1622 092898 007102 182455 -132 620 219099
375 400 32 1654 094731 005269 152606 -139 460 238832
400 425 23 1677 096048 003952 123837 -145 345 257486
425 450 11 1688 096678 003322 106471 -15 290 268590
450 475 20 1708 097824 002176 064185 -156 190 295184
475 500 9 1717 098339 001661 037156 -161 145 311883
500 525 7 1724 098740 001260 009531 -166 110 328731
525 550 9 1733 099255 000745 -043078 -17 065 360263
550 575 8 1741 099714 000286 -138629 -175 025 415922
575 600 5 1746 1 0 NUM -179 000 DIV0
1746
20 year 873 085586
-104906
099524
-07849
541 beta 116842
gamma 122575
Hs for condition 1 500 1028785 911838
1
lnssH Q
1
ln sss
s
QH
N
1124
1500
1500122 117 ln
873
122 117 675
912
sH
m
February 1 2012 36
Weibull exceedance graph
Weibull distribution
y = 11573x + 12497
R2 = 09905
0
2
4
6
8
10
0 2 4 6 8 10
Weibull Reduced variable
Str
om
heig
ht
Hss
10 100 1000 10000
February 1 2012 37
Summary
HT threshold value
Exponential
Gumbel
Weibull
150 m 163 m 136 m 122 m
HT 150 200 250 300 350 400
Ns 873 596 389 194 108 53
Hs 1500 Exponential Hs 1500 Gumbel Hs 1500 Weibull
1000 969 912
1009 950 990
948 917 963
939 893 948
908 886 917
876 818 890
February 1 2012 38
What to do if only random data are available
storm exceedance
0
200
400
600
800
01110100100010000
probability per year
Hs
s
February 1 2012 39
Example of long term data
This are
Hs-classes
February 1 2012 40
Long term (continuation)
So from this last column we can conclude
100 of time H gt 0 m s
23 of time H gt 1 m s
12 of time H gt 2 m s
001 of time H gt 9 m s
0
2
4
6
8
10
12
14
1E-071E-061E-051E-041E-031E-021E-011E+00
exceedance per year
wave
he
igh
t H
s (
m)
February 1 2012 41
From probability of waves to probability of storms
Suppose a ldquostormrdquo lasts for 12 hrs
===gt 730 stormsyear
once per year storm = 100730 = 013 =gt 67 m
once per 10 year storm = 0013 =gt 94 m
once per 100 year storm = 00013 =gt 119 m
0
5
10
15
20
1 10 100 1000 10000
return period in years
Hs o
f th
e g
ive
n s
torm
February 1 2012 42
Meteorological data
bull Not of direct importance for design
bull Can be important for hindcast of wave data and storm surge
bull Extremely important for the execution of the works (workability)
February 1 2012 43
Waves from Wind (Brettschneider)
February 1 2012 44
required soil data
February 1 2012 45
in situ test methods
February 1 2012 46
During construction
bull Quarry stone
bull Concrete
bull Local Equipment
bull Labour
bull skilled
bull cost
bull availability
bull expatriates
February 1 2012 27
Using the Gumbel distribution
exp exp ssHP
February 1 2012 28
determination of and
ln exp
1ln ln
ss
ss
ssss
GAH B
HP
HP H
1ln lnG
P
Perform linear regression
for G = A Hss - B
February 1 2012 29
data for calculation of Gumbel 150 cumul P Q ln(Qs) -ln(H) Qs G
150 175 384 384 021993 078007 422098 -056 6810 -0415046
175 200 381 765 043814 056186 389284 -069 4905 0192121
200 225 266 1031 059049 040951 357655 -081 3575 0640938
225 250 157 1188 068041 031959 332863 -092 2790 0954366
250 275 148 1336 076518 023482 302042 -101 2050 1318085
275 300 111 1447 082875 017125 270471 -11 1495 1672191
300 325 81 1528 087514 012486 238876 -118 1090 2014645
325 350 63 1591 091123 008877 204769 -125 775 2375535
350 375 31 1622 092898 007102 182455 -132 620 2608194
375 400 32 1654 094731 005269 152606 -139 460 2916351
400 425 23 1677 096048 003952 123837 -145 345 3210883
425 450 11 1688 096678 003322 106471 -15 290 3387796
450 475 20 1708 097824 002176 064185 -156 190 3816515
475 500 9 1717 098339 001661 037156 -161 145 4089424
500 525 7 1724 098740 001260 009531 -166 110 4367707
525 550 9 1733 099255 000745 -043078 -17 065 4896399
550 575 8 1741 099714 000286 -138629 -175 025 5854211
575 600 5 1746 1 0 NUM -179 000 NUM
February 1 2012 30
Gumbel exceedance graph
Gumbel distribution
y = 07234x + 1882
R2 = 09871
0
2
4
6
8
10
0 2 4 6 8 10Gumbel Reduced variable
Sto
rm h
eig
ht
Hs
s
ssG AH B
= 1A = 0723
= B =1882
February 1 2012 31
calculation of a value
1ln ln
1ln ln
1
1ln ln
1
ln ln
ss
s
s
s
s s
HP
Q
QN
N
N Q
1500
873188 073ln ln 967
1873500
sH
= 1A = 073
= B =188
February 1 2012 32
transformation of the axis
Gumbel distribution
y = 07234x + 1882
R2 = 09871
0
2
4
6
8
10
0 2 4 6 8 10Gumbel Reduced variable
Sto
rm h
eig
ht
Hs
s
ln ln s
s s
NG
N Q
Ns = 873 storms per year
Qs G
110
1100
11000
110000
677
907
1138
1368
Figure Error No text of specified style in document-1 Storm exceedance on basis of Gumbel
10 100
February 1 2012 33
Weibull distribution
exp ssHQ
February 1 2012 34
determination of the reduced variable
1
1
ln
ln
1ln
ss
ss
ss
ss
WAH B
HQ
HQ
Q H
1
lnW Q
Three variables
and
So iteration is needed
February 1 2012 35
calculation for Weibull
alfa= 124
150 cumul P Q ln(Qs) -ln(H) Qs W
150 175 384 384 021993 078007 422098 -056 6810 032522
175 200 381 765 043814 056186 389284 -069 4905 064136
200 225 266 1031 059049 040951 357655 -081 3575 091261
225 250 157 1188 068041 031959 332863 -092 2790 111202
250 275 148 1336 076518 023482 302042 -101 2050 134858
275 300 111 1447 082875 017125 270471 -11 1495 158094
300 325 81 1528 087514 012486 238876 -118 1090 180552
325 350 63 1591 091123 008877 204769 -125 775 204065
350 375 31 1622 092898 007102 182455 -132 620 219099
375 400 32 1654 094731 005269 152606 -139 460 238832
400 425 23 1677 096048 003952 123837 -145 345 257486
425 450 11 1688 096678 003322 106471 -15 290 268590
450 475 20 1708 097824 002176 064185 -156 190 295184
475 500 9 1717 098339 001661 037156 -161 145 311883
500 525 7 1724 098740 001260 009531 -166 110 328731
525 550 9 1733 099255 000745 -043078 -17 065 360263
550 575 8 1741 099714 000286 -138629 -175 025 415922
575 600 5 1746 1 0 NUM -179 000 DIV0
1746
20 year 873 085586
-104906
099524
-07849
541 beta 116842
gamma 122575
Hs for condition 1 500 1028785 911838
1
lnssH Q
1
ln sss
s
QH
N
1124
1500
1500122 117 ln
873
122 117 675
912
sH
m
February 1 2012 36
Weibull exceedance graph
Weibull distribution
y = 11573x + 12497
R2 = 09905
0
2
4
6
8
10
0 2 4 6 8 10
Weibull Reduced variable
Str
om
heig
ht
Hss
10 100 1000 10000
February 1 2012 37
Summary
HT threshold value
Exponential
Gumbel
Weibull
150 m 163 m 136 m 122 m
HT 150 200 250 300 350 400
Ns 873 596 389 194 108 53
Hs 1500 Exponential Hs 1500 Gumbel Hs 1500 Weibull
1000 969 912
1009 950 990
948 917 963
939 893 948
908 886 917
876 818 890
February 1 2012 38
What to do if only random data are available
storm exceedance
0
200
400
600
800
01110100100010000
probability per year
Hs
s
February 1 2012 39
Example of long term data
This are
Hs-classes
February 1 2012 40
Long term (continuation)
So from this last column we can conclude
100 of time H gt 0 m s
23 of time H gt 1 m s
12 of time H gt 2 m s
001 of time H gt 9 m s
0
2
4
6
8
10
12
14
1E-071E-061E-051E-041E-031E-021E-011E+00
exceedance per year
wave
he
igh
t H
s (
m)
February 1 2012 41
From probability of waves to probability of storms
Suppose a ldquostormrdquo lasts for 12 hrs
===gt 730 stormsyear
once per year storm = 100730 = 013 =gt 67 m
once per 10 year storm = 0013 =gt 94 m
once per 100 year storm = 00013 =gt 119 m
0
5
10
15
20
1 10 100 1000 10000
return period in years
Hs o
f th
e g
ive
n s
torm
February 1 2012 42
Meteorological data
bull Not of direct importance for design
bull Can be important for hindcast of wave data and storm surge
bull Extremely important for the execution of the works (workability)
February 1 2012 43
Waves from Wind (Brettschneider)
February 1 2012 44
required soil data
February 1 2012 45
in situ test methods
February 1 2012 46
During construction
bull Quarry stone
bull Concrete
bull Local Equipment
bull Labour
bull skilled
bull cost
bull availability
bull expatriates
February 1 2012 28
determination of and
ln exp
1ln ln
ss
ss
ssss
GAH B
HP
HP H
1ln lnG
P
Perform linear regression
for G = A Hss - B
February 1 2012 29
data for calculation of Gumbel 150 cumul P Q ln(Qs) -ln(H) Qs G
150 175 384 384 021993 078007 422098 -056 6810 -0415046
175 200 381 765 043814 056186 389284 -069 4905 0192121
200 225 266 1031 059049 040951 357655 -081 3575 0640938
225 250 157 1188 068041 031959 332863 -092 2790 0954366
250 275 148 1336 076518 023482 302042 -101 2050 1318085
275 300 111 1447 082875 017125 270471 -11 1495 1672191
300 325 81 1528 087514 012486 238876 -118 1090 2014645
325 350 63 1591 091123 008877 204769 -125 775 2375535
350 375 31 1622 092898 007102 182455 -132 620 2608194
375 400 32 1654 094731 005269 152606 -139 460 2916351
400 425 23 1677 096048 003952 123837 -145 345 3210883
425 450 11 1688 096678 003322 106471 -15 290 3387796
450 475 20 1708 097824 002176 064185 -156 190 3816515
475 500 9 1717 098339 001661 037156 -161 145 4089424
500 525 7 1724 098740 001260 009531 -166 110 4367707
525 550 9 1733 099255 000745 -043078 -17 065 4896399
550 575 8 1741 099714 000286 -138629 -175 025 5854211
575 600 5 1746 1 0 NUM -179 000 NUM
February 1 2012 30
Gumbel exceedance graph
Gumbel distribution
y = 07234x + 1882
R2 = 09871
0
2
4
6
8
10
0 2 4 6 8 10Gumbel Reduced variable
Sto
rm h
eig
ht
Hs
s
ssG AH B
= 1A = 0723
= B =1882
February 1 2012 31
calculation of a value
1ln ln
1ln ln
1
1ln ln
1
ln ln
ss
s
s
s
s s
HP
Q
QN
N
N Q
1500
873188 073ln ln 967
1873500
sH
= 1A = 073
= B =188
February 1 2012 32
transformation of the axis
Gumbel distribution
y = 07234x + 1882
R2 = 09871
0
2
4
6
8
10
0 2 4 6 8 10Gumbel Reduced variable
Sto
rm h
eig
ht
Hs
s
ln ln s
s s
NG
N Q
Ns = 873 storms per year
Qs G
110
1100
11000
110000
677
907
1138
1368
Figure Error No text of specified style in document-1 Storm exceedance on basis of Gumbel
10 100
February 1 2012 33
Weibull distribution
exp ssHQ
February 1 2012 34
determination of the reduced variable
1
1
ln
ln
1ln
ss
ss
ss
ss
WAH B
HQ
HQ
Q H
1
lnW Q
Three variables
and
So iteration is needed
February 1 2012 35
calculation for Weibull
alfa= 124
150 cumul P Q ln(Qs) -ln(H) Qs W
150 175 384 384 021993 078007 422098 -056 6810 032522
175 200 381 765 043814 056186 389284 -069 4905 064136
200 225 266 1031 059049 040951 357655 -081 3575 091261
225 250 157 1188 068041 031959 332863 -092 2790 111202
250 275 148 1336 076518 023482 302042 -101 2050 134858
275 300 111 1447 082875 017125 270471 -11 1495 158094
300 325 81 1528 087514 012486 238876 -118 1090 180552
325 350 63 1591 091123 008877 204769 -125 775 204065
350 375 31 1622 092898 007102 182455 -132 620 219099
375 400 32 1654 094731 005269 152606 -139 460 238832
400 425 23 1677 096048 003952 123837 -145 345 257486
425 450 11 1688 096678 003322 106471 -15 290 268590
450 475 20 1708 097824 002176 064185 -156 190 295184
475 500 9 1717 098339 001661 037156 -161 145 311883
500 525 7 1724 098740 001260 009531 -166 110 328731
525 550 9 1733 099255 000745 -043078 -17 065 360263
550 575 8 1741 099714 000286 -138629 -175 025 415922
575 600 5 1746 1 0 NUM -179 000 DIV0
1746
20 year 873 085586
-104906
099524
-07849
541 beta 116842
gamma 122575
Hs for condition 1 500 1028785 911838
1
lnssH Q
1
ln sss
s
QH
N
1124
1500
1500122 117 ln
873
122 117 675
912
sH
m
February 1 2012 36
Weibull exceedance graph
Weibull distribution
y = 11573x + 12497
R2 = 09905
0
2
4
6
8
10
0 2 4 6 8 10
Weibull Reduced variable
Str
om
heig
ht
Hss
10 100 1000 10000
February 1 2012 37
Summary
HT threshold value
Exponential
Gumbel
Weibull
150 m 163 m 136 m 122 m
HT 150 200 250 300 350 400
Ns 873 596 389 194 108 53
Hs 1500 Exponential Hs 1500 Gumbel Hs 1500 Weibull
1000 969 912
1009 950 990
948 917 963
939 893 948
908 886 917
876 818 890
February 1 2012 38
What to do if only random data are available
storm exceedance
0
200
400
600
800
01110100100010000
probability per year
Hs
s
February 1 2012 39
Example of long term data
This are
Hs-classes
February 1 2012 40
Long term (continuation)
So from this last column we can conclude
100 of time H gt 0 m s
23 of time H gt 1 m s
12 of time H gt 2 m s
001 of time H gt 9 m s
0
2
4
6
8
10
12
14
1E-071E-061E-051E-041E-031E-021E-011E+00
exceedance per year
wave
he
igh
t H
s (
m)
February 1 2012 41
From probability of waves to probability of storms
Suppose a ldquostormrdquo lasts for 12 hrs
===gt 730 stormsyear
once per year storm = 100730 = 013 =gt 67 m
once per 10 year storm = 0013 =gt 94 m
once per 100 year storm = 00013 =gt 119 m
0
5
10
15
20
1 10 100 1000 10000
return period in years
Hs o
f th
e g
ive
n s
torm
February 1 2012 42
Meteorological data
bull Not of direct importance for design
bull Can be important for hindcast of wave data and storm surge
bull Extremely important for the execution of the works (workability)
February 1 2012 43
Waves from Wind (Brettschneider)
February 1 2012 44
required soil data
February 1 2012 45
in situ test methods
February 1 2012 46
During construction
bull Quarry stone
bull Concrete
bull Local Equipment
bull Labour
bull skilled
bull cost
bull availability
bull expatriates
February 1 2012 29
data for calculation of Gumbel 150 cumul P Q ln(Qs) -ln(H) Qs G
150 175 384 384 021993 078007 422098 -056 6810 -0415046
175 200 381 765 043814 056186 389284 -069 4905 0192121
200 225 266 1031 059049 040951 357655 -081 3575 0640938
225 250 157 1188 068041 031959 332863 -092 2790 0954366
250 275 148 1336 076518 023482 302042 -101 2050 1318085
275 300 111 1447 082875 017125 270471 -11 1495 1672191
300 325 81 1528 087514 012486 238876 -118 1090 2014645
325 350 63 1591 091123 008877 204769 -125 775 2375535
350 375 31 1622 092898 007102 182455 -132 620 2608194
375 400 32 1654 094731 005269 152606 -139 460 2916351
400 425 23 1677 096048 003952 123837 -145 345 3210883
425 450 11 1688 096678 003322 106471 -15 290 3387796
450 475 20 1708 097824 002176 064185 -156 190 3816515
475 500 9 1717 098339 001661 037156 -161 145 4089424
500 525 7 1724 098740 001260 009531 -166 110 4367707
525 550 9 1733 099255 000745 -043078 -17 065 4896399
550 575 8 1741 099714 000286 -138629 -175 025 5854211
575 600 5 1746 1 0 NUM -179 000 NUM
February 1 2012 30
Gumbel exceedance graph
Gumbel distribution
y = 07234x + 1882
R2 = 09871
0
2
4
6
8
10
0 2 4 6 8 10Gumbel Reduced variable
Sto
rm h
eig
ht
Hs
s
ssG AH B
= 1A = 0723
= B =1882
February 1 2012 31
calculation of a value
1ln ln
1ln ln
1
1ln ln
1
ln ln
ss
s
s
s
s s
HP
Q
QN
N
N Q
1500
873188 073ln ln 967
1873500
sH
= 1A = 073
= B =188
February 1 2012 32
transformation of the axis
Gumbel distribution
y = 07234x + 1882
R2 = 09871
0
2
4
6
8
10
0 2 4 6 8 10Gumbel Reduced variable
Sto
rm h
eig
ht
Hs
s
ln ln s
s s
NG
N Q
Ns = 873 storms per year
Qs G
110
1100
11000
110000
677
907
1138
1368
Figure Error No text of specified style in document-1 Storm exceedance on basis of Gumbel
10 100
February 1 2012 33
Weibull distribution
exp ssHQ
February 1 2012 34
determination of the reduced variable
1
1
ln
ln
1ln
ss
ss
ss
ss
WAH B
HQ
HQ
Q H
1
lnW Q
Three variables
and
So iteration is needed
February 1 2012 35
calculation for Weibull
alfa= 124
150 cumul P Q ln(Qs) -ln(H) Qs W
150 175 384 384 021993 078007 422098 -056 6810 032522
175 200 381 765 043814 056186 389284 -069 4905 064136
200 225 266 1031 059049 040951 357655 -081 3575 091261
225 250 157 1188 068041 031959 332863 -092 2790 111202
250 275 148 1336 076518 023482 302042 -101 2050 134858
275 300 111 1447 082875 017125 270471 -11 1495 158094
300 325 81 1528 087514 012486 238876 -118 1090 180552
325 350 63 1591 091123 008877 204769 -125 775 204065
350 375 31 1622 092898 007102 182455 -132 620 219099
375 400 32 1654 094731 005269 152606 -139 460 238832
400 425 23 1677 096048 003952 123837 -145 345 257486
425 450 11 1688 096678 003322 106471 -15 290 268590
450 475 20 1708 097824 002176 064185 -156 190 295184
475 500 9 1717 098339 001661 037156 -161 145 311883
500 525 7 1724 098740 001260 009531 -166 110 328731
525 550 9 1733 099255 000745 -043078 -17 065 360263
550 575 8 1741 099714 000286 -138629 -175 025 415922
575 600 5 1746 1 0 NUM -179 000 DIV0
1746
20 year 873 085586
-104906
099524
-07849
541 beta 116842
gamma 122575
Hs for condition 1 500 1028785 911838
1
lnssH Q
1
ln sss
s
QH
N
1124
1500
1500122 117 ln
873
122 117 675
912
sH
m
February 1 2012 36
Weibull exceedance graph
Weibull distribution
y = 11573x + 12497
R2 = 09905
0
2
4
6
8
10
0 2 4 6 8 10
Weibull Reduced variable
Str
om
heig
ht
Hss
10 100 1000 10000
February 1 2012 37
Summary
HT threshold value
Exponential
Gumbel
Weibull
150 m 163 m 136 m 122 m
HT 150 200 250 300 350 400
Ns 873 596 389 194 108 53
Hs 1500 Exponential Hs 1500 Gumbel Hs 1500 Weibull
1000 969 912
1009 950 990
948 917 963
939 893 948
908 886 917
876 818 890
February 1 2012 38
What to do if only random data are available
storm exceedance
0
200
400
600
800
01110100100010000
probability per year
Hs
s
February 1 2012 39
Example of long term data
This are
Hs-classes
February 1 2012 40
Long term (continuation)
So from this last column we can conclude
100 of time H gt 0 m s
23 of time H gt 1 m s
12 of time H gt 2 m s
001 of time H gt 9 m s
0
2
4
6
8
10
12
14
1E-071E-061E-051E-041E-031E-021E-011E+00
exceedance per year
wave
he
igh
t H
s (
m)
February 1 2012 41
From probability of waves to probability of storms
Suppose a ldquostormrdquo lasts for 12 hrs
===gt 730 stormsyear
once per year storm = 100730 = 013 =gt 67 m
once per 10 year storm = 0013 =gt 94 m
once per 100 year storm = 00013 =gt 119 m
0
5
10
15
20
1 10 100 1000 10000
return period in years
Hs o
f th
e g
ive
n s
torm
February 1 2012 42
Meteorological data
bull Not of direct importance for design
bull Can be important for hindcast of wave data and storm surge
bull Extremely important for the execution of the works (workability)
February 1 2012 43
Waves from Wind (Brettschneider)
February 1 2012 44
required soil data
February 1 2012 45
in situ test methods
February 1 2012 46
During construction
bull Quarry stone
bull Concrete
bull Local Equipment
bull Labour
bull skilled
bull cost
bull availability
bull expatriates
February 1 2012 30
Gumbel exceedance graph
Gumbel distribution
y = 07234x + 1882
R2 = 09871
0
2
4
6
8
10
0 2 4 6 8 10Gumbel Reduced variable
Sto
rm h
eig
ht
Hs
s
ssG AH B
= 1A = 0723
= B =1882
February 1 2012 31
calculation of a value
1ln ln
1ln ln
1
1ln ln
1
ln ln
ss
s
s
s
s s
HP
Q
QN
N
N Q
1500
873188 073ln ln 967
1873500
sH
= 1A = 073
= B =188
February 1 2012 32
transformation of the axis
Gumbel distribution
y = 07234x + 1882
R2 = 09871
0
2
4
6
8
10
0 2 4 6 8 10Gumbel Reduced variable
Sto
rm h
eig
ht
Hs
s
ln ln s
s s
NG
N Q
Ns = 873 storms per year
Qs G
110
1100
11000
110000
677
907
1138
1368
Figure Error No text of specified style in document-1 Storm exceedance on basis of Gumbel
10 100
February 1 2012 33
Weibull distribution
exp ssHQ
February 1 2012 34
determination of the reduced variable
1
1
ln
ln
1ln
ss
ss
ss
ss
WAH B
HQ
HQ
Q H
1
lnW Q
Three variables
and
So iteration is needed
February 1 2012 35
calculation for Weibull
alfa= 124
150 cumul P Q ln(Qs) -ln(H) Qs W
150 175 384 384 021993 078007 422098 -056 6810 032522
175 200 381 765 043814 056186 389284 -069 4905 064136
200 225 266 1031 059049 040951 357655 -081 3575 091261
225 250 157 1188 068041 031959 332863 -092 2790 111202
250 275 148 1336 076518 023482 302042 -101 2050 134858
275 300 111 1447 082875 017125 270471 -11 1495 158094
300 325 81 1528 087514 012486 238876 -118 1090 180552
325 350 63 1591 091123 008877 204769 -125 775 204065
350 375 31 1622 092898 007102 182455 -132 620 219099
375 400 32 1654 094731 005269 152606 -139 460 238832
400 425 23 1677 096048 003952 123837 -145 345 257486
425 450 11 1688 096678 003322 106471 -15 290 268590
450 475 20 1708 097824 002176 064185 -156 190 295184
475 500 9 1717 098339 001661 037156 -161 145 311883
500 525 7 1724 098740 001260 009531 -166 110 328731
525 550 9 1733 099255 000745 -043078 -17 065 360263
550 575 8 1741 099714 000286 -138629 -175 025 415922
575 600 5 1746 1 0 NUM -179 000 DIV0
1746
20 year 873 085586
-104906
099524
-07849
541 beta 116842
gamma 122575
Hs for condition 1 500 1028785 911838
1
lnssH Q
1
ln sss
s
QH
N
1124
1500
1500122 117 ln
873
122 117 675
912
sH
m
February 1 2012 36
Weibull exceedance graph
Weibull distribution
y = 11573x + 12497
R2 = 09905
0
2
4
6
8
10
0 2 4 6 8 10
Weibull Reduced variable
Str
om
heig
ht
Hss
10 100 1000 10000
February 1 2012 37
Summary
HT threshold value
Exponential
Gumbel
Weibull
150 m 163 m 136 m 122 m
HT 150 200 250 300 350 400
Ns 873 596 389 194 108 53
Hs 1500 Exponential Hs 1500 Gumbel Hs 1500 Weibull
1000 969 912
1009 950 990
948 917 963
939 893 948
908 886 917
876 818 890
February 1 2012 38
What to do if only random data are available
storm exceedance
0
200
400
600
800
01110100100010000
probability per year
Hs
s
February 1 2012 39
Example of long term data
This are
Hs-classes
February 1 2012 40
Long term (continuation)
So from this last column we can conclude
100 of time H gt 0 m s
23 of time H gt 1 m s
12 of time H gt 2 m s
001 of time H gt 9 m s
0
2
4
6
8
10
12
14
1E-071E-061E-051E-041E-031E-021E-011E+00
exceedance per year
wave
he
igh
t H
s (
m)
February 1 2012 41
From probability of waves to probability of storms
Suppose a ldquostormrdquo lasts for 12 hrs
===gt 730 stormsyear
once per year storm = 100730 = 013 =gt 67 m
once per 10 year storm = 0013 =gt 94 m
once per 100 year storm = 00013 =gt 119 m
0
5
10
15
20
1 10 100 1000 10000
return period in years
Hs o
f th
e g
ive
n s
torm
February 1 2012 42
Meteorological data
bull Not of direct importance for design
bull Can be important for hindcast of wave data and storm surge
bull Extremely important for the execution of the works (workability)
February 1 2012 43
Waves from Wind (Brettschneider)
February 1 2012 44
required soil data
February 1 2012 45
in situ test methods
February 1 2012 46
During construction
bull Quarry stone
bull Concrete
bull Local Equipment
bull Labour
bull skilled
bull cost
bull availability
bull expatriates
February 1 2012 31
calculation of a value
1ln ln
1ln ln
1
1ln ln
1
ln ln
ss
s
s
s
s s
HP
Q
QN
N
N Q
1500
873188 073ln ln 967
1873500
sH
= 1A = 073
= B =188
February 1 2012 32
transformation of the axis
Gumbel distribution
y = 07234x + 1882
R2 = 09871
0
2
4
6
8
10
0 2 4 6 8 10Gumbel Reduced variable
Sto
rm h
eig
ht
Hs
s
ln ln s
s s
NG
N Q
Ns = 873 storms per year
Qs G
110
1100
11000
110000
677
907
1138
1368
Figure Error No text of specified style in document-1 Storm exceedance on basis of Gumbel
10 100
February 1 2012 33
Weibull distribution
exp ssHQ
February 1 2012 34
determination of the reduced variable
1
1
ln
ln
1ln
ss
ss
ss
ss
WAH B
HQ
HQ
Q H
1
lnW Q
Three variables
and
So iteration is needed
February 1 2012 35
calculation for Weibull
alfa= 124
150 cumul P Q ln(Qs) -ln(H) Qs W
150 175 384 384 021993 078007 422098 -056 6810 032522
175 200 381 765 043814 056186 389284 -069 4905 064136
200 225 266 1031 059049 040951 357655 -081 3575 091261
225 250 157 1188 068041 031959 332863 -092 2790 111202
250 275 148 1336 076518 023482 302042 -101 2050 134858
275 300 111 1447 082875 017125 270471 -11 1495 158094
300 325 81 1528 087514 012486 238876 -118 1090 180552
325 350 63 1591 091123 008877 204769 -125 775 204065
350 375 31 1622 092898 007102 182455 -132 620 219099
375 400 32 1654 094731 005269 152606 -139 460 238832
400 425 23 1677 096048 003952 123837 -145 345 257486
425 450 11 1688 096678 003322 106471 -15 290 268590
450 475 20 1708 097824 002176 064185 -156 190 295184
475 500 9 1717 098339 001661 037156 -161 145 311883
500 525 7 1724 098740 001260 009531 -166 110 328731
525 550 9 1733 099255 000745 -043078 -17 065 360263
550 575 8 1741 099714 000286 -138629 -175 025 415922
575 600 5 1746 1 0 NUM -179 000 DIV0
1746
20 year 873 085586
-104906
099524
-07849
541 beta 116842
gamma 122575
Hs for condition 1 500 1028785 911838
1
lnssH Q
1
ln sss
s
QH
N
1124
1500
1500122 117 ln
873
122 117 675
912
sH
m
February 1 2012 36
Weibull exceedance graph
Weibull distribution
y = 11573x + 12497
R2 = 09905
0
2
4
6
8
10
0 2 4 6 8 10
Weibull Reduced variable
Str
om
heig
ht
Hss
10 100 1000 10000
February 1 2012 37
Summary
HT threshold value
Exponential
Gumbel
Weibull
150 m 163 m 136 m 122 m
HT 150 200 250 300 350 400
Ns 873 596 389 194 108 53
Hs 1500 Exponential Hs 1500 Gumbel Hs 1500 Weibull
1000 969 912
1009 950 990
948 917 963
939 893 948
908 886 917
876 818 890
February 1 2012 38
What to do if only random data are available
storm exceedance
0
200
400
600
800
01110100100010000
probability per year
Hs
s
February 1 2012 39
Example of long term data
This are
Hs-classes
February 1 2012 40
Long term (continuation)
So from this last column we can conclude
100 of time H gt 0 m s
23 of time H gt 1 m s
12 of time H gt 2 m s
001 of time H gt 9 m s
0
2
4
6
8
10
12
14
1E-071E-061E-051E-041E-031E-021E-011E+00
exceedance per year
wave
he
igh
t H
s (
m)
February 1 2012 41
From probability of waves to probability of storms
Suppose a ldquostormrdquo lasts for 12 hrs
===gt 730 stormsyear
once per year storm = 100730 = 013 =gt 67 m
once per 10 year storm = 0013 =gt 94 m
once per 100 year storm = 00013 =gt 119 m
0
5
10
15
20
1 10 100 1000 10000
return period in years
Hs o
f th
e g
ive
n s
torm
February 1 2012 42
Meteorological data
bull Not of direct importance for design
bull Can be important for hindcast of wave data and storm surge
bull Extremely important for the execution of the works (workability)
February 1 2012 43
Waves from Wind (Brettschneider)
February 1 2012 44
required soil data
February 1 2012 45
in situ test methods
February 1 2012 46
During construction
bull Quarry stone
bull Concrete
bull Local Equipment
bull Labour
bull skilled
bull cost
bull availability
bull expatriates
February 1 2012 32
transformation of the axis
Gumbel distribution
y = 07234x + 1882
R2 = 09871
0
2
4
6
8
10
0 2 4 6 8 10Gumbel Reduced variable
Sto
rm h
eig
ht
Hs
s
ln ln s
s s
NG
N Q
Ns = 873 storms per year
Qs G
110
1100
11000
110000
677
907
1138
1368
Figure Error No text of specified style in document-1 Storm exceedance on basis of Gumbel
10 100
February 1 2012 33
Weibull distribution
exp ssHQ
February 1 2012 34
determination of the reduced variable
1
1
ln
ln
1ln
ss
ss
ss
ss
WAH B
HQ
HQ
Q H
1
lnW Q
Three variables
and
So iteration is needed
February 1 2012 35
calculation for Weibull
alfa= 124
150 cumul P Q ln(Qs) -ln(H) Qs W
150 175 384 384 021993 078007 422098 -056 6810 032522
175 200 381 765 043814 056186 389284 -069 4905 064136
200 225 266 1031 059049 040951 357655 -081 3575 091261
225 250 157 1188 068041 031959 332863 -092 2790 111202
250 275 148 1336 076518 023482 302042 -101 2050 134858
275 300 111 1447 082875 017125 270471 -11 1495 158094
300 325 81 1528 087514 012486 238876 -118 1090 180552
325 350 63 1591 091123 008877 204769 -125 775 204065
350 375 31 1622 092898 007102 182455 -132 620 219099
375 400 32 1654 094731 005269 152606 -139 460 238832
400 425 23 1677 096048 003952 123837 -145 345 257486
425 450 11 1688 096678 003322 106471 -15 290 268590
450 475 20 1708 097824 002176 064185 -156 190 295184
475 500 9 1717 098339 001661 037156 -161 145 311883
500 525 7 1724 098740 001260 009531 -166 110 328731
525 550 9 1733 099255 000745 -043078 -17 065 360263
550 575 8 1741 099714 000286 -138629 -175 025 415922
575 600 5 1746 1 0 NUM -179 000 DIV0
1746
20 year 873 085586
-104906
099524
-07849
541 beta 116842
gamma 122575
Hs for condition 1 500 1028785 911838
1
lnssH Q
1
ln sss
s
QH
N
1124
1500
1500122 117 ln
873
122 117 675
912
sH
m
February 1 2012 36
Weibull exceedance graph
Weibull distribution
y = 11573x + 12497
R2 = 09905
0
2
4
6
8
10
0 2 4 6 8 10
Weibull Reduced variable
Str
om
heig
ht
Hss
10 100 1000 10000
February 1 2012 37
Summary
HT threshold value
Exponential
Gumbel
Weibull
150 m 163 m 136 m 122 m
HT 150 200 250 300 350 400
Ns 873 596 389 194 108 53
Hs 1500 Exponential Hs 1500 Gumbel Hs 1500 Weibull
1000 969 912
1009 950 990
948 917 963
939 893 948
908 886 917
876 818 890
February 1 2012 38
What to do if only random data are available
storm exceedance
0
200
400
600
800
01110100100010000
probability per year
Hs
s
February 1 2012 39
Example of long term data
This are
Hs-classes
February 1 2012 40
Long term (continuation)
So from this last column we can conclude
100 of time H gt 0 m s
23 of time H gt 1 m s
12 of time H gt 2 m s
001 of time H gt 9 m s
0
2
4
6
8
10
12
14
1E-071E-061E-051E-041E-031E-021E-011E+00
exceedance per year
wave
he
igh
t H
s (
m)
February 1 2012 41
From probability of waves to probability of storms
Suppose a ldquostormrdquo lasts for 12 hrs
===gt 730 stormsyear
once per year storm = 100730 = 013 =gt 67 m
once per 10 year storm = 0013 =gt 94 m
once per 100 year storm = 00013 =gt 119 m
0
5
10
15
20
1 10 100 1000 10000
return period in years
Hs o
f th
e g
ive
n s
torm
February 1 2012 42
Meteorological data
bull Not of direct importance for design
bull Can be important for hindcast of wave data and storm surge
bull Extremely important for the execution of the works (workability)
February 1 2012 43
Waves from Wind (Brettschneider)
February 1 2012 44
required soil data
February 1 2012 45
in situ test methods
February 1 2012 46
During construction
bull Quarry stone
bull Concrete
bull Local Equipment
bull Labour
bull skilled
bull cost
bull availability
bull expatriates
February 1 2012 33
Weibull distribution
exp ssHQ
February 1 2012 34
determination of the reduced variable
1
1
ln
ln
1ln
ss
ss
ss
ss
WAH B
HQ
HQ
Q H
1
lnW Q
Three variables
and
So iteration is needed
February 1 2012 35
calculation for Weibull
alfa= 124
150 cumul P Q ln(Qs) -ln(H) Qs W
150 175 384 384 021993 078007 422098 -056 6810 032522
175 200 381 765 043814 056186 389284 -069 4905 064136
200 225 266 1031 059049 040951 357655 -081 3575 091261
225 250 157 1188 068041 031959 332863 -092 2790 111202
250 275 148 1336 076518 023482 302042 -101 2050 134858
275 300 111 1447 082875 017125 270471 -11 1495 158094
300 325 81 1528 087514 012486 238876 -118 1090 180552
325 350 63 1591 091123 008877 204769 -125 775 204065
350 375 31 1622 092898 007102 182455 -132 620 219099
375 400 32 1654 094731 005269 152606 -139 460 238832
400 425 23 1677 096048 003952 123837 -145 345 257486
425 450 11 1688 096678 003322 106471 -15 290 268590
450 475 20 1708 097824 002176 064185 -156 190 295184
475 500 9 1717 098339 001661 037156 -161 145 311883
500 525 7 1724 098740 001260 009531 -166 110 328731
525 550 9 1733 099255 000745 -043078 -17 065 360263
550 575 8 1741 099714 000286 -138629 -175 025 415922
575 600 5 1746 1 0 NUM -179 000 DIV0
1746
20 year 873 085586
-104906
099524
-07849
541 beta 116842
gamma 122575
Hs for condition 1 500 1028785 911838
1
lnssH Q
1
ln sss
s
QH
N
1124
1500
1500122 117 ln
873
122 117 675
912
sH
m
February 1 2012 36
Weibull exceedance graph
Weibull distribution
y = 11573x + 12497
R2 = 09905
0
2
4
6
8
10
0 2 4 6 8 10
Weibull Reduced variable
Str
om
heig
ht
Hss
10 100 1000 10000
February 1 2012 37
Summary
HT threshold value
Exponential
Gumbel
Weibull
150 m 163 m 136 m 122 m
HT 150 200 250 300 350 400
Ns 873 596 389 194 108 53
Hs 1500 Exponential Hs 1500 Gumbel Hs 1500 Weibull
1000 969 912
1009 950 990
948 917 963
939 893 948
908 886 917
876 818 890
February 1 2012 38
What to do if only random data are available
storm exceedance
0
200
400
600
800
01110100100010000
probability per year
Hs
s
February 1 2012 39
Example of long term data
This are
Hs-classes
February 1 2012 40
Long term (continuation)
So from this last column we can conclude
100 of time H gt 0 m s
23 of time H gt 1 m s
12 of time H gt 2 m s
001 of time H gt 9 m s
0
2
4
6
8
10
12
14
1E-071E-061E-051E-041E-031E-021E-011E+00
exceedance per year
wave
he
igh
t H
s (
m)
February 1 2012 41
From probability of waves to probability of storms
Suppose a ldquostormrdquo lasts for 12 hrs
===gt 730 stormsyear
once per year storm = 100730 = 013 =gt 67 m
once per 10 year storm = 0013 =gt 94 m
once per 100 year storm = 00013 =gt 119 m
0
5
10
15
20
1 10 100 1000 10000
return period in years
Hs o
f th
e g
ive
n s
torm
February 1 2012 42
Meteorological data
bull Not of direct importance for design
bull Can be important for hindcast of wave data and storm surge
bull Extremely important for the execution of the works (workability)
February 1 2012 43
Waves from Wind (Brettschneider)
February 1 2012 44
required soil data
February 1 2012 45
in situ test methods
February 1 2012 46
During construction
bull Quarry stone
bull Concrete
bull Local Equipment
bull Labour
bull skilled
bull cost
bull availability
bull expatriates
February 1 2012 34
determination of the reduced variable
1
1
ln
ln
1ln
ss
ss
ss
ss
WAH B
HQ
HQ
Q H
1
lnW Q
Three variables
and
So iteration is needed
February 1 2012 35
calculation for Weibull
alfa= 124
150 cumul P Q ln(Qs) -ln(H) Qs W
150 175 384 384 021993 078007 422098 -056 6810 032522
175 200 381 765 043814 056186 389284 -069 4905 064136
200 225 266 1031 059049 040951 357655 -081 3575 091261
225 250 157 1188 068041 031959 332863 -092 2790 111202
250 275 148 1336 076518 023482 302042 -101 2050 134858
275 300 111 1447 082875 017125 270471 -11 1495 158094
300 325 81 1528 087514 012486 238876 -118 1090 180552
325 350 63 1591 091123 008877 204769 -125 775 204065
350 375 31 1622 092898 007102 182455 -132 620 219099
375 400 32 1654 094731 005269 152606 -139 460 238832
400 425 23 1677 096048 003952 123837 -145 345 257486
425 450 11 1688 096678 003322 106471 -15 290 268590
450 475 20 1708 097824 002176 064185 -156 190 295184
475 500 9 1717 098339 001661 037156 -161 145 311883
500 525 7 1724 098740 001260 009531 -166 110 328731
525 550 9 1733 099255 000745 -043078 -17 065 360263
550 575 8 1741 099714 000286 -138629 -175 025 415922
575 600 5 1746 1 0 NUM -179 000 DIV0
1746
20 year 873 085586
-104906
099524
-07849
541 beta 116842
gamma 122575
Hs for condition 1 500 1028785 911838
1
lnssH Q
1
ln sss
s
QH
N
1124
1500
1500122 117 ln
873
122 117 675
912
sH
m
February 1 2012 36
Weibull exceedance graph
Weibull distribution
y = 11573x + 12497
R2 = 09905
0
2
4
6
8
10
0 2 4 6 8 10
Weibull Reduced variable
Str
om
heig
ht
Hss
10 100 1000 10000
February 1 2012 37
Summary
HT threshold value
Exponential
Gumbel
Weibull
150 m 163 m 136 m 122 m
HT 150 200 250 300 350 400
Ns 873 596 389 194 108 53
Hs 1500 Exponential Hs 1500 Gumbel Hs 1500 Weibull
1000 969 912
1009 950 990
948 917 963
939 893 948
908 886 917
876 818 890
February 1 2012 38
What to do if only random data are available
storm exceedance
0
200
400
600
800
01110100100010000
probability per year
Hs
s
February 1 2012 39
Example of long term data
This are
Hs-classes
February 1 2012 40
Long term (continuation)
So from this last column we can conclude
100 of time H gt 0 m s
23 of time H gt 1 m s
12 of time H gt 2 m s
001 of time H gt 9 m s
0
2
4
6
8
10
12
14
1E-071E-061E-051E-041E-031E-021E-011E+00
exceedance per year
wave
he
igh
t H
s (
m)
February 1 2012 41
From probability of waves to probability of storms
Suppose a ldquostormrdquo lasts for 12 hrs
===gt 730 stormsyear
once per year storm = 100730 = 013 =gt 67 m
once per 10 year storm = 0013 =gt 94 m
once per 100 year storm = 00013 =gt 119 m
0
5
10
15
20
1 10 100 1000 10000
return period in years
Hs o
f th
e g
ive
n s
torm
February 1 2012 42
Meteorological data
bull Not of direct importance for design
bull Can be important for hindcast of wave data and storm surge
bull Extremely important for the execution of the works (workability)
February 1 2012 43
Waves from Wind (Brettschneider)
February 1 2012 44
required soil data
February 1 2012 45
in situ test methods
February 1 2012 46
During construction
bull Quarry stone
bull Concrete
bull Local Equipment
bull Labour
bull skilled
bull cost
bull availability
bull expatriates
February 1 2012 35
calculation for Weibull
alfa= 124
150 cumul P Q ln(Qs) -ln(H) Qs W
150 175 384 384 021993 078007 422098 -056 6810 032522
175 200 381 765 043814 056186 389284 -069 4905 064136
200 225 266 1031 059049 040951 357655 -081 3575 091261
225 250 157 1188 068041 031959 332863 -092 2790 111202
250 275 148 1336 076518 023482 302042 -101 2050 134858
275 300 111 1447 082875 017125 270471 -11 1495 158094
300 325 81 1528 087514 012486 238876 -118 1090 180552
325 350 63 1591 091123 008877 204769 -125 775 204065
350 375 31 1622 092898 007102 182455 -132 620 219099
375 400 32 1654 094731 005269 152606 -139 460 238832
400 425 23 1677 096048 003952 123837 -145 345 257486
425 450 11 1688 096678 003322 106471 -15 290 268590
450 475 20 1708 097824 002176 064185 -156 190 295184
475 500 9 1717 098339 001661 037156 -161 145 311883
500 525 7 1724 098740 001260 009531 -166 110 328731
525 550 9 1733 099255 000745 -043078 -17 065 360263
550 575 8 1741 099714 000286 -138629 -175 025 415922
575 600 5 1746 1 0 NUM -179 000 DIV0
1746
20 year 873 085586
-104906
099524
-07849
541 beta 116842
gamma 122575
Hs for condition 1 500 1028785 911838
1
lnssH Q
1
ln sss
s
QH
N
1124
1500
1500122 117 ln
873
122 117 675
912
sH
m
February 1 2012 36
Weibull exceedance graph
Weibull distribution
y = 11573x + 12497
R2 = 09905
0
2
4
6
8
10
0 2 4 6 8 10
Weibull Reduced variable
Str
om
heig
ht
Hss
10 100 1000 10000
February 1 2012 37
Summary
HT threshold value
Exponential
Gumbel
Weibull
150 m 163 m 136 m 122 m
HT 150 200 250 300 350 400
Ns 873 596 389 194 108 53
Hs 1500 Exponential Hs 1500 Gumbel Hs 1500 Weibull
1000 969 912
1009 950 990
948 917 963
939 893 948
908 886 917
876 818 890
February 1 2012 38
What to do if only random data are available
storm exceedance
0
200
400
600
800
01110100100010000
probability per year
Hs
s
February 1 2012 39
Example of long term data
This are
Hs-classes
February 1 2012 40
Long term (continuation)
So from this last column we can conclude
100 of time H gt 0 m s
23 of time H gt 1 m s
12 of time H gt 2 m s
001 of time H gt 9 m s
0
2
4
6
8
10
12
14
1E-071E-061E-051E-041E-031E-021E-011E+00
exceedance per year
wave
he
igh
t H
s (
m)
February 1 2012 41
From probability of waves to probability of storms
Suppose a ldquostormrdquo lasts for 12 hrs
===gt 730 stormsyear
once per year storm = 100730 = 013 =gt 67 m
once per 10 year storm = 0013 =gt 94 m
once per 100 year storm = 00013 =gt 119 m
0
5
10
15
20
1 10 100 1000 10000
return period in years
Hs o
f th
e g
ive
n s
torm
February 1 2012 42
Meteorological data
bull Not of direct importance for design
bull Can be important for hindcast of wave data and storm surge
bull Extremely important for the execution of the works (workability)
February 1 2012 43
Waves from Wind (Brettschneider)
February 1 2012 44
required soil data
February 1 2012 45
in situ test methods
February 1 2012 46
During construction
bull Quarry stone
bull Concrete
bull Local Equipment
bull Labour
bull skilled
bull cost
bull availability
bull expatriates
February 1 2012 36
Weibull exceedance graph
Weibull distribution
y = 11573x + 12497
R2 = 09905
0
2
4
6
8
10
0 2 4 6 8 10
Weibull Reduced variable
Str
om
heig
ht
Hss
10 100 1000 10000
February 1 2012 37
Summary
HT threshold value
Exponential
Gumbel
Weibull
150 m 163 m 136 m 122 m
HT 150 200 250 300 350 400
Ns 873 596 389 194 108 53
Hs 1500 Exponential Hs 1500 Gumbel Hs 1500 Weibull
1000 969 912
1009 950 990
948 917 963
939 893 948
908 886 917
876 818 890
February 1 2012 38
What to do if only random data are available
storm exceedance
0
200
400
600
800
01110100100010000
probability per year
Hs
s
February 1 2012 39
Example of long term data
This are
Hs-classes
February 1 2012 40
Long term (continuation)
So from this last column we can conclude
100 of time H gt 0 m s
23 of time H gt 1 m s
12 of time H gt 2 m s
001 of time H gt 9 m s
0
2
4
6
8
10
12
14
1E-071E-061E-051E-041E-031E-021E-011E+00
exceedance per year
wave
he
igh
t H
s (
m)
February 1 2012 41
From probability of waves to probability of storms
Suppose a ldquostormrdquo lasts for 12 hrs
===gt 730 stormsyear
once per year storm = 100730 = 013 =gt 67 m
once per 10 year storm = 0013 =gt 94 m
once per 100 year storm = 00013 =gt 119 m
0
5
10
15
20
1 10 100 1000 10000
return period in years
Hs o
f th
e g
ive
n s
torm
February 1 2012 42
Meteorological data
bull Not of direct importance for design
bull Can be important for hindcast of wave data and storm surge
bull Extremely important for the execution of the works (workability)
February 1 2012 43
Waves from Wind (Brettschneider)
February 1 2012 44
required soil data
February 1 2012 45
in situ test methods
February 1 2012 46
During construction
bull Quarry stone
bull Concrete
bull Local Equipment
bull Labour
bull skilled
bull cost
bull availability
bull expatriates
February 1 2012 37
Summary
HT threshold value
Exponential
Gumbel
Weibull
150 m 163 m 136 m 122 m
HT 150 200 250 300 350 400
Ns 873 596 389 194 108 53
Hs 1500 Exponential Hs 1500 Gumbel Hs 1500 Weibull
1000 969 912
1009 950 990
948 917 963
939 893 948
908 886 917
876 818 890
February 1 2012 38
What to do if only random data are available
storm exceedance
0
200
400
600
800
01110100100010000
probability per year
Hs
s
February 1 2012 39
Example of long term data
This are
Hs-classes
February 1 2012 40
Long term (continuation)
So from this last column we can conclude
100 of time H gt 0 m s
23 of time H gt 1 m s
12 of time H gt 2 m s
001 of time H gt 9 m s
0
2
4
6
8
10
12
14
1E-071E-061E-051E-041E-031E-021E-011E+00
exceedance per year
wave
he
igh
t H
s (
m)
February 1 2012 41
From probability of waves to probability of storms
Suppose a ldquostormrdquo lasts for 12 hrs
===gt 730 stormsyear
once per year storm = 100730 = 013 =gt 67 m
once per 10 year storm = 0013 =gt 94 m
once per 100 year storm = 00013 =gt 119 m
0
5
10
15
20
1 10 100 1000 10000
return period in years
Hs o
f th
e g
ive
n s
torm
February 1 2012 42
Meteorological data
bull Not of direct importance for design
bull Can be important for hindcast of wave data and storm surge
bull Extremely important for the execution of the works (workability)
February 1 2012 43
Waves from Wind (Brettschneider)
February 1 2012 44
required soil data
February 1 2012 45
in situ test methods
February 1 2012 46
During construction
bull Quarry stone
bull Concrete
bull Local Equipment
bull Labour
bull skilled
bull cost
bull availability
bull expatriates
February 1 2012 38
What to do if only random data are available
storm exceedance
0
200
400
600
800
01110100100010000
probability per year
Hs
s
February 1 2012 39
Example of long term data
This are
Hs-classes
February 1 2012 40
Long term (continuation)
So from this last column we can conclude
100 of time H gt 0 m s
23 of time H gt 1 m s
12 of time H gt 2 m s
001 of time H gt 9 m s
0
2
4
6
8
10
12
14
1E-071E-061E-051E-041E-031E-021E-011E+00
exceedance per year
wave
he
igh
t H
s (
m)
February 1 2012 41
From probability of waves to probability of storms
Suppose a ldquostormrdquo lasts for 12 hrs
===gt 730 stormsyear
once per year storm = 100730 = 013 =gt 67 m
once per 10 year storm = 0013 =gt 94 m
once per 100 year storm = 00013 =gt 119 m
0
5
10
15
20
1 10 100 1000 10000
return period in years
Hs o
f th
e g
ive
n s
torm
February 1 2012 42
Meteorological data
bull Not of direct importance for design
bull Can be important for hindcast of wave data and storm surge
bull Extremely important for the execution of the works (workability)
February 1 2012 43
Waves from Wind (Brettschneider)
February 1 2012 44
required soil data
February 1 2012 45
in situ test methods
February 1 2012 46
During construction
bull Quarry stone
bull Concrete
bull Local Equipment
bull Labour
bull skilled
bull cost
bull availability
bull expatriates
February 1 2012 39
Example of long term data
This are
Hs-classes
February 1 2012 40
Long term (continuation)
So from this last column we can conclude
100 of time H gt 0 m s
23 of time H gt 1 m s
12 of time H gt 2 m s
001 of time H gt 9 m s
0
2
4
6
8
10
12
14
1E-071E-061E-051E-041E-031E-021E-011E+00
exceedance per year
wave
he
igh
t H
s (
m)
February 1 2012 41
From probability of waves to probability of storms
Suppose a ldquostormrdquo lasts for 12 hrs
===gt 730 stormsyear
once per year storm = 100730 = 013 =gt 67 m
once per 10 year storm = 0013 =gt 94 m
once per 100 year storm = 00013 =gt 119 m
0
5
10
15
20
1 10 100 1000 10000
return period in years
Hs o
f th
e g
ive
n s
torm
February 1 2012 42
Meteorological data
bull Not of direct importance for design
bull Can be important for hindcast of wave data and storm surge
bull Extremely important for the execution of the works (workability)
February 1 2012 43
Waves from Wind (Brettschneider)
February 1 2012 44
required soil data
February 1 2012 45
in situ test methods
February 1 2012 46
During construction
bull Quarry stone
bull Concrete
bull Local Equipment
bull Labour
bull skilled
bull cost
bull availability
bull expatriates
February 1 2012 40
Long term (continuation)
So from this last column we can conclude
100 of time H gt 0 m s
23 of time H gt 1 m s
12 of time H gt 2 m s
001 of time H gt 9 m s
0
2
4
6
8
10
12
14
1E-071E-061E-051E-041E-031E-021E-011E+00
exceedance per year
wave
he
igh
t H
s (
m)
February 1 2012 41
From probability of waves to probability of storms
Suppose a ldquostormrdquo lasts for 12 hrs
===gt 730 stormsyear
once per year storm = 100730 = 013 =gt 67 m
once per 10 year storm = 0013 =gt 94 m
once per 100 year storm = 00013 =gt 119 m
0
5
10
15
20
1 10 100 1000 10000
return period in years
Hs o
f th
e g
ive
n s
torm
February 1 2012 42
Meteorological data
bull Not of direct importance for design
bull Can be important for hindcast of wave data and storm surge
bull Extremely important for the execution of the works (workability)
February 1 2012 43
Waves from Wind (Brettschneider)
February 1 2012 44
required soil data
February 1 2012 45
in situ test methods
February 1 2012 46
During construction
bull Quarry stone
bull Concrete
bull Local Equipment
bull Labour
bull skilled
bull cost
bull availability
bull expatriates
February 1 2012 41
From probability of waves to probability of storms
Suppose a ldquostormrdquo lasts for 12 hrs
===gt 730 stormsyear
once per year storm = 100730 = 013 =gt 67 m
once per 10 year storm = 0013 =gt 94 m
once per 100 year storm = 00013 =gt 119 m
0
5
10
15
20
1 10 100 1000 10000
return period in years
Hs o
f th
e g
ive
n s
torm
February 1 2012 42
Meteorological data
bull Not of direct importance for design
bull Can be important for hindcast of wave data and storm surge
bull Extremely important for the execution of the works (workability)
February 1 2012 43
Waves from Wind (Brettschneider)
February 1 2012 44
required soil data
February 1 2012 45
in situ test methods
February 1 2012 46
During construction
bull Quarry stone
bull Concrete
bull Local Equipment
bull Labour
bull skilled
bull cost
bull availability
bull expatriates
February 1 2012 42
Meteorological data
bull Not of direct importance for design
bull Can be important for hindcast of wave data and storm surge
bull Extremely important for the execution of the works (workability)
February 1 2012 43
Waves from Wind (Brettschneider)
February 1 2012 44
required soil data
February 1 2012 45
in situ test methods
February 1 2012 46
During construction
bull Quarry stone
bull Concrete
bull Local Equipment
bull Labour
bull skilled
bull cost
bull availability
bull expatriates
February 1 2012 43
Waves from Wind (Brettschneider)
February 1 2012 44
required soil data
February 1 2012 45
in situ test methods
February 1 2012 46
During construction
bull Quarry stone
bull Concrete
bull Local Equipment
bull Labour
bull skilled
bull cost
bull availability
bull expatriates
February 1 2012 44
required soil data
February 1 2012 45
in situ test methods
February 1 2012 46
During construction
bull Quarry stone
bull Concrete
bull Local Equipment
bull Labour
bull skilled
bull cost
bull availability
bull expatriates
February 1 2012 45
in situ test methods
February 1 2012 46
During construction
bull Quarry stone
bull Concrete
bull Local Equipment
bull Labour
bull skilled
bull cost
bull availability
bull expatriates
February 1 2012 46
During construction
bull Quarry stone
bull Concrete
bull Local Equipment
bull Labour
bull skilled
bull cost
bull availability
bull expatriates
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