A survey of ocean wave data

19 JLJNI 9?3

ARC H LEF

r c

- ouwkunde

nische Hogeschool, De

DOCUMENTATE

DATUM:

Seminar at Southampton University The Application of Ship Motion Research

to Design

16 - 17 April, _19Z0

/.

2.

J'

etv

A survey of ocean wave data by J. A. Ewing.

National Institute of Oceanography.

Lab.

v.

Scheepsbouwkund

A survey of ocean wave data. by J.A. Ewing.

National Institute of Oceanography.

Introductjon

An adequate description of wave characteristics is

needed by naval architects in

designing

ships to operate

in a particular sea area. _{This paper gives a brief out-.}

line of the more important sources of wave data with particular reference to the North Atlantic Ocean.

Wave data can be grouped intO three classes according

to its origin. _{These three classes consist of wave}

data from visual observations, wave data from direct

measurements and wave data hindcasted from

_known

meteorol-..

ogical

conditions.

Data from visual observations.

The most extensive amount of wave data has been

derived from visual observations made by observers on

merchant ships duxiug their passage over the _{oceans. A}

comprehensive survey of' this kind of data has already been given by the Environmental Conditions Committee of

the

International

_{Ship Structures Congress (issc) in their}

reports to the Second and Third Congresses. _{In view of}

this t does not appear necessary to repeat this pz'esentat-.

ion but rather to refer to some of the more important sources of visual wave statistics.

A recent

_an4

detailed coverage of visual wave data

over the oceans is given in Hogben and Lumb (i). _These

data, covering fifty different sea areas with the

exception of the North Pacific Ocean (see Fig. 1), have

been collected by the British Meteorological _{Office from}

voluntary observing ships over a period of eight years. Tables are given of the number of observations in each of twelve direction classes for every combination of wave

2

A seasonal breakdown is also incorporated, Fig0 2

shows the wave height versus period table (all wave directions) for Area 2 of the eastern North Atlantic.

Another important source of data for the North Atlantic has been published by the U.S. Naval

Ocean-ographic Office (2). This atlas gives data for wind,

sea and swell on a monthly basis, _{Persistence of waves}

and wave period-height, wave period-direction are presented on a seasonal basis.

Walden has compiled very useful statistics of

visual observations from the weather ships in the Atlantic Ocean (3) and also data covering the east coast of

South America and the west coast of North Africa (4), Two atlases of the North Atlantic and North Pacific Oceans have been issued by the U.S. Department of

Commerce (), (6), These atlases include wave height

contours and cumulative distributions of wave height

for each of four seasons.

Wave statistics for the North Pacific Ocean have also been compiled by Yamanoucni (7), (8).

The World Meteorological Office (wMo) is concerned with collecting and disseminating wave data from visual observations and has distributed responsibility for the collection of data from different oceans among nine nations Details of this distribution and the scope of the data

are given in the report of the 3rd ISSC,

The question of the reliability of visual observations arises and this, with the exception of wave direction, can be investigated by comparing visual observations of

height and period with measurements of the waves. Two

independent investigations have been carried out with

this in mind (References (1) and (9))and both arrive at

the conclusion that visual observations of wave height are reasonably reliable and well correlated with measured wave height (in fact the significant wave height) but that visual estimates of period have low correlation with

measured mean periods and with average and modal periods

obtained by spectral analysis, _{There does not appear}

to be a reliable way of estimating wave spectra _{by fitting}

:3

Data from wave measurements:

(a) Statistics of wave height and period0

The main source of measured wave data is from weather ships operating in the North Atlantic ocean

and equipped with the NI0 shipborne wave recorder. Draper and his colleagues have published two studies

of' wave statistics at ocean weather stations'"India"

(59°N, 19°W) and"Juliett"(52° 30'N, 20

oo'w) (10),

(ii),

'Figs.

3, 4,

and 5 shOw 'the results for'státion

"india". The wave height and period statistics given

in these papfrs have been determined using simple 'analysis techniques based on theoretical studies by Cartwright and

Longuet-Higgins (12), (13). Statistics of a spectral

width parameter and also given.

Draper has recently suggested the need for a uniform method of analysis and presentation for this kind of data based on the.procedures given in references (14), (is'). Reference (15) shows, in" addition to the distributions of' wave height and period, the long term distribution of'

wave height and a wave persistence diagram, These two

distributions are shown in Fig.

6.

The prediction of

the most severe conditions which might occur over a long

period of time is clearly of grf at importance. Wave

persistence diagrams can be use4 to determine the number of' Oècurrences and duration during which waves persist at or above a specified wave height.

Statistics of waves measured with the shipborne wave recorder on light vessels around the coasts of the British Isles have also been collected by the NI0 but these are not discussed here,

(b) Wave spectra measurements.

Darbyshire (16), (17) has measured the one dimensional spectrum of a large number of recordings with the shipborne wave recorder on 0,W.S, "Weather Explorer" at stations

"India" and "Juliett" in his early investigations of wind generated waves and has derived a spectral formula (18.)

£()=

4

More recently Pierson and hIs associates (19) have analysed wave records supplied by the .NIO from weather ships at stations Alfa, India, Juliett and Kilo to

obtain 400 one dimensional spectra.0 A subset of about

50 spectra wCre.'theñ choSen to correspond to fülIy.

developed seas at five Wind speeds between 20 and

40

1.ots. Finally Pierson and Moskowitz derived the

follow-ing spectral formula for fully-developed seas based on the similarity theory of S.A. Kitaigorodski'i (20):

where '

='8.lOx 10,

3= 0.74,A)0./Q,U

wind

speed at a height of 19,5m and C) is the wave frequency in radians/sec.

Over :360 measurements of the one dimensional spectrum have been reported by Inoue (21) using vibrotron pressure transducers on the special research vessel FLIP (Floating

Instrument Platfox'm) during the month of September

_196:3.

The recordings weremade at a position 39° 20'N, 11i8°

20'W in' the Pacific Ocean,

The difficulties in recording and analysing waves in the. open ocean have -resulted in only a few measurements of the two dimensiOnal'wave spectrum (References (22) .to

(26)). ' Furthermore, these nieasureiients have usually been

taken as part of fundamental research on ocean waves

and so -cannot be considered an adequate statistical sample

for wave data purposes. The need for techniques which

can 'give a rapid 'and accurate estimate of the two diméns:or'al

wave spectrum is recognized by oceanographers. Stilvell.

(27) has shown hOw the directional' spectrum may be obtained - from a photograph of the glitter pattern of the sea surface.

This technique Seems 'a suitable one for the routine collection

of wave data0 .AEióther promising technique which is being

explored in the 'United States and in Europe uses a laser

-carried in -an aircraft to measure the wave 'profile with

-Hindcasted wave data derived from numerical wave prediction models.

Modern methods of wave prediction (28),. (29), (jo), (31) are based on the numerical integration

of the energy balance equation first proved by Longuet Higgins

(32):-E

is the directional spectrum at position X and time

as a function of wave frequency and wave direction

9

. The source function _S represents the riot.

transfer of energy to or from the spectrum at

_Cf,

due

to all

interaction

proceSses which affect the component

(j, 9).

C is the group velocity. When

S 0

the equation decribee the propagation of swell waves

at a group velocity appropriate to each frequency component

1

In the numerical integration of the partial

differential equation the directional spectrum is

re-presented by a finite number of

_components

-typically

l2directions and 1, f:requencies -

on

a grid of size

l2Onzn. x .120 rim. The wind field is assumed known at

all grid points. The integrations usually proceed

by explicit finite difference methods from an initially

assumed state of rest when there are

no

waves on the

ocean

At the present time the main uncertainty in this approach (assuming the wind field is specified correctly) is in an adequate representation of the source function A wave forecasting method is at present being developed

at Nb with the following form of source function

6

and (3 represent mechanisms of wave generation

by the wind according to two recent theories, namely the resonance mechanism of Phillips and the instability

mechanism of' Miles respectively. Some recent

ocean-ographic experiments have shown that the observed growth of waves both in the initial stage of linear growth and the subsequent stage of exponential growth cannot be

reconciled with these two theories. oC and ₍₃ are

therefore fitted to experimentally determined values of the growth rate as functions of' wind speed and direction. Wave breaking is taken into account by the second expression

in brackets. This term does not allow the spectral

density to exceed the "equilibrium level"

The term

IJ

describes the transfer of energy due to

nonlinear wave-wave interactions (33). This choice of

source function is similar to that used by Barnett (31).

Pierson

(jo)

and Gelci- (28) use other formulations

Fig. ₇ shows a comparison between measured waves and

computed results obtained using techniques similar to those described above.

As more becomes known about ocean wave processes

rational methods of wave forecasting or hindcasting should be able to give accurate estimates of the one and two

dimensional wave spectrum. When this aim is achieved

then it seems likely that, for the majority of engineering uses, hindcasted wave data in spectral form may well

supersede wave spectra measurements. As an example

of such an approach Pierson and his colleagues have

hindcasted a years set of directional wave spectra for

a grid of points over the North Atlantic ocean and this has been used to investigate the seakeeping performance

of a ship in realistic short crested seas(3L&).

Appendix 1. The relationship between wave height and

wind speed in the open ocean.

Although it is recognized that there is no unique

relationship between wave height and

wind

speed measured

over the oceans it is nevertheless useful for naval

architects to have some nominal values for this

relation-ship when wave data is not available but there is

7

Hogben (35) has tabulated over 2000 measurements of wave, heights from weather ships at station "India"

which have been supplied by the NI0 fromdáta published

in reference (io) against corresponding wind measurementà

provided by the Meteorological Office. Fig. 8 shows

the

contingency

diagram constructed from these data. The mean line through the data agrees very well with an empirical relationship 'derived by Scott (.36) from an analysis of the wave spectra measurements of

Möakowitz and his colleagues (19) and with the recommend.. ations of the 11th International Towing Tank Conference

(rrrc) which are also based on a "random" analysis of.

Moskowitz's measurements. The two empirical relationships

of Scott and the ITTC give greater values of wave height' than would be predicted for fully-developed seas at low wind speeds since they allow for the existence of swell waves, which, as shown in Fig, 8, occur frequently in

the eastern North Atlantic. At higher wind speeds the

wave heights calculated from the PiersonMoskowitz formula

exceed values from the empirical relationships since

fullydeveloped seas are quite rare, The following

table illustrates this point by showing a comparison between fully".developed wave heights after Pierson and Moskowitz, the empirical formula of Scott and the more recent reco3mendations of the 12th ITI'C at five wind

speeds.

Wind Speed

(knots)

Significant wave height (ft.) open ocean

.

Pierson..Moskovitz Scott 12th ITTC

(fully..developed seas) 20 _{7.3 11.7} 10.0 30 16,4 ' 17.3 17.2 40 29.1 . 24.7 26.5 50 45.5 31.5 ' .36.6 60 ' 65.5 39.9 48.0

Appendix 2 Nominal wave Spectra: reconimSndat ions of the ISSC and ITIC.

. . .

In the absence of environmental data in the farm

of wave spectra both the

ISSCaiid ITTC

have recommended

that a two parameter speetra formulation based on te

Pierson-Moskowiti rëpresentâtion for fully-developed

Seas should be uSed to evaluate ship performance in waes.

The two paxameters concerned are wave height and period. ISSC representation of one-dimensional spéctra

The ISSC have recommended the following form for

the one dimensional spectrum, (f).

where is the visual estimate of wave height;

significant wave height may also be used.

T

is the visual estimate of wave period

(in

eec);

averaEe period derived from the first moment of the spectrum may also

beused.

..

is wave f.requency(cyàlespersecond). ITTCrepresentationof one dimensional spectra:

The following spectral form and associated parameters have been recommended as an interim standard.by the

12th ITTC:

4 Aw5,4

(Bci

where Ci.) _{is circular wave frequency (radians}

per second).

The constants

A

and are determined from

the following considerations.

(a) If the only information available is significant

wave height in feet) then

=

g'o, Io'.

....

If information is available on the significant wave height (in feet) characteristic wave period(in sec ) then

A. I73/T14,

4

E

e9i/T.

The characteristic wave period, T , is derived in terms

of the first moment of the spectrum and may be taken as approximately equal to the observed wave period.

When there is no information on wave statistics but

the wind speed is known then the approximate relationship between wind speed and wave height given in the table

in Appendix 1 (for the 12th irrc) may be used. It is

important to note no recommendations are made for the

relation between wind speed and wave period due to the

poor correlation between these two variables0 Two dimensional wave spectra:

When it is necessary to use a two dimensional wave

spectrum the IS$C and IC recommend the _{use of a cosine}

power spreading function of the form

A

(Pie)

E(

(4 %

where _{is the wave direction referred to the}

predominant wave direction and

A (%)

is a normalizing

factor.

The exponent 'h _{has recommended values of 2(ITTC)}

and 4(ISSC) but these are likely to be modified as more wave measurements become available.

References

Hogben, N. and F.E. Lumb. "Ocean Wave Statistics"

Her Majestys Stationery Office, London, 1967. "Oceanographic Atlas of the North Atlantic Ocean.

Section IV Sea and Swell". U.S. Naval Oceanographic

Office, Publication No. 700, 1963.

Walden, H "Die Eigenschaftefl der Meereewellen

10

Deutschen Wettendienst

im NordatlantisChefl Ozean".

Seewetteramt, Publication No. 41, 1964.

Walden, H. "Der Seegang in ausgewahiten Gebieten

des Tropischen und Subtropischefl Atlantischefl Ozeans"

Deutschen Wetterdienst Seewetteramt, Publication

No. 6, 1966.

"Climatological and Oceanographic Atlas for Mariners.

Vol. 1. North Atlantic Ocean". U.S. Department

of Commerce, Washington, D.C., 1959.

"Climatological and Oceanographic Atlas for Mariners. Vol. 2. North Pacific Ocean". U.S. Department of

Commerce, Washington, D.C., 1961.

Yamanouchi, Y. et al. "Statistical Investigations

of Wind and Waves on North Pacific Ocean and

Adjacent Seas of Japan". Japanese Shipbuilding

Research, Vol. 7 (1965) and Vol. 8 (1966).

Yamanouchi, Y. et al. "On the winds and waveson

the Northern North Pacific Ocean and South adjacent

seas of Japan". Ship Research Institute paper No.5,

Tolçyo, 1965.

Hogben, N. and F.E. Lumb. (Appendix by D.E. Cartwright)

"The Presentation of wave data from Voluntary

Observing Ships". NPL, Ship Division Report, No. 49,

1964.

(io) Draper, L. and E.M. Squire. "Waves at Ocean

Weather Ship Station "India" (59°N, 19°W)".

11

(ii) Draper, L, and M.A.B. Whitaker. "Waves at

Ocean Weather Ship Station "Juliett" (52° 30'N,

200 oo'w)." Dt. hydrogr. Z. 18,

1965.

Cartwright, D.E. and N.S. Longuet-Higgins. "The

statistical distribution of the maxima of a random

function".. Proc. Roy. Soc. London, A,

237, 1956.

Cartwright, D.E. "On estimating the mean energy

of sea waves from the highest waves in

a

record".

Proc. Roy. Soc. London,. A,

247, 1938.

Draper, L. "The analysis and presentation of

wave data : a plea for uniformity". Proceedings,

10th. Conference on Coastal Engineering, Tokyo,

Vol. 1. New York: American Society of Civil

Engineers,

_1967.

(15).

Draper, L. "Waves at Sekondi, Ghana". Proceedings, 10th Conference on Coastal Engineering, Tokyo,

Vol. 1. New York; American Society of Civil

Engineers,

_1967.

Darbysbire, J, "An investigation of' storm waves

in the North Atlantic Ocean". Proc. Roy. Soc.

London, A,

230, 1955.

Darbyshire, J. "A further investigation of'

Wind.-Generated Waves". Pt. hydrogr. Z., 12,

1959.

. Darbyshire, J. "The oneidimensional spectrum in

the Atlantic Ocean and in coastal waters". Ocean

Wave Spectra, pp.

27-31.

Englewood Cliffs, N.J.:

Prentice-Hall

Inc., 1963.

(19).. Möskowitz, I., W.J. Pierson and E. Mehr. "Wave

spectra estimated from wave records obtained by

0.WSS., Weather Reporter". Technical Reports I,

11,111, NeW York University,

1962, 1963

and

1965.

(20) Pierson, WJ. and L. Moskowitz. "A proposed

spectral for, for fully.-develáped wind seas based on the similarity theory of' S.A. Kitaigorodskii".

12

Inoue, T.

"Ocean wave spectra estimated

from

three hour pressure records

obtained by FLIP".

New York University,

Geophysical Sciences

Laboratory Report No.

671, 1967.

Pierson,W.J. (èd.)

"The directional spectrum

of awind generated sea as

deterininedTfrOm:data

obtained by the Stereo Wave

Observational Project".

New YorkUxiversitY Met. Paper.

2, 1962.

Canham, H.J.S., D.E.Cartwright, G.J. Goodrich,

àndN.Hogben.

"Seakeeping trials on.O.W.S.

Weather Reporter".

Trans. R.I.N.A., 1962.

LonguetHiggiflSi M.S.

D.E.' Cartwright and N.D.

Smith.

"Observations

t the directional spectrum

of sea waves using the motions

of' a floating buoy".

Ocean Wave Spectra,PP.111136.

Englewood Cliffs,

N.J.: Prentice-Hall Inc. 1963.

Ewing, J.A.

"Some measurements: of.

the: directional

wave spectrum".

J. Mar, Res.,27, 1969.

Rudwick, P.

"Wave directions from a 1arge

Spar

buoy".

J.Mar. Res., 27, 1969.

Stilwell, D.

"Directional energy spectra of the

Sea from photographs".

J. Geophys. Res. , .74,

1.96).

Gelci, R., H. Cazale and J.

Vassal,

"The

spectro-angular method of forecasting ocean

w.ve".

Meteorologie Nationa.Le

(Ibaris), 1953.

HasselmarLfl, K.

"Grundleichungen der SeegangsvoraU-'

ssage".

Schiff'stecbnik, 7, 1960.

(o)

Pierson, W.J., L.J. Tick andL.

Baer.

"Computer

based proëedures for preparing

globalvave forecasts

and wind field analyses capable of using wave data

Obtained by a spacecraft".

Sixth Symposium on

Naval Hydrodynániics, Washington,

D.C.

1966.

(31)

Barnett, T.P.

"On the generation, dissipation

and predIct ion of Ocean wind

waves".

J. Geophys.

13

Longuet-.Higgins, M.S.: "On the transformation of

a continuous spectrum by refraction". Proc.

Camb. Phil. Soc.,

53, 1957.

Hasselmann,.K.

"Nonlinear

interactions treated

by the methods of thecretical physics. (with

application to the generation of waves .by wind)"

Proc. Roy. Soc. London, A, 299, 1967

(3z)

Wachnik, Z.G. and E.E. Zarnick. ttShip motions

predictions in realistic Short crested seas".

Proc. S.N.A.M.B..,

_1965.

Hogben, N. "Measured wave heights and wind speeds

at Weather Station "India" in the. North Atlantic".

The Marine Observer, Vol. XXXIV,

_1969.

Scott, J.R. "Somé:average wave spectra".

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Fig. 2, Table for

all

directions : Area (2).

Hogben

and

Lumb (1).

I

I___j __I.____

Iii

I

I!

I I

II

YO160I50I40I3013ouiotoogoa070 6050403020100 1020304050607080 OCQIC13OI3OI40I5QQI7020

Fig. 1. Choice of sea areas for visual wave statistics.

Hogben

and

Lumb (1).

AREA 2 ALL SEASONS

0 I0 10 W. Hht fl it Ca) Spcing 50 0 0 - 3 4 5 6789 405060 60 HdçlS m tt -(b) 60 to 15 3 4 5678910 30 30405040 Wow HigM In 440-(e) Autumn

\

\i

"0

\

\

'

\

3 4 S 6 7I9 30 30 405060 S0, WonHsiçhtiif.st-Cd)

Fig.

3.

Cumulative distributions of -wave heights at

I

15 5.-0

Fig.

4.

II

Winter 0 6 7 B 9 10 II IS IS 14 IS

Zero-Crottung Pinod in uconds -'

Spring (b) (a) 16 101 u. Summer 7 B 10 II 13 13 14

Zero-Crag Period T5 in second.

Autumn

0

-8 9 0 II IS 14 IS 16 6 7 0 9 10 II 12 13 14 IS 16

Zero - Crosiinq Per-lad Tz I' rds - Zero-Crouing Period T in .ids

TIIS DISTRIBUTION OF Z!RO-CRSING PERIODS IS GIVEN FOR EACH SEASON

TiecDISTRIBUTION OP THE SPECrRAL WWTH

P4RAMETRR IS OIVEN FOR THE WHOLE YEAR

02 0-S 04 0-5 06 07 0-B 0-9

Spectral Width Parmetir £ -.

(e)

Distributions of wave period and spectral

width at Station "India". Draper et al (10).

I 17

222

4

2471

4.. 31

I I I ,,,

1/5

5 4 I ii ." ,'2

6/5

9 3

6 I2

'I,,, 4,)(//7i\\6

,

_i 3 I

'I

4/,,13 9 IOJY 8 4

3 I I .2

/8/J\

5

4

2/ I 4 13

18 24 22I6 8

5 3 I

///_'__

_{12 2V26 3924 12/S}

₎

/

_1/

.1

I

0 ®

4

I jj6i

}

1.2 I 2 . I _______ 7Q

₈₀

₉₀

100

110 120

l3O

140 150

Zero-Crossing Period Tz in seconds

Fig. 5.

Significant wave height wave period relation

S 20 1.5 10 0.5 N C,, uJ 20 UI 0 U. 0 I8 I7DECEMBER

SHIP SPEEDS 2 KNOTS

-

1.5-Fig.

7.

d

.15 .20 2.0 - 1,0-- 0.51,0--

0.5-18

50-40 30- 20-z 10-0

....ii

I I 1,1,111 3 45 10 20 30 50 100 200 0 DURATION IN HOURS

Fig.

6.

Long term distribution of wave height (left)

and wave persistence diagram (right). Draper (15).

1.5 o: 0: 0: 0. 0: 0 I 0-_0. C) 0. 05

1

I I 0 .05 .10 OO 17 DECEMBER

SHIP SPEED: 5 KNOTS (QUESTIONABLE)

O6 17 DECEMBER

SHIP SPEED 3 KNOTS

.,

-..---

-.,---f' I I

I .ó....I,.

.10 IS .20 FREQUENCY (CPS) .20 .05 2.0 OO 18 DECEMBER SHIP SPEED3KNOTS - 1.5 - 1.0 - 0.5 0 06Z I8DECEMBER

SHIP SPEED.5 KNOTS

(QUESTIONABLE)

-I I 111111

.10 .15 .20

Computed spectra compared with measurements from

0W.S. Weather Reporter. Open and solid

circles-computed values for 60 and 120 n.m. grids. Barnett (31). I 6 6 10 U 16 17 20 WAVE KEIGHTFEE7 05 .10 .15 20 a) as 10-

/

.10 60 I 111111

19

Beoufort wind scale

1 2 3 4 6 7 8 11

Anemometer wind speed W knots

mecsured at height of 19'2 rnetres Mean of measurements

Mean plus standard deviation * Mean minus standard deviation *

Recommendation of 1966 TIC H5=(0075 W+5) feet Scott.

Because of the asymmetry of the distributions, standard

deviations obove and below were calculated separately

Fig. 8. Measured wave heights and wind speeds at

Station "india". Hogben (35).

15 10 5 Total number of comparisons 2245 selected at random from years 1957 to 1965 3

Ii--' __ra

2

-33--___II 4 PK'd

'E4N

27 18

II

6 6

HhIIH4d

WI

20

)3

4 10

2O6 67I!j.

24 3 25 6 1 6 n .r r .,,