Some Experience Gained from Analysis of Visual
and Instrumental Wave Data
from the Norwegian Continental Shelf
O. G. Houmb*)Introduction
The lach of. wave data needed for design and operation of marine structures is typical for most waters in the world
includ-ing the Norwegian seas.
A wave research program at The Norwegian Institute of Tech.: nology is partly aimed at meeting these needs and also to contri-bute to applied and basic wave research in general.
In 1960 a wave recording project was initiated in cooperation
with The Board of Maritime Works, using pressure wave recorders
at four sites on the Norwegian coast. The main reason for this work was to study waves outside harbours that are exposed to
heavy wave action. The depths at these sites were approximately
20m. The longest series of wave data covers 13 years.
During the last 4 to 5 years waves have also been recorded
using the Dutch Waverider buoy at 3 sites at depths from 80
ro 140m. These buoys measure at their moored position vertical accelerations, integrate them twice and transmit data in the form of wave elevations by radio to a recording station..usually located at a lighthouse.
The experience from the use of these buoys is that they are excellent for use in open waters, because maintenance intervals
can be in the order of one year. Furthermore they can easily
be moored at any depth on the continental shelf.
Visual wave data observed from lighthouses are also considered
in the wave research program. Data from 15 lighthouses on the Norwegian coast covering a period of 20 years were stored on
computer compatible magnetic tape. Research on these data was
supported by the Norwegian Meteorological Institute in Oslo.
The Use of Pressure Type Wave Recorders 2.1. Generai
At small depths pressure type wave recorders are usually
in-stalled close to the sea bed, where a transducer measures fluctua-tions in pressure generated by waves. In this case data were
cabled to a recording unit. on the shore.
Using 1. order wave theory pressure fluctuations are
con-verted to wave height by the formula
cosh k (dz)
zip = 'H
cosh kdwhere
p
7 = specific weight of sea water
H = wave height (vertical distance from wave crest to the following through) 2' k - , wave number L
L.
= wave length d = water depthz distance from SWL to the pressure transducer
) Member of the Division of Port and Ocean
tnstitute ofTednoIogy. Trondheim Engineering, Norwegian
914 Schiff & Hafen, SMM-Sonderausgabe, September 1974
Wave period is converted to wave length by the formula L gT2 2 tanh L 2rd where T = wave period = acceleration of gravity g
The first order theory may in practice give ars uncorrect
description of the relation between zip and H. It is, however, assumed that the difference between the actual wave height and that predicted by 1. order wave theory is stochastically
distribut-ed. This error will therefore give a very minor influence on the statistical results obtained. On this basis it is believed that the
use of higher order wave theory in converting Ap to H will
have insignificant influence on the results of the statistical
ana-lysis. It is stressed, however, that one should be very careful in considering single waves measured by means of an instrument
of the pressure type.
The recording Sites are shown on Fig. I
Pressure type wave recorders installed close to the bottom
have operational advantages compared to moored instruments,
because moorings arc normally more exposed to wear.
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2.1. ome selected results from the use of pressure type wave recorders
When pressure wave recorders are used at a depth of 18 to
20 meters waves of periods shorter than 4 to 6 seconds are
usually filtered out. Local waves do therefore not normally Occur
in the records. This, however, does not reduce the value of the data because they are mainly used in the assessment of design conditions for breakwaters, for which longer waves are most
important.
Calculations based on data from severe wave conditions reveal spectra that are relatively narrow. Normalized spectra are
compar-ed to the analytical spectra of Neumann [1], Pierson-Moskowitz
[2] and Darbyshire 13).
The normalized Neumann spectrum can be expressed as
E(f) f
E(f)
exp 3
(1-where fo is the peak frequency.
The Darbyshire spectrum in normalized form is given by
E(f) f f
E(fo)
( = ___)_9 (4.4 (-.- ) -3.4)
and the normalized Pierson-Moskowitz spectrumE(f) f f
E (fo)
- exp 1.25 (.__)_5 exp (-1.25 ()4)
Fig. 2 compares these spectra and some of those obtained at
Berlevâg, Ferkingstad and Arviksand. It is noted that the
calculat-ed spectra are more narrow than the others. Differences in the
high frequency section are partly due to the instruments cut off of locally generated sea. The calculated spectra are believed
to be most correct in the low frequency part as recent measure-ments 151 conclude that the left part of the spectrum is very
steep. 0.5 O 1.0 0.5 o O 1.0 '5f/f0 0.5 1.0 LS
FIg. 2: Normalized spectra. Comparison between the Neumann (N), Pierson Moskowltz (PM), Derbyshire (D) and calculated spectra.Rel. 141
-7
Class no. 7 includes waves from 6 to 9 m and class no. 8
from 9 to 14 m. This essentially excludes the possibility ofbasing estimates of design waves higher than, say 9,0 m on these data. It is assumed that the visually observed wave height correspond to the signigicant wave height
Schiff & Hafen, SMM-Sonderausgabe, September 1974 915
3. Results from Analyses of Visual Data
There are 45 lighthouses on the Norwegian coast where meteoro-logical observations are made. Based on a data discrimination 15
of these were selected and data comprising visual sea state, in-strumentally measured wind force an.d direction together with
surface air pressure were punched on cards which were later
transferred to magnetic tape. The data consists of4 daily observa-tions over 20 years.
The sea state is raported in classes according to Table 3.3.1.
+ r i I
iH
lrI
'!"!
uii
III.
-i
tLI4A.LH
AuN
L
- i-H .1. ---AElï. 4H H H i 4II IflI$fl
L J i-4II
-.-
-, EllhIIlPiiIi
E 15F-no.3. BRLEVÀG. ,,F.b,, 3i37, : T7 HI II -H ;,t---
IftJH..i.
-l-riyI,-H-t't-:
"\H 1/3 4.1 .-..- BerIo6 20/I 1963 .\\ \\\H 1/3 03I il
ii
Ii/II
"i
N v .. - Berlooòg'Ii
IH
Iii
¡ j-34,,
:4k \ 3/12 50010965 \"\H1/3=Z803 19637:,/
Taxble 3.3.1. Visual wave height scale, Ref. 171
Class number Wave height intervals in meters
0 o 1 0-0.1 2 0.1-0.5 3 0.5-1.25 4 1.25-2.5 5 2.5-4 6
4-6
76-9
8 9-14 9 > 14 2 3 4 3 è 7 , 73 74Fig. 3: Gumbel probailty paper
At Berlevâg wave recording has been undertaken for 13 years. Extreme values such as the highest wave pr year and the highest wave for all months were selected. These extremes were plottcd
on Gumbel probability paper. The Gumbel distribution
G (x) = exp (-exp (-(X-U) a))
where u and a are parameters, forms a straight line on this
probability paper.
Fig. 3 shows a plot of the highest wave during February 1960 to 1973. As there are only 10 observations it is concluded that the wave recorder has been out of operation in February for
four of the 14 years.
The lines on each side of the best fit lfne are called control curves. There is a probability of 0.6827 that a Gumbel distributed
variable shall fall within the control curves. The distance from
the best fit line to either of the control curves is one standart
error. The extrapolated control curves are obtained by use of
the asymptotic theory of extreme values.
The theory that a set of extreme data are Gumbel distributed
is generally accepted if the plotted points fall within the contro! interval. 0.5 1.0 1.5 f/1 2.0 0.5 IO 1.5 2.0 00 1 30 10 s -3 I.3 0.5 1.0 1.5 f/ 2.0 1.0 0.5 1.0 E (f E () 0.5 1.0 E (f) 0.5
As no other data were available, observations from one lign-house were used to estimate design conditions for a breakwater whith was built in the same area. Assuming that the visually
observed wave height, H, equals Hjj, it is experienced that
this statistical variable follows the exponential distribution so that
data can be plot as a straight line on semi-logarithmic paper.
1f we want to know the probability P(x) of exactly x ex-ceedances of a given level, Poissons law
mx P(x)
x! was applied where,
m
N = average number of exceedances of the given level
L a number of years
m = average number of exceedances in L years
T = return period (average number of years between ex-ceedances of the actual level)
If m = i we have L T whith combined with x = O gives
Q
1P(0)
e8
0.63This means that during T years there is a probability of
630/o of at least one exceedance of the event of return period T.
We are now able to draw lines for different values of m in
our estimated distribution as shown in Fig. (4).
For m = 5 we obtain
Q = i - e' 0.99
Fig. 4 is interesting because we can directly read off values of Hv that are exceeded with different probabilities in the number
of years read on the horizontal axis.
At the site represented by Fig. 4 the most adverse period
of wind generated waves in a period of 10 years was selected. Weather maps on this situation were used to determine thc wind
field, whids was used as input in a numerical wave forecasting
model [8J. The data from the 15 lighthouses were used to select this situation.
Using the wave forecasting. model to describe the wave field
a maximum value of Hji equal to 7.9 meters was hindcasted,
Fig. 4.
Visual data from the salvage vessel Famita at 57°30'N, 3°E were also analyzed to provide information on design waves and duration of storms. Through extensive data controls it was con-cluded that these data were of high quality. They were therefore used to estimate design waves for the Norwegian part of the North Sea (9]. A simple statistical model on the duration of
storms were veryfied by the use ofthese data (10].
A Tu&er wave recorder by N.I.O., UK, is now installed on
Famita. In this way visual as well as instrumental data were
available from this site.
10 100 lo.
Frequency per year (N)
Fig. 4: ExponentIal distribution of visually observed wave height. Ref. ).
916 Schiff& Hafen, SMM-Sonderausgabe, September 1974
30
80
100
Fig. 5: Waverldev mooring
4. The Use of Accelerometer Buoys in Wave Research
The Dutch Datawell Waverider (WR) .buoy seems at this time
to be the only proven wave recorder for continuous operation in open waters.
The 0.7 m diameter WR buoy measures vertical accelerations that are integrated twice to give the wave displacement. The signal is transmittet in the 27 MH2 band to a receiving station
that can be up to 50 km from the WB..
The low frequency response depends on the two integrators and the accuracy is about 30/e at 0.06 H3 and 3Q0/ at 0.03 1-1.
Experience shows that the high frequency cut off is
0.8 H.
This limit depends on the actual seize of the buoy.
Users of the WR have, at least in the North Sea experienced
some mooring problems. During the first years use of the WR this was the most frequent reason for unsuccessful operation ex-perienced in Norway. A new mooring system was then developed (Fig. 5).
Braided terylene was used to avoid spin in the rope such that
no svivels were needed. The sub surface buoy will very rarely move vertically due to waves when submerged to 30 m. The
rubber cable supplied by Datawell was easily stretched from the normal length 151 m up to 30 m. A chain was introduçed to
keep the WR's vertical axis in vertical, in order to avoid break
down of the accelerometer. To prevent corrosion no contacts
between metals of different alloys were allowed.
l/2 CHAIN
ANCHOR OF SCRAP IRON - 300 kg 20k9 CHAIN
RUBBER CABLE
BRAIDED TERYLENE
SUB SURFACE BUOY - BUOYANCY 200 kg
BRAIDED TERYLENE (Breaking sfrength 2BOOkgs)
12 This mooring system has been in continued use for mooring
of the WR buoy without any maintenance for up to 16 months 10 in waves up to 20 m high.
A great many interesting results were obtained from the ana-lyses of data recorded by the WR. The wave spectra comprise a
.s particular feature that is of importance to designers of naval
. and marine structures.
Spectral analyses of data recorded in the Lopp Sea, Fig. 1,
2 reveal distinct
differences between calculated spectra and the
Piersan-Moskowitz spectrum [Ill which naval architects now are using widely for design.
.2 One of the spectra representing a situation of steady winds
is shown in Fig. 6 together with the Pierson-Moskowitz
spec-trum of the same peak frequency.
1
1111111111H11
uIuauII_lIIIII
lIIUlui
IUIIIIflIIIIl!
11H111111H11
liii
II lIIIiIII!'IIII
uhIlIIIIIIII
lUi ________________I n°' '?::"
III.1u_
niiiiiiitiii____
iiuiuiii iiirni
lIuII1liI!!Illi
uhI_II1iI;;;;;i!:
IIIuIIpjIÎIII
liii
MI-g, s 3 2 i ¿ 3 3 17S S * 3 3 U 7*1 4 3 2 17 S 3 2 lo E . 6 o B >Tagungen, Ausstellungen
Offshore International
Exhibition vom 7.-11. Oktober
1974 In London
Auf der internationalen Offshore-Ausstel-lung auf dem Londoner Olympia-Gelände werden Firmen aus aller Welt Neuigkeiten und erprobte Produkte aus dem Offshore-Bereich ihrer Produktionsprogramme vor-stellen.
The corresponding JONSWAP spectrum is also shown in Fi 6.
'
The analytical expression for this spectrum is one of the resultsof the Joint North Sea Wave Observation Project - a
cpmpre-hensive international experimental effort undertaken in the North Sea off the Island of Sylt (5).
The analytical expression for the JONSWAP spectrum is given by 5 f E (f)= cg2 (2t)-4 f-5 exp --. where a = 0.008 fm = peak frequency = 0.07 for f fm 0.09 for f > fm y peakedness parameter
y I leads to the Pierson-Moskowitz spectrum, and y equals 3.3 for the average Jonswap spectrum.
(f_fm)2
exp
20 f m
0.05 01 0 15 0.2 0.25 0.3 0.35 04
Rg. 6: The choice of PM-spectrum Is done according to the development
of the steep forward phase of the spectrum. Ref. [11]
'Most of the spectra from the Lopp Sea fitted the Jonswap
spectrum very well with y between i and 3. The variation in y reflects the various wind conditions under which waves were measured.
The Pierson-Moskowitz spectrum in the case of a peak period
of 10 sec leads to a H113 pf 4.0 m while the calculated spectrum gives H13
5.3 m - a difference of
330/o! For comparison the average Jonswap spectrum gives J-11/3 4.9 m which is farcloser to the calculated value.
From this one may conclude that the Jonswap spectrum should
be used, at least for the North Sea and the adjacent Continental
shelves.
Conclusions
Pressure type wave recorder are found suitable for wave measurements in shallow water when waves of periods shorter
than 4 to 6 sec are not important. The data are suitable for
statistical analyses, but care must be shown when single waves
are to be reconstructed.
In cases where wave data are urgently needed for design of e.g. breakwaters visual wave observations provided from
light-houses are useful when instrumental data are not available. Hindcasting using a numerical wave forecasting model is also a useful means in such situations.
The Dutch Datawell Waverider (WR) has proved to be very satisfactory for recording of offshore waves, when the mooring problem was solved. Based on high quality wave data recorded by the WR, the JONSWAP spectrum was shown to .be more representitive for the North Norwegian Continental Shelf than
the Pierson-Moskowitz spectrum.
References
(1] Neumann, G., 1953: On ocean wave spectra and a new method of
forecasting wind generated sea. Tech.Memo No 43. B.E.B. Corps of
Engineers, Washington D.C.
t 2] Pierson. W. J. and Moskowitz, L., 1964: A proposed spectral form
for fully developed wind seas based on the similarity theory of
SA. Kitaigorodskii. J. Geophys. Res., 69 (24) pp 5181-5190
1 31 Darbyshire: An investigation of Storm waves in the North Atlantic
Ocean, Proc R. Soc. Vol 230, No 1183, July 12, 1955, pp 560-569 141 Thrum, A.: Wave analysis with special reference of short - and
long term statistics of data recorded at Ferkingstad, Arvlksand, Ber-levag and Verde. Norwegian Institute of Technology. Internal report prepared for the Board of Maritime Work, 1968 (In Norwegian) Hasselmann, K. et.ai.: Measurements of wind-wave growth and swell
decay during the Joint North Sea Wave Project (JONSWAP).
Deut-sche Hydrographiache Zeitschrift, No 12. 1973
Houmb, O. G.: Wave analysis with special reference of short- and
long term statistica of data recorded at Ferklngstad, Arvlksand,
Berle-vag and Vardo. Norwegian Institute of Technology. Internal report
prepared for the Board of Maritime Work, 1974.
Houmb, O. G. and Viggoson, G.: Probabillistic and statistical
evalua-tion of wave data as an aid for the design of maritime structures.
lnterocean Conf. Düsseldorf 1971. pp 115-120
Haug. O.: A numerical model for prediction of sea and swell.
Meteorologiske Annaier 5, No 4 (1968). Norwegian Meteorologic
in-stitute, Oslo
Haland, L., Houmb, O. G. and Pedersen. B.: Long term distribution
of North Sea waves. Norwegian Maritime Research No 1, VoI. 1, 1973, pp 3-14
tb] Houmb, O. G.: On the duration of Storms in the North Sea. ist Intl.
Conf, on Port and Ocean Engineering under Arctic Conditions.
Trond-heim 1971. pp423-439
[11] Houmb, O. G. and Rye, H.: Analysis of wave data from the Norwegian
Continental Shelf. 2nd Intl. Conf, on Port and Ocean Engineering
under Arctic Conditions. Reykjavik 1973 (In preparation)
Dieses Symposium wird vom 10.-13.
Dezember 1974 in Wagcningen/Niedcdande abgehalten werden. Veranstalter ist Nether-lands Ship Model Basin, Wageningen. Fol-. gende Themen werden behandek: The role of cavitation in propeller design; model-full scale correlation; wake field and pro-peller dynamics; propro-peller-hull interaction, excitation forces; cavitavion, noise and erosion.
Zum erstenmal findet am 29. und 30.
10. 1974 in Europa eine Tagung statt, die sich ausschließlich mit den praktischen An-wcndungsniöglichkeitcn dieser Regeltcdsnik
befaßt. Sic läuft während der 7.
Interna-tionalen Fadimesse für tMhydraulik und
Pneumatik und wird deshalb allen
Teilneh-mern die Gelegenheit bieten, den
Vorträ-gen anerkannter Fachleute zu folVorträ-gen. Auskunft: International Fluidics Services
Ltd., Carlton, Bedford, MK43 7JS.
Schiff & Hafen, SMM-Sonderusgabe, September 1974 917
Power m2/Hz
Mean Jonswad spectrum = 3.3
Pieruon - moskowitz spectrum Spectrum recording during wove growth in Lopphavet.
30 Date: 18.12.1971
Time: Approx. 21.00 Peak frequency: approx. 0.10 Hz.
Significant wove height: 5.30 m
10
/
Frequency Hz( 8]
1 91
