By Arne Kvitrud, Sondre Nordheimsgate 9, 4021 Stavanger.

Paper presented 23.4.1996, published on internet 25.9.2002.

The figures are not presented here.




The ISO/TC67/SC7/WG3 - draft have in chapter C.3.2.3 description about the wave kinematics factor : "Wave kinematics measurements support a factor in the range 0.85 to 0.95 for tropical storms and 0.95 to 1.0 for extratropical storms"

In the guidelines (1992) point it is said : "When using the design sea state method, energy distribution around the dominating wave direction may be taken into account. In the case of sea states with significant wave height less than 10 meters, the following distribution function may be used :

D (Qm - Q) = C * cos n (Qm - Q)

where Qm is the mean wave direction, and where n is selected in the area of 2-8 as the load is most unfavourable for each structure. With regard to sea states with significant wave heights exceeding 10 meters, the energy distribution should be disregarded if it gives a reduced load effect."

The values of 2-8 should be the same as kinematics reduction factors of 0.87-0.95 using the ISO reduction formula.

Noble Denton (1993) specifies a value of 0.95.


Bruce et al (1984) analysed the spreading of the sea at Ekofisk in Norway calculated the wave spreading based on the measured total platform overturning moment. The n-value is between 2 and 9 for 5 sea states having a significant wave height between 3-7m, and about 15 for a significant wave height at 11.5m. This was a jacket platform of about 70m water depth.

Heavner et al (1984) analysed the spreading of the sea at Valhall in Norway based on the wave elevation and the water particle velocity at -14m assuming linear wave theory. They calculated n-values for 4 sea states : Hs = 5.5m gave n=7, Hs = 5.7m gave n=7, Hs = 8.9m gave n=9 and Hs =10.8m gave n=19. The higher sea states indicate rather long crested waves. The spreading increases rapidly as the frequency deviates from the peak frequency. The calculations are based on measurements but it is not specified which is used, but must be a response characteristic of the platform.

Haver et al (1986) calculates the spreading based on a cos 2s (0.5*Q) basis. He describe the :

s = sp( hm0, tp, qp) * (f/fp) m where n = 0.46 * s

They refer to Mitsuyasu et al from 1975 and Hasselmann et al from 1980 who use m = 5. They recommend 5 for f > fp and -1 for f < fp.

For a dynamic deep water jacket Haver et al (1986) recommend the use of n =2.5-5.5 for ULS control and 2-7 for fatigue calculations. With 3.5 and 6 as average values. The current meter indicate a much more narrow sea than did the Miros radar and the Norwave buoy. The average value seams to be an average value of the different instruments. The values are maximum values and are not integrated over the wave spectrum.

The data analysed was according to Sverre Haver (22.3.1996) :

a) Norwave buoy data from Haltenbanken 112 cases with significant wave heights from 4 to 6m.

b) Miros radar data 18 cases significant wave height of 5.8.

c) Valhall current meter 9 cases with significant wave heights from 8 to 9.2m. Three storm periods are included (Haver, 1990).

Bole (1996) refer to Forristall from 1986 having analysed current velocity data from Fulmar in significant wave hights up to 11 meters. The mean bias was is about 15%. A k-value of 0.9 is reasonable.

Heideman and Weaver (1992) analysed data from Tern. They analysed one moderate and two major storms. In April 1991 a significant wave height up to 9m was measured. The kinematic reduction factor was found to be 0.91-0.94. In October 1994 the significant wave height was about 0.93-0.95. In January 1992 the significant wave height was up to 14m and the kinematic reduction factor about 0.93. They have done an integration over the spectrum (range 0.055 to 0.095 Hz for one of the storms) and are not using the peak value (according to Jon Heideman, fax 22.4.1996). He also write that transforming the spectra to mean water level and including all wave frequencies would have led to a smaller kinematic factor.

Heideman and Weaver (1992) also analysed data from Magnus. 0.96-0.97 for three Magnus storms. In January 1986 the waves were up to about 12.5m. The kinematic reduction factor was 0.97. Similar in December 1988 a storm with HS = 14m had kinematic reduction factor of 0.97. The December 1990 storm with HS = 12.5m had a kinematic reduction factor of 0.96. John Heideman (fax 22.4.1996) say that the structure act as a filter. The inferred spreading is probably dominated by the longer waves, which have less spreading.

Jonathan et al (1994) refer to measurements at Tern. The current measurements were at 41m below mean sea level. The wave spreading is minimised at a frequency below the spectral peak. The measurements from fixed velocity meters was analysed in two significantly different ways and got about the same result around the spectral peak. Even for the least spread frequency, the in line velocity is reduced by a factor of 0.9. The investigated sea states had significant wave hights from 8.9m to 13.8m and were from three storms.

Santala and Raines (1995) refer measurements from the CUMEX project (at Odin) giving n-factors of from 1-5 for waves up to 8m significant. They specify n-factors of 5 to 9 for sea states above 8m significant with reference to measurements at Tern.

Forristall and Ewans (1996) have analysed data from several sources. All the data indicate an increased average value when the sea state increase. They have integrated the spreading for all the frequencies in the spectrum:

a) Auk give an average from 0.85 to 0.93 when the sea states increase from 2m to 10m. Two data above 10m give a kinematic reduction factor of 0.92-0.93.

b) North Cormorant give an average from 0.82 to 0.87 when the sea states increase from 2m to 10m. Data above 10m give a kinematic reduction factor of 0.86-0.88.

c) Nordkappbanken give an average from 0.80 to 0.88 when the sea states increase from 2m to 10m. A few data above 10m give an average kinematic reduction factor of 0.88-0.89.

d) WADIC (at Ekofisk field) give an average which is dependent on the instrument. They disregard the current meter measurements. The average value of the other instruments seams to be from 0.83 to 0.88 when the sea states increase from 2m to 10m. For a sea state of about 11m the kinematic reduction factor drops to about 0.8 (correct??).

e) Fulmar have a kinematic reduction factor of about 0.91-0.92 for sea states slightly above 10m.

f) Tern have average values of 0.82-0.85 for sea states below 10m and increasing from 0.85 to 0.92 for about 14m.


Allender et al (1989) reviewed different instruments and their ability to measure wave spreading. The conclusions are based on measurements at the Ekofisk area at about 70m water depth. Some of the conclusions are :

- Miros radar overestimate wave spreading and does not show characteristics dip at spectral peak as seen by other systems

- Norwave buoy overestimate wave spreading.

- Current meter used as best estimate. But at the WADIC experiments both current meters at

-6m and -15m overestimated wave spreading.

Forristall and Ewans (1996) demonstrate that the current meter data from WADIC is influenced by the structure and conclude with minor differences between different instruments.

The platform instruments as total moment and deck accelerations give a significantly smaller spreading factor than the wave/current measurements. This difference must be caused by the behaviour of the platforms. Non of the investigators have discussed the differences nor the implication of the difference for the design of jacket structures.

Jon Heideman (fax 22.4.1996) write that transforming current meter data to mean water level will lead to a smaller kinematic factor. An increase of the kinematic reduction factor might than be expected for deep jacket structures and subsea structures than found for sea surface measurements.



According to Noble Denton (1993) commentaries to chapter : " To use such a spreading factor in reducing overall forces on a structure is debatable, and especially so for jack-up structures. There may be cases where the inclusion of the spreading in irregular seas results in higher forces for some headings. If the leg spacing corresponds to a wave period, inducing opposing wave forces for different legs coinciding with the first resonance period, the forces will in fact be amplified when spreading is introduced"

A similar conclusion is obtained by Haver et al (1986) and Haver (1990) on several dynamic structure (also a jacket structure). Haver (1990) states for a jacket structure "however, the reduction is not the most important result. If we consider a more favourable direction the reduction will of course be much less and for the most favourable one (with respect to long crested sea), the extremes will obviously increase."



The calculation of the spreading factor are according to the ISO draft is : c = SQRT ((n+1) / (n+2)). Using this formula directly the following summary can be made :


Analysed by


c- moderate sea states

c - at Hs >10m


Bruce et al

Total moment




Forristall et al

Wave measurements




Heavner et al

Platform response or current meter ?




Haver et al

Current meter



Sentral North Sea

Haver et al

Miros radar







<0.9 (up to 11m)


Forristall et al





Jonathan et al

Current meter


up to 0.9 (>8.9m)


Heideman et al

Current meter




Forristall et al

Current meter




Santala et al

Current measurements?




Heideman et al

Deck acceleration



North Cormorant

Forristall et al





Haver et al

Wave buoy




Forristall et al

Directional buoy



In the table there are a mixture of data as integrated values over the spectrum and as peak values at the peak frequency, which are reported by some observers. The "*" indicate a maximum value. Some of the investigators do not describe if the result is a maximum value or an integrated value. The most consistent data base might be the data of Forrisstall and Ewans (1996), which have done an integration, also over the water depth.

Based on all the measurements in the table above and reviewing only situations with significant wave height above 10m, an average is about 0.92 with a standard deviation of 0.04.

The wave measurements analysed by Forrisstall and Ewans (1996) indicate an average about 0.90 and a standard deviation of about 0.02 (my interpretation). The platform response data indicate an average of 0.97 and a standard deviation of 0.01.

The work performed have been based on finding the reduction of velocity. The standard state that the kinematic reduction factor also can be used on the acceleration. Have anybody evaluated the statements on the kinematic reduction factor with respect to accelerations? A single column as used now by Saga Petroleum on the wellhead platform at Varg project is also a "fixed steel structure". It is dominated by inertia forces.

The work by Forristall is based on linear wave theory, but the general load describtion is based on Stoke V, Newwave theory etc. What will the use of an other wave theory mean to the kinematic reduction factor?

The kinematics reduction factor as described in the ISO draft also include an "irregularity factor", which is not evaluated here. I have not found any documentation for such a factor. According to Jon Heideman (verbal 22.3.1996) it is a reduction which is found in long crested waves in laboratory testing. I disregard such an influence.

The proposed ISO text with values in the order of 0.95-1.0 seams reasonable conservative for the Norwegian continental shelf, as long as a high number is conservative. If a value lower than 1.0 is applied a check should also be done that the spreading is not amplifying the loads. There has not been done any evaluation if the kinematic reduction factor is a function of the water depth.

References :

Allender J, Audunson T, Barstow S F, Bjerken S, Krogstad H, Steinbakke P, Vartdal L, Borgman L and Graham C : The Wadic project; a comprehensive field evaluation of directional wave instrumentation, Ocean Engineering, Vol 16, no 5/6, 1989

Bole J : Valhall WP Project Environmental data, Amoco, Houston, 23.1.1996

Bruce R L, Lieng J T and Langen I : Ekofisk 2/4-H, final report safety assessment, Sintef report STF 88 F84055, Trondheim, Norway, 20.7.1984

Forristall G Z and Ewans K C : Worldwide measurements of wave spreading, draft Shell, 15.1.1996.

Haver S, Dalane J I and Anfindsen M : Uncertainties in the modelling of ocean waves and their effects on the structural response, Statoil report F&U-ST 88006, Stavanger, 1986.

Haver S : On the modelling of short crested sea for structural response calculation, Proceedings of the European Offshore Mechanics Symposium, Trondheim, 1990 pp 13-20.

Heavner J, Langen I and Syvertsen K : Valhall QP, EMP project, final report, Sintef report STF88 F84037, Trondheim, Norway, 26.7.1984.

Heideman J C and Weaver T O : Static wave force procedure for platform design, Civil engineering in the oceans no 5, Collage station, Texas, 1992 p 496-517.

ISO/TC67/SC7/WG3 - draft from panel 1 (metocean) and panel 2 (actions), SIPM, den Hague, 20.1.1995

Jonathan P, Taylor P H and Tromans P S : Storm waves in the northern North Sea, BOSS'94, vol 2, page 481-494, 1994

Noble Denton : Guideline for Site-specific Assessment of Mobile Jack-up Units, final draft, London 1993

Guidelines concerning loads and load effects, issued 7.2.1992.

Santala M J and Raines R D : Balder metocean and geotechnical criteria, Exxon, Houston, 20.4.1995.