Draper, L.

Driver, J. S.

Southampton (e-Prints Soton)

C—-A m NATIONAL INSTITUTE OF OCEANOGRAPHY WORMLEY, GODALMING, SURREY Winter Waves in the northern North Sea at 57°30'N 3°00'E i i i l f ® -Recorded by M.V. " F A M I T A " by L. DRAPER and J. S. DRIVER N . I . O . INTERNAL REPORT N O . A . 4 8 AUGUST 1971 NATIONAL INSTITUTE OF OCEANOGRAPHY Wormley, Godalming, Surrey. Winter Waves in the Northern North Sea at 57°30'N 3°00'E Recorded by M.V. FAMITA by L> Draper and J•S. Driver N,.1.0, Internal Report No. A.48 August 1971 CONTENTS Description of the investigation Discussion of results Acknowledgements Heferences Page 1 2 4 5 Figures; Wave Height Exceedance Autumn Winter Wave Period Occurrence A^utumn Winter Spectral Width Parameter Occurrence Autumn and Winter Scatter Diagram Autumn and Winter Persistence Diagram Autumn and Winter 'Lifetime' wave prediction graph 'Lifetime' wave prediction graph based on the technique used by Battjes Figures 1 2 3 4 5 6 7 8 - 1 -Waves have been recorded by a Shipborne Wave Recorder (Tucker, 1956) placed on M.V. FAMITA, a Norwegian rescue and meteorological vessel which is stationed in the North Sea in 40 fathoms of water 160 miles east of Peterhead at 57°30'N 3 OO'E. The record* from one winter's operation, from October 1969 - March 1970 have been analysed, mainly following the method of analymim developed by Tucker (l96l) from theoretical studies by Cartwright and Longuet-Higgins (I956i. The method of presentation is that recommended for data for engineering purposes (Draper, 1966).-Records were taken at three-hourly intervals, and the emalyais yields the following peurameter*: CaX E. = Th» sum of the distances of the highest crest and the lowest trough from the mean water level. (b) Hp = The sum at the distances of the second highest crest and the second lowest trough from the mean water level. (c) T^ = The mean zero-crossing period. (d) T^ = The mean crest period. From these measured parameters the following parameters have been calculated, after allowing for instrumental response: (e) H = The significant wave height (mean height of ® the highest one-third of the waves): this is calculated separately from both and H^,and an average taken. The relationship between the parameters is = f(Hg) where f is a factor related to the number of zero-crossings in the records (Tucker, 1963)# A similar relationship is used for the calculation of H from S_. s 2 (f) hours) ~ moat probable value of the height of the highest wave which occurred in the recording interval (Draper, 1963). (g) ^ = The spectral width parameter, which is calculated from T^ and T^ (Tucker, 1961): . 1 - (T, / The results of these measurements are expressed graphically divided into two seasons thus: Autumn: October November December Winter: January February March - 2 -For each season a graph (Figures 1 & 2) shows the cumulative distribution of significant wave height and of the most probable value of the height of the highest wave in the recording interval, hours)' The distribution of zero-crossing period is given for each season (Figures 3 & 4). The distribution of the spectral width parameter is given for the six months (Figure 5)* Figure 6 is a scatter diagram relating significant wave height to zero-crossing period, for the six months. Figure 7 is a persistence diagram for the six months. Figures 8 & 9 are 'Lifetime' wave height prediction graphs. Discussion of Results From Figures 1 & 2 may be determined the proportion of time for which or ^exceeded ajiy given height. For example, in the Winter the significant height exceeded 10 feet for 43 percent of the time, which is somewhat rougher than the winter data (1962) from Sevenstones, off Land's End (Draper and Fricker, 1965). It is considerably rougher thaji wave conditions at Smith's Knoll in the southern North Sea (Draper, 1968). The highest measured wave (H^ ) of 6l feet with a zero-crossing period T^ on the record of 13»3 seconds occurred about 15OO hr on either 27 or 28 November 1969. The uncertainty in date is caused by inadequate labelling of the chart and discontinuities in the sequence of records. The record showing the high wave is a good one and its validity ia not in doubt. There is little seasonal variation in either the wave period or spectral width parameter. The scatter diagram of Figure 6 relates the significant wave height to zero-crossing period, with the numbers of occur-rences expressed in parts per thousand; for example, the most common wave conditions were those with a significant height of between 4 and 5 feet and a zero-crossing period of between 6 . 0 and 6,5 seconds, which occurred for 33 thousandths, or 3*3 percent, of the time. The rapid attenuation of the shorter waves with depth means that the pressure units, which are necessarily situated at about 3*7 feet below mean water level, do not record the lower period waves; this is a cause of the cut-off below that period. A parameter which is sometimes of interest is the wave steepness, expressed as wave height: wave length; it may also be expressed as a decimal number. It should be noted that the steepness of a wave is not the same as the maximum slope of the water surface during the passage of a wave. Lines of constant steepness of 1 ; 20 and 1 : 40 are drawn on Figure 6. (In this case, steepness relates to significant wave height : wave length calculated from the zero-crossing period.) -3-A fairly well-defined limit of steepness is observed at approximately 1:l6 (0,06): this occurs in all stormy areas. There is a theoretical limit for a progressive wave of 1 j7 C0..14). From the persistence diagram, Figure 7, may be deduced the number and duration of the occasions- between October and March on which waves persisted at or above a given height. For example, if the limit for a particular operation of a vessel is a significant height of 8 feet, it would have been unable to operate for spells in excess of 10 hours on 46 occasions, or spells in excess of 20 hours on 32 occasions. Figure 8 enables an estimate to be made of the most probable value of the height of the highest wave likely to occur in various time intervals up to 100 years. For example the most probable value in a 50-year interval is 90ft. Figure 9 shows an alternative method of extrapolating wave data to yield estimates of extremes. It is based on the scatter diagram (Fig. 6) of significant height and zero-crossing period, and has been calculated following an example by Battjes 1970. The authors are indebted to their colleague Mr. J.A, Ewing for the calculations on which this graph is based. The values of extreme-wave heights yielded by this method are the highest of several different methods of estimating this parameter for this site. Wind Conditions The mean wind speed for the six months during which wave measurements were made has been compared with the appropriate t«n-year mean speed. Two stations, Lerwick, Shetland and Bell Rock, off the Firth of Tay were investigated by Mr. B.C. Shellaxd of the Meteorological Office. At Lerwick the mean speed for the 1969-70 winter was 15*1 knots whilst the 10-year mean was 15*3 knots. At Bell Rock the figures are 17«9 and l8,1 respectively. The differences from the 10-year mean were quite small, being less than 1 .$9^  in wind speed. The higher values at Bell Rock are due to the winds being recorded at the top of a tall lighthouse, and not at a standard height above a land station. It could be argued that to achieve 'average' conditions the measured wave heights quoted in this report should be increased by between 2 and 3 percent, depending on whether in this area wave heights are related to the wind speed to the power of 1.5 or 2. However, these differences are quite •mall and are well within the errors inherent in the measur-ing system. It is recommended that the heights (and periods also) be used without modification. -4-Acknowledgements The authors wish to express their appreciation to Norsk Selskab til Skibbrudnes Redning, and Kaire Misje and Co. for permission to operate the equipment on the vessel, and to the Officers and Crew for operating the equipment, and to the authors' colleagues for help in the analysis. The authors are very grateful to the North Sea Environmental Study Group, which has given financial assistance to expedite the analysis. -5-REFERENCES BATTJES, J,A, 1970 Long-Term Wave Height Distribution at Seven Stations around the British Isles. N.I.O. Internal Report A 44. CAKTWRIGHT, D.E. and LONGUET-HIGGINS, M.S. 19^6 The statistical distribution of the maxima of a random function. Proc. roy, Soc. A. 237, 212-2^2. DRAPER, L. 1963 The derivation of a 'design-wave' from instrumental measurements of sea waves. Proc. Inst. civ. Engrs. 26, 291-30^* DRAPER, L. and FRIGKES, H.3. 1965 Waves off Land's End. J. Inst. Navig. l8,2,l80-l87. DRAPER, L, 1966 The analysis and presentation of wave data - a plea for uniformity. Proc. 10th Conf, on Coastal Engineering, Tokyo, Chapters 1 and 2. DRAPER, L« 1968 Waves at Smith's Knoll Light Vessel, North Sea. N.I.O. Internal Report A 33* TUCKER, M.J. 1936 A Shipborne Wave Recorder. Trans. Instn. nav. Archit. Lond. 98, 236-230. TUCKER, M.J. 1961 Simple measurement of wave records. Proc. Conf. Wave Recording for Civ. Engrs. (M.1.0.) 22-3' TUCKER, M.J. 1963 Analysis of records of sea waves. Proc. Instn. civ. Engrs. 26, 304-316. PERCENTAGE EXCEEDANCE OF HS AND HMAX AUTUMN - OCTOBER TO DECEMBER too 90 .. BO . . 70 .. GO . . 50 .. 40 .. 30 .. 20 .. 10 .. *^ max(3 hours) 4 5 E 7 B 10 SO WAVE hCItSHT IN FEET 3 0 4 7 ^ ¥ * * * * 4 0 5 0 GO 7 0 8 0 1 0 0 FAM Fig.1 PERCENTAGE EXCEEOANCE OF HS Ahd HMAX WINTER - JANUARY TO MARCH 100 SO .. BO .. 70 .. GO 50 40 .. 30 .. SO .. 10 max (3 hours) 4 5 6 7 B 10 30 WAVE ttlGHT IN FEET M K K K 30 40 50 60 70 80 100 FAM Fi9.2 GRAPH OF PERCENTAGE OCCURRENCE OF TZ WITHIN HALF-SECOm INTERVALS AUTUMN - OCTOBER TO OECEIvBER 30 » I I I I I I I I I I I I I I I I I I SO . . lO .. 0 —I—I—J B I E I S ao ZERO CR0GGIN3 PERIOD IN HALF H F m O INTERVALS CALM = 0 , 0 0 PER CENT FAM Fig-3 GRAPH OF PERCENTAGE OCCURRENCE OF TZ WITHIN HALF-SETOND INTERVALS WINTER - JANUARY TO MARCH 3 0 ao .. I D . . 4—I—I—1—4—I—I—I—I—I—I—I—I—*—I—I—h 0 —I—I—I—I- I O-l—I—I—I—#-8 12 1£ ao ZERO CROSSING PERICD IN HALF 3 T T N 3 INTERVALS CALM - 0 * 0 0 PER CENT FAM Fig.4 GRAPH OF SPECTRAL WIDTH PARAMETER ^ —I—I—I—I—I—I—I—I—I—I f I—I—I—I—I—1-4—I—I—I—I—I—I—I—I—I—I—I—I—I—I—I—I—I—I—I—I—h 10 .. 5 . . -I—I—1-4—I r I M I —1—4 0 * 0 0 * 1 0 , 2 0 * 3 0 ' 4 0 * 5 0 * 6 0 * 7 SPECTRAL WIDTH PARAMETER IN TENTHS WITHIN INTERVALS OF 0 * 0 2 5 CALM - 0 * 0 0 PER CENT 0*8 0 * 9 1 * 0 FAM Fig. 5 SCATTER DIAGRAM I N PARTS PER THOUSAND + = 1 OCCURRENCE, 40 4 1—4- 4 1 1- 4 1 1 1 1 1 I I 1- 4 1 1 1—I 1 1 »-35 30 25 20 15 10 5 4 k + l/l/lB 21 10>D/5 3 /2/4 IS IB 7 1/ " 5 -'7/* 1 'ST 1^4 3 5 1 + ib/id / s / I Q/ a' 3—g-" / 4 1 1 1 h 4 H 4 1 1 1 1 1—I 1 1 1 1 1 1 1 1 1 1 1 1 1 » 1 h 7 8 9 1 0 1 1 1 2 1 3 1 4 1 5 1 5 1 7 1 8 ZERO CROSSING PERIOD IN HALF SECOND INTERVALS FAM Fig.6 NUMBER OF OCCURRENCES OF WAVE CONDITIONS EXCEEDING A GIVEN DURATION u z ULI LU w U J i LLI Q. 0-0001 0-0002 00005 0-001 0-002 0-005 0-01 0-05 0-1 0 - 2 0-5 1 2 5 10 20 30 40 50 60 70 80 90 95 98 99 99-8 99-9 99-99 FAMITA WINTER (OCT T i — i — n — r MCH INCL.) 1969-70 T 1—I I I I I—I I I I 93 ft 100 YR 90 ft 50 YR : 86 ft 25 YR / H 80 ft 10 YR 66 ft 1 YR> 5 10 20 WAVE HEIGHT-FEET 30 50 ±JL± 100 FAM FIG. 8. (ft) 12 16 20 24 32 40 48 64 80 96 • I I I I I I 1 L, A _ lOOwinters 50 " 2 0 // I winter log h (h in ft) ®io FAMITA WINTER Fig. 9 BSHI 

Winter waves in the northern North Sea at 57,30N, 3,00E recorded by M.V. 'Famita'

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