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A new empirically-based correction procedure for shipborne wave recorder data
A new empirically-based correction procedure for shipborne wave recorder data E. G. P I T T
Applied IVave Research, Little Croft, Rectory Lane, Pulborough, West Sussex Rtt20 2AD, England A new correction procedure for Shipborne Wave Recorder (SBWR) wave height data is described. The method is based on a new assessment of the available measurements of the frequency response of the SBWR using a Froude-type frequency scaling. Spectral data from the SBWR are corrected using this method and values of Hs, the significant wave height and Tz, the mean zero-crossing period are derived. The spectra appear to be reasonable while the Hs and Tz values are consistent with independent data which were also derived from spectral analysis. However, when the spectral values of Hs are co r2pared with the values of Hs derived from simultaneous chart records using the so-called Tucker-Draper method, the latter are found to be higher on average. For installations with deep pressure sensors, such as the Seven Stones lightvessel, the differences are substantial. It is argued that the differences are due to the use of an inappropriate frequency response correction. A method is derived for applying the new frequency response correction to historical Hs, Tz data. The results of this procedure are compared with the simultaneous spectral values of Hs and with independent data from the Geostat altimeter. Finally, the changes in the 50-year design wave heights brought about by the use of the new correction procedure are evaluated. These calculations are done for a number of SBWR installations whose data contribute to the U K Department of Energy's Guidance Notes. Key Words: Shipborne wave recorder, measured frequency response, non-dimensional frequency scaling, frequency response correction, characteristic frequency.
INTRODUCTION The Shipborne Wave Recorder (SBWR) was devised in tile early 1950's by Tucker 1, for the first time enabling wave measurements to be made on a routine basis in offshore areas. Since then it has been used extensively for the measurement of waves in sea areas around the British Isles and in the North-East Atlantic, as well as in other parts of the world. Considerable advances in wave-measuring instruments have been made over the last thirty years, notably with the introduction of reliable telemetering accelerometer buoys (the Datawell 'Waverider' being perhaps the best-known example), the deployment of high capability discus buoys which allow directional wave measurements to be made out to the shelf edge and beyond and the development of satellites for both data relay from remote areas and the measurement of wave height. Nevertheless in those areas where a suitable stationkeeping ship is available the SBWR remains uniquely cost-effective and because it is protected within the hull of a ship, immune from many of the dangers which beset instruments on attended moorings. These advantages have allowed measurements to be made in oceanic and coastal areas over periods of many years using temporal sampling schemes which are still not possible from Paper accepted March 1990. Discussion closes February 1992. 9 1991 ElsevierSciencePublishers Ltd 162
Applied Ocean Research, 1991, Vol. 13, No. 4
satellites and will not be for some years to come. Thus the performance of the SBWR continues to be of interest both because of the measurement programmes which are presently underway and because of the extensive historical archive. The instrument, in effect, uses the ship within which it is installed as a wave sensor, so that its response varies not only with the wavelength of the waves but also from one installation to another. Thus, uncertainties regarding the form of the frequency response of the SBWR have limited the accuracy of the measurements made.
O R G A N I S A T I O N O F T I I E PAPER The present paper describes a new empirically-based frequency response correction procedure and argues that it gives more accurate results than the method used historically. The benefits are particularly important at the higher frequencies and for installations where the pressure sensors are comparatively deeply submerged. The paper is arrangcd as follows. First an account is given of the principle of operation of the instrument, and this is followed by a derivation of the functional form of the frequency response. Then a comparison is made of the response function which has been used historically for SBWR data with the
A new empirically-based correction procedure f o r shipborne wave recorder data: E. G. Pitt
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|..
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= Sensor P a c k a g e s Fig. 1.
P - Pressure Sensor A - Vertical Accelerometer
S B W R installation (schematic)
available empirical determinations of the frequency response. A method is described whereby measurements of the frequency response from different ships may be reconciled using a non-dimensional frequency scaling. This method is then applied to measured SBWR spectra and the results assessed. Finally, a method is developed for applying the new response function to historical SBWR measurements. The results of this procedure are assessed by comparison with independent measurements, including those from satellites. Applications of the data are in areas such as offshore engineering, wave power research and the validation of wave models. For one of these applications, offshore engineering, the effect the new correction procedure has on the design wave heights estimated from the SBWR data used in the United Kingdom Department of Energy's Guidance Notes 2 is considered.
heave response is small the pressure information is relatively more important. In the latter case, however, we should note that the pressure signal is attenuated by the hydrodynamic filter effect. The use of an accelerometer and a pressure sensor on either side cancels out roll signals (both in acceleration and pressure) as well as providing some compensation for pressure fluctuations due to waves reflected from one side of the ship.
F R E Q U E N C Y RESPONSE This is a rather complicated system and in order to gain an understanding of the frequency response we suppose that the system can be replaced by a single accelerometer and a single pressure sensor mounted on a spar buoy as represented in Fig. 2. If the sea surface elevation above the mean level is given by q(t) and the heave of the buoy is h(t), then the pressure at the pressure sensor (in metres of sea water) is given by:
p(t) = d-h(t) + ~l(t)*rn(t )
PRINCIPLE OF OPERATION The SBWR consists of two instrument packages which are located within the hull below the waterline on either side of the ship at an alongships station which is close t o the pitch axis (Fig. 1). Each package consists of an accelerometer mounted in gimbals so as to measure the vertical acceleration and a pressure sensor which communicates with the ocean via a hole in the ship's side. These holes are positioned at the smallest distance below t h e mean water line which ensures that they remain submerged at all times. In practice this results in a depth of between one and three meters depending on the ship. The four signals (two from each side) are led to a central computer unit where the accelerations are doubly integrated to give the displacement at each instrument package. These signals, now two displacement and two pressure (scaled as pressure head in meters), are added and it is this composite signal which gives a measure of the wave height. Analogue electronic techniques are used throughout the system. Design and calibration aspects are discussed by Haine 3 and Crisp4; the use of vertical accelerometers mounted on short-period pendula is discussed by Tucker 5. On a small ship in long waves the heave sensor provides most of the information, while on a large ship whose
(I)
where d is the mean depth of immersion of the pressure sensor, rn is the impulse response function of the pressure attention with depth and * indicates convolution. The response of the pressure sensor can be written as
p'(t)
= p(t)*,'E(t)
(2)
ie
p'(t) = {d - h(O + q(t)*rn(O}*r,(t)
(3)
SD~Ir buoy
water surface
..,
~
q
...................................
pressure sensor ~
Fig. 2.
buoy water hr'~
I. . . . . . . . pyap_gaf_er2ev_el___
/
Shnple model of the S B W R
Applied Ocean Research, 1991, Vol. 13, No. 4
163
A new empirically-based correction proce&we for shipborne wave recorder data: E. G. Pitt Likewise, the response of the heave sensor can be written as
h'(t) : h(t)*rE(t) where rE is the impulse response of the accelerometer/ double integrator. In practice, this is just the response of the double integrator with respect to a perfect double integrator'*. The equivalent filter must be included in the pressure signal path and this is reflected in equation (2). The sum signal is given by:
Some early measurements of the response suggested that it fell more quickly with increasing frequency than is indicated by equation (5) and so the depth was multiplied by a factor c~ (usually called k). The routine analysis of SBWR data at lOS used this 'modified' form of the classical response with c~= 2.5 to give Rn(f) = exp
(-2.5(2nf)2d) g
(6)
s'(t) = h'(t) + p'(t) = tl(t)*rn(t)*rE(t) where we have ignored the constant d. Taking Fourier transforms we get
E M P I R I C A L DETERMINATIONS OF THE FREQUENCY RESPONSE
SO') = W(D.Rn(f).RE(D where W is the Fourier transform of tl. Forming the spectra we get: I
s,,0') = s~(f) • ~
1 x I RE I ~
(4)
Equation (4) is used to correct the measurements of the SBWR. Since R E can be calculated, the problem is reduced to determining Rn, the transfer function of the measured pressure fluctuations to the surface waves.
M O D E L S OF Rn: The simplest assumption that can be made is that the pressure beneath the waves is the same as it would be in the absence of the ship. Then, according to the linearised theory of water waves and assuming the ship is operating in deep water, the amplitude response, R n, is given by:
Rn(k ) = e x p ( - kd) ie
RnfJ) = exp
(-(2nf)ed)
(5)
where k is the wave number f is the frequency of the waves d is the mean depth of immersion of the pressure sensors g is the acceleration due to gravity
Table I.
~2= ~/ 2 g~ d f
(7)
31ahl dimensions o f the 5 ships (all dimensions hi metres)
Ship
Presure Sensor Depth
Channel LV OWS Cumulus OWS Weather Reporter RV Ernest Holt
2.0
SS Cairndhu
3.7
164
Several measurements of the frequency response of the SBWR have been undertaken on different ships over the years, and in view of the continuing interest in the instrument another such experiment was conducted in 1980 aboard the Trinity House lightvessel at the Channel station. This work is described in detail in Ref. 4 which discusses many aspects of the performance of the SBWR, and will be referred to frequently as 'Crisp'. Following Crisp the present author has developed methods for the correction of SBWR wave data using empirical determinations of R11 (see Ref. 6). Five sets of data were used in this work, three of which had been considered previously by Crisp. These are those made onboard O.W.S. Weather Reporter by Canahm et al. 7, those made onboard O.W.S. Cumulus by Van Aken and Bouws 8 and Crisp's own measurements on the Channel lightvessel. To these were added a set of measurements taken on the S.S. Cairndhu 9 and a set made on R V Ernest Hoh I~ These latter results are based on comparatively little data, each set being the mean of just three determinations of the response each of which was based on a single wave record. Table 1 sets out the main dimensions of the 5 ships. Figure 3 is a plot of the experimental estimates of I RH 12 against frequency, and it can be seen that there is a wide scatter in the results. Now consider equation (5). If (like Crisp) we define a sealed frequency variable:
Length
Beam
2.0
35.0
8.7
3.5
60
1.5
62.0
12.6
4.5
~ 1500
2.2
72.0
10.9
4.3
~ 1500
53.3
9.1
4.4
,,~ 1000
128.0
18.3
5.8
~ 1000
Applied Ocean Research, 1991, 1/oi. 13, No. 4
Draught
Water Depth
A new empMcally-based correction procedm'efor shipborne wave recorder data: E. G. Pitt I
I
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+
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x
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y
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~
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-
OWS
Cumulus,
m
OWS
Weather
Y
SS
Cairndhu
x
RV
Ernest
Reporter
Holt
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FREQUENCY
F~g. 3.
I
i
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I
0.25
0.3
HI
Measured vahtes of response plotted agahlst frequen O'
equation (5) gives R~/~2) =--exp(--4n~z)
(8)
and equation (6) gives
R~2, = 1 - Ao{ I -- exp[-- A,r
RI~(~2) = e x p ( - 10~zz)
(9)
In Fig. 4 are plotted the experimental estimates against ~2 as well as equation (8) and (9). It will be seen that although the measured responses do not agree well with either of the exponential forms, the scaling has reduced the spread between different ships. Equation (7) represents a Froude number scaling of the frequency with d as the length scale; in ship motion work the ship's length L is more often used a n d a scaling based on this was tried with rather satisfactory results (Fig. 5). A number of other combinations of dimensions were explored and finally a scaling based on the use of the harmonic mean of L and d was selected:
~.4= ~
grounds) and which tended to a constant at high frequencies. After some experimentation the following form was adopted:
(Ld)'/4f
- A2~-42- A3~.343} (11)
The experimental data can be expected to be progressively less reliable as the frequency decreases below 0.1 Hz , and so in order to force the fitted curve to adopt a physically reasonable shape at the lower frequencies a group of five points was added to the data for each ship. These were specified at frequencies 0.0, 0.005, 0.0101, 0.015, 0.020 Hz, the response being set to unity. Table 2 gives the values of the four constants and the rms error. N is the number of points including the five manufactured oned. Equation (1 I) was fitted to the data from each of the five ships and to the whole data set. Figures 7 and 8 show respectively the fits obtained for the Channel LV and OWS Cumulus data. The fit obtained for the whole data set is shown in Fig. 6.
(10)
Figure 6 shows I R I 2 plotted against ~.4 (the fitted line is equation (11) ahead).
F I T r l N G F O R M U L A E TO THE MEASURED RESPONSE DATA Since neither the 'classical' hydrodynamic attenuation formula nor its 'modified' form fit the experimental data well it was decided to use a completely empirical approach. A function was sought which tended to unity at very low frequencies (this was expected on physical
APPLICATION OF THE RESPONSE CORRECTION The IOS wave climate programme uses data from SBWR's installed on a number of Ocean Weather Ships (OWS) in the North East Atlantic Ocean and on lightvessels (LV) in British coastal waters. Over most of the period from the 1950's to the present the data were recorded as 12-minute samples using pen and paper chart. They were analysed using the so-called Tucker-Draper (TD) method to give estimates of Hs, the significant wave height and Tz, the apparent (low-pass filtered) mean
Applied Ocean Research, 1991, Vol. 13, No. 4 165
A
new empirically-based correction procedure for shipborne wave recorder data: E. G. Pitt !
1.
-
t
x
-
~._xJv
Modified f response
0.5
-
,
Classical response
x
Y
v
Oo
I
I
...
v
9
I
;
0.5
O. FREOUENCY
F~. 4.
Measured vahtes of response plotted against ~z (Ke)' MS in Fig. 3)
I
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X §
I.
--
X + +
+
+
)E
Y4-1~
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~+
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X + Y +
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y.'~ + X y +
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+x+x~
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' O.
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166
1
. . . . .
O.S
I
~x ~ x z X Xv ~(y~ -
. . . .
1.
Measured values of response plotted against ~1 (Key as in Fig. 3)
Applied Ocean Research, 1991, Vol. 13, No. 4
I 1 .S
Y Y
Y Y
i
i
FREOUENCu
Y
I 2,
Y
I,
A new empirically-based correction procedure for shipborne wave recorder data: E. G. Pitt Table 2. Fittingconstantsfor equation 12for the 5 ships Ship
A0
Channel LV OWS Cumulus OWS Weather Reporter RV Ernest Holt SS Cairndhu AII ships
At
A2
The information which is of interest includes the following:
A3
n
N
0.8468
0.4876
-6.4058 26.691
0.044330
0.7734
1.0832
- 19.048 64.048
0.0260 28
0.8258
- 1.0047
0.83725
I. D o the spectra corrected using equation (4) and (11) seem reasonable and do they agree with independent data? 2. H o w well do the values of Hs derived from the uncorrected spectra agree with the uncorrected Hs derived from the T D analysis of the charts? 3. H o w well do the values of Hs derived from the corrected spectra agree with the corrected Hs derived from the T D analysis of the charts?
8.9790 3.7864 0.0440 22
2.2130 -21.234
0.82108 0.27094 0.81027 0.50723
54.182
0.0877 23
-7.4233 40.096 -8.1996 35.790
0.0531 24 0.0690127
Figure 9 shows six spectra from the Seven Stones lightvessel plotted on log-log axes along with a saturated spectrum defined by S = flf-s with fl = 0.00076 m 2 sec-~ Apart from a suggestion of a dip at about 0.25 Hz they are not unreasonable. Certainly they are much more realistic than spectra corrected using equation (6) which 'blow u p ' at the higher frequencies. Figure 10 shows Hs derived from the uncorrected spectra plotted against the uncorrected Hs from the T D analysis. As might be expected from theoretical considerations ~4, the T D estimates of Hs agree well with those from the spectra. In all the comparisons the (least squares) best fit line which passes through the origin is shown. Figure 11 shows Hs derived from the corrected spectra plotted against the corrected Hs(TD). On average the Hs(TD) values are 2 1 % greater than the spectral values, with some of the smaller values of Hs(TD) being double the spectral values. During 1985 there was a period when spectral data were available from both a Waverider (W/R) to the West of St Mary's, Isles of Seilly and the Seven Stones lightvessel. Spectra from the latter had been corrected
zero-crossing period TM. The heights were corrected using equation (6) evaluated at a characteristic frequency f~, w h e r e f ~ = l/Tz. In the early 1980's microcomputers were installed on the ships fitted with SBWR's and spectral analysis of the data was performed at source, the results being written to magnetic tape. Details of the analysis procedure are to be found in Ref. 6 and in recent lOS wave data reports t3. For a considerable overlap period the data continued to be recorded on chart rolls both to provide a back-up and in particular to allow a comparison to be made between the chart roll and spectral results. Data from Ocean Weather Station Lima, the Seuen Stones lightvessel, the Chamtel lightvessel and the Dowsing lightvessel are considered in Ref. 6 - here we concentrate mainly on the Seven Stones data.
X
-F
X I.
~
~
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+
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,v
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y
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0.5
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I~
Fig. 6. ~leasured vahtes of response plotted agahlst ~.4 with equation (11) fitted (Key as & Fig. 3)
Applied Ocean Research, 1991, Vol. 13, No. 4
167
A new empirically-based correction proceclttrefor shipborne wave recorder data: E. G. Pitt
4-
I~
+ +
44-
+
+
4-
0.5.
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Fig. 7.
Channel LV results plotted against 44 with equation (11) fitted
I.
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Fig. 8.
168
0.$
0 IVS cumuhts results plotted against 44 with equation (11) fitted
Applied Ocean Research, 1991, 1/ol. 13, No. 4
FREOUEHCY
i~
A new empirically-based correction procedure for shipborne ,'ave recorder data: E. G. Pitt 95
711
EI~
2.117 S.82 0
I1~
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~
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SEVEN STCt~2S0 FEBRUARy - ~AY 1985
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Fig. 9. Spectra from the S e v e n Stones lightvessel corrected using frequency variable ~.,~
Comparison of Hs(spectral) with Hs(TD)
using equation (11). The two sites are about 22 km apart and the W]R is considered to be better exposed, nevertheless comparisons of simultaneous observations from the two systems are of interest. Figure 12 shows the comparison of Hs, with the W/R giving values which on average are about 7% higher. The correlation coefficient of 0.93 is good considering the geographical separation of the sites. Figure 13 shows the corresponding comparison for Tz. This shows that the S e v e n S t o n e s (SBWR) values exceed
SEVEN S I C ~ S SEVEN S f 0 1 ~ S .
SB~JR , SCILLY U/R
APRIL - M~Y 1985
I0. I0.-
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z
~
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o. 0.
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,
,
5. W/R
10.
IIs ( S p . c ~ - u l )
Fig, 12. Comparison of Hs(spectral) measured by the SBWR on the Seven Stones lightvessel with Hs(spectral) measured by the Isles of Scilly W/R
Applied Ocean Research, 1991, Vol. 13, No. 4
169
A new empirically-based correction procedure for shipborne wave recorder data: E. G. Pitt SEVEN STONES S~-IR 9 SCZLLY U / R
. . . .
IS.'
I
.
9
.
.
I ..9
.
.
correction function evaluated at a single characteristic frequency, f o where f~ is taken as the reciprocal of the mean zero-crossing period of the record9 Therefore
.
1
Hs(TD) = Hs'(TD) x ~
1 x I RE(f~) I
Where fc = 1/Tz
IO.-
9
-
.
9
9
,:-.~
.,::,
..'.~. ! .~.;
R n is given by equation (6) and Hs' is the uncorrected Hs.
.
.~. ....
.'d2...-:.'.;".
Hs(Spectral) = 4@~0-o
"
Where m o = ALES; x ~
tt~ 5 . - -
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1 x -1RE~)I 2
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The first task was to investigate the operation of the scalar correction method. To do this we used the spectral data and plotted
|SplCt;rol)
Fig. 13. Comparison of Tz(spectral) measured by the SBIVR on the Seven Stones lightvessel with with Tz(speetral) measured by the Isles of Scilly IV]R
m'oQ(l/Tc) against AJT,S;Q~) where m~ is the zeroth moment of the uncorrected spectrum (in general the nth moment of the spectrum will be defined by m. = AfXSif'i") and Q = I/R~t x 1/I REI 2 as previously defined.
the Scilly Isles (W/R) values by 4% on average, with a tendency fo r the values to approximate each other closely at the longer periods and to diverge at the shorter periods. This is as one would expect given the higher frequency limit to which the moments are summed in the W/R analysis scheme (0.64 Hz) compared with 0.48 Hz for the SBWR system. The evidence presented above suggests:
Te is the characteristic period and was taken as T'I ( = m;/m'x). The result for Seven Stones is shown in Fig. 14 and similarly remarkable results were obtained for the other vessels. Clearly, the scalar correction method can be used with very high statistical confidence. However there is a bias, the scalar corrected values being 11% lower than
a) The new correction function is giving sensible results when applied to the spectra and b) The use of the 'modified' formula, equation (6), in the TD method leads to overestimation of Hs. The installation on the Seven Stones lightvessel had comparatively deep pressure sensors with d = 2.6 m, and the overestimation was considerable. For vessels with smaller values of d, for example OWS Starella and OWS Cumulus which jointly attended the Lima station, the overestimation was less. Further discussion of the results is contained in Ref. 6.
SEVEN STOh~SI APRZL - flAY 19~5
5.--
g 8
RECORRECTING HISTORICAL WAVE H E I G H T DATA In view of the discrepancies between the spectral Hs and Hs(TD) there is a need to develop a method for correcting the historical data to the new standard. This is not entirely "straightforward because the correction processes are fundamentally different. In the spectral method the response correction function is applied to each spectral estimate and the corrected spectrum is summed to estimate the spectral moments m.. H s is then calculated as 4x~o~ In the TD method the uncorrected Hs is estimated and then a scalar correction is derived as the
170
Applied Ocean Research, 1991, VoL 13, No. 4
E
I
O.
I
o.
5. m 0
Fig. 14. Comparison ofm'o correctedby the scalar method with the fidly-corrected m o
A new empirically-based correction procedure for shipborne wave recorder data: E. G. Pitt S E V [ t i StONESl FEgUARy -
Table 3. Comparisons between mofidly corrected and m o usbzg a scalar correction Io.
Station
Slope (Scalar: f u l l )
Correlation Coeff
OWS Lima
0.8948
0.9987
Seven Stones LV
0.8929
0.9997
Dowsing LV
0.9082
0.9967
Channel LV
0.8741
0.9988
the fully corrected values. Table 3 shows the results for all four vessels. Reference 6 contains further discussion. Here we report that calculations using simulated spectra and a response defined by equation (11) gave rather more scattered results, but with the same bias of about 11%. Since the only period parameter available in the historical TD data is the apparent value of Tz, we require a relationship between this and 7"1, the filtered or apparent or uncorrected value of Tl. Because the variety of spectral forms found in nature is so wide and the counting process used in the estimation of Tz(TD) so difficult to model, it was considered most practical to assume that Tz(TD) and T] were related by a simple scale factor and to determine this empirically. Table 4 gives the main results. In addition a numerical simulation was undertaken and this gave rather similar results. On the basis of the foregoing we are now in a position to formulate a correction equation for the historical Hs(TD) data:
Hs'(TD) Hs, = {x/Ssv x v/Q(f~)}
(13)
Where HsR is the corrected value of Hs Hs'(TD) is the uncorrected T D estimate of Hs Ssv is the empirical coefficient relating the scalar corrected tn; to the fully corrected mo 1
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Fig. 15. Comparison of Hs(TD) recorrected using the tzew scheme with Hs(speetral)
Table 5 gives the slopes and correlations for the comparisons. Figure 16 shows the ratio of the new correction to the historical correction as a function of Tz. (The corrections for OWS Ctmnthts and Starella which jointly attended Ocean Weather Station Lhna were very similar).
C O M P A R I S O N WITH S A T E L L I T E DATA
This formula was used to recorrect the Hs(TD) data from the four ships and these were compared with Hs (spectral); the results for Seven Stones are shown in Fig. 15. Since Sse varies only slightly from ship to ship, the mean of the four values was used ie Ssv -- 0.8925 with standard deviation 0.014. ST'~ Tz is more problematical; for these data the value for each ship was used as appropriate. In general, however, the mean value is used.
A radar altimeter mounted on an orbiting satellite gives an estimate of Hs. The only satellite which has flown in recent years with this instrument is the US satellite Geosat, which gave estimates averaged over one second, seven kilometres apart, with an accuracy goal of 0.5 m rms or 10% whichever was greater. Dobson et a115 compared the estimates from Geosat with 116 measurements of Hs from the US National Data Buoy Center network. They found that the satellite estimates were on average about 0.4 m lower than the corresponding buoy values and that the difference between the two was independent of wave height. The maximum observed Hs in this comparison was only about 6 m, however. A more recent analysis by Srokosz 16, using more measurements
Table 4. Tz(TD)
Table 5.
Tz(TD) x ST'~ Tz where ST'~Tz is the empirical coefficient relating T1 from the uncorrected spectrum to Tz(TD).
Comparison between T I from the uncorrected spectra and Comparison between recorrected H s ( T D) and spectral Hs
Station
Slope (T'1: Tz)
Correlation Coeff
Station
Slope (lts• : fts(spectral))
Correlation Coeff
OWS Lima
1.0724
0.8951
OWS Lima
1.0482
0.9611
Seven Stones LV
1.0518
0.9183
Seven Stones LV
!.0026
0.9347
Dowsing LV
1.0076
0.9557
Dowsing LV
0.9903
0.9751
Channel LV
!.1262
0.8615
Channel LV
0.9505
0.9690
Applied Ocean Research, 1991, Vol. 13, No. 4
171
A new empirically-based correction procedure for shipborne wave recorder data: E. G. Pitt PRESSURE SENSOR DEPTH CORRECTION FUNCTIONS I
,
t
I
,
,
l
,
.
--
I
I
,
CHANNEL
LV SBWR OVERPASS
/
~To.Es
........... ~ ........... LInA' ........
SEVEN STONES Hs Prom GEOSAT
I r
DO~SING
6"14
7"14
~.32
/
.
.
.
.
.
.
.
:~
.
.
.
.
.
.
.
3.42 3.25 3.51 3.56 3.60 3.20
3.15 3.20
3.02 2.49 5 0 " N -0.5
I 4.
6.
I
8.
I
I
I0. 12. TZ ( s e c o n d s }
14.
~ . 16. Ratio ~ the new correction to the o ~ as a fimetion ~
o~ H..~-
from the network with values up to 9 m, gives a linear relationship, with the Geosat estimate around 0.87 that of the buoy value (and insignificant intercept). A comparison of data from Geosat (in 17-day repeat orbit) with SBWR measurements from OWS Lima is shown in Fig. 17 (Geosat's track passed within a few kilometres of the Ocean Weather Station; the SBWR values were obtained by linear interpolation of the values recorded every 1.5. hours). The offset of 0.4 m found by Dobson et al. and the relationship found by Srokosz are also shown. The data appear to agree reasonably well with Dobson's findings, but in fact, because of the poor statistics of the comparison (there are only 11 data pairs) either line would be an equally valid description. Moreover, if the SBWR values were recorrected using the historical method (leading to increases of the order of 5-10 %) these data too would be adequately described by either of the two lines. The new correction procedure produces large changes to the values of Hs from the Chamzel and Seven Stones LV's so that comparison with Geosat data should give clearer support for one or other correction method. Unfortunately, the SBWR in the Chmmel LV was not working on the few occasions that Geosat passed overhead (at 17-day intervals). Note also that even though its track missed Seven Stones by about 15 km the measurements from the satellite suggest sheltering by the Isles of Scilly, as can be clearly seen in Figs 18a and 18b,
+lV -50"N
2.08
.~"2.42 9 2.70 2.97 3.16 3.28 3.14 3.21 s e ~ VALUES 3.07 2.82 -~
3.03 2.76
3.b
2.85 2.67 l
|
I
I
1
l
t
I
I
i
I
I
I
I
I
I
I
;'14
6"14
7"14
DAY 326 YEAR 1986 TTi'IE 0001 H o u r s SEVEN STONES LV SBLIR Hs Prom GEOSAT OVERPASS 7%
6~
5"W
I
, 4,. 119 . . . . . .
I
. . . . . . . . .
4.27 4.05
4.27 4.46
4.77 4.58 4.34
4.52 4.37 -LV
4:19
3.68
5 0 " N --
--S0"N
~4).-3.60 3.82 4.08 4.43 4.71
4.96 4.93
SBWRvAtc[~ ,-.~
+
~.~-~.~
4.93 4.83 5.02 +.7-g'.o 4.85 4.98 ,J~,a
4.99
4.92 5.32
I
6"14
7"14
;'[J
343 YEAR 1 9 8 6 TIME 0 1 1 4 H o u r s
DAY 12
10'
Fig. 18. Chart o f the Scilly Isles showhlg Geostat and S B I V R measurenlents o f Hs
s
s S
.J ~
8-
6-
sr
9
----"
SrokosZ
4-
2-
10 Radar altimeter
Fig. 17. Comparison o f S B W R and satellite althneter measurements of Hs at O W S Lima
172 Applied Ocean Research, 1991, Vo/. 13, No. 4
taken from Ref. 17. Notwithstanding these imponderables, we show on each figure the values of Hs estimated using the historical and the new correction procedures (the range of values given in Fig. 18b refer to measurements taken four hours before and two hours after the satellite transit). It will be seen that the LV values using the new procedure are in better agreement with the satellite values. Indeed, if the satellite values are increased by 0.4 m after Dobson et al. or increased by 13% as proposed by Srokosz the agreement is very good.
A new empirically-based correction procedure f o r shipborne wave recorder data: E. G. Pitt Table 6. Esthnatesof ttsSO (m)
Site
Approx position
Hss~ using historical correction
Hs5~ new correction
OWS Lima St Gowan LV 7 Stones LV 50~ 6~ Channel LV
57~ 20~ 51891765~ 14.5 50~ 3~
21.5 13.3 13.0 12.1
20.4 12,4 10% 10.4
Thus we conclude that where sufficient data exist they indicate that the use of the new correction procedure leads to values of Hs which agree better with satellite altimeter data than the use of the historical correction method.
C H A N G E S I N D E S I G N WAVE H E I G H T All the available wave data for the four principal SBWR stations in the Institute of Oceanographic Sciences wave climate study were reeorreeted using the new procedure and the values of Hs s~ the fifty-year value of significant wave height, were calculated. The magnitudes of the reductions in Hs s~ are shown in Table 6. This shows estimates provided by Carter x8 obtained by fitting the original and revised data to a Fisher-Tippett Type I distribution. For the two stations in the English Channel, Chmmel LV and Seven Stones LV the average reduction in wave height resulting from using the new correction procedure rather than the old is rather more than 20 %. However, the changes in the correction factors are strong functions of Tz (see Fig. 16), being greatest for the shorter period waves which are generally of lower height and least for long period waves among which the larger waves are to be found. The effect on the extrapolation process is such that the increase in the design wave height is less than the increase on the average wave height.
CONCLUSIONS By using a non-dimensional frequency sealing it has been shown that it is possible it reconcile the several experimental measurements of the frequency response of the SBWR which are available. The resulting response does not match the exponentia! form which has been used historically and so an empirical formula was developed to fit the experimental data. When applied to measurements of spectra made by SBWR instaIiations, the results are reasonable (with reference to a theoretical saturated spectrum) and the estimates of Hs and Tz derived from the spectra are consistent with independent spectrally-derived data. However, the spectral Hs differs from the Tucker-Draper estimate from the corresponding pen-chart record, Hs(TD), the latter being higher on average. For installations with comparatively deep pressure sensors, such as the Seven Stones LV, the differences are substantial, being 21% on average, with the shorter period (lower) waves being factors of two or more higher
Reduction in Hss~ 5% 7% 14%
in some cases. For installations with comparatively shallow pressure sensors, such as the Dowsing LV, the differences are small. At Ocean Weather Station //ma where the wave climate is such that there is a low incidence of short period waves, the differences are modest overall even though the pressure sensor depth is in the middle of the range. In view of these discrepancies, a method was devised for recorrecting the historical Hs(TD) data to the new standard. The results were compared with the corresponding spectrally-derived values and with independent data, notably those from the Geosat altimeter, and found to be satisfactory. To demonstrate the effect on the statistics of wave height, the available data from the principal stations in the IOS wave climate study were recorrected and the 50-year design values of Hs, Hs 5~ were estimated. The reduction brought about by the use of the new correction ranged from 10-15% for the English Channel s i t e s t o about 5 % for Ocean Weather Station Lima. For other analyses which put emphasis on the whole data set, for example fatigue calculations, the changes may also be significant.
ACKNOWLEDGEMENTS My thanks are due to J. A. Ewing for bringing the SS Cairndhu and the RV Ernest Holt response data to my attention; to D. J. T. Carter for help with the comparison between SBWR and Geosat altimeter measurements of Hs, and to S, Bacon for providing Fig. 16. Messrs. Bacon and Carter jointly undertook the computations to provide the information for Table 6. The research described in this paper was undertaken at the Institute of Oceanographic Sciences (Deacon Laboratory), Wormley, England and was supported financially by the United Kingdom Department of Energy. The preparation of this paper was supported by the UK Department of Energy.
REFERENCES ! 2 3
Tucker,M. J. A shipborne wave recorder, Transactions of the Royal Institute of Naval Architects, 1956,98, 236-250 Dept of Energy Offshore Installations: Guidance on design and construction, Part 11 Section 2: Enviromnental considerations, 1989 Haine, R. A. Second Generation Shipborne Ware Recorder Transducer Technology, Vol 2, 25-28, 1980
Applied Ocean Research, 1991, Vol. 13, No. 4
I73
A new empirically-based correction procedure f o r shipborne wave recorder data: E. G. Pitt 4
Crisp, G. N. An Experimental Comparison ofa Shipborne Ware Recorder and a IVaverider Buoy Conducted at the Channel Light Vessel, Institute of Oceanographic Sciences Report, No. 235
5
Tucker, M. J. The accuracy of wave measurements made with vertical accelerometers, Deep Sea Research, 5, 185-192 Pitt, E. G. The Application of Empirically Determined Frequency
6
11 12
Response Functibns to SBWR data, 7
8 9
10
174
Institute of Oceanographic Sciences Report, No. 259 Canham, H. J. S., Cartwright, D. E., Goodrich, G. J. and Hogben, N. Seakeeping trials on ocean weathership Weather Reporter. Transactions of the Royal Institute of Naval Architects, 104, 447-492. Van Aken, H. M. and Bonws E. Frequency response of a shipborne wave recorder, Proceeding of the International Symposium on lt~re Measurement and Analysis, 1974, 281-300 NPL. Report on Analysis of Ship Motion Trials Data for Cairndhu. National Physical Laboratory Coordinating Committee for Research into the Seagoing Qualities of Ships, Report No. 6 (Unpublished manuscript) NPL. Report on Analysis of Ship Motion Trails Datafor Ernest
Applied Ocean Research, 1991, Vol. 13, No. 4
13 14 15
16 17 18
Holt, National Physical Laboratory Coordinating Committee for Research into the Seagoing Qualities of Ships, Report No. 7 (Unpublished manuscript) Tucker, M. J. Analysis of records of sea waves, Proceedings of the Institute of Civil Engineers, 26, 305-316 Draper, L. The analysis and presentation of wave data-a plea for uniformity, Proceedings of the lOth Conference on Coastal Engineering, Vol. I, Tokyo, September, 1966 Bacon, S. Waves Recorded at the Dowsing Light Vessel 1970-1985, Institute of Oceanographic Sciences Report, No. 262 Tann, H. M. The Estimation of Ware Parametersfor the Design of Offshore Structures, Institute of Oceanographic Sciences Report, No. 23 Dobson, E. Monaldo, F, Goldhirsh, J. and Wilkerson, J. Validation of Geosat altimeter-derived wind speeds and significant wave heights using buoy data, John ttopkins APL Teeh. Digest, 8 (2), 222-233 Srokosz, M. Personal communication Bacon, S. and Carter, D. J. T. tihres Recorded at Seven Stones Light Vessel, 1962-1986, Institute of Oceanographic Sciences Report, No. 268 Carter, D.J.T. Personal communication
Applied IVave Research, Little Croft, Rectory Lane, Pulborough, West Sussex Rtt20 2AD, England A new correction procedure for Shipborne Wave Recorder (SBWR) wave height data is described. The method is based on a new assessment of the available measurements of the frequency response of the SBWR using a Froude-type frequency scaling. Spectral data from the SBWR are corrected using this method and values of Hs, the significant wave height and Tz, the mean zero-crossing period are derived. The spectra appear to be reasonable while the Hs and Tz values are consistent with independent data which were also derived from spectral analysis. However, when the spectral values of Hs are co r2pared with the values of Hs derived from simultaneous chart records using the so-called Tucker-Draper method, the latter are found to be higher on average. For installations with deep pressure sensors, such as the Seven Stones lightvessel, the differences are substantial. It is argued that the differences are due to the use of an inappropriate frequency response correction. A method is derived for applying the new frequency response correction to historical Hs, Tz data. The results of this procedure are compared with the simultaneous spectral values of Hs and with independent data from the Geostat altimeter. Finally, the changes in the 50-year design wave heights brought about by the use of the new correction procedure are evaluated. These calculations are done for a number of SBWR installations whose data contribute to the U K Department of Energy's Guidance Notes. Key Words: Shipborne wave recorder, measured frequency response, non-dimensional frequency scaling, frequency response correction, characteristic frequency.
INTRODUCTION The Shipborne Wave Recorder (SBWR) was devised in tile early 1950's by Tucker 1, for the first time enabling wave measurements to be made on a routine basis in offshore areas. Since then it has been used extensively for the measurement of waves in sea areas around the British Isles and in the North-East Atlantic, as well as in other parts of the world. Considerable advances in wave-measuring instruments have been made over the last thirty years, notably with the introduction of reliable telemetering accelerometer buoys (the Datawell 'Waverider' being perhaps the best-known example), the deployment of high capability discus buoys which allow directional wave measurements to be made out to the shelf edge and beyond and the development of satellites for both data relay from remote areas and the measurement of wave height. Nevertheless in those areas where a suitable stationkeeping ship is available the SBWR remains uniquely cost-effective and because it is protected within the hull of a ship, immune from many of the dangers which beset instruments on attended moorings. These advantages have allowed measurements to be made in oceanic and coastal areas over periods of many years using temporal sampling schemes which are still not possible from Paper accepted March 1990. Discussion closes February 1992. 9 1991 ElsevierSciencePublishers Ltd 162
Applied Ocean Research, 1991, Vol. 13, No. 4
satellites and will not be for some years to come. Thus the performance of the SBWR continues to be of interest both because of the measurement programmes which are presently underway and because of the extensive historical archive. The instrument, in effect, uses the ship within which it is installed as a wave sensor, so that its response varies not only with the wavelength of the waves but also from one installation to another. Thus, uncertainties regarding the form of the frequency response of the SBWR have limited the accuracy of the measurements made.
O R G A N I S A T I O N O F T I I E PAPER The present paper describes a new empirically-based frequency response correction procedure and argues that it gives more accurate results than the method used historically. The benefits are particularly important at the higher frequencies and for installations where the pressure sensors are comparatively deeply submerged. The paper is arrangcd as follows. First an account is given of the principle of operation of the instrument, and this is followed by a derivation of the functional form of the frequency response. Then a comparison is made of the response function which has been used historically for SBWR data with the
A new empirically-based correction procedure f o r shipborne wave recorder data: E. G. Pitt
I
I
|..
[]
= Sensor P a c k a g e s Fig. 1.
P - Pressure Sensor A - Vertical Accelerometer
S B W R installation (schematic)
available empirical determinations of the frequency response. A method is described whereby measurements of the frequency response from different ships may be reconciled using a non-dimensional frequency scaling. This method is then applied to measured SBWR spectra and the results assessed. Finally, a method is developed for applying the new response function to historical SBWR measurements. The results of this procedure are assessed by comparison with independent measurements, including those from satellites. Applications of the data are in areas such as offshore engineering, wave power research and the validation of wave models. For one of these applications, offshore engineering, the effect the new correction procedure has on the design wave heights estimated from the SBWR data used in the United Kingdom Department of Energy's Guidance Notes 2 is considered.
heave response is small the pressure information is relatively more important. In the latter case, however, we should note that the pressure signal is attenuated by the hydrodynamic filter effect. The use of an accelerometer and a pressure sensor on either side cancels out roll signals (both in acceleration and pressure) as well as providing some compensation for pressure fluctuations due to waves reflected from one side of the ship.
F R E Q U E N C Y RESPONSE This is a rather complicated system and in order to gain an understanding of the frequency response we suppose that the system can be replaced by a single accelerometer and a single pressure sensor mounted on a spar buoy as represented in Fig. 2. If the sea surface elevation above the mean level is given by q(t) and the heave of the buoy is h(t), then the pressure at the pressure sensor (in metres of sea water) is given by:
p(t) = d-h(t) + ~l(t)*rn(t )
PRINCIPLE OF OPERATION The SBWR consists of two instrument packages which are located within the hull below the waterline on either side of the ship at an alongships station which is close t o the pitch axis (Fig. 1). Each package consists of an accelerometer mounted in gimbals so as to measure the vertical acceleration and a pressure sensor which communicates with the ocean via a hole in the ship's side. These holes are positioned at the smallest distance below t h e mean water line which ensures that they remain submerged at all times. In practice this results in a depth of between one and three meters depending on the ship. The four signals (two from each side) are led to a central computer unit where the accelerations are doubly integrated to give the displacement at each instrument package. These signals, now two displacement and two pressure (scaled as pressure head in meters), are added and it is this composite signal which gives a measure of the wave height. Analogue electronic techniques are used throughout the system. Design and calibration aspects are discussed by Haine 3 and Crisp4; the use of vertical accelerometers mounted on short-period pendula is discussed by Tucker 5. On a small ship in long waves the heave sensor provides most of the information, while on a large ship whose
(I)
where d is the mean depth of immersion of the pressure sensor, rn is the impulse response function of the pressure attention with depth and * indicates convolution. The response of the pressure sensor can be written as
p'(t)
= p(t)*,'E(t)
(2)
ie
p'(t) = {d - h(O + q(t)*rn(O}*r,(t)
(3)
SD~Ir buoy
water surface
..,
~
q
...................................
pressure sensor ~
Fig. 2.
buoy water hr'~
I. . . . . . . . pyap_gaf_er2ev_el___
/
Shnple model of the S B W R
Applied Ocean Research, 1991, Vol. 13, No. 4
163
A new empirically-based correction proce&we for shipborne wave recorder data: E. G. Pitt Likewise, the response of the heave sensor can be written as
h'(t) : h(t)*rE(t) where rE is the impulse response of the accelerometer/ double integrator. In practice, this is just the response of the double integrator with respect to a perfect double integrator'*. The equivalent filter must be included in the pressure signal path and this is reflected in equation (2). The sum signal is given by:
Some early measurements of the response suggested that it fell more quickly with increasing frequency than is indicated by equation (5) and so the depth was multiplied by a factor c~ (usually called k). The routine analysis of SBWR data at lOS used this 'modified' form of the classical response with c~= 2.5 to give Rn(f) = exp
(-2.5(2nf)2d) g
(6)
s'(t) = h'(t) + p'(t) = tl(t)*rn(t)*rE(t) where we have ignored the constant d. Taking Fourier transforms we get
E M P I R I C A L DETERMINATIONS OF THE FREQUENCY RESPONSE
SO') = W(D.Rn(f).RE(D where W is the Fourier transform of tl. Forming the spectra we get: I
s,,0') = s~(f) • ~
1 x I RE I ~
(4)
Equation (4) is used to correct the measurements of the SBWR. Since R E can be calculated, the problem is reduced to determining Rn, the transfer function of the measured pressure fluctuations to the surface waves.
M O D E L S OF Rn: The simplest assumption that can be made is that the pressure beneath the waves is the same as it would be in the absence of the ship. Then, according to the linearised theory of water waves and assuming the ship is operating in deep water, the amplitude response, R n, is given by:
Rn(k ) = e x p ( - kd) ie
RnfJ) = exp
(-(2nf)ed)
(5)
where k is the wave number f is the frequency of the waves d is the mean depth of immersion of the pressure sensors g is the acceleration due to gravity
Table I.
~2= ~/ 2 g~ d f
(7)
31ahl dimensions o f the 5 ships (all dimensions hi metres)
Ship
Presure Sensor Depth
Channel LV OWS Cumulus OWS Weather Reporter RV Ernest Holt
2.0
SS Cairndhu
3.7
164
Several measurements of the frequency response of the SBWR have been undertaken on different ships over the years, and in view of the continuing interest in the instrument another such experiment was conducted in 1980 aboard the Trinity House lightvessel at the Channel station. This work is described in detail in Ref. 4 which discusses many aspects of the performance of the SBWR, and will be referred to frequently as 'Crisp'. Following Crisp the present author has developed methods for the correction of SBWR wave data using empirical determinations of R11 (see Ref. 6). Five sets of data were used in this work, three of which had been considered previously by Crisp. These are those made onboard O.W.S. Weather Reporter by Canahm et al. 7, those made onboard O.W.S. Cumulus by Van Aken and Bouws 8 and Crisp's own measurements on the Channel lightvessel. To these were added a set of measurements taken on the S.S. Cairndhu 9 and a set made on R V Ernest Hoh I~ These latter results are based on comparatively little data, each set being the mean of just three determinations of the response each of which was based on a single wave record. Table 1 sets out the main dimensions of the 5 ships. Figure 3 is a plot of the experimental estimates of I RH 12 against frequency, and it can be seen that there is a wide scatter in the results. Now consider equation (5). If (like Crisp) we define a sealed frequency variable:
Length
Beam
2.0
35.0
8.7
3.5
60
1.5
62.0
12.6
4.5
~ 1500
2.2
72.0
10.9
4.3
~ 1500
53.3
9.1
4.4
,,~ 1000
128.0
18.3
5.8
~ 1000
Applied Ocean Research, 1991, 1/oi. 13, No. 4
Draught
Water Depth
A new empMcally-based correction procedm'efor shipborne wave recorder data: E. G. Pitt I
I
1
I
+
I. --
x
+
y
x+ +
~
_4-
+
+
I
+
Channel LV
-
OWS
Cumulus,
m
OWS
Weather
Y
SS
Cairndhu
x
RV
Ernest
Reporter
Holt
I Y
x+ I
4-
+
-
x+
X X + _
0.S X
y
y
l(
tl(
y
4-
X X
y
3~
+ ~
3~
I
+
Y
Y
~
4-
+
Y
~.
.
O.
.
.
.
I
0.05
. . . .
I
0.1
. . . .
I
0.15
. . . .
I 0.2
!
I
i
i
I
|
FREQUENCY
F~g. 3.
I
i
I
I
0.25
0.3
HI
Measured vahtes of response plotted agahlst frequen O'
equation (5) gives R~/~2) =--exp(--4n~z)
(8)
and equation (6) gives
R~2, = 1 - Ao{ I -- exp[-- A,r
RI~(~2) = e x p ( - 10~zz)
(9)
In Fig. 4 are plotted the experimental estimates against ~2 as well as equation (8) and (9). It will be seen that although the measured responses do not agree well with either of the exponential forms, the scaling has reduced the spread between different ships. Equation (7) represents a Froude number scaling of the frequency with d as the length scale; in ship motion work the ship's length L is more often used a n d a scaling based on this was tried with rather satisfactory results (Fig. 5). A number of other combinations of dimensions were explored and finally a scaling based on the use of the harmonic mean of L and d was selected:
~.4= ~
grounds) and which tended to a constant at high frequencies. After some experimentation the following form was adopted:
(Ld)'/4f
- A2~-42- A3~.343} (11)
The experimental data can be expected to be progressively less reliable as the frequency decreases below 0.1 Hz , and so in order to force the fitted curve to adopt a physically reasonable shape at the lower frequencies a group of five points was added to the data for each ship. These were specified at frequencies 0.0, 0.005, 0.0101, 0.015, 0.020 Hz, the response being set to unity. Table 2 gives the values of the four constants and the rms error. N is the number of points including the five manufactured oned. Equation (1 I) was fitted to the data from each of the five ships and to the whole data set. Figures 7 and 8 show respectively the fits obtained for the Channel LV and OWS Cumulus data. The fit obtained for the whole data set is shown in Fig. 6.
(10)
Figure 6 shows I R I 2 plotted against ~.4 (the fitted line is equation (11) ahead).
F I T r l N G F O R M U L A E TO THE MEASURED RESPONSE DATA Since neither the 'classical' hydrodynamic attenuation formula nor its 'modified' form fit the experimental data well it was decided to use a completely empirical approach. A function was sought which tended to unity at very low frequencies (this was expected on physical
APPLICATION OF THE RESPONSE CORRECTION The IOS wave climate programme uses data from SBWR's installed on a number of Ocean Weather Ships (OWS) in the North East Atlantic Ocean and on lightvessels (LV) in British coastal waters. Over most of the period from the 1950's to the present the data were recorded as 12-minute samples using pen and paper chart. They were analysed using the so-called Tucker-Draper (TD) method to give estimates of Hs, the significant wave height and Tz, the apparent (low-pass filtered) mean
Applied Ocean Research, 1991, Vol. 13, No. 4 165
A
new empirically-based correction procedure for shipborne wave recorder data: E. G. Pitt !
1.
-
t
x
-
~._xJv
Modified f response
0.5
-
,
Classical response
x
Y
v
Oo
I
I
...
v
9
I
;
0.5
O. FREOUENCY
F~. 4.
Measured vahtes of response plotted against ~z (Ke)' MS in Fig. 3)
I
I
I
X
X §
I.
--
X + +
+
+
)E
Y4-1~
Y + +
~+
Y
-
X
X + Y +
O,S
X ]K
y.'~ + X y +
x
~
Y ~y~
y +
+x+x~
O~
' O.
Fig. 5.
166
1
. . . . .
O.S
I
~x ~ x z X Xv ~(y~ -
. . . .
1.
Measured values of response plotted against ~1 (Key as in Fig. 3)
Applied Ocean Research, 1991, Vol. 13, No. 4
I 1 .S
Y Y
Y Y
i
i
FREOUENCu
Y
I 2,
Y
I,
A new empirically-based correction procedure for shipborne wave recorder data: E. G. Pitt Table 2. Fittingconstantsfor equation 12for the 5 ships Ship
A0
Channel LV OWS Cumulus OWS Weather Reporter RV Ernest Holt SS Cairndhu AII ships
At
A2
The information which is of interest includes the following:
A3
n
N
0.8468
0.4876
-6.4058 26.691
0.044330
0.7734
1.0832
- 19.048 64.048
0.0260 28
0.8258
- 1.0047
0.83725
I. D o the spectra corrected using equation (4) and (11) seem reasonable and do they agree with independent data? 2. H o w well do the values of Hs derived from the uncorrected spectra agree with the uncorrected Hs derived from the T D analysis of the charts? 3. H o w well do the values of Hs derived from the corrected spectra agree with the corrected Hs derived from the T D analysis of the charts?
8.9790 3.7864 0.0440 22
2.2130 -21.234
0.82108 0.27094 0.81027 0.50723
54.182
0.0877 23
-7.4233 40.096 -8.1996 35.790
0.0531 24 0.0690127
Figure 9 shows six spectra from the Seven Stones lightvessel plotted on log-log axes along with a saturated spectrum defined by S = flf-s with fl = 0.00076 m 2 sec-~ Apart from a suggestion of a dip at about 0.25 Hz they are not unreasonable. Certainly they are much more realistic than spectra corrected using equation (6) which 'blow u p ' at the higher frequencies. Figure 10 shows Hs derived from the uncorrected spectra plotted against the uncorrected Hs from the T D analysis. As might be expected from theoretical considerations ~4, the T D estimates of Hs agree well with those from the spectra. In all the comparisons the (least squares) best fit line which passes through the origin is shown. Figure 11 shows Hs derived from the corrected spectra plotted against the corrected Hs(TD). On average the Hs(TD) values are 2 1 % greater than the spectral values, with some of the smaller values of Hs(TD) being double the spectral values. During 1985 there was a period when spectral data were available from both a Waverider (W/R) to the West of St Mary's, Isles of Seilly and the Seven Stones lightvessel. Spectra from the latter had been corrected
zero-crossing period TM. The heights were corrected using equation (6) evaluated at a characteristic frequency f~, w h e r e f ~ = l/Tz. In the early 1980's microcomputers were installed on the ships fitted with SBWR's and spectral analysis of the data was performed at source, the results being written to magnetic tape. Details of the analysis procedure are to be found in Ref. 6 and in recent lOS wave data reports t3. For a considerable overlap period the data continued to be recorded on chart rolls both to provide a back-up and in particular to allow a comparison to be made between the chart roll and spectral results. Data from Ocean Weather Station Lima, the Seuen Stones lightvessel, the Chamtel lightvessel and the Dowsing lightvessel are considered in Ref. 6 - here we concentrate mainly on the Seven Stones data.
X
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~
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Fig. 6. ~leasured vahtes of response plotted agahlst ~.4 with equation (11) fitted (Key as & Fig. 3)
Applied Ocean Research, 1991, Vol. 13, No. 4
167
A new empirically-based correction proceclttrefor shipborne wave recorder data: E. G. Pitt
4-
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+ +
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168
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Applied Ocean Research, 1991, 1/ol. 13, No. 4
FREOUEHCY
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A new empirically-based correction procedure for shipborne ,'ave recorder data: E. G. Pitt 95
711
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Comparison of Hs(spectral) with Hs(TD)
using equation (11). The two sites are about 22 km apart and the W]R is considered to be better exposed, nevertheless comparisons of simultaneous observations from the two systems are of interest. Figure 12 shows the comparison of Hs, with the W/R giving values which on average are about 7% higher. The correlation coefficient of 0.93 is good considering the geographical separation of the sites. Figure 13 shows the corresponding comparison for Tz. This shows that the S e v e n S t o n e s (SBWR) values exceed
SEVEN S I C ~ S SEVEN S f 0 1 ~ S .
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APRIL - M~Y 1985
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Fig. 10. Comparison of Hs fi'om the uncorrected spectrum with the uncorrected value of Hs(TD)
,
,
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10.
IIs ( S p . c ~ - u l )
Fig, 12. Comparison of Hs(spectral) measured by the SBWR on the Seven Stones lightvessel with Hs(spectral) measured by the Isles of Scilly W/R
Applied Ocean Research, 1991, Vol. 13, No. 4
169
A new empirically-based correction procedure for shipborne wave recorder data: E. G. Pitt SEVEN STONES S~-IR 9 SCZLLY U / R
. . . .
IS.'
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9
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correction function evaluated at a single characteristic frequency, f o where f~ is taken as the reciprocal of the mean zero-crossing period of the record9 Therefore
.
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1 x I RE(f~) I
Where fc = 1/Tz
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"
Where m o = ALES; x ~
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The first task was to investigate the operation of the scalar correction method. To do this we used the spectral data and plotted
|SplCt;rol)
Fig. 13. Comparison of Tz(spectral) measured by the SBIVR on the Seven Stones lightvessel with with Tz(speetral) measured by the Isles of Scilly IV]R
m'oQ(l/Tc) against AJT,S;Q~) where m~ is the zeroth moment of the uncorrected spectrum (in general the nth moment of the spectrum will be defined by m. = AfXSif'i") and Q = I/R~t x 1/I REI 2 as previously defined.
the Scilly Isles (W/R) values by 4% on average, with a tendency fo r the values to approximate each other closely at the longer periods and to diverge at the shorter periods. This is as one would expect given the higher frequency limit to which the moments are summed in the W/R analysis scheme (0.64 Hz) compared with 0.48 Hz for the SBWR system. The evidence presented above suggests:
Te is the characteristic period and was taken as T'I ( = m;/m'x). The result for Seven Stones is shown in Fig. 14 and similarly remarkable results were obtained for the other vessels. Clearly, the scalar correction method can be used with very high statistical confidence. However there is a bias, the scalar corrected values being 11% lower than
a) The new correction function is giving sensible results when applied to the spectra and b) The use of the 'modified' formula, equation (6), in the TD method leads to overestimation of Hs. The installation on the Seven Stones lightvessel had comparatively deep pressure sensors with d = 2.6 m, and the overestimation was considerable. For vessels with smaller values of d, for example OWS Starella and OWS Cumulus which jointly attended the Lima station, the overestimation was less. Further discussion of the results is contained in Ref. 6.
SEVEN STOh~SI APRZL - flAY 19~5
5.--
g 8
RECORRECTING HISTORICAL WAVE H E I G H T DATA In view of the discrepancies between the spectral Hs and Hs(TD) there is a need to develop a method for correcting the historical data to the new standard. This is not entirely "straightforward because the correction processes are fundamentally different. In the spectral method the response correction function is applied to each spectral estimate and the corrected spectrum is summed to estimate the spectral moments m.. H s is then calculated as 4x~o~ In the TD method the uncorrected Hs is estimated and then a scalar correction is derived as the
170
Applied Ocean Research, 1991, VoL 13, No. 4
E
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o.
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Fig. 14. Comparison ofm'o correctedby the scalar method with the fidly-corrected m o
A new empirically-based correction procedure for shipborne wave recorder data: E. G. Pitt S E V [ t i StONESl FEgUARy -
Table 3. Comparisons between mofidly corrected and m o usbzg a scalar correction Io.
Station
Slope (Scalar: f u l l )
Correlation Coeff
OWS Lima
0.8948
0.9987
Seven Stones LV
0.8929
0.9997
Dowsing LV
0.9082
0.9967
Channel LV
0.8741
0.9988
the fully corrected values. Table 3 shows the results for all four vessels. Reference 6 contains further discussion. Here we report that calculations using simulated spectra and a response defined by equation (11) gave rather more scattered results, but with the same bias of about 11%. Since the only period parameter available in the historical TD data is the apparent value of Tz, we require a relationship between this and 7"1, the filtered or apparent or uncorrected value of Tl. Because the variety of spectral forms found in nature is so wide and the counting process used in the estimation of Tz(TD) so difficult to model, it was considered most practical to assume that Tz(TD) and T] were related by a simple scale factor and to determine this empirically. Table 4 gives the main results. In addition a numerical simulation was undertaken and this gave rather similar results. On the basis of the foregoing we are now in a position to formulate a correction equation for the historical Hs(TD) data:
Hs'(TD) Hs, = {x/Ssv x v/Q(f~)}
(13)
Where HsR is the corrected value of Hs Hs'(TD) is the uncorrected T D estimate of Hs Ssv is the empirical coefficient relating the scalar corrected tn; to the fully corrected mo 1
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Table 5 gives the slopes and correlations for the comparisons. Figure 16 shows the ratio of the new correction to the historical correction as a function of Tz. (The corrections for OWS Ctmnthts and Starella which jointly attended Ocean Weather Station Lhna were very similar).
C O M P A R I S O N WITH S A T E L L I T E DATA
This formula was used to recorrect the Hs(TD) data from the four ships and these were compared with Hs (spectral); the results for Seven Stones are shown in Fig. 15. Since Sse varies only slightly from ship to ship, the mean of the four values was used ie Ssv -- 0.8925 with standard deviation 0.014. ST'~ Tz is more problematical; for these data the value for each ship was used as appropriate. In general, however, the mean value is used.
A radar altimeter mounted on an orbiting satellite gives an estimate of Hs. The only satellite which has flown in recent years with this instrument is the US satellite Geosat, which gave estimates averaged over one second, seven kilometres apart, with an accuracy goal of 0.5 m rms or 10% whichever was greater. Dobson et a115 compared the estimates from Geosat with 116 measurements of Hs from the US National Data Buoy Center network. They found that the satellite estimates were on average about 0.4 m lower than the corresponding buoy values and that the difference between the two was independent of wave height. The maximum observed Hs in this comparison was only about 6 m, however. A more recent analysis by Srokosz 16, using more measurements
Table 4. Tz(TD)
Table 5.
Tz(TD) x ST'~ Tz where ST'~Tz is the empirical coefficient relating T1 from the uncorrected spectrum to Tz(TD).
Comparison between T I from the uncorrected spectra and Comparison between recorrected H s ( T D) and spectral Hs
Station
Slope (T'1: Tz)
Correlation Coeff
Station
Slope (lts• : fts(spectral))
Correlation Coeff
OWS Lima
1.0724
0.8951
OWS Lima
1.0482
0.9611
Seven Stones LV
1.0518
0.9183
Seven Stones LV
!.0026
0.9347
Dowsing LV
1.0076
0.9557
Dowsing LV
0.9903
0.9751
Channel LV
!.1262
0.8615
Channel LV
0.9505
0.9690
Applied Ocean Research, 1991, Vol. 13, No. 4
171
A new empirically-based correction procedure for shipborne wave recorder data: E. G. Pitt PRESSURE SENSOR DEPTH CORRECTION FUNCTIONS I
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from the network with values up to 9 m, gives a linear relationship, with the Geosat estimate around 0.87 that of the buoy value (and insignificant intercept). A comparison of data from Geosat (in 17-day repeat orbit) with SBWR measurements from OWS Lima is shown in Fig. 17 (Geosat's track passed within a few kilometres of the Ocean Weather Station; the SBWR values were obtained by linear interpolation of the values recorded every 1.5. hours). The offset of 0.4 m found by Dobson et al. and the relationship found by Srokosz are also shown. The data appear to agree reasonably well with Dobson's findings, but in fact, because of the poor statistics of the comparison (there are only 11 data pairs) either line would be an equally valid description. Moreover, if the SBWR values were recorrected using the historical method (leading to increases of the order of 5-10 %) these data too would be adequately described by either of the two lines. The new correction procedure produces large changes to the values of Hs from the Chamzel and Seven Stones LV's so that comparison with Geosat data should give clearer support for one or other correction method. Unfortunately, the SBWR in the Chmmel LV was not working on the few occasions that Geosat passed overhead (at 17-day intervals). Note also that even though its track missed Seven Stones by about 15 km the measurements from the satellite suggest sheltering by the Isles of Scilly, as can be clearly seen in Figs 18a and 18b,
+lV -50"N
2.08
.~"2.42 9 2.70 2.97 3.16 3.28 3.14 3.21 s e ~ VALUES 3.07 2.82 -~
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4.99
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Fig. 18. Chart o f the Scilly Isles showhlg Geostat and S B I V R measurenlents o f Hs
s
s S
.J ~
8-
6-
sr
9
----"
SrokosZ
4-
2-
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Fig. 17. Comparison o f S B W R and satellite althneter measurements of Hs at O W S Lima
172 Applied Ocean Research, 1991, Vo/. 13, No. 4
taken from Ref. 17. Notwithstanding these imponderables, we show on each figure the values of Hs estimated using the historical and the new correction procedures (the range of values given in Fig. 18b refer to measurements taken four hours before and two hours after the satellite transit). It will be seen that the LV values using the new procedure are in better agreement with the satellite values. Indeed, if the satellite values are increased by 0.4 m after Dobson et al. or increased by 13% as proposed by Srokosz the agreement is very good.
A new empirically-based correction procedure f o r shipborne wave recorder data: E. G. Pitt Table 6. Esthnatesof ttsSO (m)
Site
Approx position
Hss~ using historical correction
Hs5~ new correction
OWS Lima St Gowan LV 7 Stones LV 50~ 6~ Channel LV
57~ 20~ 51891765~ 14.5 50~ 3~
21.5 13.3 13.0 12.1
20.4 12,4 10% 10.4
Thus we conclude that where sufficient data exist they indicate that the use of the new correction procedure leads to values of Hs which agree better with satellite altimeter data than the use of the historical correction method.
C H A N G E S I N D E S I G N WAVE H E I G H T All the available wave data for the four principal SBWR stations in the Institute of Oceanographic Sciences wave climate study were reeorreeted using the new procedure and the values of Hs s~ the fifty-year value of significant wave height, were calculated. The magnitudes of the reductions in Hs s~ are shown in Table 6. This shows estimates provided by Carter x8 obtained by fitting the original and revised data to a Fisher-Tippett Type I distribution. For the two stations in the English Channel, Chmmel LV and Seven Stones LV the average reduction in wave height resulting from using the new correction procedure rather than the old is rather more than 20 %. However, the changes in the correction factors are strong functions of Tz (see Fig. 16), being greatest for the shorter period waves which are generally of lower height and least for long period waves among which the larger waves are to be found. The effect on the extrapolation process is such that the increase in the design wave height is less than the increase on the average wave height.
CONCLUSIONS By using a non-dimensional frequency sealing it has been shown that it is possible it reconcile the several experimental measurements of the frequency response of the SBWR which are available. The resulting response does not match the exponentia! form which has been used historically and so an empirical formula was developed to fit the experimental data. When applied to measurements of spectra made by SBWR instaIiations, the results are reasonable (with reference to a theoretical saturated spectrum) and the estimates of Hs and Tz derived from the spectra are consistent with independent spectrally-derived data. However, the spectral Hs differs from the Tucker-Draper estimate from the corresponding pen-chart record, Hs(TD), the latter being higher on average. For installations with comparatively deep pressure sensors, such as the Seven Stones LV, the differences are substantial, being 21% on average, with the shorter period (lower) waves being factors of two or more higher
Reduction in Hss~ 5% 7% 14%
in some cases. For installations with comparatively shallow pressure sensors, such as the Dowsing LV, the differences are small. At Ocean Weather Station //ma where the wave climate is such that there is a low incidence of short period waves, the differences are modest overall even though the pressure sensor depth is in the middle of the range. In view of these discrepancies, a method was devised for recorrecting the historical Hs(TD) data to the new standard. The results were compared with the corresponding spectrally-derived values and with independent data, notably those from the Geosat altimeter, and found to be satisfactory. To demonstrate the effect on the statistics of wave height, the available data from the principal stations in the IOS wave climate study were recorrected and the 50-year design values of Hs, Hs 5~ were estimated. The reduction brought about by the use of the new correction ranged from 10-15% for the English Channel s i t e s t o about 5 % for Ocean Weather Station Lima. For other analyses which put emphasis on the whole data set, for example fatigue calculations, the changes may also be significant.
ACKNOWLEDGEMENTS My thanks are due to J. A. Ewing for bringing the SS Cairndhu and the RV Ernest Holt response data to my attention; to D. J. T. Carter for help with the comparison between SBWR and Geosat altimeter measurements of Hs, and to S, Bacon for providing Fig. 16. Messrs. Bacon and Carter jointly undertook the computations to provide the information for Table 6. The research described in this paper was undertaken at the Institute of Oceanographic Sciences (Deacon Laboratory), Wormley, England and was supported financially by the United Kingdom Department of Energy. The preparation of this paper was supported by the UK Department of Energy.
REFERENCES ! 2 3
Tucker,M. J. A shipborne wave recorder, Transactions of the Royal Institute of Naval Architects, 1956,98, 236-250 Dept of Energy Offshore Installations: Guidance on design and construction, Part 11 Section 2: Enviromnental considerations, 1989 Haine, R. A. Second Generation Shipborne Ware Recorder Transducer Technology, Vol 2, 25-28, 1980
Applied Ocean Research, 1991, Vol. 13, No. 4
I73
A new empirically-based correction procedure f o r shipborne wave recorder data: E. G. Pitt 4
Crisp, G. N. An Experimental Comparison ofa Shipborne Ware Recorder and a IVaverider Buoy Conducted at the Channel Light Vessel, Institute of Oceanographic Sciences Report, No. 235
5
Tucker, M. J. The accuracy of wave measurements made with vertical accelerometers, Deep Sea Research, 5, 185-192 Pitt, E. G. The Application of Empirically Determined Frequency
6
11 12
Response Functibns to SBWR data, 7
8 9
10
174
Institute of Oceanographic Sciences Report, No. 259 Canham, H. J. S., Cartwright, D. E., Goodrich, G. J. and Hogben, N. Seakeeping trials on ocean weathership Weather Reporter. Transactions of the Royal Institute of Naval Architects, 104, 447-492. Van Aken, H. M. and Bonws E. Frequency response of a shipborne wave recorder, Proceeding of the International Symposium on lt~re Measurement and Analysis, 1974, 281-300 NPL. Report on Analysis of Ship Motion Trials Data for Cairndhu. National Physical Laboratory Coordinating Committee for Research into the Seagoing Qualities of Ships, Report No. 6 (Unpublished manuscript) NPL. Report on Analysis of Ship Motion Trails Datafor Ernest
Applied Ocean Research, 1991, Vol. 13, No. 4
13 14 15
16 17 18
Holt, National Physical Laboratory Coordinating Committee for Research into the Seagoing Qualities of Ships, Report No. 7 (Unpublished manuscript) Tucker, M. J. Analysis of records of sea waves, Proceedings of the Institute of Civil Engineers, 26, 305-316 Draper, L. The analysis and presentation of wave data-a plea for uniformity, Proceedings of the lOth Conference on Coastal Engineering, Vol. I, Tokyo, September, 1966 Bacon, S. Waves Recorded at the Dowsing Light Vessel 1970-1985, Institute of Oceanographic Sciences Report, No. 262 Tann, H. M. The Estimation of Ware Parametersfor the Design of Offshore Structures, Institute of Oceanographic Sciences Report, No. 23 Dobson, E. Monaldo, F, Goldhirsh, J. and Wilkerson, J. Validation of Geosat altimeter-derived wind speeds and significant wave heights using buoy data, John ttopkins APL Teeh. Digest, 8 (2), 222-233 Srokosz, M. Personal communication Bacon, S. and Carter, D. J. T. tihres Recorded at Seven Stones Light Vessel, 1962-1986, Institute of Oceanographic Sciences Report, No. 268 Carter, D.J.T. Personal communication