Table Of ContentElsevier Oceanography Series 24B
THE NORTHWEST
EUROPEAN SHELF SEAS
:
THE SEA BED AND THE
SEA IN MOTION
11. PHYSICAL AND CHEMICAL
OCEANOGRAPHY, AND PHYSICAL
RESOURCES
Edited by
F.T. BANNER, M.B. COLLINS and K.S. MASSIE
Department of Oceanography, University College of Swansea, Swansea, Great Britaiii
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V
Contributing Authors
R.J. BAILEY Exploration and Production Dept., BP Trading Ltd., Britannic House, Moor Lane, London,
EC2Y 9BU, U.K. (formerly: UCNW Marine Science Laboratories, Menai Bridge, North Wales)
F.T. BANNER Department of Oceanography, University College, Swansea, West Glamorgan, SA2 8PP, U.K.
and Department of Geology, University College London, Gower Street, London WClE 6BT,
U.K.
P. BISHOP Department of Geology, University College, Gower Street, London, WCl E 6BT, U.K.
K.F. BOWDEN Department of Oceanography, The University of Liverpool, Bedford St. North, P.O. Box 147,
Liverpool, L69 3BX, U.K.
D.J. BLUNDELL Department of Geology, Chelsea College, University of London, 27 1, King Street, London, W6
9L2, U.K.
J.D. BURTON Department of Oceanography, The University, Southampton, SO9 5NH, U.K.
V.N.D. CASTON British Petroleum Co. Ltd., Britannic House, Moor Lane, London, ECZY 9BU, U.K.
M.B. COLLINS Department of Oceanography, University College, Swansea SA2 8PP, West Glamorgan, U.K.
S.J. CULVER Department of Paleobiology, Smithsonian Institution, Washington, D.C. 20560, U.S.A. and
Department of Oceanography, University College, Swansea SA28PP, U.K.
M.R. DOBSON Department of Geology, University College of Wales, Aberystwyth, Cards, SY23 3DB, U.K.
L. DRAPER Marine Information and Advisory Service, Institute of Oceanographic Sciences, Brook Road.
Wormley, Godalming, Surrey, GUS SUB, U.K.
D. HAMILTON Department of Geology, Queen's Buildings, University Walk, University of Bristol, Bristol, BS8
ITR, U.K.
D.M. HAKDING Department of Forestry and Wood Science, University College of North Wales, Bangor,
Gwynedd, LL57 2UW, U.K.
D.A. HUNTLEY Department of Oceanography, Dalhousie University, Halifax, Nova Scotia, CANADA. (formerly
at the Institute of Coastal Oceanography and Tides, Bidston Observatory, Birkenhead, Cheshire,
L43 7RA, U.K.).
E.J.W. JONES Department of Geology, University College London, Gower Street, London, WCl E 6BT, U.K.
A.J. LEE Ministry of Agriculture, Fisheries and Food, Fisheries Laboratory, Lowestoft, Suffolk, NR33
OHT, U.K.
K.S. MASSIE Department of Oceanography, University College, Swansea SA2 8PP, West Glamorgan, U.K.
J. MAUCHLINE Scottish Marine Biological Association, Dunstaffnage Marine Research Laboratory, P.O. Box 3,
Oban, Argyll, Scotland, U.K.
R.D. PINGREE Institute of Oceanographic Sciences, Brook Road, Wormley, Godalming, Surrey, GU8 SUB,
U.K.
E.M. WILSON Department of Civil Engineering, The University, Salford, M5 4WT, U.K.
M.L. YOUNG Department of Oceanography, The University, Southampton, SO9 SNH,'U.K.
301
Chapter 9
Tides on the North-W est European Continental Shelf
D.A. HUNTLEY
Introduction shelf edge. Accurate measurement of mean sea level, on
the other hand, is proving important, particularly in
In this chapter we are primarily concerned with the detecting long term trends in tide and surge levels on the
tidal motion of the seas of the north-west European shelf.
continental shelf, the periodic ebb and flow of the water
in indirect response to the gravitational attraction of the
sun and moon. The first part of the chapter considers Observations
observational techniques for measuring both elevations
and currents in the tide, and discusses methods of pre- EarQ observations
dicting tidal elevation at individual stations. The suc-
ceeding sections then draw together the observations in- The earliest recorded observations of tides on the
to a coherent picture of tide propagation on the shelf. north-west European continental shelf seem to have been
For each of the main sea areas, early qualitative explana- made by Pytheas of Marseilles in about 320 B.C. Pytheas
tions of tidal motion are outlined, and the results of made a voyage of discovery in which he circumnavigated
more modem quantitative modelling techniques, general- the British Isles and he reported seeing tides which rose
ly based on computer simulation, are described. This is to a height of 120 ft. (36 m) on the coast of Britain, a
followed by a short section dealing with the highly gross overestimate typical of tidal observations even as
asymmetric tidal motion experienced in the shallow late as the 17th century. Pytheas also knew of the con-
waters of estuaries and tidal rivers. This section considers nection between the tides and the motion of the moon,
the methods of modelling tidal response in these impor- and the details of this connection were slowly unfolded
tant areas, where ports and towns are often situated and by other scholars during the following centuries. How-
where the tidal regime is likely to be modified by coastal ever, following the collapse of the Roman Empire, and
engineering. In a later section we depart from considera- extending into the 15th or 16th century, knowledge of
tion of strictly tidal phenomena to discuss the most com- tides, in common with other spheres of learning, became
mon source of error in predictions of tide levels, that dominated by philosophical speculation, often of a very
caused by the presence of storm surges, the abnormally obscure kind, generally about the origin of the tides.
high or low sea levels resulting from the action of atmo- Such speculation was usually unrelated to observations,
spheric pressures and winds on the sea surface. The sec- although the indications are that seamen were gaining
tion reviews the present understanding of the generation considerable unwritten knowledge of the movement of
and propagation of these surges on the shelf seas, and de- the tides. The outstanding exceptions to the lack of con-
scribes the techniques in use or being developed to pre- cern for observational accuracy in the writing of this
dict them from weather forecasts. Finally, in the last period are the works of the Venerable Bede (673-739).
section of the chapter, three areas of recent interest in Bede was a monk who wrote from Northumbria, on the
tidal research are discussed. Yielding of the solid earth in north-east coast of Britain, and, significantly, had impor-
response to tidal forces is now known to be surprisingly tant connections with the island-dwelling monastic com-
large and may have an important effect on the sea tides munity of Lindisfarne. In his works on tides, Bede shows
themselves. Internal tides, occurring in density stratified himself fully conversant with the sailor’s knowledge of
waters, may also be important, particularly close to the the sea, and is concerned to provide theories which ex-
plained the observations rather than indulge in philosoph- until 1640 that the first systematic observations of tides
ical speculation. He observed that ebbing tides usually for scientific purposes were made, by Jeremiah Horrocks
last longer than flood, an effect now known to be due to (1617?-1641). He studied the tides at Liverpool for
the propagation of tides in shallow water. Local knowl- about three months and was hoping to collect a full year
edge told him that both the passage of the moon and the of observations, but his early death prevented this and
tide were retarded by about 50 min every 24 hrs, and the records have not survived.
that although high water did not necessarily occur in During the 1650’s a Dorsetshire clergyman named
places with the same longitude as soon as the moon Joshua Childrey (1623-1670) compiled a compendium
reached the meridian or an identical interval afterwards, of natural phenomena which included records of ab-
nevertheless at any one place, high water always occurred normally high tides both in his own experience and from
when the moon was in the same place in the sky. This historical records. Deacon (1971) records some of the
observation, providing the “port establishment” of a correspondence which Childrey had with contemporary
place, formed an important part of tidal predictions right scientists from which it is clear that at least some scien-
up to the beginning of the present century. Bede was also tists at last recognised the importance of accurate obser-
aware of the ability of the wind to alter both the time vations in testing tidal hypotheses. In particular, Child-
and height of high water. When considering the overall rey’s observations lead him to challenge Wallis’s (1616-
flow of the tides around the British Isles, Bede made the 1703) theory that tides were caused by accelerations on
important observation that: the earth’s surface due to its rotation, on the grounds
“We know, we who live on the many-sided shore of that it did not explain the observed variation of tide
the British Sea, that when this sea begins to flow, inthe height with the time of the year, nor the importance of
same hour another will begin to ebb”. the wind. At the same time Sir Robert Moray (1608-
The conclusion was that tides were caused by move- 1673) was making tidal observations in the Western Isles
ment of water from place to place, though later writers of Scotland from which he was able to deduce that the
continued to develop explanations of the tides which re- ebb and flood,,of the tide and the monthly progression
quired changes in the total volume of water during a tidal of high tides were both nearly sinusoidal.
cycle. In an attempt to explain the tidal flow around the With the Restoration in England and the establish-
British Isles, Bede called attention to the common ob- ment of the Royal Society in 1662, the new move to-
servation that times of high water got progressively later wards accurate observation of the tides was given fresh
as one travelled southwards down the east coast of impetus. In 1666, at Wallis’s suggestion, the Royal Soci-
Britain. He deduced from this that tidal streams flowed ety asked Lord Brouncker to find tide observers on the
in from the “boundless northern sea”, dividing at the Thames, and asked Sir Robert Moray to draw up instruc-
north of Scotland and passing southwards down either tions for making observations both of the rate of ebb
side of Britain to meet again in the Solent, a deduction and flood and the variation of tide height. Wallis had en-
roughly correct for the North Sea, though not for the visaged observations of water height against a simple
western coast. vertical graduated pole, but Moray designed a complete-
Bede’s writings were widely circulated but it was not ly new type of tide measuring instrument as part of a
until the approach of the 13th century that science began tidal observatory, which, he suggested, should be built at
to move forward again and concentrated attempts were places with a large tidal range. Unfortunately Moray’s
made to record and explain the observed tides around plans were too ambitious for their time, and for the next
British shores. Gerald of Wales (c. 1 146-c. 1220) record- 160 years, although great progress was made in the theo-
ed observations of the tides in the Irish Sea, and found retical understanding of tidal motion in particular by the
that the tides on the Irish coast were ebbing as tides on publication of Newton’s “Principia” in 1687, and the
the opposite English coast were in flood, from which he work of French mathematicians, dominated by Laplace
deduced that there was a rocking motion of the tides in (1749-1827), tidal observations were still made by the
the Irish Sea. The earliest British tide tables also date ancient method of estimating mean water level against a
from this time. They forecast, in a very crude way, the vertical tide staff. Murdoch Mackenzie the elder (d. 1797)
times of high water at London Bridge and are credited to ruefully noted that, although the new theories might
John Wallingford, who died Abbot of St. Albansin 1213. delude the academics into thinking the problem solved,
Although the Renaissance produced important advan- the real motion of the water remained “as inexplicable
ces in the understanding of the motion of the Solar SYS- and as little known as ever”. ,
tem, a great gulf remained between the scientists and Nevertheless, with increasing overseas trading in the
those with first hand knowledge of the tides. It was not early part of the 19th century, the need for accurate tide
303
measurements became more pressing. On the suggestion is measured by a float, usually of wood, which is con-
of the Royal Society, Henry Palmer designed a self- nected to a counter-weight by a string running over a
recording tide gauge, based on the plans of Moray, and series of pulleys at the top of the well. In Moray’s orig-
published his design in 1831, the same year as Lubbock inal design the pulleys were used to drive dials which
published the first of an important series of papers on would be read to give the instantaneous water level. In
the prediction of tides. Palmer’s tide gauge enabled the Palmer’s self-recording gauge, the pulleys act through
complete shape of the tide elevation curve to be recorded, gearing to move a pen which records the tide elevation
in contrast to previous records of high and low water on a cylindrical drum of paper rotated at a known speed
only, and would operate unattended for long periods. by a clockwork motor. The basic components are shown
The first gauge was set up in London in 1828 and was diagrammatically in Fig. 9.1; Harris (1894-1908) gives a
quickly followed by others at Sheerness, Portsmouth, complete description of the design. Figure 9.2 is a typical
Plymouth and Bristol. The first volume of the Admiralty record, from the gauge in Alfred Dock, Liverpool, Eng
Tide Tables was published in 1833 using results from the land, and shows the variation in water level over a fort-
London, Sheerness, Portsmouth and Plymouth gauges. night. The paper has been removed from a drum which
With these developments, scientific development of tidal rotated once every 24 hrs, so that the predominantly
studies had at last begun. semi-diurnal tide, lagging by about 50 min in every 24
hrs, appears progressively displaced from day to day.
Measuring tide elevations The succession of tidal range from a large spring range to
a much smaller neap range is clear from this record.
The Palmer-Moray tide gauge is still the most impor- This gauge forms the pattern for most of the tide
tant instrument for measuring tide elevation on the shelf gauges now operating around the shelf sea coasts. Figure
seas. Its essential feature is a “stilling well”, a well reach- 9.3 shows the distribution of those tide gauges around
ing to below the level of low water. This well is con- the north-west European shelf sea coasts considered suf-
nected to the sea by a narrow orifice which serves to ficiently reliable to be used by the UNESCO Permanent
dampen the influence of short period surface waves while Service for Mean Sea Level, but there are many more tide
allowing the well level to follow accurately the long wells in use by local and port authorities. In some cases
period tidal movement; the basic principle, first suggested minor modifications to the original design are incorpo-
by Moray, has recently been studied in detail by Shipley rated. In some gauges, for example, the pen drive system
(1963) and Noye (1972). The level of water in the well is replaced by a digital recorder which records the in-
L
CYLINDRICAL
Fig. 9.2. A typical tide-well tide gauge record. Alfred Dock,
Fig. 9.1. Schematic diagram of a Palmer-Moray tide gauge. Liverpool, 22 May-5 June, 1963.
304
&
~ L E R W ~ C K
BERGEN
sTAvANEtJ
MALiN HEAD ESBJER
&
SCARBOROUGH
TERSCHELLING
0UBLiN.t
HARLINGEN
4 DELFZIJL
IJMUIDEN
LHOEK
VAN HOLLANO
BREST
Fig. 9.3. Locations of first class tide gauge stations on the continental shelf seas. The underlh-ed stations are those used in the Storm
Surge Flood Warning System in Great Britain.
stantaneous water level every fifteen minutes by punch- also in operation in the Thames estuary, where it is neces-
ing holes in paper tape which can then be read directly sary to guide tankers the SO miles (80 km) from the river
by a digital computer. This arrangement avoids the back- mouth to the principal oil refineries of the estuary
lash and friction errors associated with the mechanical (Balestrini, 1968; White, 1972). Radio telemetry is used
pen drive and also avoids the extra step of converting the to convey the instantaneous water levels measured by
analogue pen record into digital form manually before the tide gauges to the pilots navigating ships upriver.
computer processing. The first gauges using this method Although the Palmer-Moray tide gauge has proved
of recording have now been installed at Buckie (North satisfactory for neady 150 years, increases in ship
Scotland) and on the east coast of Britain at Lowestoft draughts and the interest in long-term measurements of
and Southend. A sophisticated system of tide gauges is mean sea level have made a reappraisal of tide gauge
305
accuracy necessary. Oil tankers with a draught of perhaps significant proportion of the mean depth. Edmund Halley
15 m are now expected to navigate channels with a clear- seems to have been the first person to make systematic
ance as small as 1 m and the increasing size and numbers observations of offshore tides, by soundings, as part of
of tankers are eroding this margin of error even further, the hydrographic surveys of the shelf seas begun in the
despite potentially disastrous consequences in the event second half of the 17th century. His chart of tides and
of an accident. In addition, long periods of tide gauge tidal streams in the English Channel was published in
records are being used to detect changes in mean sea 1701. Modern interest has centred on sea-bed mounted
level of fractions of a niillimetre/year. Against this back- pressure sensors whose output is generally recorded digi-
ground, Lennon (1967, 1968, 1971) has assessed the tally in a self-contained unit also placed on the sea bed.
relative importance of mechanical errors, siltation of the
well orifice, water density changes during a tidal cycle in
an estuary, “draw-down’’ due to tidal streams flowing
past the orifice and wave set-down and set-up, to the
total error of a Palmer-Moray type tide gauge, and he
estimates that the total error can be as large as 0.3 m for
a badly sited tide gauge. “Draw-down” due to rapid flow
past the well orificc has been further tested by laboratory
and field experiments by llalliwell and Perry (1968,
1969), who conclude that measurements in streams in
excess of 0.25 m/s are unacceptable.
In view of these potential inaccuracies, important
tide gauges, such as those shown in Fig. 9.3, are now
carefully chosen for their siting, and are checked at least
once a year by the van der Casteele test (Lennon, 1968),
which is capable of detecting and diagnosing sources of
error. New forms of tide gauge are also being developed.
Lennon (197 1) describes the current development of an
electronic version of the simple tide staff consisting of a
string of discrete electrodes coated with plastic so as to
form parallel plate capacitors with the sea water. The
i 2
instantaneous water level is measurcd to 2 cm every 50m
5a’ ROCK ALL
using an electronic unit mounted at the head of the staff, 0 .Sit es occupied to date with
position numbers
and electronic filtering should yicld the tide elevation to
t‘ Sites lo be OccupieE
0.1%.
Shore Dasd retorders
Another form of tidc gauge, much simpler to install relevant to this prcqramm
than the Palmer-Moray gauge, though somewhat less 200 m depth contour
accurate, is the bubbler gauge. In this gauge, gas from a 54
cylinder is blown down a flexible tube and bubbles out
of the open end, which is mounted below the low water
mark at a known datum level. For small rates of gas flow,
the pressure in the tube, measured by a mercury manom-
eter, depends on the pressure at the immersed end due to A
the water height above it, and, with suitable corrections
for water density, yields the water height itself. These
gauges are now being used at temporary coastal sites and LA CHAPtLLt BANK
1 I -1-
offshore drdling rigs in the shelf seas and are found to
give an accuracy of better than 1.5 cm (Pugh, 1972). Fig. 9.4. a. The Bidston Continental Shelf Tide Gauge ready to
be lowered onto sea bed. The central sphere contains the auto-
Measurement of tide elevation away from the coastal matic recording apparatus and the vertically rnrmnted cylinders
boundaries of the shelf seas is of considerable impor- are two different types of water pressure sensor. The complete
apparatus is about 1 m high. Froin Skinner and Rae (1973).
tance to a proper understanding of the propagation of
b. Geographical distribution of continental shelf tidal records.
tides (e.g., see Heaps, I969a), as well as for navigation in From Collar and Cartwright (1972). (Reprinted with permission
some of the shallow sea areas where the tidal range is a from DeepSea Research, 1972. Pergamon Press Ltd.)
306
A typical sea-bed module is shown in Fig. 9.4a. Sensor tides. Initially he hoped to find a simple relationship be-
stability (see, e.g., Skinner and Rae, 1973) and recovery tween high water times at different ports but in this he
of the modules after one month or more on the seabed failed, and had to be content with finding empirical con-
are the major development problems at present, but stants to predict the tides at each place. The basis of
records taken with an offshore gauge by Collar and Cart- Lubbock’s “non-harmonic” method was to predict the
Wright (1972) during a programme to make tide measure- times and heights of high and low water on the basis of
ments along the western edge of the European continen- astronomical variables such as the age of the moon and
tal shelf (Fig. 9.4b) show that accurate, low-noise records the declination and parallax of the moon and sun. Thus.
can be obtained in this way. for example, the height of high water was determined
from the mean high water height for the port by adding
Tide predictions successive corrections for the age, declination, parallax,
diurnal inequality and so on.
One of the main purposes of obtaining long records The “harmonic” method of tide prediction, which is
of tidal elevation at a point is to use the past records for now used for most ports of the shelf seas, and indeed of
the predxtion of future tides. In view of the generally the world, was developed by Sir W. Thomson (Lord
large and variable tides on the north-west European con- Kelvin) following the formation of a committee for the
tinental shelf it is perhaps not unexpected that most of purpose in 1867. The method was further developed by
the techniques for analysing and predicting tides were Sir George Darwin (1890), whose technique involved the
developed for these shelf seas. manual analysis of a year’s hourly heights. The basic
Surprisingly, prediction of tides was not attempted on premise of the harmonic method is that since, as Laplace
any scientific basis until the important work of Lubbock (1 799) had shown, the astronomical forces generating
in the 1830’s. Prior to this time, and even after it, tide the tides can be expressed as the sum of a series of con-
prediction was an obscure art, jealously guarded often as tinuous sine wave components of astronomically deter-
a family trade, a typical example being the Liverpool mined frequencies, the tide at a port must also contain
Tide Tables begun in 1770 by the Holden brothers and those same frequency components, though with ampli-
produced with very little modification right up until tudes and phases which will vary from place to place.
1924 (Rossiter, 1972b). Sir John William Lubbock, Tide records from a port are therefore analysed to obtain
sometime Vice-president and Treaurer of the Royal Soci- the amplitude and phase of the component sine waves at
ety, must be considered the founder of scientific predic- each astronomical frequency and the resulting sine
tion of tides for the shelf seas. His chief concern was the waves can readily be extrapolated to the future and sum-
reduction of large quantities of observational data into a med to predict the tide curve at future times.
manageable form from which he could predict future Laplace’s harmonic expansion of the astronomical
TABLE 9.1
Comparison of equilibrium and observed tide amplitudes and phases
(K = lag of the phase of the tidal constituent behind the phase of the corresponding equilibrium constituent at the place)
Darwin Period Equilib
Designation
~
Long Period
Mf 321h.84 2.03 2.35 243.4 2.29 231.1 3.11 18.0 1.95 85.6 2.10 10.5 2.59 207.6
Diurnal species
0, 25h.82 9.12 13.53 46.0 11.13 112.4 1.99 284.9 9.36 29.8 5.52 344.2 1.68 308.1
PI 24h.01 4.54 3.60 186.1 6.04 262.1 2.13 90.3 3.63 163.8 2.53 95.9 3.12 52.6
23h.93 13.69 11.31 201.9 16.28 281.4 5.12 82.3 10.61 116.1 1.65 104.5 10.58 51.6
Kl
Semidiurnal species
N2 1231.66 1.64 25.42 351.9 43.04 138.1 10.55 23.1 36.03 258.1 31.64 128.8 29.81 96.9
12h.42 8.53 130.18 19.1 230.0 161.1 65.65 52.4 118.82 282.6 169.13 143.0 153.01 122.4
M2
12h.00 3.98 44.53 16.2 16.12 210.4 16.18 114.5 59.13 319.1 60.26 198.3 55.66 154.6
s2
1 lh.91 1.08 12.28 53.0 21.95 208.8 4.39 116.8 18.04 311.3 11.28 196.1 16.46 153.5
K2
*Equilibrium tide elevations calculated for latitude 54”N.
307
tide generating potential was developed in detail by
Doodson (192 1) and has recently been updated by Cart-
Wright and Tayler (1971) and Cartwright and Edden
(1973). Doodson recognised the main astronomical peri-
ods as a lunar day. a lunar month, a year, the lunar
perigee period of 8.85 years, the period of regression of
lunar nodes, 18.61 years, and the period of solar perigee,
20,900 years. Tidal component frequencies are then lin-
ear combinations of the frequencies corresponding to
these periods, and divide into “species” centred around
0, 1 or 2 cycles per lunar day, and subdivide within each @
species into “groups”, differing by 1 cycle per month, LULL L L L
and “constituents”, differing by 1 cycle per year, with HOURS
further division by hyperfine splitting due to perigee and
nodal regression. Clearly a large number of terms are
generated this way, so that for analysis of real tides only
the most important frequencies are used. These are deter-
mined on the basis of their importance in the notional
“equilibrium tide”, a surface of constant gravitational
potential which the sea would take up on the surface of
the earth in the absence of inertia and of land masses.
Doodson found that about 400 terms were needed when
a limiting amplitude of times the largest term was
chosen, and he assumed that, although the amplitudes of
the frequency components in the real sea would differ
from the equilibrium amplitudes, nevertheless relative
amplitudes would be approximately comparable, so that
very small equilibrium Components would also be negli-
gible in real tides. Table 9.1 shows the leading constants
from Doodson’s expansion of the equilibrium tide, with
the observed amplitudes and phases at some typical shelf
sea ports added for comparison.
On the shallow shelf seas, tide curves are further com- 3
plicated by the presence of significant sine wave compo-
nents with frequencies which are sums and differences of Oislorted tides- Southampton
the basic astronomical frequencies. These additional Fig. 9.5. a. Typical tide gauge records for Southampton, showing
components are generated in shallow water by non-linear the double high water. b. Synthesis of the Southampton tide
curves from semi-diurnal and quarter-diurnal tide components.
interaction, due to friction forces at the sea bed and the
increased amplitude of the tide wave relative to the mean
water depth. An example of the effect of this shallow and sixth-diurnal terms to represent the shallow-water
water interaction can be seen at Southampton. In Fig. distortion. This technique, with a modification to allow
9.5a the typical tide curves for Southampton show the for the analysis of only 29 days of data(Doodson, 1954),
well-known double high water; in Fig. 9.5b the semi-di- forms the basis of most tide predictions carried out in
urnal component (A) is combined with a quarter-diurnal the British Isles. Early predictions were made by ana-
component (B), generated by non-linearity in (A), to lysing past tide records by hand and then synthesising
produce a double high water similar to that at South- future tides from the derived harmonic constants by
ampton (but see below). means of highly complex mechanical “tide-predicting
Doodson’s classic paper of 1928 proposes a complex machines” (Doodson and Warburg, 1941). These labori-
sequence of digital filtering to separate 60 pairs of har- ous procedures have now been superceded by the use of
monic constants (amplitude and phase) of chosen fre- digital computers, and Lennon (1965) describes the
quencies from a year of hourly observations of tide eleva- present computer-based analysis and prediction treat-
tion; the chosen frequencies include semi-, ter-, quarter- ment. The Institute of Oceanographic Sciences at Birken-
