Tide and Time – a history of tidal science in Liverpool

This short film, by Andy Lane, Andy Heath and Craig Corbett, is part of the Tide and Time exhibition at the National Oceanography Centre, Liverpool. The exhibition showcases two tidal prediction machines – the Roberts-Légé and the Doodson-Légé. The film also explores the history of tidal science in Liverpool and its development as a port.

Enjoy!

Finding the Amplitudes and Phases to use for the Bidston Tide Prediction Machines

Philip Woodworth, 23 May 2017

There is a lot of renewed interest in tide prediction machines and, after many years hidden away in storerooms, some of the machines made in the UK are on permanent display once again. Kelvin’s original 10-component machine is now part of the new Winton Gallery for Mathematics at the Science Museum in London alongside Ishiguro’s storm surge simulator. Two of the machines that were used at Bidston can now be seen at the National Oceanography Centre building in Brownlow Street in Liverpool.

As you may know from articles mentioned in the Resources section of this web site, the tide prediction machines were a way of simulating the tide in terms of its many harmonic components. Each component would be represented by an amplitude and phase lag, called the ‘harmonic constants’, and the machine, which can be considered as a sort of analogue computer, would be programmed to run by providing it with these constants. Of course, the constants would differ from port to port.

That raises the obvious question of where people like Arthur Doodson, and the other operators of the machines, got their constants from in the first place. This short article reviews the main characteristics of one of the machines (the so-called Doodson-Légé machine now on display at NOC) and then attempts to answer the question of how Doodson obtained the constants.

The Doodson-Légé Machine

The Doodson-Légé machine simulates the variations of the ocean tide by representing the tide as a combination of 42 constituents, each of which has a particular amplitude (h) and phase lag (g). The values of h and g are ‘programmed’ into the settings of the 42 wheels, and the nickel tape that wraps around and connects all the wheels serves to sum up all the constituents.

Figure 1. Some of the wheels of the Doodson-Légé Machine (from Doodson, 1951).

What are these constituents? Mathematically, the total tide htotal at time t can be expressed as a sum of many cosine series (one for each constituent). We can write this schematically as:

htotal(t) = i=1,…,42 hi cos(ωitgi)

where hi, gi and ωi are the amplitude, phase and angular speed of constituent i, and ωi = 2π / Ti with Ti its period. The periods of the 42 constituents correspond to the known main lunar and solar frequencies which contribute to the tide. Most of them have values around either 12 or 24 hours (semi-diurnal and diurnal tides), some have smaller values (shallow-water tides) and a few have values up to a year (the long period tides). The two largest constituents in many parts of the world, including Liverpool, are called:

M2, with a period of 12 h 24 min (the main semi-diurnal tide from the Moon with a period of half a lunar day) and

S2, with a period of 12 h (the main semi-diurnal tide from the Sun with a period of half a solar day).

At Liverpool, M2 and S2 have amplitudes of 3.13 and 1.01 m respectively. Because our day is 24 hours, the S2 tide will repeat itself twice a day exactly at the same time every day (shown in red below). M2 has a larger amplitude and repeats twice a lunar day (a little later each time) as shown in blue. They combine by ‘beating together’ to give a classic ‘semi-diurnal’ tide where M2 and S2 together result in a total tide that is larger and smaller over a fortnight, called spring and neap tides.

Figure 2.
Figure 3.

You can appreciate that simply by combining the separate contributions of these two constituents (M2 and S2), we already have a curve which starts to look something like the real tidal variation at Liverpool over a fortnight.

The fact that the tide can be parameterised this way, as a simple addition of harmonics (but many more than two), made it technically easy to invent machines such as the D-L machine that could sum them up. Some machines could handle 40 or more constituents. That was important in order to be able to handle the many smaller constituents that contribute to the tide (not just M2 and S2). Also, in other parts of the world, the total tide can have very different characteristics to that at Liverpool and so the machines needed to be able to handle their particular constituents. See Pugh and Woodworth (2014) for a discussion of why these different types of tide occur.

Obtaining the Harmonic Constants to give to the D-L Machine

As mentioned, the D-L machine has 42 wheels (or constituents), which means that we need 84 numbers to ‘programme’ it (i.e. the amplitude and phase for each constituent for the port in question). Once it has been set up correctly, then it can be run to predict the tide at the port for many years in the future (or past).

But how did Doodson know what these 84 numbers were in the first place?

The 84 numbers come from analysis of previous observations of the tide at the port using a tide gauge. Normally one year of data was adequate, with observations of the water level every hour (i.e. about 9000 values in a year). The team of people who worked with Doodson (called his ‘computers’) usually worked with values of water level in units of 1/10 of a foot and expressed as integers. There is a lot of arithmetic involved in this work and integers are much easier to deal with than real numbers.

His method of analysis of the hourly values made use of ingenious arithmetical filters designed to emphasise the importance of each constituent in turn and so, after a lot of work, arrive a set of estimates of amplitude and phase for all 42 that could be used to programme the machine. The work was very labour intensive, involving endless integer arithmetic by someone who could add up properly. Analysis of a year of data could take a ‘computer’ a few days or a week. The procedures are described in Doodson (1928) and Doodson and Warburg (1941) although be warned that a reader has to devote some hours to understand them.

Now, the people in those days before digital computers could not readily handle 9000 hourly water level values in most of their work, and it turns out that for Doodson’s tidal analysis it is not necessary, as long as the data is good quality. Doodson invented a set of filters which would convert the hourly information into daily numbers, which are just as useful for the tidal analysis, and have 24 times less the bulk of the original data.

For the semi-diurnal constituents these filters are called X2 and Y2 and are a set of simple integer arithmetic weights applied to the hourly values for each day. (They can be thought of as representing the real and imaginary parts of the variations. For people used to studying satellite altimeter data from space the outputs of the filters are akin to the aliasing that occurs in tidal lines using ‘repeat track’ data.)

The method they used was to list the hourly values from hours 0 to 23 each day on a page, one line for each day, and then have a cardboard cut-out with holes for the hours which had to be multiplied by a filter weight. These cut-outs were called stencils. The weight value itself was written on the cardboard, black for a positive weight and red for a negative weight.

Figure 4. An original cardboard filter for X2 showing holes to show through the hours with data that had to be multiplied either by positive (black) or negative (red) weights. There were many pieces of cardboard like this for many types of filter.

The X2 filter for a particular day used data for hours 0-23 on that day and also hours 24 to 28 (i.e. hours 0-4 on the next day), spanning 29 hours total. The integer weights were:

x2=[1,0,2,0,1,0,−2,0,−4,0,−2,0,2,0,4,0,2,0,−2,0,−4,0,−2,0,1,0,2,0,1,0,0,0]

Note the central value of the filter shown in red. The Y2 weights were (using hours 3-23 on the required day and 24-31 on the next day):

y2=[0,0,0,1,0,2,0,1,0,−2,0,−4,0,−2,0,2,0,4,0,2,0,−2,0,−4,0,−2,0,1,0,2,0,1]

Note that the central value is 3 hours different from that of X2. So the two filters sampled orthogonal (or real and imaginary) components of the semi-diurnal variation.

Figure 5. An original cardboard filter for Y2 showing holes to show through the hours with data that had to be multiplied either by positive (black) or negative (red) weights.

Nowadays, we can easily apply these filters to our example Liverpool data using a computer and the daily record of X2 and Y2 time series for Liverpool then look something like:

Figure 6.

You can see it has much the same information content as Figure 3 (i.e. variation over a fortnight and with two sets of amplitudes and phases) but with 24 times fewer numbers. The constant parts (the offsets) of the red and blue curves come from S2, because S2 is the same every day. And the cyclic parts come from M2, which varies over a fortnight. The red and blue offsets give the amplitude and phase of S2, and the amplitudes and phases of the cyclic parts give the amplitude and phase of M2.

So the first task of the ‘computer’ person was to calculate X2 and Y2 for each day (the work was done by hand of course, or sometimes with the novelty of an adding machine) and write the values for each day in a table with 12 columns (for 12 months of the year), with some columns having 29 rows, and some 30 rows. X2 (or Y2) values for days from the start to the end of the year (i.e. about 360 values) would be listed down column 1 first, then down column 2 etc. until the year was completed in column 12.

The second step is harder to describe but in fact is the most important. The X2 (or Y2) values in each of the columns of the 12 months in the first table were multiplied by different sets of integer weights to maximise the importance of the many different constituents with slightly different frequencies (called ‘daily multipliers’, see Table XV of Doodson, 1928). In addition, sums of the X2 (or Y2) values in each month, listed in each column of the first table, were multiplied by further several sets of integer weights for each month (called ‘monthly multipliers’, see Table XVI of Doodson, 1928). In our idealised example, after a lot of arithmetic, that readily leads to 4 numbers i.e. the 2 each we need for M2 and S2.

The different constituents with periods around 12 hours (other than M2 and S2) have names like 2N2, Mu2, N2, L2, K2 etc. (and it will be seen that they all have their own wheels on the machine). They will all contribute to the hourly water levels to make the total tide plot of hourly values more complicated (Figure 3), and also to contribute individually to the X2 and Y2 values (Figure 6). The results of the filtering in the second step, by means of the daily and monthly multipliers, produces values that have contributions in different amounts from each semi-diurnal constituent. Therefore, the information from the second step needs to be recombined, using linear combinations of each parameter in a process that Doodson called ‘Correction’, in order to provide information specific to each constituent. This was also labour intensive but it was straightforward once a clearly-defined procedure could be explained to a ‘computer’. The method is described in great detail in his 1928 paper with a worked example for Vancouver (which has some mistakes that do not matter).

Doodson then had all the amplitudes and phases that he needed to programme the machine. (In fact, the long-period tides were treated differently but they are not important for this note.) All the amplitudes and phases were written down on a special ‘constants card’ for the port in question which the machine operator would use whenever the machine was required for setting up for that port and year in the future; Figure 7a,b shows the front and reverse of an example card.

The top part of the first card shows amplitudes for each constituent in the order they appear on the machine for Hilbre Island for 1987 and 1988. The amplitudes are in metres and the lunar ones are slightly different each year because of the nodal variations (the ‘f’ factors). You can see the amplitudes for the solar constituents such as S2 are the same both years. The lower part of the card shows the values of frequency * amplitude for each year, with an overall scaling factor, which represents the rate of change of the constituent.

The amplitudes are programmed onto the shafts (also called ‘amplitude blocks’) for each wheel on the front of the machine using a Vernier screw, and the values of frequency * amplitude are programed similarly on the back of the machine (i.e. the machine is a ‘double sided’ one, in effect two separate machines, one for the heights and one for the rates). Finally the phases for each constituent, shown on the reverse of the card for each year (e.g. Figure 7b), are programmed onto the wheels at the front of the machine using the rotating dials. In order to rotate the dials, it is first necessary to release the associated clutch, remembering to tighten it up again before running the machine, otherwise the contribution of the particular constituent would not be included in the total tide. These phases are not phase lags (or they would be the same for both years) but are values of V+u-g, where ‘V’ is the astronomical argument for the start of the year, ‘u’ is the nodal correction, and ‘g’ is the phase lag. These can all be readily computed for each year once one knows ‘h’ and ‘g’, as explained above.

Figure 7(a).
Figure 7(b).

Was this Method of Doodson the Best or Easiest for Finding the Amplitudes and Phases?

The Doodson method described above was by no means the first. You can find many papers from the 19th century which have lists of amplitudes and phases for the various constituents computed in different ways (e.g. see Baird and Darwin, 1885).

For example, in the 19th century there had been methods:

  • The British Association method, as used by Kelvin, Roberts and Darwin. This was the method used by Roberts to determine amplitudes and phases with which to programme his earlier tide prediction machines.
  • Darwin’s own later method.
  • A method used by the US Coast and Geodetic Survey.
  • Börgen’s method in Germany.

The methods differed in the amount of labour involved, in how well they could eliminate the overlap of information from different constituents in the derivation of the amplitudes and phases, and in the completeness of the analysis. The BA method was the most arduous for the ‘computer’ person.

Doodson’s method was largely an extension, and more complete version, of that employed by Darwin many years before. As always with Doodson, it was devised with more than one eye on subsequent application of the tidal information for use by the prediction machines. Doodson was excellent at handling numbers (and, as important, in showing how his ‘computers’ could handle the numbers) and the method he devised, although complicated and long-winded, was perfectly adapted to routine working by people with basic mathematical skills.

Finally, we can refer to the work of Lord Kelvin (William Thomson), who not only invented the ‘Kelvin Machines’, as the Tide Prediction Machines (TPMs) like the Doodson machine were called, but also invented a mechanical analyser which he thought should be capable of the numerical tidal analysis described above. His prototype ‘tidal analyser’ allowed for determining 5 constituents and a later one allowed for 11. The 5 constituent machine can be seen at Glasgow University, while the 11 constituent machine is in the Science Museum, and both are described by Hughes (2005).

However, Kelvin’s analysers were not successful and so hand-calculated computations of the Darwin and Doodson type were needed for many years. Nowadays, all the tidal analysis of a year of data can be performed in a split second on a modern computer using methods that have many similarities to those of Doodson (see Pugh and Woodworth, 2014).

Acknowledgements

Valerie Doodson and Ian Vassie are thanked for comments on a first draft of this article.

References

Baird, A.W. and Darwin, G.H. 1885. Results of the harmonic analysis of tidal observations. Philosophical Transactions of the Royal Society, 34, 135-207.

Doodson, A.T. 1928. The analysis of tidal observations. Philosophical Transactions of the Royal Society, A 227, 223-279.

Doodson, A.T. 1951. New tide-prediction machines. International Hydrographic Review, 28(2), 88-91 and 6 plates.

Doodson, A.T. and Warburg, H.D. 1941. Admiralty Manual of Tides, His Majesty’s Stationery Office, 270pp.

Hughes, P. 2005. A study in the development of primitive and modern tide tables. PhD Thesis, Liverpool John Moores University.

Pugh, D.T. and Woodworth, P.L. 2014. Sea-level science: Understanding tides, surges, tsunamis and mean sea-level changes. Cambridge: Cambridge University Press. ISBN 9781107028197. 408pp.

Tide & Time Exhibition opens

The Tide & Time Exhibition  is now open to the public.

The exhibition – at the National Oceanography Centre in Liverpool – showcases some of the fascinating achievements made in the Liverpool area in understanding and predicting the tides. The highlights of the exhibition are the rare Roberts-Légé and Doodson-Légé tide prediction machines, extraordinary analogue computers that calculate the rise and fall of the ocean tide. See these beautifully intricate machines up and running at the only place in the world where you can see two of them together.

Bidston Observatory was the home of the Roberts-Légé and Doodson-Légé tide prediction machines while they were still in use. The machines are now owned by National Museums Liverpool, who have carefully restored them to working condition.

Tide & Time is open to the public once a month (usually the first Tuesday of each month from 15:00 to 16:00) or by special arrangement for group visits and events. See this page for information on planning your visit and how to book.

The exhibition will also be open to the public during LightNight Liverpool on Friday 19th May 2017 from 17:00 to 22:00.

The Doodson-Légé machine in the 1990s in the reception area of the Proudman Oceanographic Laboratory. The machine is now on display at the National Oceanography Centre in Liverpool.

 

Earth Tides and Ocean Tide Loading

Trevor F. Baker, 2 November 2016

Research on Earth tides and ocean tide loading has an even longer history at Bidston Observatory than the work on ocean tides. This article gives a brief overview of the developments in these research areas following the measurements at Bidston in 1909 by John Milne, with particular emphasis on the contributions of the research groups at Bidston to the advances in these topics.

Introduction.

Most people are aware of tides in the oceans, but are surprised to hear that there are also tides in the solid Earth. Figure 1 shows the gravitational tidal forces caused by the moon (the tidal forces caused by the sun are just under half of those from the moon). The ocean tides have a complicated spatial distribution because the oceans respond dynamically to these forces. In the case of the solid Earth, to a first approximation there is nearly a static response to these forces. Therefore the simple picture of two tidal bulges, one towards the moon (sun) and one opposite to the moon (sun) is appropriate for the Earth tide. Following the work of Kelvin and G. H. Darwin in the late nineteenth century, it is known that the response is mainly elastic and that the average rigidity of the Earth is similar to steel. The combined lunar and solar tidal deformation of the Earth is up to 40 centimetres in range at the Earth’s surface in low to mid-latitudes. The Earth tide in an Earth without any oceans is usually called the Earth’s body tide.

Figure 1. The gravitational tidal forces on the Earth caused by the moon, which is on the right of the figure.
Figure 1. The gravitational tidal forces on the Earth caused by the moon, which is on the right of the figure.

In addition, the weight of the ocean tides deforms the solid Earth, giving a time varying deformation as the surface mass of the ocean tides moves around the Earth. This is usually called the ocean tide loading deformation. The Earth’s body tide and the ocean tide loading can be decomposed into the same set of tidal frequencies. The spatial distribution of the ocean tide loading is however more complicated, not only because of the spatial variations of the ocean tides, but also because both the near field ocean tides and the far field ocean tides have an effect at any given point. For example, for the principal lunar tidal harmonic M2 (with a period of 12.42 hours) the vertical displacement of the Earth’s surface reaches maximum amplitudes of 4 to 5 cm. in some areas (e.g. south-west UK, north-east Brazil and Central America). On the continents, it only decreases slowly with distance from the coast reaching typically 1 cm. at distances of the order of 500 to 1000 km. from the ocean.

From the point of view of solid Earth geophysics, the main interest in measuring the tidal deformations of the Earth is to determine the Earth’s rheology as a function of depth. The tidal frequencies are very well known and offer the opportunity to measure the response of the Earth at lower frequencies than those involved in seismology. The body tide gives important information on the lower mantle and the Earth’s liquid core. The ocean tide loading, since it involves shorter wavelengths on the Earth’s surface, gives new information on the upper mantle. The main challenges in this research are to make accurate measurements and to use accurate ocean tide models. Although the displacements mentioned above are fairly large, it has only in relatively recent years that advances in space geodesy have enabled useful direct measurements of these displacements. For most of the past century the main technique that was used for these measurements was using very sensitive tiltmeters. Later, sensitive strainmeters became available and from the 1950s onwards sensitive relative gravimeters began to be used for tidal work.

For anyone requiring more detailed information on the above, the review articles by Baker (1984), Harrison (1985), Zuern (1997) and Agnew (2015) are recommended.

Early Measurements of Ocean Tide Loading at Bidston.

John Milne was born in Liverpool in 1850 and is often called the father of modern seismology. From 1875-1895 he was a professor in Japan, where he was involved in the design and building of seismographs for the study of Japanese earthquakes. He was the inventor of the horizontal pendulum seismograph. In 1895, he returned to England and lived at Shide on the Isle of Wight where he installed a seismic observatory He set up 7 seismic observatories in England, including in the cellar at Bidston and then went on to set up a global seismic network. After discussions with G. H. Darwin concerning ocean tide loading, Milne and his Japanese assistant, Hirota, brought a horizontal pendulum seismometer to Bidston in 1909, specifically to measure tidal loading, in collaboration with the Director, W. E. Plummer. The horizontal pendulum was set up in order to measure the tilt in the north-south direction. The results were published in Nature (Milne, 1910) and clearly show the tilt down towards the Irish Sea (1.5 miles away) at high tide:-

“The buildings in towns along sea-boards twice a day are tilted seawards. When the tide flows out these movements are reversed. The deflection of the pendulum by tidal load and attraction, although greater than might be expected, is, however, very small. At Bidston it is about 0.2’’, or 1 inch in 16 miles.”

New tidal tilt observations were made in the Bidston cellar in the 1930s. Doodson and Corkan (1934) used a Milne-Shaw seismometer for one month of observations. In 1934, funds were used from a Cambridge mathematics prize that was awarded to Proudman to purchase a new Milne-Shaw seismometer. Beginning in March 1935, one year of observations of the north-south tilt were made using this instrument (Corkan, 1939).

After the second world war, from 1947-1955, Professor Rudolf Tomaschek from Germany worked in the UK at the Anglo-Iranian Oil Company (now BP) in collaboration with the University of Cambridge. He established a tilt and tidal gravity measuring station in the ICI salt mine at Winsford in Cheshire. During this period, he was a regular visitor at Bidston Observatory. At Winsford, he used 2 Tomaschek-Schaffernicht horizontal pendulum tiltmeters (T1 and T2), which were constructed in 1937 and operated previously at Berchtesgaden in Germany. He also designed a smaller horizontal pendulum (P1) which was built in Cambridge in 1950. For the tidal gravity measurements at Winsford, he made visual observations using a Frost gravimeter for 8 days and he also made similar measurements at a few other UK sites. The quoted accuracy for these tidal gravity measurements was of the order of+/- 4% in amplitude. After Tomaschek returned to Germany, his horizontal pendulums were modified and used by the Bidston research group in the research described below.

Geoff Lennon made further observations of the north-south tilt at Bidston using the Milne-Shaw seismometer between 1952 and1954. For the International Geophysical Year 1957-1958 there were increased efforts to make observations of Earth tides around the world. In the Bidston cellar, modified Milne-Shaw seismometers were used to measure the tilts in both the north-south and east-west directions from July 1957 to December 1958 (Lennon, 1959). During the IGY, Slichter’s group at the University of California Los Angeles (UCLA) made tidal gravity measurements at various sites around the world using the newly available Lacoste and Romberg ET (Earth Tide) continuously recording gravimeters. Bidston was one of the chosen sites and the gravimeter was installed by Chris Harrison.

Large Systematic Errors in Tidal Tilt Measurements.

During the 1960s and 1970s there was a large expansion in the number of sites around the world measuring Earth tides, particularly tidal tilt. This usually involved adapting and using a tunnel in a disused mine, but Askania also developed a two component vertical pendulum for use in boreholes. In 1969, Lennon and Vanicek set up a site for measuring tilt in a disused lead mine near Llanrwst in North Wales, 20 km. from the Irish Sea. This was at a depth of 41 metres and was less affected by temperature changes than the Bidston cellar and therefore was more suitable for geophysical investigations. The Bidston cellar provided a useful test site for comparing various tiltmeters, before installation in the tunnel at Llanrwst (Figure 2 shows one day of the record from the Askania vertical pendulum tiltmeter installed in the Bidston cellar in 1971). The various tidal tilt measurements around the world were giving conflicting results between sites several kilometres apart and were also proving difficult to understand using available Earth models. These problems led to the development of several types of tiltmeter and many efforts to check the calibrations of the tiltmeters. What was difficult to understand was that, although anomalous results were very common, the sensitivity and quality of the tilt records were extremely good. The tiltmeters have typical resolutions of 0.2 msec of arc (i.e. less than one ten millionth of a degree) and the signal to noise ratios are similar to a coastal tide gauge.

Figure 2. The north-south and east-west tidal tilts recorded in the Bidston cellar in 1971 using the Askania vertical pendulum tiltmeter. The off-sets are calibrations, which were made automatically by displacing small masses on the pendulum. At high tide in the eastern Irish Sea, the tilt at Bidston is down towards the Irish Sea with an amplitude of about 100 milliseconds of arc.
Figure 2. The north-south and east-west tidal tilts recorded in the Bidston cellar in 1971 using the Askania vertical pendulum tiltmeter. The off-sets are calibrations, which were made automatically by displacing small masses on the pendulum. At high tide in the eastern Irish Sea, the tilt at Bidston is down towards the Irish Sea with an amplitude of about 100 milliseconds of arc.

The results from the various tiltmeters at different positions within the Bidston cellar had already shown some anomalies of up to 20%. However, the problem became much clearer with the new tilt measurements at Llanrwst. The Tomaschek horizontal pendulums T1 and T2 were set up in the centre of the tunnel and operated continuously for 2 years (1969-1971). The Askania vertical pendulum tiltmeter was fixed to the rock wall approximately 15 metres along the tunnel from the horizontal pendulums. For M2, it gave results in reasonable agreement with the horizontal pendulums in the azimuth of the tunnel. However, in the azimuth across the tunnel the Askania M2 amplitude was about 40% lower. It was clear that the cavity itself was causing the problem with the tilt measurements. A pair of papers in Nature suggested that strain-tilt coupling due to the cavity was causing all the problems with tidal tilt measurements around the world (King and Bilham, 1973; Baker and Lennon, 1973). The tidal strain field causes additional local tilting around the cavity itself, the exact amount depending on the detailed geometry and elastic constants. Thus, the basic problem is not with the tiltmeters themselves, but with the local situation of the instrument. Any type of tiltmeter faithfully records the tilt signal at that point. The problem is that it is simultaneously measuring the tidal tilt and some combinations of the components of the tidal strain field. This neatly explains why there are anomalies, but still high quality tilt records. Further observations at Llanrwst are discussed in Baker (1980a). These show that even in the centre of the tunnel the M2 tilt amplitude can differ by 5% for positions only 50 cm. apart.

In 1972, W. E. Farrell (CIRES, University of Colorado, USA) published a seminal paper which, for the first time, showed how to compute the deformations due to surface mass loading on a spherical, radially stratified, gravitating, elastic Earth model. In 1973, I successfully applied to Chris Harrison and Bill Farrell for a Visiting Fellowship at CIRES in Boulder, Colorado and during a sabbatical from 1973-4, I made tidal loading computations for the British Isles, in order to further interpret our tidal tilt and tidal gravity observations. Model computations of ocean tide loading tilt (and strain) were used to show that an observation accuracy of about 1% is required in order to improve existing models of the crust and upper mantle derived from seismology (Baker, 1980a). There is no way that this accuracy can be guaranteed if there are unknown local strain-tilt coupling effects on the instrument. During the 1970s, there were many efforts by groups around the world investigating these strain-tilt coupling problems. It was soon realised that further strain-tilt coupling arises from the topography and from lateral variations in geology. The University of Cambridge, Department of Geodesy and Geophysics, research group showed that strainmeters in tunnels also gave anomalous tidal results, sometimes up to 30-40% in amplitude, caused by strain-strain coupling. With the difficulties of making accurate tidal measurements in tunnels, some groups turned their efforts to borehole tilt measurements. When these also started to give some anomalous tidal results, these were also abandoned. Eventually, 10 or so years after the developments of 1973, most tidal tilt and tidal strain activities around the world were abandoned. Some borehole tilt and strain measurements and long baselength tiltmeter (e.g. water tube tiltmeter) and strainmeter measurements still continue on volcanoes and in earthquake fault zones, but the emphasis is now on longer term changes in tilt or strain before or after events rather than on tidal work. Recently, Pugh, Woodworth and Bos (2011) measured lake tides in Loch Ness, in Scotland, using sub-surface pressure gauges and found that M2 had amplitudes of approximately 1.5 mm. The loch is effectively a 35 km. long tiltmeter and they found good agreement with ocean tide loading models.

Tidal Gravity Measurements in Britain.

Fortunately, the Bidston research group had 2 new LaCoste and Romberg ET gravimeters ET13 and ET15 and the research efforts began to be focussed more on these instruments as the problems with tidal tilt became increasingly apparent. After initial measurements in the Bidston cellar, a project to measure tidal gravity at other sites in Britain was undertaken between 1972 and 1975 (Baker, 1980b). The observations were made for 2 to 4 months at each site and for most of the measurements, a recording sensitivity of 2.5 cm. per microgal was used (1 microgal = one millionth of a cm/sec/sec or approximately one billionth of g, the acceleration of gravity at the Earth’s surface; the tidal gravity amplitude is typically 100 microgals). From 1971-1972, John Kuo from Columbia University, New York, had a sabbatical at the University of Cambridge. He used a Geodynamics TRG-1 gravimeter to make tidal gravity measurements at Cambridge. The gravimeter was then used to make measurements at Bidston and Herstmonceux.

Figure 3. The right hand side shows the observed M2 ocean tide loading and attraction using tidal gravimeters, together with the contours of the amplitudes from model computations using early ocean and shelf tide models (Baker, 1980b). On the left are the M2 vertical displacement amplitudes computed with a modern ocean tide model.
Figure 3. The right hand side shows the observed M2 ocean tide loading and attraction using tidal gravimeters, together with the contours of the amplitudes from model computations using early ocean and shelf tide models (Baker, 1980b). On the left are the M2 vertical displacement amplitudes computed with a modern ocean tide model.

Figure 3 (right hand side) shows the observed M2 ocean tide loading amplitudes at each site (the M2 tidal gravity on an Earth without oceans has been removed from the observations). It can be seen that the observed M2 ocean tide loading is a maximum of 12.4 microgals at Redruth in Cornwall and a minimum of 0.5 microgals at Bidston. The observed M2 amplitude is 6.0 microgals at Taunton, in Somerset, and the whole of the south-west of England is tilting downwards towards the Atlantic, when the ocean tides are high off the south-west of England. The contours show the M2 ocean tide loading computed for an elastic Earth model (Baker, 1980b). For the global oceans, the M2 ocean tide model of Hendershott and Munk was used and for the seas around the British Isles, the Bidston shelf tide model of Roger Flather was used for the loading input on the Earth. It can be seen that away from the large tidal loading in the south-west of Britain, the M2 loading decreases to zero under the Irish Sea, in the eastern English Channel and off the north-east of Scotland. In these three areas, the local M2 sea tides are in anti-phase with the loading from the Atlantic Ocean to the south-west of Britain and the loads cancel. Although there is a complicated spatial variation of the M2 loading around Britain, the tidal gravity observations are in good agreement with the model computations. The left hand side of Figure 3 shows the M2 ocean tide loading vertical displacements for Europe computed using a modern global ocean tide model (a finite element ocean tide model from the Toulouse group). It can be seen that there is a very similar spatial variation around Britain to that found from the earlier tidal gravity work. The relationship between gravity variations and vertical displacement is between 2 and 3 microgals per cm. The gravity variation also has a component from the vertical gravitational attraction of the ocean tide, which affects the relationship between gravity variation and displacement.

Tidal Gravity Measurements Worldwide.

In the early 1980s, there were major controversies internationally concerning the interpretation of the large number (about 300) of tidal gravity observations that had been made around the world. The M2 and O1(period 25.82 hours) results for the tidal gravity stations that were available in the databank of International Centre for Earth Tides (ICET), were corrected for ocean tide loading and attraction using the latest global ocean tide model (the Schwiderski one degree model). The results were given in terms of the M2 and O1 gravimetric factors, where the gravimetric factor is the ratio between the observed tidal amplitude and the amplitude of M2 or O1 on an undeformable Earth without oceans (i.e. the vertical component of the tide generating force). The problem was that the corrected gravimetric factors were totally inconsistent with the new body tide model of John Wahr (University of Colorado, USA). Even on the continents, at large distances from the oceans, the corrected gravimetric factors were typically between 1% and 4% larger than the Wahr model. As well as the overall offset, the 4% scatter was hard to explain. Some papers attributed the scatter to the effects of lateral heterogeneities in Earth structure and a correlation with heat flow measurements was suggested. These important discrepancies were a major challenge, which we decided to investigate with our LaCoste and Romberg ET gravimeters.

One obvious problem was that the majority of tidal gravity measurements had continued to be made with astatized gravimeters in the deflection mode e.g. LaCoste and Romberg G and D gravimeters and Geodynamics gravimeters. Astatized gravimeters use a mass on a spring, where the winding of the spring and the geometry are designed in order to give a high mechanical amplification of the movement of the mass. A tidal change in gravity gives a deflection of the mass, which is detected electronically using a capacitance transducer. The first problem is that the deflection sensitivity (millivolts per microgal) is time varying, because it is affected by environmental tilts of the gravimeter. The second problem is that the response of the spring in the astatized gravimeter is affected by hysteresis. This makes it difficult to determine the sensitivity accurately and also gives an amplitude response that differs between the tidal bands and also significant phase lags at tidal frequencies. For these reasons, Lucien LaCoste always said that these instruments should not be used in deflection mode and this was the reason that he designed the ET gravimeters, where the mass is continuously nulled by feedback, so that the spring does not change its length.

In the tidal gravity work in Britain described above, our LaCoste and Romberg gravimeters had the LaCoste mechanical servos in which the signal from the capacitance transducer is used to turn the measuring screw and continuously keep the mass in the same position. We found that being mechanical, the system had breakdowns fairly often, which made it difficult to obtain the required continuous records of several months duration. It was therefore decided to change ET13 and 15 to electrostatic feedback. On the recommendation of Walter Zuern from the Black Forest Observatory in Germany, we asked Jerry Larson of Maryland Instrumentation, USA, to build electrostatic feedback systems for our ET gravimeters. He had successfully built feedback systems for the important UCLA ET gravimeter station at the South Pole and ET19 at the Black Forest Observatory.

LaCoste and Romberg gave a measuring screw calibration factor for ET gravimeters with a quoted accuracy of 0.1%. However, comparing ET13 and ET15 at Bidston (Baker, 1980b) had shown that they gave results differing by 0.5% in amplitude. Before making any new observations, it was therefore decided to calibrate the measuring screws ourselves. About 85% of the signal recorded by a tidal gravimeter is just the vertical component of the astronomical tidal force and therefore accuracies of the order of 0.1% are required for investigating the body tide deformation component or the ocean tide loading. The ET gravimeters were taken to the vertical calibration line in the fire escape of a 19 storey building at the University of Hannover, which had been established by Wolfgang Torge and colleagues. This solved the discrepancy in the manufacturer’s calibration factors (it later turned out that other LaCoste ET gravimeters also had discrepancies of up to about 1%). Our ET gravimeters were then used to make a profile of measurements across Europe (Baker, Edge and Jeffries, 1989, 1991). Continuous tidal gravity data were obtained for a few months at Brussels, Bad Homburg (Germany), Zurich and Chur in Switzerland. In Europe, the O1 tidal harmonic is particularly useful for testing the body tide models, because the ocean tide loading and attraction correction is very small (less than 0.4% of O1). The Schwiderski global ocean tide models augmented with the Flather tidal model on the European shelf were used for the loading and attraction model computations. The corrected observations were used to test the Dehant-Wahr elastic and anelastic body tide models. For both M2 and O1 the agreements with the body tide models are of the order of 0.1% in amplitude and 0.1 degrees in phase. This was the first time in tidal gravity that accuracies of 0.1% had been achieved and this is a factor of 10, or more, improvement over previous tidal gravity measurements. The measurements in Brussels showed that the ‘standard’ O1 amplitude at Brussels was 1.2% too high. This ‘standard’ O1 amplitude in Brussels had been used to normalise the calibrations of many of the tidal gravimeters before they were used around the world and this led to the bias in the International Centre for Earth Tides databank discussed above. Our profile of observations from Brussels to the Alps in Switzerland showed that in this area at the 0.1% level there is no dependence of the gravimetric factors on lateral changes in Earth structure or correlations with heat flow. The only reasonable explanations that are left for the scatter of the earlier gravimetric factors are the problems of astatized gravimeters without feedback discussed above.

From the mid-1980s onwards, superconducting gravimeters (SGs) developed by the GWR company in the USA, began to be deployed at a few sites around the world. In these instruments, instead of a test mass on a spring in the usual relative gravimeters, the test mass is a superconducting sphere supported by the force gradient of the magnetic field generated by a pair of superconducting current carrying coils. Again the mass is kept in a fixed position using an electrostatic feedback force. These instruments have very high signal to noise ratios and the drift rates are very small, which makes them very suitable for measuring the long period tides. The SGs were not calibrated and the user had to provide their own calibration of millivolts per microgal. This was usually done by recording in parallel with a spring gravimeter and therefore the accuracy was no better than the spring gravimeter. Later, parallel recording with an early generation of absolute gravimeters was used to provide a calibration. In the late 1990s, parallel recording for several days with the new Micro-g LaCoste FG5 absolute gravimeter began to be used to provide calibrations accurate to 0.1%. A global network of observatories with superconducting gravimeters was set up and from 1997 coordinated under the Global Geodynamics Project (GGP) run by David Crossley (University of St. Louis, USA) and Jacques Hinderer (University of Strasbourg, France).

Baker and Bos (2003) computed the O1 and M2 ocean tide loading and attraction at 15 GGP stations using the 10 latest ocean tide models. The model results were then used to correct the observations at each station in order to test the Dehant, Defraigne and Wahr body tide models. At most of the European and global stations the corrected observations agreed with the models at the 0.1% level, thus verifying the conclusions of our work with spring gravimeters described above. The notable exceptions were discrepancies of order 0.3% at Metsahovi (Finland), Esashi (Japan) and Wuhan (China). Later tests at these stations confirmed that the discrepancies were due to calibration errors, rather lateral heterogeneities in Earth structure. The O1 results in Europe, for both spring gravimeters and SGs, give phase lags of the order of a few hundredths of a degree. At this stage, it is not yet clear whether this is a phase lag in the Earth’s body gravity tide or remaining errors in the determinations of the phase lags in the gravimeters.

Baker and Bos (2003) also used the GGP results, together with our LaCoste ET measurements in Wuhan (China) and Curitiba (Brazil), to assess the different ocean tide models that were available. The earlier model of Schwiderski was shown to have errors in several areas. The FES series of ocean tide models have significant errors in the western Pacific as shown by the tidal gravity observations in China, Japan and Australia. In contrast, Bos, Baker, Rothing and Plag (2002) used tidal gravity measurements on Spitzbergen to show that the FES99 ocean tide model gave an excellent fit to the gravity results and was even better than the regional Arctic Ocean tidal models.

GPS Measurements of Ocean Tide Loading.

Baker, Curtis and Dodson (1995) used GPS observations near the Newlyn tide gauge to show that GPS had reached the stage where it could be used to measure ocean tide loading displacements. Over the years, GPS improved even further and long continuous GPS time series became available for a very large number of sites around the world. At the same time, the global ocean tide models continued to improve substantially as more satellite altimetry data became available. These two developments gave the opportunity to re-visit the ocean tide loading investigations by using direct measurements of the tidal displacements. A project with the University of Newcastle to take advantage of these developments was successfully completed. Bos, Penna, Baker and Clarke (2015) used continuous GPS observations from stations in western Europe with 3 to 6 years of data between 2007 and 2013. Kinematic precise point positioning was used to measure the M2 ocean tide loading displacements at 259 sites covering the area from the north of Scotland to southern Spain and from western France to Switzerland and Germany. The high spatial density of the GPS results showed an excellent spatial coherency for the observed M2 vertical loading amplitudes and phases across Europe and the accuracies are about 0.2 mm. These measurement accuracies, together with the accuracy of the ocean tide model loading input onto the Earth, made it possible, for the first time, to investigate the Earth models of the crust and upper mantle. The research shows clear evidence that there is anelastic dispersion in the asthenosphere (depths from 80 to 220 km.) which gives a reduction in the shear modulus of 8-10% at tidal frequencies compared to seismic frequencies. This dispersion in the asthenosphere can be represented by a frequency independent Q from seismic to tidal frequencies, with Q = 80.

Ocean Tide Loading Corrections for Geodetic Measurements.

The models of the Earth’s body tides and ocean tide loading discussed above are also required for make corrections to precise geodetic measurements that are being used to determine longer term crustal movements. These can be tectonic movements or the movements associated with rebound or subsidence following the melting of the major ice sheets. In the 1990s, we started a collaborative project with the University of Nottingham to make continuous GPS measurements near UK tide gauges, together with absolute gravity measurements using the new FG5 absolute gravimeter. These measurements are required for separating the vertical crustal movements at tide gauges from the long term changes in mean sea levels (Teferle, Bingley, Williams, Baker and Dodson, 2006; Williams, Baker and Jeffries, 2001). This work was funded by NERC and the flood defence agencies (MAFF, DEFRA and the Enviroment Agency). We are also collaborating with the NERC Satellite Laser Ranging (SLR) facility at Herstmonceux to make absolute gravity measurement in parallel with the SLR and continuous GPS measurements. The absolute gravimeter works on the principle of measuring the positions of a falling mass in a vacuum using a laser interferometer and has an accuracy of about 1 to 2 microgals. Figure 4 shows 24 hours of observations with the FG5 at Paul, near Newlyn. All corrections have been applied except the corrections for ocean tide loading and attraction. The very clear signal with an amplitude of about 20 microgals shows the large ocean tide loading and attraction in the south-west of England (see Figure 3). Loading due to storm surges also causes deformations over a wide area, which have to be taken into account e.g. a 1.5 metre storm surge on the east coast of England causes Liverpool to be displaced downwards by about 1 cm.

Figure 4. 24 hours of absolute gravity observations for a site near Newlyn in the south-west of England using the Micro-g LaCoste FG5-103 absolute gravimeter. The large signal with an amplitude of about 20 microgals is the ocean tide loading and attraction (see also Figure 3). This is corrected at the next stage of data processing.
Figure 4. 24 hours of absolute gravity observations for a site near Newlyn in the south-west of England using the Micro-g LaCoste FG5-103 absolute gravimeter. The large signal with an amplitude of about 20 microgals is the ocean tide loading and attraction (see also Figure 3). This is corrected at the next stage of data processing.

References

  • Agnew, D. C. (2015), Earth Tides, in Treatise on Geophysics, G. Schubert (ed), Second Edition, Vol. 3, 151-178, Elsevier
  • Baker, T. F. (1980a), Tidal tilt at Llanrwst, North Wales: Tidal loading and Earth structure, Geophys. J. R. astr. Soc., 62, 269-290.
  • Baker, T. F. (1980b), Tidal gravity in Britain: tidal loading and the spatial distribution of the marine tide, Geophys. J. R. astr. Soc., 62, 249-267.
  • Baker, T. F., (1984), Tidal deformations of the Earth, Sci. Prog. Oxf., 69, 197-233.
  • Baker, T. F. and M. S. Bos (2003), Validating Earth and ocean tide models using tidal gravity measurements, Geophys. J. Int., 152(2), 468-485.
  • Baker, T. F., D.J. Curtis and A. H. Dodson (1995), Ocean tide loading and GPS, GPS World, 6(3), March 1995, 54-59.
  • Baker, T. F., R. J. Edge and G. Jeffries (1989), European tidal gravity: animproved agreement between observations and models, Geophys. Res. Lett., 16, 1109-1112.
  • Baker, T. F., R. J. Edge and G. Jeffries (1991), Tidal gravity and ocean tide loading in Europe, Geophys. J. Int., 107, 1-11.
  • Baker, T. F. and G. W. Lennon (1973), Tidal tilt anomalies, Nature, 243, 75-76.
  • Bos, M. S., T. F. Baker, K. Rothing and H.-P. Plag (2002), Testing ocean tide models in the Nordic Seas with tidal gravity observations, Geophys. J. Int., 150, 687-694.
  • Bos, M. S., N. T. Penna, T. F. Baker and P. J. Clarke (2015), Ocean tide loading displacements in western Europe: 2. GPS-observed anelastic dispersion in the asthenosphere, J. Geophys. Res. Solid Earth, 120, doi:10.1002/2015JB011884.
  • Corkan, R. H., (1939), The analysis of tilt records at Bidston, Monthly Not. R. astr. Soc. Geophys. Suppl., 4(7), 481-497.
  • Doodson, A. T. and R. H. Corkan (1934), Load tilt and body tilt at Bidston, Monthly Not. R. astr. Soc. Geophys. Suppl., 3(6), 203-212.
  • Harrison, J. C. (1985), Earth Tides. In Benchmark Papers in Geology Series, pp 419. Van Nostrand Reinhold, New York.
  • King, G. C. P. and R. Bilham (1973), Tidal tilt measurements in Europe, Nature, 243, 74-75.
  • Lennon, G. W. (1959), A report on the progress of work on IGY tilt observations at Bidston, Proceedings of the Third International Symposium on Earth Tides, Trieste, 1959.
  • Milne, J. (1910), Surface deformation and the tides, Nature, 82 (2102), 427.
  • Pugh, D.T., P. L. Woodworth and M. S. Bos (2011), Lunar tides in Loch Ness, Scotland, J. Geophys. Res., 116, C11040, doi:10.1029/2011JC007411.
  • Teferle, F. N., R. M. Bingley, S, D. P. Williams, T. F. Baker and A. H. Dodson (2006), Using continuous GPS and absolute gravity to separate vertical land movements and changes in sea-level at tide gauges in the UK., Phil. Trans. Soc. A, 364, 917-930.
  • Williams, S. D. P., T. F. Baker and G. Jeffries (2001), Absolute gravity measurements at UK tide gauges, Geophys. Res. Lett., 28, 2317-2320.
  • Zurn, W. (1997), Earth tide observations and interpretation. In Wilhelm, H., Zurn, W, and Wenzel, H-G. (eds)., Tidal Phenomena, pp. 77-94, Springer-Verlag, Berlin.
Figure 5. Graham Jeffries (left), Trevor Baker (right) and Machiel Bos (centre). Machiel came from the Netherlands to Bidston from 1996-2000 to do his PhD. on research into ocean tide loading. He now works at the University Beira Interior, Portugal and has continued to collaborate with Bidston/NOC on various projects.
Figure 5. Graham Jeffries (left), Trevor Baker (right) and Machiel Bos (centre). Machiel came from the Netherlands to Bidston from 1996-2000 to do his PhD. on research into ocean tide loading. He now works at the University Beira Interior, Portugal and has continued to collaborate with Bidston/NOC on various projects.

Bidston recollections

John Huthnance, 7 Oct 2016.

I joined IOS Bidston (as it was then) in October 1977. The validity of my appointment could be questioned as the appointment letter came from DB Crowder (the Bidston administrator) who left before I arrived.

It was a good time to join. There were about 80 staff in total, few enough to give a “family” atmosphere with the feeling that everyone knew everyone else. Several colleagues had been taken on during the early 1970s but it was still a time of expansion rather than otherwise.   Scientists like myself had a fairly free hand to pursue promising lines of research within a fairly broad remit. I enjoyed a feeling of support from fellow scientists to do just this. Much of the funding came through a consortium of several government departments with an interest in our research. The negotiations were at some distance from most of the scientists who did not have to spend much time writing proposals, yet it was good to know of “user” interest in our work, always a characteristic of Bidston science. It was still possible to be “the” expert in a topic, a rarity today. I was lucky.

Everyone was expected to go to sea at least once. My first experience was a long trip in October 1978 on RRS Discovery from South Shields to Recife (Brasil)! We had calm across the Bay of Biscay but gradually increasing seas as time progressed. Green terminal screens on board added to my discomfort. It also got hot enough to affect some of the electronics and the salinometer bath struggled to maintain any standard temperature. My struggles with the latter resulted in being one of many co-authors on a paper about steric height around the equator – as I discovered when the paper was published.

My next research “cruise” was less exotic, to the North Sea on RRS John Murray. The picture shows the arrangement for under-way surface sampling – a CTD (device for measuring the conductivity and temperature of sea water at a known depth) in a bucket lashed to the side.

Arrangement for under-way surface sampling
Arrangement for under-way surface sampling

I have seen some changes in the “style” of research – some for the better! In the 1980s John Bowman (Chief Executive of NERC) told us that if we wanted students, we should get a university job. Now student supervision is encouraged (and helped by being in Liverpool). When I started, current meter data processing typically involved printing out all the recorded values. Models were semi-analytic or had reduced dimension or coarse resolution. My thesis compared a few tidal harmonic constants between measurements and a simple model. Now we have millions of observed values, billions of model output values, and we need computer programs to translate these to something viewable. In the end, science wants to compare two independent numbers for the same quantity. With the “Big Data” that modern science generates, is it harder to think what we are aiming at?

 

North Sea Project - monthly surveys
North Sea Project – monthly surveys

Another change is towards “inter-disciplinary science”. I have been a believer in this owing to early good experience: a seminar at Bidston by John Allen (University of Reading) about sand transport gave me an idea for how sand banks might grow (I had already published about the character of tidal flow around the Norfolk sand banks). The “flip” side to inter-disciplinarity is the overhead of communication with a wider group of scientists. Anyway, Bidston (now Proudman Oceanographic Laboratory – POL) saw this in a big way in NERC’s first “Community Project”, the North Sea Project (formally 1987-1992). John Howarth and I were respectively coordinators of the monthly “surveys” (see figure) and intervening “process studies” for 15 months in 1988-89. I recall a “spat” with Philip Radford (PML) at the concluding 1993 Royal Society Discussion meeting. I showed a diagram characterised by physics-ecosystem. Philip countered with physics-ecosystem. These are of course quite compatible, differing only by which part is under the microscope.

The North Sea Project was followed by the “Land-Ocean Interaction Study” LOIS in the 1990s with POL at the centre of coastal, shelf-edge and modelling studies. Such large-scale projects with many participants involved a Steering group and many rail trips to London. At the same time (and possibly inspired by NERC) the EU Marine Science and Technology Programme (MAST) began. My main involvement was in “Processes in Regions of Freshwater Influence” (PROFILE; two phases), “Ocean Margin Exchange” (OMEX; two phases) – both inter-disciplinary – and “Monitoring Atlantic Inflow to the Arctic” (MAIA) which somehow managed to be only physics. MAST projects had several European partners; the beaten track became the M56 for Manchester airport and flights to partners’ laboratories, EU Brussels and MAST gatherings in rather nice places (e.g. Sorrento, Vigo, . . ).

After formation of Southampton Oceanography Centre SOC, there was an April 1st announcement setting up the “Centre for Coastal Marine Science” CCMS in the mid-1990s as a counterpart to SOC. CCMS incorporated PML, POL and SAMS and resulted in more trekking, to Plymouth and Oban. This was good for inter-lab communications but management went awry, especially regarding finances, and POL became “independent” again (within NERC) in 2001. 2001 was also the year of design for the new building for POL in Liverpool (pictured). There were several reasons for unhappiness about this; building down to a price, inevitable open-plan offices (being cheaper and set by Swindon precedent), more time and expense of commuting for most staff. I had the “joy” being project “sponsor”. In building procurement this does not mean having the money but rather liaison between the “owner” (NERC with the money) and the design team. I was in the architect’s Birmingham offices on “9/11”.

POL's new building in Liverpool
POL’s new building in Liverpool

After more than a year’s delay on completing the Liverpool building, we finally left Bidston at the beginning of December 2004.

Tidal Curiosities – The Whirlpool of Corryvreckan

Judith Wolf, 1 Sep 2016.

Most people know that the tide rises and falls periodically at the coast but not everyone is as aware of the periodic flood and ebb of tidal currents. These are of particular importance for mariners and need to be taken into account for navigation. Where currents become particularly strong, they can become known as a ‘tidal race’, which can be unnavigable at certain states of the tide.

Around the coast of the British Isles are many locations where a tidal race forms, usually in a constricted channel between two islands or an island and the mainland. In Scotland, between the islands of Jura and Scarba is the famous ‘Whirlpool of Corryvreckan’ – possibly the third largest whirlpool in the world (after Saltstraumen and Moskstraumen, off the coast of Norway). The Gulf of Corryvreckan, also called the Strait of Corryvreckan, is a narrow strait between the islands of Jura and Scarba, in Argyll and Bute, off the west coast of mainland Scotland.

Corryvreckan, between the islands of Jura and Scarba
Corryvreckan, between the islands of Jura and Scarba

The name ‘Corryvreckan’ probably derives from two words ‘Coire’ which in Irish means cauldron and ‘Breccán’ or ‘Breacan’, which may be a proper noun i.e. the name of an individual called Breccán, although this has also been translated as ‘speckled’ from the adjective brecc ‘spotted, speckled’ etc. combined with the suffix of place – an.

There is an Old Irish text known as Cormac’s Glossary written by the King and Bishop of Cashel, Cormac mac Cuilennáin who died in the year 908. The text is written in the form of a dictionary combined with an encyclopaedia. In it are various attempts at providing explanations, meanings and the significances of various words. At entry 323 it provides probably the fullest description of the Coire Breccáin of the early Irish material:

‘a great whirlpool which is between Ireland and Scotland to the north, in the meeting of various seas, viz., the sea which encompasses Ireland at the north-west, and the sea which encompasses Scotland at the north-east, and the sea to the south between Ireland and Scotland. They whirl around like moulding compasses, each of them taking the place of the other, like the paddles… of a millwheel, until they are sucked into the depths so that the cauldron remains with its mouth wide open; and it would suck even the whole of Ireland into its yawning gullet. It vomits iterum {again & again} that draught up, so that its thunderous eructation and its bursting and its roaring are heard among the clouds, like the steam boiling of a cauldron of fire.’

Corryvreckan Whirlpool, photo by Russ Baum, CC BY-SA 2.0
Corryvreckan Whirlpool, photo by Russ Baum, CC BY-SA 2.0.
https://commons.wikimedia.org/w/index.php?curid=2720206
Corryvreckan Whirlpool, photo by Walter Baxter
Corryvreckan Whirlpool, photo by Walter Baxter, CC BY-SA 2.0.
https://commons.wikimedia.org/w/index.php?curid=33579199

Corryvreckan is also very close to the island of Iona, famous for St Columba, and some of the tales about the whirlpool relate to this saint and his companions, praying to be spared from falling into it, while sailing from Ireland. In one story St Columba is supposed to have encountered and recognised the bones of one Brecan, supposed to have drowned in the whirlpool with his ship and crew, years before. However, there is some dispute as to whether the location of this event was off Scotland or in another whirlpool off northern Ireland.

More recently, in mid-August 1947, the author George Orwell nearly drowned in the Corryvreckan whirlpool. Orwell had fled the distractions of London in April 1947 and taken up temporary residence to write on the isolated island of Jura. On the return leg of a boating daytrip, Orwell seems to have misread the local tide tables and steered into rough seas that drove his boat near to the whirlpool. When the boat’s small engine suddenly sheared off from its mounts and dropped into the sea, Orwell’s party resorted to oars and was saved from drowning only when the whirlpool began to recede and the group managed to paddle to a rocky outcrop about a mile off the Jura coastline. The boat capsized as the group tried to disembark, leaving Orwell, his two companions, and his three-year-old son stranded on the uninhabited outcrop with no supplies or means of escape. They were rescued only when passing lobstermen noticed a fire the party had lit in an effort to keep warm. Orwell’s one-legged brother-in-law Bill Dunn was reputedly the first person to swim across the 300ft deep, mile-wide channel. Nowadays there are regular boat trips and diving trips for tourists.

As the flood tide enters the narrow area between the islands of Jura and Scarba it speeds up to 8.5 knots (>4m/s) and meets a variety of underwater seabed features including a deep hole and a pyramid-shaped basalt pinnacle that rises from depths of 70 m to 29 m at its rounded top. These features combine to create eddies, standing waves and a variety of other surface effects. Flood tides and inflow from the Firth of Lorne to the west can drive the waters of Corryvreckan into waves of more than 30 feet, and the roar of the resulting whirlpool can be heard ten miles away.

Image from Hebridean Wild website
Image from Hebridean Wild website.
http://www.hebridean-wild.co.uk/about.html

Although dangerous when the flood or ebb tide is running and particularly when the wind is blowing ‘against the tide’ (when choppy seas make it very dangerous), it can be safely crossed at slack water when the weather is calm. This is where accurate tidal predictions come into their own, to identify the safe passage times of slack water, although detailed modelling of these areas of complex bathymetry is still a challenge.

Tide and Storm Surge Modelling at Bidston Observatory

Philip L. Woodworth, 4 August 2016.

One of the main objectives of the research at Bidston Observatory was to understand more about the dynamics of the ocean tides, that is to say, the physical reasons for why the tide propagates through the ocean as it is observed to do. Before the advent of digital computers, the only way to approach these questions was from basic mathematical perspectives, in which eminent scientists such as Pierre-Simon Laplace in France excelled in the 19th century, and in which Joseph Proudman at Bidston was an acknowledged expert in the 20th century.

Similarly, there has always been considerable interest in the reasons for large non-tidal changes in sea level, including in particular those which occur due to the ‘storm surges’ generated by strong winds and low air pressures in winter. For example, following the Thames floods of January 1928, Arthur Doodson at Bidston chaired a committee for London County Council that undertook a detailed study of the reasons for the storm surge that caused the flooding, and made recommendations for protecting the city in the future.

These areas of research were revolutionised in the mid-20th century, stimulated by public concerns following the major floods and loss of life in East Anglia in 1953 (Figure 1c,d), and finally made possible by the availability of modern computers in the 1960s. An important person in using computers in this work at Bidston was Norman Heaps, who joined the staff in 1962 and was eventually joined by a group of ‘modellers’ and ‘student modellers’ including Roger Flather, Judith Wolf, Eric Jones, David Prandle and Roger Proctor.

(As a digression, we may also mention the attempted simulation in this period of storm surges using electronic circuits, in effect analogue computers, by Shizuo Ishiguro, the father of the novelist Kazuo Ishiguro, at the Institute of Oceanographic Science at Wormley in Surrey. These devices were made redundant by digital computers. Ishiguro’s equipment can be seen at the Science Museum in London.)

Computer modelling of the tides has many similarities to the modelling of storm surges. In both cases, there are external forces involved: gravitational due to the Moon and Sun in the case of the tides, and meteorological (winds and air pressure changes) in the case of storm surges. These forces are exerted on the water surface inducing currents and redistributing volumes of water.

So the first thing a modeller has to know is how much the forces are. These are provided from astronomy in the case of the tides, and from meteorology for storm surges (e.g. information from the Met Office). In the case of the 1953 storm surge, the effect of the wind can be appreciated from Figure 1(a) which shows a deep depression crossing from west to east and strong winds from the north pushing water into the southern part of the North Sea. The winds are especially important in this case: their force is determined by the ‘wind stress’, which is proportional to the square of the wind speed, and the dynamics are such that a greater surge occurs when wind stress divided by water depth is maximum. In other words, bigger surges occur in shallower waters, such as those of the southern North Sea or the German Bight.

Figure 1. Images from the 1953 North Sea storm surge that resulted in over 2500 fatalities, mostly in the Netherlands and eastern England. (a) Meteorological chart for 1 February 1953 (0 hr GMT) with the track of the storm centre shown by black dots in 12-hour steps from 30 January (0 hr) to 1 February (0 hr); (b) maximum computed surge throughout the area (cm); (c) flooding at Sea Palling on the Norfolk coast of England; (d) the Thames Barrier, an example of the considerable investment in coastal protection in the United Kingdom and Netherlands following the 1953 storm. For image credits, see Pugh and Woodworth (2014).
Figure 1. Images from the 1953 North Sea storm surge that resulted in over 2500 fatalities, mostly in the Netherlands and eastern England. (a) Meteorological chart for 1 February 1953 (0 hr GMT) with the track of the storm centre shown by black dots in 12-hour steps from 30 January (0 hr) to 1 February (0 hr); (b) maximum computed surge throughout the area (cm); (c) flooding at Sea Palling on the Norfolk coast of England; (d) the Thames Barrier, an example of the considerable investment in coastal protection in the United Kingdom and Netherlands following the 1953 storm. For image credits, see Pugh and Woodworth (2014).

The next problem is to determine what the impact of these forces is, and for that the computer solves sets of mathematical equations at each point on a grid distributed across the ocean (e.g. Figure 2); these equations are in fact the same ones that Proudman and others used but could not be applied in this way at the time. The output of the models consists of long records of sea level changes and of currents at all points in the grid: as an example, Figure 1(b) provides a map of the maximum resulting surge during the 1953 storm surge event. Layers of ‘nested models’ enable very detailed information to be provided to coastal users in particular localities.

Figure 2. The grid used for the numerical surge model employed in the current UK operational surge forecasting system. Only a section of the grid is shown to give an impression of model resolution and matching of a finite-difference grid to a coastline. The complete grid covers the entire northwest European continental shelf from 40° to 63° N and eastwards of 20° W. The model is forced by winds and air pressures covering the entire North Atlantic and Europe on a 0.11° grid indicated by dots. From Pugh and Woodworth (2014).
Figure 2. The grid used for the numerical surge model employed in the current UK operational surge forecasting system. Only a section of the grid is shown to give an impression of model resolution and matching of a finite-difference grid to a coastline. The complete grid covers the entire northwest European continental shelf from 40° to 63° N and eastwards of 20° W. The model is forced by winds and air pressures covering the entire North Atlantic and Europe on a 0.11° grid indicated by dots. From Pugh and Woodworth (2014).

As Figure 1 demonstrates, surge modelling is particularly important to people who live at the coast. The Met Office can provide data sets of winds and air pressures up to 5 days ahead, which can be used to force the computer models. And, because the models can thankfully run faster than ‘real-time’, they can provide forecasts of what the likely magnitudes of storm surges will be several days ahead, enabling flood warnings to be issued. In the case of London, the operational warnings can be used to decide whether or not to close the Thames Barrier (Figure 1d).

These forecast techniques, developed at Bidston by Norman Heaps, Roger Flather and others, were first used operationally at the Met Office in 1978, and successor models, which are conceptually the same, are still used there, providing warnings to the Environment Agency. Similar schemes have been adopted by other agencies around the world. Storm surge models developed at Bidston have also been applied to areas such as the Bay of Bengal where surges can be considerably larger than around the UK and where there has been a large loss of life on many occasions.

Modelling at Bidston later developed into studying the 3-dimensional changes in the ocean that result in the transport of sediments or pollutants (‘water quality modelling’) or that have impacts on ecosystems. Modelling has also been applied to topics such as the safety of offshore structures and renewable energy. The same sort of computer modelling is now used throughout environmental science. For example, the models that the Met Office uses for weather forecasting, or the Hadley Centre uses to predict future climate use the same principle of solving physical equations on a grid.

But every modeller knows that their model provides only an approximate representation of the real world, and to help the model along there is sometimes a need to include real measurements into the model scheme, in order to constrain the mathematical solutions on the grid. These are called ‘assimilation models’, of which forecast weather models are the most obvious examples.

This enables us to return to tide modelling. Scientists at Bidston developed many regional models of the ocean tide for engineering applications as well as scientific research. These models tended to have ‘open boundaries’ where the region of the model grid meets the wider ocean. In these cases, it is normal to prescribe ‘boundary conditions’ which specify the tide at the boundary, and which are in effect a form of data assimilation. However, if one wants to make a tide model for a large region or for the whole ocean, with no boundaries, it was found that there were problems with obtaining acceptable results, as the assumptions which go into the computer codes were not universally applicable or missed some aspects of the tidal dynamics. Assimilation of sea level measurements by tide gauges and from space by radar satellites provided a solution to these problems.

In the last decade, a number of excellent parameterisations of the global ocean tide have become available. Some of these parameterisations are based purely on measurements from space (e.g. Figure 3), others are based on computer tide models that make use of only the known dynamics, and others are hybrid models that employ data assimilation. The two latter schemes provide information on tidal currents as well as tidal elevations. All three techniques are in agreement to within 1-2 cm which is a superb achievement. Proudman could never have dreamed of knowing the tide around the world so well, and it is thanks to him and others at Bidston leading the way that we now have an understanding of why the tide is so complicated.

Figure 3. Co-tidal chart of the M2 ocean tide: global map of lines joining places where high tides for M2 occur simultaneously, and places with equal tidal range. The lines indicate Greenwich phase lag every 30°, a lag of zero degrees being shown by the bold line, and the arrows showing the direction of propagation. The colours show amplitudes. Map provided by Richard Ray (Goddard Space Flight Center) for Pugh and Woodworth (2014).
Figure 3. Co-tidal chart of the M2 ocean tide: global map of lines joining places where high tides for M2 occur simultaneously, and places with equal tidal range. The lines indicate Greenwich phase lag every 30°, a lag of zero degrees being shown by the bold line, and the arrows showing the direction of propagation. The colours show amplitudes. Map provided by Richard Ray (Goddard Space Flight Center) for Pugh and Woodworth (2014).

The tide and surge models we have described above are usually operated in 2-dimensional mode (i.e. with the currents at each point in the grid taken as averages through the water column), and such model codes are relatively straightforward to construct and fast to run. A big change since the early days of the 1960s that first saw their construction is that modellers nowadays tend not to write their own codes, but instead adapt sophisticated modelling code packages written by others. This enables them to construct the 3-dimensional models of much greater complexity that are now used in research.

Numerical computer modellers now comprise one of the largest groups of scientists in oceanography laboratories such as the National Oceanography Centre in Liverpool (the successor of Bidston Observatory). Their models provide a way to make maximum use of oceanographic measurements from ships, satellites and robotic instruments in the ocean (and the ocean is a big place and there are never enough measurements) and a way to forecast how conditions in the ocean might evolve. It is inevitable that oceanography and many other aspects of science will rely on modelling more in the future.

 

Some References for More Information

  • Cartwright, D.E. 1999. Tides: a scientific history. Cambridge University Press: Cambridge. 292pp.
  • Heaps, N.S. 1967. Storm surges. In, Volume 5, Oceanography and Marine Biology: an Annual Review, edited by H.Barnes, Allen & Unwin, London, pp.11-47.
  • Murty, T. S., Flather, R. A. and Henry, R. F. 1986. The storm surge problem in the Bay of Bengal. Progress in Oceanography, 16, 195–233, doi:10.1016/0079-6611(86)90039-X.
  • Pugh, D.T. and Woodworth, P.L. 2014. Sea-level science: Understanding tides, surges, tsunamis and mean sea-level changes. Cambridge: Cambridge University Press. ISBN 9781107028197. 408pp.
  • Stammer, D. and 26 others. 2014. Accuracy assessment of global barotropic ocean tide models. Reviews of Geophysics, 52, 243-282, doi:10.1002/2014RG000450.
  • Wolf, J. and Flather, R.A. 2005. Modelling waves and surges during the 1953 storm. Philosophical Transactions of the Royal Society, A, 363, 1359–1375, doi:10.1098/rsta.2005.1572.

Tide Gauges and Bidston Observatory

Philip L. Woodworth, 4 August 2016.

Everyone knows that the level of the sea goes up and down. Most of these changes in level are due to the ocean tide (at Liverpool the level changes due to the tide by more than 8 metres at ‘spring tides’), but changes of several metres can also occur due to ‘storm surges’ that occur during bad weather, while slow changes in level can take place due to climate change and because of the geology of the adjacent land.

Changes in sea level are measured by devices called ‘tide gauges’: the more suitable name of ‘sea level recorders’ has never been widely adopted in the UK although Americans often call them ‘water level recorders’. There are as many types of tide gauge such as:

Vertical scales fixed to a jetty or dock entrance.

These were simple ‘rulers’ (sometimes called ‘tide poles’ or ‘tide boards’), by means of which the sea level could be measured by eye. An example is shown in Figure 1.

Figure 1. A simple ‘tide pole’ or ‘tide board’ installed vertically in the water by means of which the water level can be estimated by eye.
Figure 1. A simple ‘tide pole’ or ‘tide board’ installed vertically in the water by means of which the water level can be estimated by eye.
Float and stilling well gauges.

This way of measuring sea level was first proposed by Sir Robert Moray in the mid-17th century. However, over a century went by before the first practical systems were introduced at locations in the Thames during the 1830s. They quickly become the standard way of measuring sea level and by the end of the 19th century they had spread to major ports around the world.

A stilling well is a vertical tube with a hole at its base through which sea water can flow. The level inside will be, in principle, the same as that of the open sea outside, but energetic wave motion will be damped (or ‘stilled‘) inside due to the hole acting as a ‘mechanical filter’. In the well is a float which rises and falls with the water level, and is attached via a wire over pulleys to a chart recorder driven by an accurate clock. The rise and fall of the water level is thereby recorded as a line traced by a pen on paper charts that are regularly replaced, the charts finding their way to a laboratory such as that at Bidston Observatory, where an operator ‘digitises’ the pen trace and so provides the measurements of sea level.

Figure 2(a) demonstrates how the level of the float is recorded on the paper chart, while Figure 2(b) is a photograph of the tide gauge station at Holyhead where there are two exceptionally large stilling wells.

Figure 2a. An example of a float and stilling well tide gauge. In modern gauges of this type, the recording drum and the paper charts are replaced by digital shaft encoders and electronic data loggers.
Figure 2a. An example of a float and stilling well tide gauge. In modern gauges of this type, the recording drum and the paper charts are replaced by digital shaft encoders and electronic data loggers.
Figure 2b. Two large stilling wells at Holyhead in North Wales.
Figure 2b. Two large stilling wells at Holyhead in North Wales.

This type of gauge is of historical importance as they were used for almost two centuries (although with modern improvements such as replacing the paper charts with modern electronic data loggers) and so data from them make up the data sets of sea level change that are nowadays archived at the Permanent Service for Mean Sea Level (PSMSL) in Liverpool and used for studies into long-term climate change. During the 19th century, most of these gauges were operated in the UK by the major ports, and even by the railway companies which operated ferries. Bidston Observatory operated one at Alfred Dock in Birkenhead for many years. A number of countries still operate float and stilling well gauges although most in the UK have been replaced with other types.

Pressure gauges.

These gauges measure sea level by recording water pressure with the use of a pressure sensor that is installed well below the lowest likely level of the water. The recorded pressure will be the sum of two forces pressing on the sensor: the pressure due to the water above it (which will be the sea level times the water density and acceleration due to gravity) and the pressure of the atmosphere pressing down on the sea surface. In practice, the latter can be removed from the pressure measurement using what is called a ‘differential’ sensor, thereby, after some calculation, providing a measurement of the sea level.

We mention two types of pressure sensor below, which were both developed at Bidston. One type (the bubbler pressure gauge) has been used at 45 locations around the UK for several decades and remains the main technology for sea level measurements in this country. Until recently (mid-2016), this large network was operated for the Environment Agency by a group at Bidston called the Tide Gauge Inspectorate, and then, following relocation, at the National Oceanography Centre in Liverpool.

Ranging tide gauges.

These devices consist of a transducer that is installed over the sea so that it can transmit a pulse down to the water, where the pulse is reflected back and recorded by the transducer, so measuring the time taken to travel down and back. If one knows what the speed of the pulse is, then one can readily compute the height of the transducer above the sea, and so measure sea level. The transmitted pulse can be either an acoustic one (sound), or electromagnetic (radar) or optical (light). During the last decades of the 20th century, acoustic systems became very popular and replaced float gauges, and even replaced pressure gauges in some countries. However, they have since been largely replaced in their turn by radar gauges for several reasons. One simple reason is relative cost. However, radar gauges are potentially more accurate than acoustic systems owing to the speed of a radar pulse, unlike sound, being independent of air temperature. Optical ranging gauges use lasers to transit the pulses but, to my knowledge, are used in only two countries (Canada and South Korea).

Bidston Observatory had expertise in all of these types of tide gauge, but three can be mentioned in which Bidston scientists took a special lead.

Bubbler pressure gauges.

In the late 1970s, the Institute of Oceanographic Sciences (IOS, as Bidston Observatory was then known) was encouraged by the government to see if the new types of tide gauge then becoming available would be suitable for replacing the float and stilling well gauges then standard in the UK. This led to a programme of research by David Pugh and others into the use of different types of pressure gauge, including the bubbler gauge, and the curiously-named ‘non-bubbling bubbler gauge’ which we shall not explain.

Bubbler gauges were not invented at Bidston but they were developed there into practical instruments. They offered advantages over other pressure sensor systems in which the sensors themselves are installed in the water. In a bubbler system, the only equipment in the water is a tube through which gas flows at a rate sufficient to keep the tube free of water, such that the pressure in the tube is the same as that of the water head above the ‘pressure point’ at the end of the tube (Figure 3). The pressure sensor itself is located safely at the ‘dry land’ end of the tube, so there are no expensive electronic components that could be damaged in the water. If the tube is damaged it is simple and cheap to replace. The only drawback is that a diver is needed to install the tube, although the same need for a diver applies to all other pressure systems.

Figure 3. A outline of the bubbler pressure gauge system. (From Pugh and Woodworth, 2014).
Figure 3. A outline of the bubbler pressure gauge system. (From Pugh and Woodworth, 2014).

Comparisons of the old (float and stilling well) and new (bubbler) gauges were made at various locations, including at the important tide gauge station at Newlyn in Cornwall. In addition, the way that they measure sea level was thoroughly understood from both theoretical and experimental perspectives. The conclusion of the research was that bubbler pressure gauges could be reliably installed across the network. Bubblers are now standard in the UK and Ireland although they have since been replaced in countries such as the USA by other systems.

‘B’ gauges (where B stands for Bidston).

These gauges were developed in the 1990s by Bob Spencer, Peter Foden, Dave Smith, Ian Vassie and Phil Woodworth for the measurement of sea level at locations in the South Atlantic. They are rather complicated to explain in this short note, but the gist of the technique is that it uses three pressure sensors to measure sea water pressure (as in a bubbler gauge) and also maintain the datum (measurement stability) of the data in the record. ‘B gauges’ are probably the most accurate and stable types of tide gauge ever invented, but they are expensive (because of the requirement for three sensors) and were never developed commercially. Nevertheless, the principle of the ‘B technique’ was eventually incorporated into the way the bubblers were operated in the UK network, which remains the situation today.

Radar tide gauges.

Bidston Observatory cannot claim to have invented radar tide gauges; these radar transducers were developed first for the measurement of liquids and solids in giant industrial tanks, and were then applied to the measurement of river levels. However, Bidston can claim to have been one of the first laboratories to have used radar gauges for measuring sea level, a one year comparison of radar and bubbler data from Liverpool having shown that radar was a suitable technique for a tide gauge (Figure 4). Radar gauges have since fallen in price, are even more accurate than they were, can be readily interfaced to any kind of computer, and consume less power (an important feature in remote locations where gauges have to be powered from solar panels). They have become the standard technique for measuring sea level around the world and look like remaining so in the future.

Figure 4. A radar tide gauge at Gladstone Dock in Liverpool. The gold-coloured radar transducer transmits pulses down to the water and so measures sea level. The grey box on the wall is a satellite transmitter that sends the data to the laboratory.
Figure 4. A radar tide gauge at Gladstone Dock in Liverpool. The gold-coloured radar transducer transmits pulses down to the water and so measures sea level. The grey box on the wall is a satellite transmitter that sends the data to the laboratory.

Some References for More Information

  • Bradshaw, E., Woodworth, P.L., Hibbert, A., Bradley, L.J., Pugh, D.T., Fane, C. and Bingley, R.M. 2016. A century of sea level measurements at Newlyn, SW England. Marine Geodesy, 39(2), 115-140, doi:10.1080/01490419.2015.1121175.
  • IOC. 2015. Manual on Sea Level Measurement and Interpretation. Manuals and Guides 14. Intergovernmental Oceanographic Commission. Volumes I-V may be obtained from http://www.psmsl.org/train_and_info/training/manuals/.
  • Pugh, D.T. and Woodworth, P.L. 2014. Sea-level science: Understanding tides, surges, tsunamis and mean sea-level changes. Cambridge: Cambridge University Press. ISBN 9781107028197. 408pp.
  • Woodworth, P.L., Vassie, J.M., Spencer, R. and Smith, D.E. 1996. Precise datum control for pressure tide gauges. Marine Geodesy, 19(1), 1-20.

Bidston Observatory and Its Tide Prediction Machines

This article originally appeared in the newsletter of the Friends of Bidston Hill in February 2016. It is reproduced here with the permission of the author.

The role of Bidston Observatory has changed several times through the years. In its early decades, following the decision in the 1860s by the Mersey Docks and Harbour Board to move the Liverpool Observatory from Waterloo Dock to Bidston Hill, the focus was on astronomical measurements. These were required in order, amongst other things, to determine accurately the latitude and longitude of the site. Famous names involved included John Hartnup and his son (also John) and W.E. Plummer. Other areas of science undertaken by the Observatory included meteorology and seismology. In addition, it provided several local services, such as the calibration of accurate chronometers for port users and precise timing via the “One O’Clock Gun”.

By the 1920s, the Observatory had become ‘moribund’ (to quote from the excellent book by David Cartwright) and, after the death of its then Director Plummer, the decision was made to combine its work with that of the University of Liverpool Tidal Institute, with both to be located at Bidston. The latter had been founded in 1919 on the university campus in Liverpool with Joseph Proudman as Director and Arthur Doodson as Secretary, with funding from several sources including the major Liverpool shipping companies. The formal amalgamation of the Observatory and the Tidal Institute took place in 1929.

Proudman is another famous name, with Bidston Observatory later becoming known as the Proudman Oceanographic Laboratory. However, it is Arthur Doodson who is more relevant to this article. In the first year of the Tidal Institute, Doodson and Proudman began work on the problem of predicting tides, especially in shallow waters. They also undertook an evaluation of the benefits of mechanical tide prediction machines, which had been invented in the late 19th century by Lord Kelvin (William Thomson) and later developed by Edward Roberts. In effect, they were ‘analogue computers’. By 1924 Doodson had taken delivery of a brand new tide machine, the so-called ‘Bidston Kelvin machine’ thanks to the generosity of Liverpool ship-owners. Then in 1929, with all staff now installed at Bidston, he acquired and refurbished the so-called ‘Roberts machine’ which had been constructed by Roberts in 1906. The Roberts family had used this machine as part of a business of providing tidal predictions to the government but, due to the death of Roberts’ son, were no longer able to continue.

The Bidston Kelvin Machine and (inset) Arthur Doodson (from Parker, 2011)
The Bidston Kelvin Machine and (inset) Arthur Doodson (from Parker, 2011)

The Roberts machine was in many ways superior to the Kelvin machine, being capable of predicting 40 ‘constituents’ of the tide instead of 29. Such machines can only have a decent stab at simulating the tide at all thanks to the fact that the tide is capable of being described as the sum of individual harmonic constituents. Constituents can be thought of as cosines with particular frequencies (or periods) that are known from astronomy. So, for example, two of the most important constituents are called M2 and S2. These come from the Moon and Sun respectively with periods of 12 hours 25 minutes for M2 and 12 hours exactly for S2. These two terms are responsible for the regular twice-daily tide we have at Liverpool. However, many more constituents than these two are required to do a decent job of simulating the real tide to the accuracy required, and a machine with as many constituents as possible is highly desirable.

The Roberts machine at an exhibition in Paris in 1908. This machine is now on display at the National Oceanography Centre in Liverpool.
The Roberts machine at an exhibition in Paris in 1908. This machine is now on display at the National Oceanography Centre in Liverpool.

These two machines were responsible for many important achievements in the Observatory’s history. Bidston had become the undoubted centre of excellence in tidal research, both from theoretical perspectives (primarily Proudman) and on more practical bases such as the provision of tidal predictions worldwide using these machines (primarily Doodson). Doodson was excellent at devising techniques for handling numbers within complicated scientific calculations that nowadays would be undertaken by digital computers. He also became an expert in the technical design and construction of the tide prediction machines.

Although important individual machines were constructed in Germany and the USA, the majority of the 33 ever made (24 machines) were designed and manufactured in the UK, in either London, Glasgow or Liverpool. The UK was the only country to export machines to other countries. The construction of the majority of the machines made after 1920 was supervised, one way or another, by Arthur Doodson. These included a series of machines made after World War II, of which one (called locally the “Doodson-Légé machine”) was to be found in the lobby of the main POL building for many years until the move of the laboratory to the Liverpool campus in 2004.

The Doodson-Légé machine in the 1990s in the reception area of the Proudman Oceanographic Laboratory. The machine is now on display at the National Oceanography Centre in Liverpool.
The Doodson-Légé machine in the 1990s in the reception area of the Proudman Oceanographic Laboratory. The machine is now on display at the National Oceanography Centre in Liverpool.

Two of the three machines at Bidston have an importance in a notable period in the Observatory’s history, in providing tidal predictions during World War II and, in particular, for the D-Day landings and in other military operations around the world. These were the Kelvin and Roberts machines, which were located in separate buildings at the Observatory during the 1940s in case of bomb damage. The Kelvin machine, Doodson’s first, is now to be found in good condition at the headquarters of the French Hydrographic Service in Brest. Its disposal by Bidston after the war was a financial requirement in order to obtain funding for the Doodson-Légé machine.

The Roberts and Doodson-Légé machines are still located in Liverpool and are now owned by the Liverpool Museum. Recently, they have both been refurbished excellently and are capable of working as well as they can in order to show how things were done at Bidston, before the advent of digital computers in the 1960s saw their demise as the Observatory’s main technical assets.

Both machines are now on long-term loan from the Museum to the National Oceanography Centre in Brownlow Street on the Liverpool University campus, NOC being the successor to POL and therefore the ‘spiritual home’ of the machines. They are available for viewing by the public but arrangements must be made beforehand with the NOC Administration.

For anyone interested in Bidston Observatory and these machines, there is more to read. For an excellent introduction to tidal science, see Cartwight (1999), while histories of the Observatory and the people who worked there are given by LOTI (1945), Jones (1999) and Scoffield (2006). Aspects of Doodson’s career have been described by Carlsson-Hislop (2015). An ‘inventory’ (or overview) of tide prediction machines can be obtained from me, while the story of the use of the Kelvin and Roberts machines in World War II is given by Parker (2011).

Philip L. Woodworth
National Oceanography Centre,
6 Brownlow Street,
Liverpool L3 5DA
December 2015

References

  • Carlsson-Hislop, A. 2015. Human computing practices and patronage: anti-aircraft ballistics and tidal calcuations in First World War Britain. Information and Culture: A Journal of History, 50, 70-109, doi:10.1353/lac.2015.0004.
  • Cartwright, D.E. Tides: a scientific history. Cambridge University Press: Cambridge, 1999. 292pp.
  • LOTI. 1945. Liverpool Observatory and Tidal Institute. Centenary Report and Annual Reports for 1944-5. Available from P.L. Woodworth.
  • Jones, J.E. (original date 1999) From astronomy to oceanography: a brief history of Bidston Observatory. http://noc.ac.uk/f/content/downloads/2011/proudman-history.pdf.
  • Parker, B. 2011. The tide predictions for D-Day. Physics Today, 64(9), 35-40, doi:10.1063/PT.3.1257. Available from http://scitation.aip.org/content/aip/magazine/physicstoday/article/64/9/10.1063/PT.3.1257.
  • Scoffield, J. 2006. Bidston Observatory: The place and the people. Merseyside: Countyvise Ltd. 344pp.