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.


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:


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):


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).


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


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.


My early life at Bidston Observatory

Joyce Scoffield

Originally, from 1955, I worked in the Met Office at Speke Airport (later to be called Liverpool Airport and subsequently John Lennon Airport). I very much enjoyed being a weather observer – sending observations up to the control tower to be passed on to aircraft, but the job involved shift work, which included regular night duties. This was fine till I got married in 1961. At that stage, I became less enthusiastic about shift work and about the amount of travelling involved between Greasby and the airport: bus – ferry – bus – at least an hour each way. I didn’t drive in those days.

So I decided to look for another job. Bidston Observatory came to mind. It was much nearer home and I knew they had a weather station there. So I wrote to the Director asking him if there were any job vacancies. He – Dr. Rossiter – invited me to go for interview and duly offered me a job! It was as easy as that in 1961. Nowadays, with high competition for every post, people can’t believe that it could ever be that easy.

I was a very basic assistant at Bidston – one of 10 girls who were classed as ‘computers’. We operated tidal prediction machines – large machines consisting of gears, weights and pulleys which could be set to represent the contributions of sun, moon, location, etc. to the tides of a port. You can read all about these machines in other articles on this site.

The scientific programs which turned these numbers into tidal predictions were written by the scientists – them upstairs! – it was all way beyond our understanding. We just operated the machines by foot pedals and a hand wheel and wrote down the answers – the more senior girls scanned our numbers looking for obvious errors. When plotted on a graph, the figures would form a smooth curve representing the pattern of the tide on consecutive days at the port concerned. Once the figures had been accepted as correct, we had to write them down on prepared forms – using pen and ink – no biros allowed – neat handwriting was essential for the job! There was a darkroom in the basement where our carefully written-out tables were photographed before being sent to the port authority concerned. This was a typically old-fashioned dark room with trays of chemical developers, subdued red lights, etc. In those days we did tidal predictions for many parts of the Commonwealth.

Another of the girls’ duties was to maintain a daily weather diary. At 9 am each day – Saturdays, Sundays and Christmas Day included – the duty observer would take readings from the thermometers in the Stevenson’s Met. Screen sited on the Observatory lawn, change the temperature and humidity charts on the analogue instruments also sited in the met screen and change the chart in the tipping bucket rain gauge, as well as measuring any rainfall recorded in the rain bottle. The observer would then go up to the roof to change the daily sunshine card in the Campbell-Stokes sunshine recorder. The sun’s rays were concentrated through a solid glass ball to produce a burn on the specially-treated card. In the summer, this recorder was located on the roof of the ‘Dines cabin’ – the climb up the ladder to this site could be rather precarious on a windy day. In winter, the sunshine recorder was moved to the outside of one of the domes accessed from inside the dome by a small door (again up steps) facing due south. Because the sun is a lot lower in the sky in winter, and needing a smaller range of exposure, this was obviously safer for the staff than the outside summer climb.

Inside the ‘Dines cabin’ was the Dines anemometer recording wind speed and direction on an analogue chart. There again the observer changed the chart on the instrument’s cylinder. The final job was to note the visibility from all sides of the roof. On fine days, we had a great view over Liverpool with the Pennines in the distance. To the north, we could see Blackpool and occasionally Black Coombe in Southern Scotland. To the west, we could see the Great Orme and the Snowdonia range.

Taking the retrieved charts and the sunshine card, the observer returned to the office and calculated three hour readings for the past 24 hours and entered them into the weather diary. These diaries were beautifully produced for us by a company in Liverpool and, I believe, they are now housed in the Wirral Libraries Archive in the Cheshire Lines Building in Birkenhead.

Photo of the One O'Clock Gun, still sited in Birkenhead
The One O’clock Gun is still sited in Birkenhead

Another job for the duty observer was to fire the one o’clock gun at precisely 1 pm Mondays to Fridays. This was a tradition dating back to the building of the Observatory in 1866, when accurate time was not available to the business people of Liverpool. A very accurate clock in the Observatory was connected by landline to a gun sited at Morpeth Dock, on the Birkenhead side of the Mersey. When the observer flicked a switch at Bidston the gunfire was heard in Liverpool (the gun having first been duly primed by a docker at Morpeth). The practice was discontinued at Bidston in 1969, but still continues at observatories in other parts of the world.

The girls had little association with the scientists who were mostly men. At coffee time – strictly 1045-1100 am (we daren’t overstay our time limit) – the men stood round the marble fireplace in the old dining room and the girls sat at the tables. There was little communication between the two groups. Incidentally, the girls prepared the coffee on a rota bases – strictly 50% warm milk – heated in a pan and 50% water. When the coffee was ready, spot on 1045 am, we pressed a buzzer – I think it was 2 buzzes for coffee break – to summon the staff from upstairs.

At lunch time, on a fine day, the menfolk would often take a brisk walk over Bidston Hill usually talking shop. The girls tended to sit on the observatory front door step eating their sandwiches.

It was quite a hierarchical situation at the observatory in those days – a total staff of only about 18 people – a sort of strict family atmosphere – and always quiet. I enjoyed working there.

When I was expecting my first baby in 1964, people seemed quite relieved. It was several years since anyone had become a mum and they had thought there was a hoodoo on the place! Dr. Rossiter was very solicitous towards me when I became pregnant – he insisted on my desk being moved downstairs to save me having to climb anywhere or do anything at all strenuous. There was no thought of my returning to work after having the baby. Mums did not return to work in those days! In the event, I did return to Bidston part time when my younger son was nine years old and attitudes towards working mums were starting to ease.

More stories of life at Bidston Observatory at this time can be found in my book “Bidston Observatory: The Place and the People” (Countryvise Ltd. 2006. ISBN: 978190121687).

Reflections on Time

Kevin F. Taylor

I was recently invited to attend a garden party to celebrate 150 years of the Bidston Observatory, hosted by Stephen and Mandy Pickles on Saturday 17 September 2016 in the grounds of Bidston Lighthouse. This gave me a deep sense of déjà vu, as it reminded me so much of my first day as a member of Bidston staff at the start of 1972.

On that day, I drove up the same well-worn drive, past the sandstone wall entrance, and into the grounds. On my right hand side was a lawn that was shortly to be occupied by the new Proudman Building. But in early 1972 that area looked almost the same as it does now, except for a small vegetable patch that was attended to by a Mr. Connell. He and his family occupied the cottages that belonged to the lighthouse and had been built by the Mersey Docks and Harbour Board. On that balmy Saturday evening in September, I thought it quite strange that, here I was celebrating 150 years of the Observatory, and yet the ‘new’ Proudman Building had been built and demolished (in early 2013) within little more than 40 years, a fraction of the Observatory’s lifetime.

The nostalgia continued as I parked my car behind the rear of the Observatory in almost the same spot as I had on that first day at work. I remembered thinking back; my father would quite often force me to join him on one of his marathon walks. One of his favorite treks was from Moreton to Bidston, then over the Vyner Road footbridge, past the windmill, around the Observatory boundary wall down to the village, then home. In the 1950s and early 60s, I was infatuated by science fiction and men-from-outer-space movies, and TV dramas like Quatermass and Doomwatch. For me, looking over the walls surrounding the Observatory presented all kinds of mysteries: What secrets were hidden inside the huge white domes? My youthful and vivid imagination had no bounds in ‘them days’.

On my first day in 1972, I now had the chance to look at the Observatory from the inside out, as opposed to the outside in. How exciting! As I got out of my car and approached the entrance, a gentleman in front of me held the door open and greeted me with the words “Hello Kevin, glad to see you are joining us”. We then passed through the vestibule door and continued to chat in the hallway for a good ten minutes. He then finished by saying “you will be with Dr. Skinner’s group. I will take you to his office”. He gave a quick knock on the door, popped his head around, and said “Sorry Len, Kevin is not late, my fault I kept him chatting”. I was later taken through to the rear of the building for the mid-morning tea break when the same gentleman entered. I turned to one of the staff and asked “who the nice man was”. “That is Dr. Rossiter our director” was the reply. I was then informed that he was the brother of that brilliant actor Leonard Rossiter from the Rising Damp and Reginald Perrin television shows (come to think of it, they did look alike). [Editor’s Note: see mention of Rossiter and other Bidston Directors in an article by Graham Alcock].

So, allow me to digress about a couple of things that have struck me about time, and why I have given the title of this article as ‘Reflections on Time.’ It seems to me that we have different perceptions of time depending on the situation. For example, my first day at the Observatory was over forty years ago, and yet on that recent Saturday in September, it felt like only yesterday. Another example concerns my grandmother, who was 104 years of age when she passed away. When she was born in 1889, the Observatory building had been completed (in 1866) only 23 years before. So, why were we so concerned with celebrating the Observatory as an ‘historic building’, when my memories of my grandmother do not feel ‘historic’? She was just my Nan. So, time is a funny business.

One of the main reasons for the Observatory was to provide accurate time. This gives me a chance to refer to a hero of mine called John Harrison, who had nothing to do directly with the Observatory but, of course, also had an important role in our maritime history. When a fleet of warships ran aground with the loss of many lives and ships due to bad navigation, a vast reward was offered by the King to anybody who could come up with a good way to improve navigation at sea. The main problem was how to calculate longitude, and many ideas were offered: for example, a crazy scheme for anchoring old redundant ships at fixed positions apart, distributed across the whole ocean. The establishment was convinced that the only way that longitude could be calculated, was by using the stars and planets. Harrison in the meantime concentrated on trying to develop a precision marine chronometer. His theory, that longitude could be calculated by the use of time to good precision, was treated with great disdain.

To prove his theory, he would be entirely dependent on producing an accurate timepiece. This proved to be a formidable task. Not only had it to overcome a ship’s movement, but temperature played a significant part in the reliability of the timepieces he produced. Originally, clocks used a pendulum and weight with an escapement movement, but temperature would increase and decrease the length of the pendulum, making the precision he was looking for unsatisfactory. He spent many years trying to overcome this, by making the pendulum out of metal rods with different thermal coefficients of expansion, but alas to no avail. It was not until the latter part of his life that he produced the famous Harrison timepiece. The connection to the Observatory in this story is, of course, that the calibration of marine chronometers was subsequently to form an important part of activities at Bidston, in addition to the astronomical work in establishing the longitude of the port of Liverpool.

Accurate time has historically not been very important for most ordinary people – the sun came up, the sun went down, and what happened in between was neither here nor there. However, for those people who did need accurate timing (on land), the development of affordable watches and clocks, supplemented by sundials, was enabling decent and routine measurements of time by the end of the 18th century. One way of providing accurate timing information to the general population was by the use of time balls controlled by nearby observatories such as Bidston. A time ball was a large sphere (a ball) on top of a shaft positioned on the roof of a prominent building. At precisely midday (or another time such as 1 pm), the sphere would be dropped and people (including ships’ captains) would set their watches. This was a satisfactory situation only when visibility due to the weather allowed the time ball to be seen. Instead, the time balls were eventually complemented by an audible signal such as made by a canon. Hence, the famous Liverpool “One O’clock Gun” came into being. Originally the Liverpool Observatory was located at Waterloo Dock, and the gun (a remnant of the Crimean War) was fired from the Liverpool side of the Mersey. An improvement was made by moving the Observatory from Liverpool to the highest point on the Wirral side of the river, but close to the Dock Estate, this being Bidston Hill. The gun was relocated to Morpeth Dock in Birkenhead, and was now fired directly by an electrical signal from the Observatory.

Time eventually became a significant factor in everyone’s life, and now controls our lives more and more. Everyone knows about the advent of the industrial revolution, and the development of the railway, and the national adoption of Greenwich Mean Time. Now we are controlled by our smart-phones by time that comes from space via GPS satellites. Everyone is in a hurry or we’ll be ‘late’.

So I have been thinking back to that first day at work. At that time, I had many questions, such as “Why is the Observatory called The Institute of Coastal Oceanography and Tides, or ICOT for short?” Or, “What has oceanography got to do with astronomical observations?” These questions were answered for me over the years as I got to understand the relationships between the heavens and earth, and in particular the relationships between time and the tides, and so the ocean, and how these topics have evolved to become a crucial part of everyday life.

This has been a very brief look, from my perspective, at ‘time’ and at some small aspects of life at Bidston Observatory. It would take many volumes to do it justice to it regarding topics such as the development of tide tables, the use of precise instruments (e.g. for earth tides), the collection of oceanographic data from around the world, the fieldwork at many locations etc. Perhaps other people can cover these topics on this web site. Some of the world’s most famous oceanographic scientists have worked at or passed through the Observatory during its history. I feel very fortunate to have experienced a small part of the wealth of that Bidston history. And I hope that its historical significance is appreciated by future generations.


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.


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.


  • 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.

Directing Bidston

Graham Alcock, 21 October 2016

I joined Bidston in 1972 and took early retirement in 2000, having survived five name changes (Institute of Coastal Oceanography and Tides, Institute of Oceanographic Sciences, Proudman Oceanographic Laboratory, Centre for Coastal and Marine Science and back to the Proudman Oceanographic Laboratory). Here are anecdotes about some of the Directors during that time.

I only met ICOT’s Director, Jack Rossiter, when he was chair of my interview panel in May 1972, because unfortunately he died before I was appointed. The subsequent ICOT Acting Director, Geoff Lennon, had a turn of phrase – “it occurs to me” – and that was used in my letter of appointment, suggesting that I might like to join a scientific cruise in September 1972, pre-dating my actual appointment date of 1 October. What Geoff omitted to say was that the cruise was on the RRS John Murray, an ex-fishing trawler rumoured to have been bought by NERC for £1, which had such a nasty rolling motion in anything higher than a Force 2 breeze that it was always difficult to encourage Bidston staff to go on it. That was my introduction to “wet” oceanography – subsequently I always preferred the “dry” oceanography remotely carried out by land-based radar and space-borne satellites.

The first of the frequent reorganisations of NERC’s marine science occurred in 1973, when Bidston became part of IOS, together with what had been the National Institute of Oceanography at Wormley and the Unit of Coastal Sedimentation at Taunton. Scientific rationalisation brought the Tides staff at Wormley to Bidston and David Cartwright was appointed as IOS Assistant Director.

David was a world-class researcher and an elected Fellow of the Royal Society; but as he said on his interview for The British Library’s “Voices of Science”, he “wasn’t temperamentally suited to getting too much involved with administration”. I remember attending an IOS meeting at Wormley to allocate funding for the year (in my capacity as responsible for contracted and commissioned research at Bidston), when David left early to catch his train back to Birkenhead before Bidston finances had been fully discussed and agreed. James Crease said: “I suppose we had better allocate some funds to Bidston”.

I worked on a number of projects for David and although he was the senior author of our joint papers he used the format of listing the authors in alphabetical order. For the George Deacon 70th Birthday commemorative volume of “Deep Sea Research”, we wrote a paper on our analysis and interpretation of telephone cable voltages across the English Channel to provide information on the ocean current flow. The DSR Editor knew of David but not me, and on his assumption that the first named author was the senior author, his acceptance letter (no emails then) to us was addressed to Professor Alcock; much to our amusement.

Another project that I worked on with David was the analysis of data from SEASAT – the first satellite dedicated to oceanography. In the 1970s, our visit to Venice for a SEASAT Workshop enabled David to indulge in two of his passions: railways (Liverpool – London – Calais – Venice is some train ride) and wine (his wife was French). A very good bottle consumed by us on the return rail journey was paid for using a pile of Italian Lire left over when we had discovered that our Hotel accommodation had been paid by the Workshop organisers.

After our successful campaign in the late 1980s against Bidston’s closure and transfer to Wormley, Bidston became autonomous and was renamed the Proudman Oceanographic Laboratory. (The IOS Taunton site was closed and staff transferred to Bidston or Wormley.) Brian McCartney was appointed POL Director and, in my opinion, the next eight years were Bidston’s halcyon days: we reported directly to NERC HQ, without an intervening level of bureaucracy of IOS or later CCMS or NOC.

Brian always let Group and Project leaders have a full say at the Management Committee; especially at the annual allocation meeting (consequently it sometimes went on for two days); so I felt that if you inevitably didn’t get all the money or equipment that you had bid for, you still accepted his final decisions because you had had a fair hearing. Brian was also careful to include all “Prime-movers” (the researchers) in the vision and major decisions that directed our strategy. In those ways, I believe that he made sure that all staff felt that they had had some input in formulating the strategy that POL took under his Directorship, with ensuing collective responsibility and underpinning the Bidston “family” atmosphere that John Huthnance mentions in his article.

Brian had been Head of the Engineering Group at Wormley, so it was not surprising that technology development at Bidston thrived during his Directorship. Bidston became one of the few European laboratories with the capability of developing and deploying oceanographic instruments in the coastal zone, shallow or deep water. Together with our expertise in the analysis and interpretation of the data and the world-class hind-casting and fore-casting modelling expertise developed under Norman Heaps’ leadership, Bidston’s scientists and engineers were in great demand for European Community/Union oceanography projects. Not bad for an organisation later accused of scientific isolation because it was on a hill five miles away from Liverpool University.

Under Brian’s leadership, POL became the host laboratory for the North Sea Project, the first large “Community Research Project”, involving many other research institutes and university research departments. We developed a strategy of funding all our Laboratory Science and Technology Projects from a triple combination of Commissioned Research (mainly from the DoE, MAFF and MoD), EC/EU Programmes and the NERC Science Budget; giving us some financial stability.

Happy days!

With the movement of IOS Wormley to Southampton University in the 1990s, NERC carried out yet another reorganisation of its marine science, lumping its remaining oceanographic laboratories at Bidston, Oban and Plymouth, into a “Centre” for Coastal and Marine Science. Jackie McGlade was appointed to what I always considered was a poisoned chalice of a job as the CCMS Director. (CCMS was disbanded in 2000, the then NERC Chief Executive admitting that the CCMS experiment had failed.) Jackie faced a fair degree of hostility from some senior staff, particularly at Plymouth where her office was situated, as staff at the three previously autonomous laboratories tried to work out what exactly was the purpose of the “Centre”.

I worked closely with Jackie on aspects of commissioned research and scientific applications across CCMS and got on well with her. She tended to be quite open about what she felt (perhaps that’s what some senior CCMS staff didn’t like) and because of this I was probably the first Bidston staff member to find out about the proposed closure of Bidston and transfer to Liverpool; a decision that had been taken by the then Bidston Director, without, as far as I know, any consultation with Bidston staff (the Management Committee had been an early casualty of his appointment.) Jackie and I were travelling on the London Underground, back from a meeting with an Intellectual Property lawyer, when Jackie asked me what I thought about the plan to close Bidston and move everyone to Liverpool University. I was non-committal.

Frank Field, MP for Birkenhead, had been a main factor in NERC’s decision not to close Bidston in the 1980’s and I informed him of the decision. I was summoned to the Bidston Director’s office and told, in no uncertain terms, that he was the Director and made the decisions, which I had to obey as a member of his staff without discussion. I demurred. I took early retirement in 2000, having thoroughly enjoyed most of the time at Bidston and working for most of the Directors.

(The British Libraries’ “Voices of Science” is at As well as David Cartwright, other oceanographers interviewed are James Cease, Anthony Laughton, John Woods and Philip Woodworth.)

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.

A brief history of Bidston Observatory

Bidston Observatory was built in 1866, when the expansion of Waterloo Dock forced Liverpool Observatory to re-locate to Bidston Hill. It was built alongside Bidston Lighthouse and Signals Station, on land owned by the Mersey Docks and Harbour Board. George Fosbery Lyster was the architect.

George Fosbery Lyster
George Fosbery Lyster

John Hartnup, astronomer and Assistant Secretary to the Royal Astronomical Society, had been the Director of Liverpool Observatory since it was built in 1843. Amongst his achievements was the calculation of the longitude of Liverpool, which was important for navigation and the development of the port. He presided over the move to Bidston Hill, and continued as director of Bidston Observatory until his retirement in 1885, when he was succeeded by his son. The second director, John Hartnup Jr  died on 21 April 1892, when he fell from the roof of the Observatory while making meteorological observations.

Bidston Observatory and Lighthouse, postmarked 1907
Bidston Observatory and Lighthouse, postmarked 1907

Over the years, the emphasis of the Observatory’s work shifted from astronomy to other things, but always in the tradition of Time and Tide, so important to the port of Liverpool.

Of Time. The progression from observations of the stars, to the determination of longitude, to the calibration of chronometers was a natural one. The Observatory’s two levels of cellars and other features made it especially suited for calibrating chronometers under controlled conditions of temperature and seismic vibrations. Mariners sent their chronometers from all over the empire for calibration at Bidston. The One-O-Clock gun at Morpeth Dock was signalled from Bidston Observatory.

Of Tide. Ever since Liverpool’s harbour-master William Hutchinson (the same fellow who pioneered the use of parabolic reflectors in lighthouses on Bidston Hill) took the first extended series of tidal measurements over a period of nearly thirty years, Liverpool had led the world in tidal studies. This work became centred at Bidston Observatory when the Liverpool Tidal Institute was set up there under Joseph Proudman’s direction after World War I. Arthur Doodson’s work with mechanical computers for tide prediction happened here. One of his machines was used to predict the tides for the D-Day landings.

Observatory staff by the original one-o-clock gun, after its removal to Bidston Hill from Morpeth Dock.
Observatory staff by the original one-o-clock gun, after its removal to Bidston Hill from Morpeth Dock.

In 1969, the Natural Environment Research Council (NERC) took over responsibility for the Observatory. Oceanographic research continued to expand under their auspices. During the 1970’s, the Joseph Proudman Building was constructed in the former kitchen gardens of Bidston Lighthouse.

In 1989, the Observatory, Lighthouse and the perimeter wall enclosing them became Grade-II listed buildings.

In 2004, the Proudman Oceanographic Laboratory moved from Bidston Hill to a new building at the University of Liverpool. Their oceanographic research is still continuing today, but now in the guise of the National Oceanography Centre.

The departure of the Proudman Oceanographic Laboratory from Bidston Hill began a 12-year limbo. NERC’s original plan to sell the site to a developer aroused opposition from local pressure groups, and the spectre of an eleven-story high-rise residential development was averted. In 2012, NERC applied for and obtained planning permission and listed buildings consent (now lapsed) to convert the Observatory into four residential apartments. Later that year, the Joseph Proudman Building was demolished. Having put the Observatory to the market on several occasions, NERC finally sold it in 2015 to a developer (Bidston Observatory Developments Limited), who had outbid a community-led consortium. This was the lowest point in the Observatory’s history. A period of systematic neglect saw a rapid deterioration of the fabric of the building and the appearance of the grounds, exacerbated by water ingress, unpaid bills and a winter with no heating, and the Observatory was nominated to the Victorian Society’s list of the top ten endangered buildings of 2016.

Fortunately, the Observatory was sold again in September of 2016. The new owners have announced their intentions to operate the Observatory as a not-for-profit artists’ research centre and to incorporate an exhibition celebrating the Observatory’s scientific heritage.