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.