Celebrating 100 years of tidal science on Merseyside

To mark the 100th anniversary of the Liverpool Tidal Institute (LTI), a celebratory meeting on ‘The ocean tide and the Port of Liverpool’ was held at the Merseyside Maritime Museum in May 2019. The LTI’s buildings at Bidston Observatory in Birkenhead are a well known local landmark, so the meeting attracted great interest from the general public as well as from academia, and there were almost 200 people in the audience

Tide prediction machines at the Liverpool Tidal Institute

The 100th anniversary of the Liverpool Tidal Institute (LTI) was celebrated during 2019. One aspect of tidal science for which the LTI acquired a worldwide reputation was the development and use of tide prediction machines (TPMs). The TPM was invented in the late 19th century, but most of them were made in the first half of the 20th century, up until the time that the advent of digital computers consigned them to museums. This paper describes the basic principles of a TPM, reviews how many were constructed around the world and discusses the method devised by Arthur Doodson at the LTI for the determination of harmonic tidal constants from tide gauge data. These constants were required in order to set up the TPMs for predicting the heights and times of the tides. Although only 3 of the 30-odd TPMs constructed were employed in operational tidal prediction at the LTI, Doodson was responsible for the design and oversight of the manufacture of several others. The paper demonstrates how the UK, and the LTI and Doodson in particular, played a central role in this area of tidal science

The tidal measurements of James Cook during the voyage of the Endeavour

The main priority of the first of James Cook's famous voyages of discovery was the observation of the transit of Venus at Tahiti. Following that, he was ordered to embark on a search for new lands in the South Pacific Ocean. Cook had instructions to record as many aspects of the environment as possible at each place that he visited, including the character of the tide. This paper makes an assessment of the quality of Cook's tidal observations using modern knowledge of the tide, and with an assumption that no major tidal changes have taken place during the past two and half centuries. We conclude that Cook's tidal measurements were accurate in general to about 0.5 ft (15 cm) in height and 0.5 h in time. Those of his findings which are less consistent with modern insight can be explained by the short stays of the Endeavour at some places. Cook's measurements were good enough (or unique enough) to be included in global compilations of tidal information in the 18th century and were used in the 19th century in the construction of the first worldwide tidal atlases. In most cases, they support Cook's reputation as a good observer of the environment

Tidal science before and after Newton

This chapter discusses two contrasting periods of research in tidal science, before and after Newton. The first period was marked by speculative theories, a disregard of observational evidence by some protagonists, and a lack of mathematical rigor. The second period, benefitting from the insight provided by Newton's Principia, demonstrated greater attention to tidal observations and a greater application of mathematics. One particular development that followed from the second period was Bernoulli's demonstration that data and mathematics could be combined in the production of useful tide tables for semidiurnal regimes. It is suggested that, with the benefit of hindsight, tidal science has progressed during identifiable eras of research, with us experiencing at the present time a particularly interesting era of tidal measurement and modeling

The global distribution of the M1 ocean tide

The worldwide distribution of the small degree-3 M1 ocean tide is investigated using a quasi-global data set of over 800 tide gauge records and a global tide model. M1 is confirmed to have a geographical variation in the Atlantic consistent with the suggestion of Platzman (1984b) and Cartwright (1975) that M1 is generated in the ocean as a consequence of the spatial and temporal overlap of M1 in the tidal potential and one (or at least a small number of) diurnal ocean normal mode(s). As a consequence, it is particularly strong around the UK and on North Sea coasts (amplitudes ∼10 mm). This analysis shows that their suggestion is also consistent to a great extent with the observed small amplitudes in the Pacific and Indian oceans. However, there are differences at the regional and local level which require much further study via more sophisticated ocean tidal modelling. By contrast, what is called the M1' tide (a combination of several degree-2 lines in the tidal potential with frequencies close to that of M1) is shown to have a geographical distribution consistent with expectations from other degree-2 diurnal tides, apart from locations such as around the UK where tidal interactions introduce complications. As far as I know, this is the first time that these small tidal constituents have been mapped on a global basis and, in particular, the first time that the ocean response to the degree-3 component of the tidal potential has been investigated globally

The nodal dependence of long-period ocean tides in the Drake Passage

Almost three decades of bottom pressure recorder (BPR) measurements at the Drake Passage, and 31 years of hourly tide gauge data from the Vernadsky Research Base on the Antarctic Peninsula, have been used to investigate the temporal and spatial variations in this region of the three main long-period tides Mf, Mm and Mt (in order of decreasing amplitude, with periods of a fortnight, a month and one-third of a month, respectively). The amplitudes of Mf and Mt, and the phase lags for all three constituents, vary over the nodal cycle (18.61 years) in essentially the same way as in the equilibrium tide, so confirming the validity of Doodson's nodal factors for these constituents. The amplitude of Mm is found to be essentially constant, and so inconsistent at the 3σ level from the ±13% (or  ∼ ±0.15mbar) anticipated variation over the nodal cycle, which can probably be explained by energetic non-tidal variability in the records at monthly timescales and longer. The north–south differences in amplitude for all three constituents are consistent with those in a modern ocean tide model (FES2014), as are those in phase lag for Mf and Mt, while the phase difference for Mm is smaller than in the model. BPR measurements are shown to be considerably superior to coastal tide gauge data in such studies, due to the larger proportion of non-tidal variability in the latter. However, correction of the tide gauge records for non-tidal variability results in the uncertainties in nodal parameters being reduced by a factor of 2 (for Mf at least) to a magnitude comparable (approximately twice) to those obtained from the BPR data

Reanalyses of Maskelyne's tidal data at St. Helena in 1761

The construction of an electronic data set of the tidal measurements made at St. Helena in 1761 by Nevil Maskelyne is described. These data were first analysed by Cartwright (1971, 1972) in papers which have importance within studies of changing tides. However, Cartwright's data files were never archived for the benefit of other researchers, demonstrating that “old data” at risk can sometimes take the form of electronic rather than paper records. In the present paper, the newly digitised Maskelyne data have been reanalysed by several techniques in order to obtain an updated impression of whether the tide has changed at that location in over two and a half centuries. This new data set may be found via https://doi.org/10.5285/e66db85a-eaae-6665-e053-6c86abc0bfb9 (Woodworth and Vassie, 2022). Our main conclusion, consistent with that of Cartwright, is that the major tidal constituent (M2) has changed little. However, the results of the various techniques demonstrate how difficult it is to obtain reliable conclusions for the smaller constituents

The status of measurement of the Mediterranean mean dynamic topography by geodetic techniques

We review the measurement of the mean dynamic topography (MDT) of the Mediterranean using ellipsoidal heights of sea level at discrete tide gauge locations, and across the entire basin using satellite altimetry, subtracting estimates of the geoid obtained from recent models. This ‘geodetic approach’ to the determination of the MDT can be compared to the independent ‘ocean approach’ that involves the use of in situ oceanographic measurements and ocean modelling. We demonstrate that with modern geoid and ocean models there is an encouraging level of consistency between the two sets of MDTs. In addition, we show how important geodetic MDT information can be in judging between existing global ocean circulation models, and in providing insight for the development of new ones. The review makes clear the major limitations in Mediterranean data sets that prevent a more complete validation, including the need for improved geoid models of high spatial resolution and accuracy. Suggestions are made on how a greater amount of reliable geo-located tide gauge information can be obtained in the future