Tidal Science explained

How do the Moon and Sun control the tides? How do we use this knowledge to make predictions?

About tides

Tides are very long-period waves that move through the oceans in response to the forces exerted by the moon and sun. Tides originate in the oceans and progress toward the coastlines where they appear as the regular rise and fall of the sea surface.

The water masses of our oceans carry heat, oxygen and nutrients across seventy percent of our planet, so an understanding of currents and tides is important for many reasons. A knowledge of the tides has always been fundamentally important for safety and for commerce and trade. Mariners need to know the time of high water so they can safely bring their ships into port without running aground, and those making a living from the coast – for example, people fishing on low-water mudflats – need to know when to leave before the tide comes back in. An understanding of tides is also crucial for coastal management, and for investigating features and any patterns of change in the marine environment.


The gravitational tidal forces from the Moon try to pull the water in the ocean in two directions. First, it can be appreciated that the gravitational pull of Moon is stronger in that part of the ocean nearest the Moon, than in the solid part of the Earth beneath the ocean, with the result that a bulge of water develops on the moonward side of the ocean. Second, the forces are stronger in the solid Earth than in that part of the ocean distant from the Moon, with the result that a corresponding bulge develops in the ocean on the other side of the globe.

As the Earth rotates beneath the Moon, the bulges move around the earth and therefore we experience rises and falls in the level of the water – tides. As the earth rotates beneath the Moon in a lunar day (24 hours and 50 minutes), and as there are two bulges, we get a tide every half lunar day (a little over 12 hours).

The Sun also pulls on the water in the ocean, and generates tides every half of a solar day (exactly 12 hours). When the effects of this solar pull align with those of the pull of the Moon, we experience spring tides. When they are pulling at right angles to each other we experience neap tides. A spring-neap cycle takes place over a fortnight.

However, this is a very simplified description of the tidal forces rather than the tides themselves, which are the response of the ocean basins to those forces. As a result, it transpires that the spatial patterns of the real ocean tides are much more complex than those described above, although the temporal characteristics of the tides (primarily twice a day around the UK) are much the same.

Spring tides diagram

Neap tides diagram

In many locations, the tidal pattern will not match the diagram above. The land masses on earth and a number of other factors introduce layers of complexity. There are places with only one tidal rise and fall each day, many with multiple peaks, and still others which experience none at all.

Despite these complexities, with enough recorded data on the rise and fall of water levels at a given location, it is possible to analyse the information and obtain a repeating pattern which can be used to tell you expected water levels there at any time in the past or future. Harmonic analysis breaks down an observed tidal curve (no matter how complex) into a series of regular sine wave components. When the amplitude and frequency of enough of these components is known, the original curve can be reproduced for any point in time.

The tides have a longer history of continual research than any other aspect of what is now called physical oceanography. The connection between tides and the movement and phases of the Moon was always clear, and early mariners and fishermen observed the time interval between the Moon's highest ascent above the horizon and the time of the next high water to develop simple prediction methods. They knew that the tidal range varied throughout the month, and increased toward times of full or new Moon.

150BC Seleucus of Babylon noted the times and heights of high and low waters at the northern end of the Persian Gulf, and recognised that the difference in height between high waters on a given day varied throughout the month and was greatest when the Moon was farthest north or south of the equator.
  In the centuries which followed, tide prediction continued to be based on observed correlations between water levels and excursions of the moon or sun.
  It was recognised that the differences between two high tides in a given day were greater at the solstices than at the equinoxes. A tide table printed in China in 1056 for Yanguan on the Qiantang River includes different sections for different seasons.
1546 The Brouscon tidal almanac produced for the king of France. This contained charts for dozens of harbours. A pocket-sized version on vellum was used by most mariners at that time.
1687 Newton explained how the tides are generated in Philosophiae Naturalis Principia Mathematica, showing that the generation of tides depends on both the gravitational attraction of the Moon and the centrifugal force of the Moon–Earth orbit. Gravitational attraction pulls Earth and the Moon toward each other. But they are also centrifugally pushed apart as they both orbit their joint center of mass. On the side closest to the Moon, gravitation pulls the water outward in a tidal bulge, and on the opposite side, centrifugal repulsion causes an equivalent water bulge. Any point on the sea will have two high tides a day as Earth rotates through these bulges. This explanation does not consider the effects of land masses and hydrodynamic effects (such as the resonance of each ocean basin).
1738 Daniel Bernoulli refined Newton’s equilibrium theory to produce tide tables that better incorporated several other important astronomical frequencies.

Pierre Simon Laplace described how the oceans respond dynamically to gravitational effects of the Moon and Sun. He used calculus to derive three equations for the global ocean, one based on conservation of mass and the other two based on momentum conservation in two horizontal directions. These equations became the foundation for hydrodynamic modelling of the oceans and the study of geophysical fluid dynamics.

The equations could not be fully solved until the advent of digital computing. But they demonstrated that all the energy of the tide is concentrated at only a few specific astronomical frequencies. At many locations most of the energy is found at three semi-diurnal frequencies: 1.93 cycles per day (due to the Moon), 2.00 cycles per day (due to the Sun), and 1.90 cycles per day (due to the eccentricity of the lunar orbit). In some locations, three other diurnal frequencies resulting from asymmetry introduced by the tilt of Earth’s axis play an important role. Laplace proposed that it would be possible to accurately predict the tide if the energy at each of the most important astronomical frequencies were calculated – an insight at the heart of all future tide-prediction methods.


William Thomson (who became Lord Kelvin in 1892) used Laplace’s idea to develop the harmonic method for analysing time series of tide measurements to determine how much energy there is at each tidal frequency. This method required no understanding of hydrodynamics. One simply needed to analyse a long-enough data record at each location so that the energies at the most important astronomical frequencies could be separated from each other. These could then be used to calculate tides at that location for any point in time. He developed the first Tide Prediction Machine designed to carry out calculations based on this method in 1872–1873.

Independently, William Ferrel of the US Coast and Geodetic Survey also developed a technique for harmonic analysis and prediction in the early 1880s inspired by Laplace.

It was recognised that harmonic constants could also be calculated for other tidal frequencies that represent other orbit variations in the Earth-Moon-Sun system – giving greater predictive accuracy. In addition, non-linear shallow-water effects can transfer tidal energy to still other frequencies, and so over time those frequencies were included in the harmonic prediction method. These so-called over-tides involve higher harmonics of the basic astronomical frequencies, and they are what make a tide curve for shallow water look distorted when compared with the simple cosine curve for deep water, for example, showing a faster rise and slower fall.

Over time, Tide Prediction Machines became better developed, and predictions could be made for an entire year for all major ports and harbours around the world where data had been taken and harmonically analysed. For those so-called reference stations, the heights and times of all predicted high and low waters were published in annual tide tables. For ‘secondary stations’ without sufficient data for harmonic analysis, high and low tide differences from a nearby reference station were calculated for daily prediction of local tides. By the early 1900s, this practice was commonplace.

1960 Digital computers became able to to perform the same calculations. In the decades which followed, their efficiency increased, and the information available became better and better. During the same period developments in measuring tides also moved on apace and the combination of information gained through these research methods continued to be used to help people better traverse and understand our oceans.

Exploiting the harmonic method for tidal analysis and prediction requires lots of data. Frequent water-level measurements must be made (usually hourly) for several weeks. The longer the data series, the more harmonic components one can quantify and the more accurate the resulting tide prediction capability would be.

How do you measure the height of the sea surface?

Many different technologies and methods have been used. Until the early 19th Century, sea-level measurements were made using tide poles or staffs. The earliest form of self-recording tide gauges were introduced in the UK during the 1830s. These mechanical float and stilling well gauges became the primary means of sea-level measurement for over 150 years, and continue to operate at some UK locations today. However, they are generally auxiliary systems to newer pressure gauges. In recent decades, many countries have adopted acoustic gauges or radar gauges as their standard means of sea-level measurement.

Find out more about tides and tide measurements from The National Tidal and Sea Level Facility →

Developments in satellite technology have also played a big part in enhancing our ability to measure water heights - both in transmitting data from measurement stations, and in actually making measurements, as with TOPEX/Poseidon satellite launched in 1992 to record the changes in sea level and continued to the present day by the JASON series of missions. Oceans are not the only part of our planet which are affected by gravitational forces, and satellite observations have also helped the study of earth tides – the displacement of the solid Earth's surface caused by the gravity of the Moon and Sun.

Tide Predicting Machines provide a mechanical solution to the problem of summing values of component waves of different sizes which travel at different speeds. They are analogue computers which use the motion of wheels and pulleys to simulate the rise and fall of the ocean tide. Settings of each wheel are programmed to match the amplitude and phase of different components of a tidal pattern. A wire band connects all the wheels and serves to sum their motion. A pen connected to the wire will draw the resulting tidal pattern.

Records from a tide gauge at any particular port were analysed by Doodson’s methods and the resulting analysis would be used to ‘program’ a tide predicting machine. The machine could then be used to predict the tides at that port for any desired date.

Computed predictions from these machines, and their modern digital equivalents, are used to help inform navigation and better understanding of our oceans. The astronomically-forced tides are not the only influence on water surface height; meteorological effects such as air pressure and strong winds make an impact as well. Using supercomputers these are often predictable as well, but generally on much shorter time scales. Combining tidal and meteorological information through numerical modelling provides a powerful forecasting tool which can help those operating offshore, and to protect our coastal communities through early warning systems for coastal flooding.