Estimates for tide water levels were once made using tidal prediction machines, which were beautifully engineered mechanical devices.
These were a type of analogue computer and the predictions were surprisingly accurate considering how many factors affect the tides. In addition to the influence of the sun and the moon, these include the effects of orbital wobbles of the Earth, the depth and contours of the seabed, and the shape of the coastline.
Indeed, some modern software programs take account of eighty or more so-called harmonics which, superimposed on each other, define the shape and timing of the tidal cycle.
In the UK, tidal predictions are made by the UK Hydrographic Office and the National Tidal and Sea Level Facility (NTSLF), which is part of the National Oceanography Centre. Predictions are readily available on websites and in the tide tables on sale at newsagents and RNLI shops in most seaside resorts. The estimates are used by shipping operators, boating and fishing enthusiasts and many others.
If you are interested in the history of tidal prediction, it is worth looking online to find photographs and drawings of tidal prediction machines as some could be considered a work of art.
Typically they had numerous wheels and pulleys of different sizes to represent the different harmonics to consider. These contributions would be aggregated by a wire or tape running through the machine, with the resulting predictions drawn on a chart or displayed on a dial.
Less than a hundred were built worldwide and one of the last and most elaborate was designed and operated at the former Bidston Observatory on the Wirral: the Doodson-Legge machine.
Used until the 1960s, at one time about two-thirds of the world’s ports relied on its predictions for shipping operations.
Although the observatory is now closed, in collaboration with National Museums Liverpool this machine has been rebuilt and is on display at an exhibition called Tide & Time at NTSLF in Liverpool. This is open to the public on one day each month with another earlier machine also on display. The visits are accompanied by an interesting talk on the history of the pioneering work done on tidal science in Liverpool and on the Wirral.
If you are interested in the history of tidal prediction in Liverpool and the Wirral, I say more about this in The Mersey Estuary: A Travel Guide, along with information on how tidal bores form and other tidal phenomena such as surge. Click this link for details.