How Are Tides Predicted? Adding Up Cycles That Were Worked Out Long Ago

The tide is driven by the gravitational pull of the moon and sun on the ocean, and the motions of those bodies are known with great precision far into the future, which means the driving forces can be calculated exactly. What is not calculable from first principles is how any particular stretch of coast responds, since the shape of the basin, the depth, the coastline and the friction all modify the arriving wave enormously, producing ranges of a few centimetres in some places and over fifteen metres in others. The solution splits the problem, taking the driving forces from astronomy and the local response from measurement, and that combination is why predictions are excellent for places with a long record and unreliable for places without one.

The prediction is a sum of components, each a simple oscillation with a fixed period:

• •The main lunar semidiurnal component, with a period of about twelve hours and twenty five minutes, which usually dominates
• •The main solar semidiurnal component, at exactly twelve hours
• •Daily components arising from the tilt of the earth, which dominate in some parts of the world
• •Fortnightly variation from the interaction of the lunar and solar components, giving spring and neap tides
• •Monthly and yearly components from the shapes and tilts of the orbits
• •Components with periods of years and decades, including one of about 18.6 years from the precession of the lunar orbit

The strength and timing of each component at a given place is extracted from a record of measured water levels, which is the part requiring patience. A tide gauge records the level continuously, and a year of data allows the components to be separated reliably, since components with similar periods can only be distinguished by observing long enough for them to drift apart. Nineteen years of record captures the longest of the significant cycles. The analysis producing these constants was done by hand in the nineteenth century and then by remarkable mechanical computers, machines with a pulley and wire arrangement that summed the components physically and drew the resulting curve, which were used to produce published tables for decades before electronic computation replaced them. The constants for a port change slowly if the harbour is dredged or the coastline altered, which requires the analysis to be repeated.

The enormous variation in tidal range between places has specific causes worth naming. Resonance is the main one, since a bay or channel whose natural period of oscillation is close to the tidal period amplifies the arriving wave enormously, which is why a few places have ranges above fifteen metres while an open coast nearby has two. Funnelling concentrates the same volume of water into a narrowing space, raising the level. Shallowness distorts the shape of the wave, making the rise faster than the fall in many estuaries and producing a tidal bore in a few rivers where the leading edge steepens into a wave that travels upstream. The rotation of the earth organises the tide into systems that circulate around points of almost no tide, which is why some places, including parts of the Mediterranean and the Baltic, have almost no tide at all.

The published prediction is the astronomical tide alone, and the actual water level differs from it for reasons the method cannot include. Atmospheric pressure raises or lowers the sea directly, with roughly a centimetre for each millibar of departure from average. Wind piles water against a coast or drives it away, which can add or subtract a metre or more in a severe storm and is the mechanism behind the most damaging coastal floods. River discharge raises levels in estuaries. Sustained changes in ocean circulation and temperature produce departures over seasons. The difference between the prediction and the observation is called the surge and is forecast separately by models, and serious coastal flood warnings come from combining a high predicted tide with a forecast surge, which is why the worst events happen when a storm coincides with a spring tide.

Astronomical driving forces are calculable exactly, while the local response to them is not, so prediction takes the forces from theory and the response from a measured record. The tide is summed from components with fixed periods, the largest completing in about twelve hours and twenty five minutes. Published times exclude weather, and a storm surge on top of a spring tide causes the worst floods.