Glossary

Harmonic prediction

Harmonic prediction is the method behind every authoritative tide table in the world. NOAA uses it for US stations. The UK Hydrographic Office uses it for the Admiralty TotalTide product. Germany's Bundesamt für Seeschifffahrt und Hydrographie (BSH) uses it. So does France's SHOM, Portugal's Instituto Hidrográfico, Australia's Bureau of Meteorology. The technique dates to William Thomson (Lord Kelvin) in the 1860s and has been refined continuously since.

The input is decades of measured water level at a specific tide gauge — typically hourly or sub-hourly readings going back to at least the 1970s, and at long-record stations like The Battery in New York the record runs back to 1856. Tidal analysts decompose that record into a sum of sine waves, each matching a known gravitational forcing: the principal lunar semidiurnal M2, the principal solar S2, the larger lunar elliptic N2, the diurnal lunar K1, the diurnal solar O1, and dozens of smaller harmonics. The frequencies of those sine waves are fixed by celestial mechanics; only the amplitudes and phases at this specific gauge are unknowns to fit.

To predict a future tide at the same gauge, you sum the fitted constituents forward in time. Done well, the result is accurate to within a few minutes and a few centimetres under normal weather. The method cannot capture anything not in the original record — storm surge, wind setup, river discharge, secular sea-level rise beyond the calibration window. For TideTurtle's accuracy framing per source see methodology, and for the difference between this and the surface-level datum you measure heights against, see the datum entry.