Tide Oscillation Height Time Calculator

Tide oscillation and height

Most coasts run on a semidiurnal lunar cycle with period T ≈ 12 h 25 min, which works out to two highs and two lows per lunar day. A plain sinusoidal model does the job: h(t) = (A/2)·sin(2π·t / T), where A is the tidal range. When the Moon and Sun line up at new or full Moon, their gravitational pull adds up and you get syzygy, or spring tides. At quadrature, around the first and last quarter, the two forces partly cancel and the tides go slack into neaps. Along the Brazilian coast the range runs from roughly 3 m at Fortaleza to 6 m near Marajó, which is what feeds the Amazon pororoca tidal bore. A 2.4 m amplitude over a 12.42 h cycle is about what you'd expect on the Southeast coast.

Applications

Coastal navigation and port access, where deep-draught vessels wait for high water at Santos and Itajaí. Surf forecasting, since Saquarema and Itacoatiara only fire on specific tide windows. Recreational fishing, because estuary species feed on the incoming tide. Marine biology and its intertidal zonation, the engineering of berths and offshore platforms, and tide gauge calibration by the Brazilian Navy.

FAQ

Why 12 h 25 min and not 12 h flat? The Moon moves about 12.2° per day along its orbit, so a lunar day stretches to 24 h 50 min. Half of that is the semidiurnal gap between consecutive high tides.

What is the difference between spring and neap tides? Spring tides show up near new and full Moon, with the range at its widest. Neap tides happen near the quarters, with the range at its narrowest. The whole thing repeats about every 14.8 days.

Why is the Marajó range so large? The funnel-shaped estuary of the Amazon resonates with the semidiurnal forcing. That resonance amplifies the open-ocean tide and, on certain spring tides, sets off the pororoca bore.