How we compute the tide

The tide at a harbour is the sum of a few dozen cosines, each one the harbour's measured answer to one motion of the Moon or the Sun. That is not a metaphor; it is the method every published tide table uses, and the one on every plate we print.

1. 01

   The station's constants

   NOAA publishes, for each station, the amplitude and phase of up to 37 tidal constituents, the measured response of that harbour to the Moon and Sun. We use those numbers as published, public domain, and name the station on the plate.

2. 02

   The astronomy

   Each constituent has a speed fixed by astronomy (M2, the main lunar tide, runs every 12 h 25 m) and a node factor that drifts over the Moon's 18.6-year cycle. We compute both for the year in question, the way NOAA's own tables do.

3. 03

   The sum

   The height at any minute is the datum plus the sum of every constituent's cosine. For the ribbon we sample every fifteen minutes; for the calendar we find each high and low water by bisection, to the minute.

4. 04

   The check

   Before a plate is drawn, the engine's highs and lows for five stations are compared with NOAA's own published predictions for the same week. The receipts are in the repository's tests.

5. 05

   What it is not

   A prediction from astronomy, not a forecast from weather. Wind, pressure and river flow move the water too, and no printed table can know them a year ahead. The plate says so in its footer.

61 stations today, all NOAA. The engine is the one behind Semidiurnal, our free tide clock, vendored into this shop at a named commit so the preview and the print cannot drift apart. See a station's own numbers on its page, for instance the station list.