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Halls Harbour, Nova Scotia; and Halls Harbour, six hours later.

* General stuff about tides and tide prediction (this page).

* Samples of today's tide predictions from the National Ocean Service and from the WWW Tide and Current Predictor.

* About Water Levels, Tides and Currents (includes some history of tide prediction) from the NOAA/NOS website.

* Tide Spectra and Tide Sounds: The predicted tidal record for various ports interpreted as musical scores.

* The Song of the Tides: 3000 hours from Ancona and Venice, arranged for woodwinds, marimba by Levy Lorenzo.

* More detailed information about Harmonic Analysis of Tides.

* A nice Calculus with Calculators exercise: The Priming/Lagging of the Tides.

* References.

**NOTE:** Some of this information appears in a 3-part
column
I wrote in April-June 2001 for "What's New in Mathematics" on
the American Mathematical Society webpage. Part III of the column
has a lovely JAVA animation of a tide predictor, due to Bill
Casselman.

Tides and history: The tide predictions for D-Day by Bruce Parker, in
*Physics Today*.

**TIDE PREDICTION. **
People going into or out of a harbor, or anchoring near
a shore, need to know in advance about the behavior of the tide.
The tide is caused by the pull of the sun and the moon on the
oceans, and the rotation of the earth, but its exact pattern
at any particular spot on the coast depends very strongly
on the shape of the coastline and on the profile of the sea floor
nearby. So even though the forces that move the tide are
completely understood, the tides at any one spot are
essentially impossible to calculate theoretically. What we can
do is to record the height of the tide
at that spot over a certain period of time, and
use these measurements to predict the tides in the future.
Here is a typical tide record: this graph shows the height of the
water over fourteen days.

This figure shows the tidal record for two weeks (January 1-14, 1884) at Bombay. The tide was recorded on a cylindrical sheet that turned once every 24 hours. Each daily curve is labelled with its date. Some obvious features: there are usually two high tides and two low tides each day; the tides come about 50 minutes later each day; during the two-week period there is considerable variation in the daily pattern of highs and lows; there is usually a difference in height between two consecutive high tides (the

Times of high tides are computed and published by the National Ocean Service. For a current sample, click here. For a complete analysis of one location (Port Aransas, Texas) with an interesting tidal pattern, click here. The method used today in the United States is a modification of the method called ``harmonic analysis.'' In fact, until 1965 tide predictions were generated by machines along the lines of this one

The Tide Predicter (Kelvin, opposite p. 304).

designed by Kelvin (then Sir William Thomson) in 1873,
based on a suggestion of Beauchamp Tower's for
summing several trigonometric functions with independent
periods. This machine is the embodiment of the
harmonic method of prediction of tides.

Math Dept SUNY Stony Brook

tony at math.stonybrook.edu

May 20 1999

links updated March 17 2013

New musical material added May 23 3015

October 5 2015