This page in Bosnian
This page in Swedish
This page in Georgian
This page in Croatian
This page in Estonian
This page in Kazakh
This page in Ukrainian
This page in Azerbaijanian
This page in Thai
This page in Belarusian
This page in Chinese
Tides and Tide Prediction
Halls Harbour, Nova Scotia; and Halls Harbour, six hours later.
from Greenberg, p.128A
* General stuff about tides and tide prediction (this page).
of today's tide predictions from the National Ocean Service
and from the
WWW Tide and Current Predictor.
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.
NOTE: Some of this information appears in a 3-part
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
Tides and history: The tide predictions for D-Day by Bruce Parker, in
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 diurnal inequality). [From
G. H. Darwin's Encyclopaedia Britannica article,
now available online. Note that in this
graph, time increases to the left.]
Times of high tides are computed
and published by the National Ocean Service. For a current
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
Fonts adjusted January 28, 2020
Links updated July 20, 2020