[thedoc (OP)]

Chloe asked the Naked Scientists:
   What determines whether the tide is low or high, when the full moon is visible.  The pattern appears to be inconsistent, yet there must be an explanation if the moon controls the tide, right?
What do you think?

[evan_au]

How does the moon impact the tides?

The Moon has a major impact on driving the tides, due to its proximity to Earth. The Sun is farther away, and has less impact, but still significant.

Tides would be easy to predict if there were no continents, the Earth was not rotating, and the ocean had a uniform depth.

However, in the present epoch, North-South continents (Africa-Europe and North/South America) block the flow of the tidal bulge around the Earth; the velocity that a wave can propagate at the equator is less than the speed of rotation of the Earth, and so the tides fragments into local oscillations, which rotate around points in the mid-ocean which have almost no tides.

The amplitude and phase of the tide is affected by the angle between the Sun and the Moon, but also by the depth of the ocean, and the distance from these central tide-free points.

The pattern appears to be inconsistent

For many years, tides were monitored in each port, and predicted based on the history of tides at that port.
Some ports have 2 tides per day, some have 1 per day, and some have a combination.
While nearby ports had similar tides, there was no overall pattern.

Now, however, we have GPS which can measure the height of ships in the open ocean, and so determine tides away from fixed ports. And we have satellites which use radar to measure the height of the ocean and its waves precisely, all around the world.

This has revealed global tide patterns which were not visible from ports:
See: http://en.wikipedia.org/wiki/File:M2_tidal_constituent.jpg

As I understand it, in this map:

• The white "stars" are the central points in the oceans which have almost no tide. (There is also one "hidden" inside New Zealand.)
  
• The lack of tide is indicated by the dark blue color.
  
• The lines radiating from the star are at hourly intervals; the number of lines indicate the number of tides per day.
  
• The arrow indicates the direction around the star in which the tide circulates.
  
• The spacing of the lines indicates how rapidly the tide changes.
  
• The red and black areas (farthest from the stars) have the most extreme tides.

[evan_au]

Here is an animation of world tides, where blue represents a low tide, and red represents a high tide:

[evan_au]

I came across this table of "Tidal Constituents" - the values you can plug into a tidal model for a particular port, using the method of "Harmonic Analysis" - something that people may also recognize as "Fourier Analysis".

An oddity in this article is that the land can rise and fall by up to half a meter at the equator, under the influence of tides from the Sun and Moon. This will subtract from the water depth measured at that port.

when the full moon is visible

This happens monthly, and it is described by a component M_m, which has a fairly small maximum amplitude of 20mm. The full moon does not have much impact on the tides.

What determines whether the tide is low or high

There are cyclic components that produce 2 high tides per day ("Semi-Diurnal") due to the action of the Moon (M₂) and Sun (S₂). The Moon's contribution (up to 384mm vertical amplitude) is more than twice the Sun's contribution (maximum 179mm). The maximum amplitudes are experienced on the equator, with diminishing effects towards the poles.

There are also cyclic components that produce 1 high tide per day ("Diurnal"), but these have less amplitude than the Semi-Durnal tides. They have most impact at latitudes around 45° North and South, but less towards the equator and poles.

So, depending on your latitude, you will have a different ratio of 1 or 2 tides per day.

Once these Tidal Constituents are measured and calculated for a given port, they can be fed into a machine to predict future tides. Today these calculations are done by computers, but you can see some of the earlier steampunk contraptions used for predicting tides by following the links on the following page:
http://tidesandcurrents.noaa.gov/predmach.html