How Tides Work

Tides are the result of gravitational forces from the moon, sun, and other celestial bodies. These forces, combined with the benthic environment, create predictable oscillations in water levels that can be modeled as a sum of sinusoidal waves called harmonic constituents.

Tide predictions are created by adding up the effects of potentially hundreds of factors like the location of the sun, the moon, and the benthic environment. These constituents are derived from analyzing past water levels.

Harmonic Constituents

Single Constituent

You can think of each tidal constituent as a sine wave. For example, below is a single constituent, M2, or "Principal lunar semidiurnal constituent" for Monterey, California during the first week of January 2018:

If this constituent, which measures the regular effect of the moon on water levels, were the only one that affected the tides, then tides would go up and down in a regular pattern.

Multiple Constituents

However, once you add more constituents to measure more effects, it gets complicated. To simplify, let's take just four constituents and plot them for the same location:

All Constituents

Just for fun, let's take a look at all the defined constituents:

Combined Prediction

If we add all these constituents together, they cancel each other or amplify each other, leading to an accurate tide prediction:

Constituent Properties

Each tidal constituent is defined by three key properties that determine its contribution to the overall tide prediction:

• • Amplitude: The strength of this constituent's effect on water levels, typically measured in meters or feet.
• • Phase (Epoch): The timing offset relative to an astronomical reference, measured in degrees.
• • Speed: How quickly this constituent oscillates, measured in degrees per hour.

Where Tidal Constituents Come From

Harmonic Analysis

Tidal constituents are derived by running harmonic analysis on observed water levels. This involves fitting sinusoidal functions to historical tide gauge data to extract the amplitude and phase of each constituent.

Published Data

Some agencies, like NOAA, publish tidal constituents that are available on their website and via an API. Other agencies do not provide constituents directly, but do provide data on observed water levels that can be analyzed.

Further Reading

To learn more about tidal constituents and harmonic analysis, these resources are helpful:

• Theory of the Harmonic Model of Tides
  An exhaustive description of how Pytides and Neaps handle tidal constituents.
• NOAA Overview of Harmonics
  Official NOAA documentation on harmonic constants.
• About Harmonic Constants and Sub Station Corrections
  The classic XTide description of harmonic constituents.