How to know what ocean wave measurements really show?

You are sitting out on the pier one day watching the waves roll by (not quite a song lyric, but you have the image). Each wave slowly rolls under your feet. You see the water rise and fall along the barnacle covered piling. You definitely have a sense of which direction that wave is moving. The top of the wave is a few feet above the bottom of the wave.  That's your wave height. It takes about ten seconds between the peak of two waves. So, that's your wave period. Wave height is how high the wave is from crest to trough and wave period is the time between those troughs and crests. Simple right?

Description of ocean waves from the Coastal Data Information Program (CDIP).

But wait ... it took 10 seconds for the first one to pass, 12 seconds for the next one, which was a foot higher, and then a bunch of smaller waves that are moving faster. This is not quite as straightforward as the single height and period we see coming from NOAA or other information sources.

The reason, as anyone who watches the ocean for any time knows, is that the surface is a mix of waves of different lengths, heights, and directions all mixing together. An average condition, sometimes referred to as the sea state, does emerge, but all those waves jumble together. So, what measurements are the buoys giving us? The buoys measure the vertical motion of the sea surface and compile all of those height measurements into what's called an energy spectrum. The energy spectrum is the amount of wave energy (which is the height of a wave squared) split up into frequencies (frequency = 1/period). There are many reasons energy spectra are used to describe ocean waves, but primarily they provide scientists and engineers an easy way to compile complex information resulting from measuring the sea surface.

It helps to break down a single spectrum to better comprehend it. The figure below shows a spectral measurement from a NOAA wave buoy. The spectra is essentially the "raw" data coming out of a wave measurement buoy. It is compilation of the wave data over 20 minutes. The plot shows the energy (that's roughly our wave height squared) on the Y-axis, frequency on the bottom X, and period on the top X.

Image of the Monterey Bay NOAA NDBC buoy 46042 spectral wave energy. 

The wave spectra has a dominant or peak period that we see from the NOAA measurements. That's the easiest part to pick out. It's just the peak along that little spectrum and is about 10 seconds or at a frequency of 0.1 Hertz on this plot. Another one we see from the NOAA buoys is the average period. It is the average period of all of the waves over a time period. However, in my opinion the dominant period usually tells us what we are interested in, but it can miss longer period swells like a good south swell in Hawaii or California. That's where we may look for a second peak in the higher periods (lower frequencies) in the spectra.

Then there is also the height, but that expresses as energy in the spectral plots. How do we get a wave height from this? Fortunately, we can easily calculate a significant wave height form the spectra. It's the average of the highest one third (highest 30%) of the waves measured in a 20 minute time period. The way we do this mathematically is we sum up the area under the spectra, take the square root, and multiply it by 4.

The wave heights and periods are all essentially based on the vertical motion of the buoy. If you are more interested in the math definitely dig in here: NOAA Wave Measurement Description

Wave directions are determined from either the horizontal moving or tilting of the buoy.  Think of an object floating on the sea surface.  As a wave moves past, the object moves forward then backward as the wave moves past. Also, its going to tilt forward and backward along the face and back of the wave. The measurements of these motions are also compiled into what's called a directional spectrum. It is similar to an energy spectrum, but it tells us which direction the waves are coming from over a 20 minutes period. AND .. if there are two swells in the water, it will measure both of the directions and be able to discern the height spectra of each.

Below is a directional spectrum from a CDIP buoy in Monterey Bay. Think of these plots like a compass with each direction representing where wave energy is coming from. Now instead of a line spectrum like the previous graph, we have colors to represent our higher (red) and lower (blue) wave energy. The plot shows the most wave energy (red) coming from about 300 degrees (west-northwest). We can also see some wave energy from the southerly direction. We have a little bit of south swell in the water.

Directional spectra from CDIP buoy in Monterey Bay.

Amazing stuff and maybe a little more complicated than most people thought, but now that you're in the know, share the knowledge!

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