How do wave buoys work?
Wave buoys don’t look like much more than your standard ocean-floatin’ buoy, but they are clever little devices. Everything on the forecast page (height, period, direction, spread) can get pulled out of 30 minutes of one of these buoys watching itself move around. No cameras, no radar, no sensors reaching down toward the bottom; just a ball of electronics and some elegant signal processing that turns the buoy’s wiggling into a description of the sea surface.
Inside a Sofar Spotter, a common surface wave buoy for shorter deployments, the GPS records where the hull sits in three dimensions 2.5 times per second. Older designs like the Datawell buoys use accelerometers and tilt sensors to get the same information a different way. Either way, the whole measurement comes from one point in the water, three axes of motion, and about half an hour of recording.
Water particles in a passing wave don’t just go up and down. They trace circles in deep water, moving forward on the crest and back in the trough, and the buoy rides those orbits. The diameter of each orbit at the surface is roughly equal to the wave height, so big waves make the buoy swing through big circles and small waves through small ones. Vertical motion tells us how tall the wave is, while horizontal motion at the same instant tells us which way it’s going. In deep water, the vertical and horizontal motions are locked a quarter-cycle apart, which is what makes the math work cleanly. The direction the wave is traveling shows up in whether that horizontal motion is mostly east-west, mostly north-south, or some mix of the two.
Thirty minutes of motion data gets fed through something called a Fast Fourier Transform, which splits a signal over time into its constituent frequencies. A 15-second swell shows up as a peak near 0.067 Hz (1 divided by 15). A 6-second wind chop shows up higher (1 divided by 6). The frequency spectrum is what a wave buoy actually produces, and everything else makes use of it. Significant wave height is a statistic computed from the area under the curve. Peak period is the frequency where the curve is tallest. A messy sea with several things happening at once turns into a clean plot of energy against frequency, where separate swells become separate peaks instead of overlapping confusion.
At each frequency, direction is encoded in how vertical motion correlates with horizontal motion. A wave from the west pulls the buoy up and east-west together. A wave from the south pulls up and north-south. Sorting those correlations by frequency gives us a bearing for each component of the seastate. More simply: if there are two swells, one from the south and one from the west, we can pick that out of the data. A second pair of correlations tells us how tightly the waves at a given frequency stack around that direction, which is where directional spread comes from. A clean groundswell shows up as a narrow peak with a sharp direction. Local wind chop smears across the compass as the buoy is tossed around.
While the measurement of offshore swells is relatively stable and straightforward, what arrives at the break takes a few more steps that introduce a lot of error in prediction. But we all know that about the forecasts.
Further Reading:
You have to love a buoy. This one is about 50km from where I live and is my online go-to first thing before walking down to the lookout to check what is actually hitting.