Replaying a real recording · Puerto Romano, Marbella

How do you measure a wave?

This water is not an animation loop. It is 205 seconds of sea, recorded off Marbella by Puerto Romano — the small solar buoy behind marola.surf — and rebuilt from its spectrum, wave by wave. The buoy is riding its own data.

Scroll — in four short acts you'll know exactly how bobbing becomes a number
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Act I · The recording

Five times a second,
the buoy feels itself fall.

There is no camera and no radar in the water. Inside the sealed hull an inertial sensor measures one thing: vertical acceleration — the lift and drop you'd feel in your stomach on a small boat.

Every wake cycle the buoy holds still and listens: 1,024 samples at 5 Hz — 205 seconds of raw motion, in metres per second squared. This trace is the actual record, exactly as it came up the cellular link.

To a person this wiggle is noise. No two seconds repeat, and the height of the sea is nowhere to be seen in it. The trick is to stop reading it left to right — and start asking what it is made of.

Act II · The unweaving

Every sea is a sum
of simple waves.

Joseph Fourier's 200-year-old idea: any wiggle, however messy, can be rewritten — exactly — as a stack of pure sine waves, each with its own period, strength and timing.

The Fast Fourier Transform is the recipe-reader. Watch the recording peel apart: these sinusoids are its real ingredients. Add them back together and you get the original trace, sample for sample.

Now line the ingredients up by frequency and let the height of each bar say how much energy it carries. This is the sea's spectrum — its fingerprint. Short chop on the right, long swell on the left.

Act III · The alchemy

From shaking
to shape.

We recorded acceleration, but you want height. Calculus connects them: a wave of frequency f accelerates (2πf)² times harder than it displaces. To get back to metres, every bar is divided by (2πf)⁴.

That divisor is astonishingly steep. Energy at a 60-second period is amplified about 160,000× more than energy at 3 seconds. Slow bins get a colossal megaphone. Remember that — it's the loaded gun on the wall.

Add up the area under the height spectrum — call it m₀ — and a century-old formula gives the headline number: Hs = 4√m₀, significant wave height: the average of the biggest third of waves, the number sailors actually experience.

Height isn't the only number hiding in the spectrum. The tallest bar names the sea's rhythm: flip its frequency over and you get the peak period, Tp = 1/f — here, one wave every 3.5 seconds. Long periods mean slow, powerful strides of swell; short ones mean fussy, wind-whipped water.

And the dashed line at 8 seconds tells you where the waves came from. Shorter than 8 s is chop — wind-sea being made here, right now; longer is swell that travelled to reach you. Each side's area gets its own 4√ to become chop height and swell height — and Marola's five states lean hardest on chop, because chop is what makes the water feel messy.

Act IV · The instrument room

Your turn at the bench.

Six real records from Puerto Romano. The whole pipeline you just scrolled through runs live in your browser — change anything and watch the sea, the spectrum and the verdict react.

Where the pipeline stops trusting slow bins. The firmware ships at 0.04 Hz (25 s).

The 8-second line splits local wind-sea from travelled swell.

A zero-rate gyro bias in °/s. The injected signal is the actual contamination band-passed out of the 27 Aug record, scaled to your bias.

A true story

The afternoon the sea
was 32 metres tall.

On 27 August 2026 Puerto Romano sat in a calm 0.4 m sea and reported waves the size of office blocks. The culprit was a lie 1.5 degrees per second wide: the gyroscope's zero-rate bias had drifted, the fused "which way is up" tilted ~15°, and a slow whisper of gravity leaked into the vertical channel. Divided by (2πf)⁴, the whisper became a mountain range.

You can reproduce it upstairs with the red slider — the same record, the same maths. Note what doesn't move: the chop band. Short waves live where the megaphone is quiet, which is exactly how the fault was diagnosed from shore.

The fix shipped the same week — the gyro now re-zeroes itself every single wake cycle, while the buoy is electrically still — and the record "Honest again" in the picker is the same buoy, the same afternoon, measuring truthfully once more.

We publish our failures on purpose. An instrument you can trust is one whose mistakes you're allowed to watch.