The open ocean is a vast basin where almost no one measures the wind directly. Fixed platforms are rare and expensive, and satellite scatterometers, instruments that probe the surface with radar, need ground truth for calibration. Coastal zones have such data, but far from shore, there's a void.
The MELODI drifting buoy, a small sphere with a satellite navigation receiver and a motion sensor, tackles this differently. Instead of just measuring wave height, it listens to the full spectrum (set of frequencies) of accelerations it experiences while afloat. Older buoys of this kind used only a narrow frequency band, the "equilibrium range" of the spectrum, where wave energy stops growing. That gave errors of 1–2 m/s and confusion about direction in light winds. MELODI takes the whole picture.
First, a complex model, the teacher, is trained on satellite data. This is a regularized regression (a fitting method with protection against overfitting) with error correction. It achieves an error of 0.9 m/s, nearly matching the accuracy of the satellites themselves. Then, using symbolic regression, the teacher is distilled into compact formulas that can be embedded directly into the buoy's processor. One formula relies solely on the wave spectrum (error ~1.0 m/s), while another adds data on the buoy's own motion (0.93–0.94 m/s).
Wind direction is reconstructed from wave moments — characteristics of the asymmetry of oscillations in the wind-wave band. The error is about 9 degrees. This is comparable to the disagreement between different satellites and stationary buoys. In essence, a small drifting sphere has learned to see the wind as well as multi-million-dollar orbital platforms, and twice as accurately as its predecessors. Winds up to 18 m/s are determined confidently, while stronger gusts are flagged as unreliable, the buoy honestly says when it's uncertain.
Before MELODI, drifting buoys for wind measurement used the "equilibrium range" principle of the wave spectrum, proposed by Japanese oceanographer Yoshiaki Toba in the 1970s. He noticed that at certain frequencies, wave energy stops depending on the duration of wind forcing and is determined only by wind speed.
The idea of a swarm of drifting sensors reading the weather from waves recalls the "Myriads" from Stanisław Lem's novel The Invincible — except instead of mechanical flies, the ocean is plied by weather-sensing spheres.