On New Year's Day 1995, a storm was raging in the North Sea. The Draupner E oil platform, run by the company Statoil, stood in the middle of it. Waves rolling past averaged about 12 meters tall. The platform had been engineered to handle waves of this size.
At 3:20 in the afternoon, a laser instrument pointing down at the sea recorded something different. A single wave 25.6 meters tall rose out of the water and struck the platform. That is about 2.13 times the height of the waves around it. The wave damaged the lower deck and equipment. The sea then returned to its 12 meter pattern as if nothing had happened.
The rogue wave appeared once, in the middle of an ordinary storm pattern, and then the pattern returned.
Engineers were stunned. A wave twice as tall might be expected to hit about twice as hard. Yet the damage was far worse than double. Scientists later compared the two waves' energy. Wave energy depends on amplitude, which is the distance from average sea level up to the crest. A wave's full height, from trough to crest, is about twice its amplitude. Doubling height doubles amplitude, so the ratio is the same either way. Energy grows with the square of that ratio. Squaring 2.13 gives about 4.5. The rogue wave carried roughly 4.5 times the energy of an ordinary storm wave.
A side view of a water wave drawn as a smooth up and down line. A dashed horizontal line across the middle is labeled Average Sea Level. The top of the bump is labeled Crest. The bottom of the dip is labeled Trough. A vertical arrow from the dashed line up to the crest is labeled Amplitude. A longer vertical arrow from the trough up to the crest is labeled Wave Height. A horizontal arrow from one crest to the next is labeled Wavelength. A note beside the arrows reads: Wave height is about two times the amplitude. If one wave is twice as tall as another, its amplitude is also twice as big.
Amplitude is measured from average sea level to the crest, while wave height is measured from trough to crest.
Wave energy does not grow the same way height grows. It grows like the area of a square. Draw a square on graph paper with sides 1 box long. It covers 1 box. Now make each side 2 boxes long. It covers 4 boxes, not 2. Doubling the side gives 4 times the area, because 2 times 2 is 4. Wave energy works the same way with amplitude. Amplitude is how far the wave rises above average sea level. Make the amplitude about 2.13 times bigger, and the energy becomes 2.13 times 2.13, which is about 4.5 times bigger. That is why a wave that was only about twice as tall hit with about four and a half times the energy.
Before that day, many scientists doubted that such waves existed. Sailors had told stories of giant waves appearing from nowhere, but no instrument had ever captured one. The Draupner measurement was the first ever recorded by scientific equipment. Researchers including Haver in 2004 and Adcock and others in 2011 studied the record closely. The New Year's Day wave proved that rogue waves are real. It also showed why one such wave can be far more dangerous than its height alone suggests.
