Rogue Waves and the Complacency of Scientists with Models

I saw a fascinating program last night on the Science Channel. (Yeah, I actually watched some TV. Doesn’t happen often.) It was about “rogue” or “killer” waves at sea. Apparently mariners have been reporting them for centuries, but up until 1995 scientists had a nice “linear model” that described ocean waves, and it predicted that a 100-foot monster wave might happen once every 10,000 years on Earth — basically never. So, they figured the mariners were just telling tall tales the way that fishermen do. The fact that the world’s multibillion-dollar shipping industry loses an average of one ship **per week** without explanation was written off to corrosion or “human error”.

Until New Year’s Day, 1995, when an oil rig in the middle of the North Sea recorded a 100-foot wave going by during a storm. Oops.

By examining where most rogue wave reports come from (many off the SE coast of South Africa), some bright scientist figured out that when big waves and wind meet an oncoming current (such as storms from the South Atlantic moving up towards the Indian Ocean, meeting the warm narrow fast Aghulas Current flowing the other way along the African coast), waves can become much larger and steeper.

Okay, problem solved, scientists happy. Shipping industry happy too, because now they can just tell their captains what to steer around.

Until March 2001, when two cruise ships in the middle of the South Atlantic each met 100-foot rogue waves, only days apart, and were almost destroyed. There were no currents or other local features to explain the occurrences.

So an intrepid scientist in Germany got access to a radar satellite capable of measuring wave heights with sufficient precision, and started scanning satellite data for evidence of waves so high they shouldn’t exist. To everyone’s surprise, including her, she found dozens within a three-week window. All over the place.

A physicist in Italy (but with a notably American accent) thinks that ocean waves can be modeled by the “nonlinear Schrödinger equation”. One of his model-generated solutions looks almost exactly like the profile of the 1995 New Years’ Day wave that was recorded by the oil platform. If he’s right, it means that there are two kinds of waves out there: the normal sinusoidal “linear” waves, and — hidden among them — some scattered nonlinear waves with subtly different shapes. These rogues are usually indistinguishable from the linear waves, but every once in a while they go into a strange mode where they suck energy from their adjacent neighbors and rear up into monsters for a little while, then subside again.

Mariners have described this as a “rogue sea”. I swear I’ve seen this phenomenon myself, when watching a stormy ocean from shore; every now and then an unusually large wave seems to rise up somewhere, then drop again.

Part of what fascinates me about this story is the utter faith that “scientists” (as a monolithic entity, granted) had in the “linear model”: so much that they flat-out rejected numerous and continuing eyewitness accounts of rogue waves. (Let’s assume that the program’s representation of prevailing attitudes is accurate.) And the shipping and ship-design industries had complete faith in what scientists said, and built and navigated their ships accordingly. The world’s fleet of ocean-faring vessels can generally withstand 40-foot seas, but not 100-foot waves with steep faces and deep troughs. Because, after all, those can’t exist.

It took the incontrovertible evidence of the 1995 New Years’ Day wave recorded by the oil rig to cause a reexamination of the belief that such waves can’t happen, and further in-your-face evidence (literally, for too many crew and passengers) to cause a reexamination of our model for ocean wave dynamics in general. The unexplained disappearance of one ship per week was insufficient.

I suppose that shouldn’t be too surprising. One of the earliest findings of educational research was how firmly entrenched “misconceptions” are, and how emotionally difficult it is for students (or anyone) to let go of a model that has proven at least partially successful for them.

I gather that the Schrödinger model is not yet firmly established, but the existence of rogue waves is. Personally, I’ll think twice next time I consider taking a boat out in rough seas… Or next time I hear a scientist arguing that some piece of data “must” be spurious because it doesn’t fit the model we “know” is true.

The question is, what do **you** believe so strongly that you might be rejecting contradictory evidence?