Dashing rogues: freak ocean waves pose threat to ships, deep-sea oil platforms.

In February 1933, the Navy tanker USS Ramapo was steaming its way from the Philippines to San Diego in the midst of an exceptionally strong storm. The 146-meter-long ship was buffeted by near-hurricane-force winds. Early on the morning of Feb. 7, a wave far larger than the others surrounding the ship overtook the Ramapo from behind.

As the stern of the ship dropped into the trough in front of the wave, an officer on the bridge noted that from his vantage point, the crest of the oncoming wave lined up with an observation platform on the ship's mast. Basic geometry puts the wave at more than 34 m tall, the highest ever observed.

Rogue waves like the one that struck the Ramapo occupy a special place in nautical lore. They've smashed into cruise ships, sunk oil-drilling platforms, and terrorized seafarers in fictional accounts for 2,000 years, from Virgil's Aeneid to this summer's film remake Poseidon.

Although rogue waves--also called freak waves or monster waves--are most often encountered during storms or bad weather, they can appear even in calm seas, and they almost always show up with little warning. Scientists once assumed that rogue waves strike any particular patch of ocean only once every several millennia, but oceanographic data now suggest that the waves are much more common.

New mathematical analyses indicate how rogue waves form in some instances and how long these monsters last before they blend back into the surrounding waves. These models suggest that rogue waves build up and dissipate more readily than lore and past research had indicated. The new analyses may enable scientists to better predict where rogue waves will strike--data well worth knowing for the captains of oceangoing vessels.

BIG & TALL "There's no clear definition of what a rogue wave is," says Paul C. Liu, an oceanographer with the National Oceanographic and Atmospheric Administration in Ann Arbor, Mich.

Scientists don't have many detailed shipboard measurements of rogue waves because they tend to appear without warning, and bobbing ships make poor observation platforms.

A wave typically achieves rogue status not by growing to a certain minimum size but by exceeding the surrounding waves by a certain proportion. The basis for comparison is an oceanographic parameter called significant wave height, which researchers typically calculate by taking the average of the tallest one-third of the waves in a particular patch of ocean. Many scientists define a wave as a rogue if it's 2.2 times as tall as the significant wave height.

Besides their size, rogue waves differ from their tamer kin in their shape. The peaks and troughs of ripples that spread from a gentle disturbance in the water have the approximate shape of a smoothly curving sine wave. But the larger an ocean wave is, the more its profile diverges from a sine wave.

"Real waves have higher crests and shallower troughs than sines," says Al R. Osborne, an oceanographer at the University of Turin in Italy. And rogue waves take these shape changes to the extreme. Their crests are often described as "mountains of water" and their troughs as "holes in the sea".

When a ship drops into the trough in front of a rogue wave, "it's like riding a down elevator" says C. Linwood Vincent, an oceanographer at the Office of Naval Research in Arlington, Va.

According to some scientists' models, any particular spot in the ocean should encounter a rogue wave every 10,000 years or so--about the time since the most recent ice age ended. However, data gathered by instruments on relatively stable platforms and on buoys hint that such big waves occur much more frequently than that.

Take, for instance, the data gathered by sensors mounted on a gas-drilling platform that stands in 100-m-deep water off the southern coast of South Africa. That spot, near the imaginary boundary between the Indian and Atlantic Oceans and on the edge of the Agulhas Current, lies within an ocean region well known among mariners for its abundance of rogue waves (SN: 11/23/96, p. 325).

Between 1998 and 2003, the platform's radar equipment measured wave heights twice each second for 20 minutes out of each hour. Of the more than 50,000 data sets gathered during those 6 years, almost 1,600 included at least one wave that measured more than twice that hour's significant wave height, Liu's threshold for rogue-wave status.

In other words, the chance of encountering a rogue wave during any hour spent at this spot was about 3.1 percent. Liu and his South African colleague Keith R. MacHutchon presented their findings in June at the International Conference on Offshore Mechanics and Arctic Engineering in Hamburg, Germany.

Most of the South African rogues were between two and three times the size of their companions, says Liu. In rare cases, however, the rogue waves towered over their peers even more. Six waves measured between three and four times the size of surrounding waves, and another four were more than four times the size of their neighbors. One previous model had suggested that a quadruple-size rogue wave would appear only once every several million years.

In 2004, Liu and another group of colleagues analyzed data gathered by buoy-mounted equipment in the South Atlantic east of Rio de Janeiro between March 1991 and June 1995. Of the nearly 7,500 data sets that the researchers analyzed, 276 included a wave that measured at least twice the size of its companions. So, the chance of encountering a rogue wave during any hour spent at this spot was about 3.7 percent, slightly higher than that found at the site near South Africa.

OCEAN IN MOTION Despite similarities in the frequency of rogue waves at the two sites that Liu and his colleagues analyzed, the root causes of the waves are probably very different.

The seas off South Africa are geographically complicated and highly dynamic, says Liu. The Agulhas Current flows into the area from the northeast, while the prevailing winds in the region blow from the southwest. As a result of that opposition, the winds--which often have blown uninterrupted over long distances--strike the faces of tall, current-driven waves and cause them to stack up even higher. Also, the shape of the seafloor and the coastline steers the waves as they travel through the area, sometimes creating chaotic encounters between wave clusters traveling in different directions at various speeds.

"Surrounded by such a varied assortment of dynamic interactions, it should not be surprising that very large rogue waves could appear from time to time," Liu and his colleagues note.

The buoy data from near South America tell a different story, however. They suggest that rogue waves can occur in relatively calm seas as well as in rough weather, says Liu. The researchers found rogues during periods when significant wave height measured 12 m, but also when significant wave height was as low as 50 centimeters.

Should the smaller waves really be considered rogues? Yes, Liu argues, because they stand out from their peers.

The Office of Naval Research's Vincent agrees. "We're all interested in 100-foot waves," he adds, but a smaller rogue wave in relatively calm waters can pose a threat to fishing boats or pleasure craft.

ADDING UP Scientists underestimated the frequency of rogue waves for many years because they presumed that real ocean waves behave as mathematically ideal waves do: When two theoretical 1-m-tall waves cross paths, they briefly form a wave that's 2 m tall. Physicists call this the principle of linear superposition.

But just as ocean waves don't maintain a perfect sine wave profile, they don't often follow the principle of linear superposition. Instead, they usually stack up to make a wave that's larger than the sum of its parts.

When large numbers of waves are generated by the same phenomenon--a strong storm, say, or an ocean current--they travel in groups called wave trains. Individual waves in a train can pass energy back and forth among themselves, for example when large waves overtake and briefly subsume smaller ones. Over the course of 5 or 10 minutes, relatively benign waves can become "much more exciting," says Osborne.

Moreover, the amplifying interactions between two wave trains traveling in different directions--a condition called crossing seas--can really pump up a wave, he and his colleagues report in the Jan. 13 Physical Review Letters. Not only do the rogue waves grow taller in crossing seas than they do within a single wave train, they're also more likely to form in the first place. Many ships lost in rough weather have gone down in crossing seas, the researchers note.

Computer simulations indicate that the rogues can form quickly in crossing seas, says Mattias Marklund of Umea University in Sweden. For instance, when two trains of 3-m-tall waves intersect at an angle of about 22[degrees], waves 10 m tall appear after just 11 minutes. Marklund and his colleagues report their findings in the Sept. 1 Physical Review Letters.

Similar analyses suggest that rogue waves can disappear almost as quickly as they form. During one computer simulation that featured several trains of 3-m waves, a 7-m rogue formed in a little over 7 minutes, says Victor P. Ruban of the Landau Institute for Theoretical Physics in Moscow. However, just 3 minutes later--after traveling only 1.2 kilometers--the wave had already dissipated its energy and shrunk back to the size of its peers.

With such mathematical techniques, scientists may predict the conditions that spawn rogue waves. Indeed, in addition to their weather projections, the European Centre for Medium-Range Weather Forecasts is now issuing rogue-wave forecasts on an experimental basis, says Peter Janssen of the centre in Reading, England.

Researchers there have divided the world's seas into 40-km-by-40-km areas, and they use data about ocean currents and the weather in those regions to estimate the distribution of wave sizes that mariners can expect. The forecasters issue a warning for an area when one wave out of every 3,000 there is likely to be a rogue.

The center has issued rogue-wave forecasts for about 3 years, but the slow trickle of reports from the open ocean has slowed the verification of the forecasts. Shipping companies don't like to share details about their routes and positions, but Janssen says that he occasionally hears from captains who have encountered a rogue wave that his center had predicted.

The forecasts are important for a variety of seafarers, including workers on oil platforms and on ships laying underwater cables and pipelines, says Vincent. Captains on oil tankers and cargo ships plying the open ocean--the nautical equivalent of long-haul truckers--often seek the shortest and most economical routes to their destinations, sometimes passing closer to a storm than is prudent.

An unexpectedly large wave could disrupt some naval operations at sea, including those in which ships have pulled alongside each other to transfer people, cargo, or fuel. Accurate forecasts of when and where rogue waves could strike will enable captains to steer clear of risky routes and reach distant duty stations as safely as possible, says Vincent.

Although menacing waves have different of causes, identifying the conditions under which some of these rogues form may cut the risk of ships being caught by surprise.