Then, as suddenly as the waves had appeared, they were gone. The boat turned and limped back to Barcelona. A few decades ago, rogue waves of the sort that hit the Louis Majesty were the stuff of salty sea dogs’ legends. No more. Real-world observations, backed up by improved theory and lab experiments, leave no doubt any more that monster waves happen – and not infrequently. The question has become: can we predict when and where they will occur? Science has been slow to catch up with rogue waves. There is not even any universally accepted definition. One with wide currency is that a rogue is at least double the significant wave height, itself defined as the average height of the tallest third of waves in any given region. What this amounts to is a little dependent on context: on a calm sea with significant waves 10 centimetres tall, a wave of 20 centimetres might be deemed a rogue. If that seems a little lackadaisical, for a long time the models oceanographers used to predict wave heights suggested anomalously tall waves barely existed. These models rested on the principle of linear superposition: that when two trains of waves meet, the heights of the peaks and troughs at each point simply sum.

It was only in the late 1960s that Thomas Brooke Benjamin and J.E. Feir of the University of Cambridge spotted an instability in the underlying mathematics. When longer-wavelength waves catch up with shorter-wavelength ones, all the energy of a wave train can become abruptly concentrated in a few monster waves – or just one. Longer waves travel faster in the deep ocean, so this is a perfectly plausible real-world scenario. The pair went on to test the theory in a then state-of-the-art, 400-metre-long towing tank, complete with wave-maker, at the a UK National Physical Laboratory facility on the outskirts of London. Near the wave-maker, which perturbed the water at varying speeds, the waves were uniform and civil. But about 60 metres on they became distorted, forming into short-lived, larger waves that we would now call rogues (though to avoid unwarranted splashing, the initial waves were just a few centimetres tall). We now know that rogue waves can arise in every ocean. That casts historical accounts in a new lightand rogue waves are thought to have had a part in the unexplained losses of some 200 cargo vessels in the two decades preceding 2004. It took a while for this new intelligence to trickle through. “Waves become unstable and can concentrate energy on their own,” says Takuji Waseda, an oceanographer at the University of Tokyo in Japan. “But for a long time, people thought this was a theoretical thing that does not exist in the real oceans.”

Theory and observation finally crashed together in 1995 in the North Sea, about 150 kilometres off the coast of Norway. New Year’s Day that year was tumultuous around the Draupner sea platform, with a significant wave height of 12 metres. At around 3.20pm, however, accelerometers and strain sensors mounted on the platform registered a single wave towering 26 metres over its surrounding troughs. According to the prevailing wisdom, this was a once-in-10,000-year occurrence. The Draupner wave ushered in a new era of rogue-wave science, says physicist Ira Didenkulova at Tallinn University of Technology in Estonia. In 2000, the European Union initiated the three-year MaxWave project. During a three-week stretch early in 2003, it used boat-based radar and satellite data to scan the world’s oceans for giant waves, turning up 10 that were 25 metres or more tall. We now know that rogue waves can arise in every ocean. The North Atlantic, the Drake Passage between Antarctica and the southern tip of South America, and the waters off the southern coast of South Africa are particularly prone. Rogues possibly also occur in some large freshwater bodies such as the Great Lakes of North America. That casts historical accounts in a new light and rogue waves are now thought to have had a part in the unexplained losses of some 200 cargo vessels in the two decades preceding 2004.

So rogue waves exist, but what makes one in the real world? Miguel Onorato at the University of Torino, Italy, has spent more than a decade trying to answer that question. His tool is the non-linear Schrödinger equation, which has long been used to second-guess unpredictable situations in both classical and quantum physics. Onorato uses it to build computer simulations and guide wave-tank experiments in an attempt to coax rogues from ripples. Gradually, Onorato and others are building up a catalogue of real-world rogue-generating situations. One is when a storm swell runs into a powerful current going the other way. This is often the case along the North Atlantic’s Gulf Stream, or where sea swells run counter to the Agulhas current off South Africa. Another is a “crossing sea”, in which two wave systems – often one generated by local winds and a sea swell from further afield – converge from different directions and create instabilities. Crossing seas have long been a suspect. A 2005 analysis used data from the maritime information service Lloyd’s List Intelligence to show that, depending on the precise definition, up to half of ship accidents chalked up to bad weather occur in crossing seas.

In 2011, the finger was pointed at a crossing sea in the Draupner incident, and Onorato thinks it might also have been the Louis Majesty’s downfall. When he and his team fed wind and wave data into his model to “hindcast” the state of the sea in the area at the time, it indicated that two wave trains were converging on the ship, one from a north-easterly direction and one more from the south-east, separated by an angle of between 40 and 60 degrees. Simpler situations might generate rogues, too. Last year, Waseda revisited an incident in December 1980 when a cargo carrier loaded with coal lost its entire bow to a monster wave with an estimated height of 20 metres in the “Dragon’s Triangle”, a region of the Pacific south of Japan that is notorious for accidents. A Japanese government investigation had blamed a crossing sea, but when Waseda used a more sophisticated wave model to hindcast the conditions, he found it likely that a strong gale had poured energy into a single wave system far larger than conventional models allowed. He thinks such single-system rogues could account for other accidents, too – and that the models need further updating. “We used to think ocean waves could be described simply, but it turns out they’re changing at the same pace and same time scale as the wind, which changes rapidly,” he says. In 2012, Onorato and others showed that the models even allow for the possibility of “super rogues” towering as much as 11 times the height of the surrounding seas, a possibility since borne out in water-tank experiments.

With climate change potentially whipping up more intense storms, such theoretical possibilities are becoming a serious practical concern. From 2009 to 2013, the EU funded a project called Extreme Seas, which brought shipbuilders together with academic researchers including Onorato, with the aim of producing boats with hulls designed to withstand rogue waves. That is a high-cost, long-term solution, however. The best defence remains simply knowing when a rogue wave is likely to strike. “We can at least warn that sea states are rapidly changing, possibly in a dangerous direction,” says Waseda. Various indices have been developed that aim to convert raw satellite and sea-state data into this sort of warning. One of the most widely used is the Benjamin-Feir index, named after the two pioneers of rogue-wave research. Formulated in 2003 by Peter Janssen of the European Centre for Medium-Range Weather Forecasts in Reading, UK, it is calculated for sea squares 20 kilometres by 20 kilometres, and is now incorporated into the centre’s twice-daily sea forecasts. “Ship routing officers use it as an indicator to see whether they should go through a particular area,” says Janssen. The ultimate aim would be to allow ships to do that themselves. Most large ocean-going ships now carry wide-sweeping sensors that determine the heights of waves by analysing radar echoes.

Computer software can turn those radar measurements into a three-dimensional map of the sea state, showing the size and motions of the surrounding swell. It would be a relatively small step to include software that can flag up indicators of a sea about to go rogue, such as quickly changing winds or crossing seas. Such a system might let crew and passengers avoid at-risk areas of a ship. The main bar to that happening is computing power: existing models can’t quite crunch through all the fast-moving fluctuations of the ocean rapidly enough to generate fine-grained warnings in real time. For Waseda, the answer is to develop a central early warning system, such as those that operate for tsunamis and tropical storms, to inform ships about to leave port. Thanks to our advances in understanding a phenomenon whose existence was doubted only decades ago, there is no reason now why we can’t do that for rogue waves, says Waseda. “At this point it’s not a shortage of theory, but a shortage of communication.”

- New Scientist Seven giants In 2007, Paul Liu at the US National Oceanic and Atmospheric Administration compiled a catalogue of more than 50 historical incidents probably associated with rogue waves. Here are some of the most significant: 1498 Columbus recounts how, on his third expedition to the Americas, a giant wave lifts up his boats during the night as they pass through a strait near Trinidad. Supposedly using Columbus’s words, to this day this area of sea is called the Bocas del Dragón – the Mouths of the Dragon. 1853 The Annie Jane, a ship carrying 500 emigrants from England to Canada, is hit. Only about 100 make it to shore alive, to Vatersay, an island in Scotland’s Outer Hebrides.

1884 A rogue wave off West Africa sinks the Mignonette, a yacht sailing from England to Australia. The crew of four escape in a dinghy. After 19 days adrift, the captain kills the teenage cabin boy to provide food for the other three survivors. 1909 The steamship SS Waratah disappears without trace with over 200 people on board off the coast of South Africa – a swathe of sea now known for its high incidence of rogue waves. 1943 Two monster waves in quick succession pummel the Queen Elizabeth cruise liner as it crosses the North Atlantic, breaking windows 28 metres above the waterline. 1978 The German merchant navy supertanker MS München disappears in the stormy North Atlantic en route from Bremerhaven to Savannah, Georgia, leaving only a scattering of life rafts and emergency buoys. 2001 Just days apart, two cruise ships – the Bremen and the Caledonian Star – have their bridge windows smashed by waves estimated to be 30 metres tall in the South Atlantic.

- New Scientist