It came out of the storm; a sudden wall of water as tall as a 10-storey building. On deck, explorer Jules Dumont d’Urville estimated the wave loomed at least 30 metres high – and it was bearing down fast on his ship, the Astrolabe. Somehow, they made it back to shore, losing just one man on that dangerous crossing of the Indian Ocean in 1826.

But when Dumont d’Urville, known as France’s Captain Cook, and his crew later recounted the tale of the monster wave, no one believed them. As far as the scientists of the 19th century were concerned, what the sailors had seen was impossible: no wave could reach more than nine metres. For centuries, ships’ disappearances at sea were blamed on pirates or misadventure, and stories of giant waves dismissed as readily as legends of sea monsters.

Then in 1995, a sensor on a Norwegian oil rig captured proof of what Dumont d’Urville had faced: a wave 26 metres tall, more than twice the size of any recorded in the area in the hours before – taller even than the hypothetical waves that scientists then believed could happen only once every 10,000 years. That same year, when the ocean liner Queen Elizabeth 2 was struck by a 27-metre tall wave en route from Britain to New York, scientists had to admit something else: these so-called rogue waves weren’t just possible, they happened relatively frequently. Facing down that 1995 wave, the QE2 captain said it looked as if they were headed for the white cliffs of Dover.

So, what are rogue waves exactly? And are we getting any better at predicting (and outlasting) them?

What are rogue waves?

Today, the monster wave of sailors’ nightmares has a formal scientific definition: a rogue wave is at least twice as high as recent waves around it. It can rise and disappear quickly out of a stormy sea but it can come out of nowhere too – in calm waters. Professor Nail Akhmediev, a theoretical physicist at the Australian National University, has been working to predict rogue waves through equations. He says survivors will sometimes describe otherwise good sailing weather, “clear skies”, before the monster wave appears. Such phenomena can even swallow rescue helicopters as they swing down to the water.

In more than 40 years at sea, marine engineer Karsten Petersen says he never saw a more terrifying wave than the monster that crashed on deck during a voyage across the Pacific Ocean from Singapore to the United States in 1977. From the bridge, he managed to photograph it (below) – snapping some of the world’s few images of a rogue wave.

When the water crashed on deck, more than 22 metres above sea level, Petersen, now retired, recalls the heart-stopping moment they weren’t sure if the ship was underwater or still afloat. Looking out of the bridge windows was “like looking into a water tank,” he says. “No sky, no horizon, no ship in front of you – only water.” But “like a miracle”, the white mist cleared, and the tanker pressed on through the wild seas, although with heavy damage.

Peter van Duyn also spent many years sailing the world: captaining ships, weathering hurricanes and cyclones and skirting icebergs, in the 1970s and ’80s – before rogue waves were accepted science. “I’ve seen some big, big waves,” he says. “But back then there was no proof and it is hard to judge the exact size on the bridge of a ship. When you got back on land, they’d just say you were dreaming.”

“They found the sub split into three parts on the bottom of the sea but it hadn’t been attacked by anything or anyone.”

Rogue waves are not tsunamis – those waves are triggered by a large displacement of water due to an event such as an earthquake, volcanic eruption or landslide. They affect the entire water column. At sea, you might not even notice a tsunami wave rolling under you but near the shore, as it enters the shallows, those waves can climb to terrifying heights, often kilometres wide.

Rogue waves, meanwhile, are generally thought of as those at the surface, although Akhmediev says there are also giant, unexpected waves deep below, sometimes called rogue internal waves. It’s believed one such monster tore apart an Indonesian submarine and killed all 53 on board in 2021 in the Bali Sea. That wave may have been up to 100 metres tall.

“There was no other explanation,” says Akhmediev of the tragedy. “They found the sub split into three parts on the bottom of the sea but it hadn’t been attacked by anything or anyone.” The area is a known hotspot for such sea turbulence, scientists say, and satellite images taken at the time also revealed waves on the surface, likely “ripples” from a giant wall of water surging below.

Aside from eagle-eyed sailors, Akhmediev says there are now many ways to detect rogue waves, from measuring pressure at the bottom of the ocean to special buoys drifting the seas gauging wave heights.

‘[Rogue holes] can be even steeper than the rogue wave, and very dangerous too – this great hole opening suddenly in the sea.’

“If you counted out all the ocean waves one by one, it’s estimated that one wave out of every 10,000 would be a rogue,” he says. “So there would be at least 10 of them at any one time in the ocean. Of course, luckily, there’s not that many ships out there [compared to the vast ocean], so not many will encounter them.”

In 2004, scientists using satellite data from the European Space Agency spotted at least 10 significant rogue waves, each 25 metres or higher, within just three weeks. At the time, the agency said rogue waves were likely to have sunk most of the 200 supertankers and container ships over 200 metres long that had gone down in severe weather over the previous two decades.

Sometimes, in a phenomenon known as the “three sisters”, giant waves will strike in threes. In 2010, two people were killed when three such rogues hit the Louis Majesty cruise ship off the coast of Spain.

“The first didn’t do much damage but the second and third blew out the glass and flooded into multiple decks,” Akhmediev says. Multiple rogue waves were also to blame for the 1998 Sydney to Hobart yacht race tragedy – in those wild waters, six lives and five boats were lost.

Then in 2012, Akhmediev and his colleagues proved the existence of another oddity: rogue holes, the inverse of a rogue wave where the depth of the trough (the wave’s lowest point) can be twice as big as its crest. “So they can be even steeper than the rogue wave, and very dangerous too – this great hole opening suddenly in the sea,” he says.

How do rogue waves form?

If weather forecasting is complicated, oceans are an even more complex beast, Akhmediev says. The wind whips up waves, driving them across the seas for thousands of kilometres. But everything from the geography of bays and ocean floor to the movements of the Earth and moon – even the amount of salt in the swells – can affect how these waves form.

Still, there are two main schools of thought to explain rogue waves in physics. The simplest is known as linear theory. It argues that when two wave crests meet they can merge into one wave twice as big (just as a trough meeting a crest can cancel it out and flatten the sea). Sometimes different columns of waves “or wave trains” will collide, often when different currents run into each other, forming huge waves for short periods.

“Think of cars travelling at speed,” says Akhmediev. “Every now and then, there’s a pile-up.”

At certain hotspots, scientists can see this in action. The most infamous is off the southeast coast of Africa, says van Duyn, where the fast-moving Agulhas current collides with waters from the Indian and Southern oceans. This can have an amplifying effect on the waves, making them steeper, like focusing light from a magnifying glass.

When scientists at Oxford recreated that 1995 wave that hit the oil rig near Norway, known as the Draupner wave, in a tank in the lab, they saw something that looked remarkably similar to the great wave depicted by Japanese artist Katsushika Hokusai in his iconic 19th-century print Under the Wave off Kanagawa.

But they also found that the dynamics of how waves break change when two peaks crisscross. If they meet at the right angle, sometimes they can line up to a rogue.

This linear theory does not explain many elements of waves, though, including why some rogues form on seemingly calm waters in the middle of nowhere. “And we know waves don’t act in a nice linear way,” where the size of a rogue is in perfect proportion to the waves it came out of, says Akhmediev. That’s why he and many mathematicians are increasingly looking to the strange world of quantum physics for an explanation. “All particles act like waves, after all, even on a subatomic level,” he says.

Under their “non-linear theory”, waves not directly interacting can sometimes share energy. “Like cars, they carry enormous amounts of energy,” he says. “And sometimes it can grow”, leeching out from other surrounding waves and “concentrating into a single rogue”.

In 2012, he and German scientists tested their own solution in the lab – with one unfortunate Lego pirate, whose ship they capsized by generating a freak wave in otherwise calm waters. (“Our pirate survived it though, he now lives on my desk,” Akhmediev laughs.) The experiment revealed that rogue waves can be even bigger than previously thought, more than five times the size of others around them in a phenomenon they dubbed “super rogue waves”.

How do you survive a rogue wave?

Captains suddenly confronted with a rogue have few good choices, says van Duyn, who is now a maritime expert. If a giant wave smashes on deck, it can conk out a ship’s engines and other systems or wash away its crew and cargo. Even worse, he says, is a rogue wave hitting you at night. “If you can’t see it coming, you don’t have any chance to steer the ship.”

Ideally, he says, you’d want to sail head-on into such a wave. Being hit from the side risks a capsizing. Of course, going bow-first up that steep cliff of water comes with its own dangers. If the wave is big enough, the drag could tear the ship apart. That’s why ships wrecked in such disasters are often found in pieces, even with holes punched through their hulls by the water.

“Sometimes when ships disappear, they’re found completely broken in two,” says van Duyn. “It doesn’t happen as often now, luckily, as we build ships better. Even some of the wild waves I’ve been up against, I’ve never really thought we were about to sink.” When van Duyn was sailing in the 1980s, at least one ship vanished every day at sea. Today, the global fleet is far larger but losses have been more than halved as ship design improves.

“I’ve lost steering before on a ship, and we couldn’t keep it head-on to the wave. Things got precarious.”

But experts, including Akhmediev, warn that ships are still not built to withstand the force of rogue waves – many, many metric tonnes more than standard waves. Many ships are built to weather waves only about 11 metres high, yet a review found every ship was likely to encounter at least one 20-metre wave over a 25-year lifetime.

“You can design ships better but obviously that’s going to cost,” says van Duyn. “And you can’t design for everything. They thought they’d made the Titanic unsinkable with all those extra compartments and bulkheads, but she still went down. Or maybe you’ll end up making it too strong, or too heavy.”

Steel on a ship needs to be flexible, not just strong, to move with the sea. Standing on the bridge you can often see it flexing at the bow. “It would snap otherwise,” he says. “Ships are designed to roll to a certain extent too in storms, but once they are bent over at 40, 50 degrees, they start to take on water. I’ve lost steering before on a ship, and we couldn’t keep it head-on to the wave. Things got precarious, but we managed to right it.”

Ageing ships, as well as improperly loaded cargo holds or inferior steel, can lower the odds of outlasting such a wave, he says. So can decisions made at sea. Ships often opt to slow down and ride out bad weather, but when they are on tight logistical deadlines, ferrying the world’s supplies, time is money. When the Suez Canal was blocked by one optimistic (and 400-metre-long) container ship for six days in 2021, for example, ships instead braved the turbulent waters around southern Africa to make their deadlines. “They had to go into the rogue wave territory we usually avoid,” van Duyn says.

Are we getting better at predicting rogue waves?

Even though scientists are still debating the (likely multiple) causes of rogue waves, they are already trying to predict them. “We’re really at the beginning of that now,” says Akhmediev. In the US, the National Oceanic and Atmospheric Administration (NOAA) is working on an hourly forecast for potentially hazardous ocean conditions called WAVEWATCH III.

Other mathematicians argue for calculating and then charting the most efficient way rogues can form, to factor in both the linear and nonlinear theories. Trials of this approach in wave tanks have been fairly accurate, although lab conditions are never the real-world chaos that sailors encounter.

Whatever the algorithm, the trick is making predictions fast enough to be of use to ships. On the high seas, conditions can shift minute to minute, let alone hour to hour. Akhmediev points again to the example of street traffic. It might be fairly easy to measure a car’s speed and distance already travelled, but to predict exactly where that car will be in an hour’s time, factoring in traffic lights, other cars, weather and more, he says, is “very tricky maths indeed”. Science pulls it off (to some extent) with weather forecasts, but he says the sea is even slippier to divine than the atmospheric rivers on high. To predict rogue waves, you need to know “in detail the initial conditions of the sea, so you have to be scanning all the nearby waves somehow”.

“Maybe we could watch from space and relay that down to many ships at once. Clouds do make that difficult though.”

Akhmediev and his international collaborators have an idea to build such a scanner for ships, which could continuously calculate risk factors. “Or maybe we could watch from space and relay that down to many ships at once,” he says. “Clouds do make that difficult though.”

Meanwhile, as climate change fuels wilder storms across the globe, scientists warn it will drive bigger rogue waves in some areas too. In places such as the Arctic, where melting ice is opening up new shipping routes, annual wave heights are tipped to climb by six metres. Australia too will likely see its waves grow by 15 per cent if the world hits 2 degrees of warming.

Off the western seaboard of the US, data from a decade of buoys suggests rogue waves may be happening less often, as storm systems shift, but reaching bigger heights when they do. In the south, University of Melbourne oceanographer Professor Ian Young has been studying the impact of climate change on waves for more than 30 years and has found that, on average, waves in the volatile Southern Ocean have grown by about 30 centimetres since 1985 as extreme winds become more frequent.

“The science [of rogues] is a lot better now than in my day,” says van Duyn. “But a lot of it will still come down to good seafaring. And hoping, when you see it, you get the chance to grab the wheel.”

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