Rogue waves were only recently accepted as well-established, and they have some big problems that got in their way of their acceptance: their rarity and difficult observing conditions for them.
In 1826, French scientist and naval officer Captain Jules Dumont d'Urville reported waves as high as 108 ft (33 m) in the Indian Ocean with three colleagues as witnesses, yet he was publicly ridiculed by fellow scientist François Arago. In that era it was widely held that no wave could exceed 30 ft (9 m).[19][20] Author Susan Casey wrote that much of that disbelief came because there were very few people who had seen a rogue wave, and survived; until the advent of steel double-hulled ships of the 20th century "people who encountered 100-foot rogue waves generally weren't coming back to tell people about it."[21]
Like the Aenid in 1865, though 4 out of its 6 crewmembers survived. The Wikipedia lists mention three rogue-wave hits on lighthouses, in 1861, 1900, and 1985.
Ocean liners and cruise ships that survived rogue waves are the SS Kronprinz Wilhelm (1901), RMS Etruria (1903), RMS Lusitania (1910), RMS Homeric (1924), RMS Olympic (1926, sister ship of Titanic), RMS Majestic (1934), RMS Queen Mary (1942, came close to capsizing), SS Michelangelo (1966), RMS Queen Elizabeth 2 (1995), Bremen (2001), Caledonian Star (2001), Norwegian Dawn (2005), Louis Majesty (2010).
Yes, the Lusitania that was sunk in WWI, and yes, the Queen Mary that is now in Long Beach CA.
From damage on ships, one could estimate the heights of waves, but hard evidence of rogue-wave heights was collected only relatively recently. In 1984, a big wave was recorded at an oil and gas platform in the Gorm field in the North Sea: 11 meters high. But the most convincing one was recorded in 1995 at the Draupner natural-gas platform in the North Sea. The Draupner wave, as it was eventually named, was nearly 20 meters high, far above the wave heights of about 5 m a few minutes before and after it. The wave caused some minor damage, providing additional evidence of its existence.
In 2000 the British oceanographic vessel RRS Discovery recorded a 29-metre (95 ft) wave off the coast of Scotland near Rockall. This was a scientific research vessel and was fitted with high quality instruments. The subsequent analysis determined that under severe gale force conditions with wind speeds averaging 21 metres per second (41 kn) a ship-borne wave recorder measured individual waves up to 29.1 metres (95.5 ft) from crest to trough, and a maximum significant wave height of 18.5 metres (60.7 ft). These were some of the largest waves recorded by scientific instruments up to that time. The authors noted that modern wave prediction models are known to significantly under-predict extreme sea states for waves with a significant height (Hs) above 12 metres (39.4 ft). The analysis of this event took a number of years, and noted that "none of the state-of-the-art weather forecasts and wave models — the information upon which all ships, oil rigs, fisheries, and passenger boats rely — had predicted these behemoths." Put simply, a scientific model (and also ship design method) to describe the waves encountered did not exist. This finding was widely reported in the press, which reported that "according to all of the theoretical models at the time under this particular set of weather conditions waves of this size should not have existed".[1][13][29][35][36]
Rogue waves have more recently been observed with radar satellites, and they have been observed over much of the world's ocean area.
A big problem with recognizing them was that their existence was much more probable than what one would conclude from a very common model of wave-height variation: a Gaussian model. That's
\( \frac{1}{\sqrt{2\pi\sigma}} e^{-x^2/(2\sigma^2)} \)
for variable x and standard deviation (sigma). More than a few stdevs, one gets very steep falloff, and rogue waves were much more common than what one predicts with such a model.
It is now well accepted that rogue waves are a common phenomenon. Professor Akhmediev of the Australian National University, one of the world's leading researchers in this field, has stated that there are about 10 rogue waves in the world's oceans at any moment.[41] Some researchers have speculated that approximately three of every 10,000 waves on the oceans achieve rogue status, yet in certain spots — like coastal inlets and river mouths — these extreme waves can make up three out of every 1,000 waves, because wave energy can be focused.[42]
Rogue waves also happen in lakes, like Lake Superior in the Great Lakes.
Rogue wave and 
