Introduction
When waves of two to three times greater than the Significant Wave Height (SWH) are observed they are described as extreme or rogue waves. Extreme waves are however not freak, as they are sometimes described. Although rare, they are natural and satellite observation has shown they are far more common than previously thought. Research by Mark Donelan and Anne-Karin Magnusson [1] in 2007 showed that rogue waves occur roughly twice daily at any given location during a storm.
Max Wave Height
Ocean waves are never exactly the same height because waves travelling at different speeds and/or in different directions interact with each other to form new waves and the height of waves in the ocean exhibits a Rayleigh distribution. This means there are a lot more small waves than large waves. It also means that if you wait long enough a really big wave will occur.
Figure 1 shows the probability of waves of different heights in the North Atlantic from observations by satellite altimeters. Heights are shown on the x axis and probabilities of occurrence on the y axis. In the North Atlantic a significant wave height of 2.5m occurs most frequently, around 25% of the time.
The Rayleigh distribution for ocean waves shows approximately one wave in 3,000 will be 2 times larger than the SWH. If we know the SWH (primary forecast parameter), we can estimate the maximum wave height that will occur in a given period of time. The table below shows the ratios for the occurrence of waves of different heights:
| Wave Height | Ratio |
| Average height | 0.64 |
| Significant wave height (H1/3) | 1 |
| Highest 10% | 1.29 |
| Highest (HMAX) in 3 hours | 1.87 |
| Highest (HMAX) in 12 hours | 2.25 |
| Highest (HMAX) in 24 hours | 2.35 |
To determine any one of the wave sizes, take SWH and multiply it by the applicable ratio. For example, at a point in the ocean, over a 3 hour period, if the significant wave height is 4m, the average height is 2.56m (4 x 0.64), the highest 10% of the waves will be 5.16m (4 x 1.29) and the highest waves will be 7.48m (4 x 1.87).
The ratios in the table are for a point in the ocean and the actual period will be determined by the wave encounter period, which is a function of the wave period and the vessel’s course and speed. As a practical rule of thumb, the maximum wave that is likely to be encountered is approximately double the SWH.
Extreme or rogue waves
Analysis of satellite derived observations in the MAXWAVE and GLOBWAVE projects has confirmed what mariners have long suspected, that extreme waves occur more often in some areas than others. Extreme waves were most frequent among strong currents, in the South Atlantic and under hurricane conditions. The highest wave observed in a 2 year study period was during the southern winter when a wave of about 30 meters was found in the South Atlantic (see Figure 2 below) when the SWH was 10m [2].
MAXWAVE correlated the occurrence of weather related ship accidents with sea-state and found that the SWH and wave period alone did not explain casualties. Dangerous sea state conditions were found to occur when there were rapid changes in the sea state parameters close to the accident time. A common situation at the time of the accident or just after it is crossing sea conditions, when the swell and the wind sea are at right angles as shown in Figures 3 and 4.
Research has also shown that extreme waves are more likely in regions where there is focussing by variations in water depth and/or currents [3], the rapid increase in energy drives wave interactions that enhance the likelihood of extreme waves.
Warnings
As a result of the MAXWAVE research, Meteo France have created a cross sea index which they use as a warning criterion (Toffoli et al., 2003). The WMO Manual on Marine Meteorological Services (WMO No. 558) has been amended to include “in addition, phenomena like breaking seas, cross seas and risk of abnormal/Maxwaves waves shall also be included, if needed and feasible.”
Where is there the highest probability of extreme waves occurring?
Outside of tropical revolving storms, the areas where the conditions are thought to be favourable to the occurrence of rogue waves are shown in Figure 5. The storm tracks in the North Atlantic and the Southern Ocean feature, as do the Norwegian Sea, the Grand Banks, South West of Australia stretching into the Great Australian Bight and Cape Agulhas.
The conditions under which extreme waves are most likely to occur off Cape Agulhas are described in the NGA Pilot [7] and are characteristic of those found elsewhere. They occur following fast moving winter depressions ahead of which the winds flow in the same direction as the Agulhas current, often resulting in the current increasing by 1-2 knots from its usual speed. After the frontal passage a rapid wind shift occurs and this is when freak waves are likely to happen. Such waves have an extremely short lifespan, lasting in most cases 30 seconds to 1 minute.
Freak waves generated in the Agulhas Current are unusually steep with short periods, as opposed to bell shapes in common with most ocean waves. This results in a large trough preceding the wave. Since the Agulhas current core runs seaward of the 100 fathom line, the advice is to keep inshore of the 100 fathom (180m) line. Similar conditions occur to these occur off the Grand Banks as depressions coming off the North American continent deepen and re-enforce the Gulf Stream and similarly the Leeuwen current off SW Australia.
Extreme waves in the Norwegian Sea and North Sea have been linked to intense Polar Lows. A re-analysis [9] of the conditions leading to the renowned ‘Draupner Wave’, which was measured at 25.6 m by a downward-looking laser at the North Sea Draupner gas platform on 1 Jan 95, indicates partly crossing-sea conditions at the platform at the time of the event. Nonlinear interactions may also have contributed; these are discussed below.
Competing Theories
The differences in the focussing and cross seas explanations arise from the environmental modification and resulting linear addition of waves. Although supported by observations this is not a complete solution and an alternative nonlinear explanation has also been proposed [10]. This argues that rogue waves could be produced by mechanisms that amplify and focus long-wavelength fluctuations. Work continues, but in the meantime mariners should remain vigilant in the areas indicated by MAXWAVE and GLOBWAVE, which provide the most practical guidance to date.
Stay connected and safe.
References:
1. Mark A. Donelan, Anne-Karin Magnusson. The Making of the Andrea Wave and other Rogues. Scientific Reports, 2017; 7: 44124 DOI: 10.1038/srep44124
2.Rosenthal, W. Results of the MAXWAVE project. Institute of Coastal Research, Geesthacht, Germany
3.Janssen, T.T and Herbes, T.H.C, (“Nonlinear wave statistics in a focal zone,” Journal of Physical Oceanography Volume 39: Issue 8
6. Toffoli A., J.M. Lefevre, J. Monbaliu, H. Savina, E. Bitner-Gregersen, 2003, Freak Waves: Clues for Prediction in Ship Accidents?, Proc of the ISOPE 2003, Hawaii.