Waves are the children of the wind. But how far can we exactly predict the size of a wave or ocean swell based on a given wind scenario?
Oceanography, meteorology, and physics are three key sciences that pretty much help us explain the wave phenomenon.
The intertwined knowledge provided by these specific scientific studies improves, among many other useful things, the quality of surf forecasts.
How big? How long? How powerful? How perfect?
The questions that many surfers and water people pose now have quite accurate answers thanks to the iterative work of the scientific community.
In 1974, William G. Van Dorn, a Chicago-born oceanographer from the Scripps Institution of Oceanography, published a book that would become a reference in the field: "Oceanography and Seamanship."
Before the release of the book, Van Dorn studied tsunamis for two decades and was involved in the US nuclear testing program in the South Pacific, including the hydrogen bomb test at Enewetak Atoll in 1952.
He was a surfer, skier, and diver.
Statistical Nature of Wave Heights
In his book "Oceanography and Seamanship," Van Dorn presented a scientifically backed illustration of how wind conditions over a given fetch and duration statistically determine the range of wave heights in a fully developed sea.
In his example, he considered a steady wind of about 33 miles per hour (30 knots or 53.1 kilometers per hour) blowing for 24 hours over an uninterrupted distance of 340 miles (547 kilometers).
Under these conditions, he concluded that the sea state is characterized by a distribution of wave heights rather than a single uniform height.
Specifically, his example showed that:
- 10 percent of all waves are less than 3.6 feet (1.1 meters) high;
- The most frequently occurring wave height is about 8.5 feet (2.6 meters);
- The average (mean) wave height is approximately 11 feet (3.4 meters);
- The significant wave height - defined as the average height of the highest one-third of waves - is around 17 feet (5.2 meters);
- Conversely, 10 percent of waves exceed 18 feet (5.5 m), and the average height of the top 10 percent is about 22 feet (6.7 meters);
- There is roughly a 5 percent chance that, among every 200 waves (which pass in about 30 minutes), a single wave will exceed 35 feet (10.7 meters);
- Over a longer period (about five hours, equivalent to roughly 2,600 waves), there's a 5 percent chance of encountering a wave taller than 40 feet (12.2 meters);
The Lessons Learned
What's really interesting about William G. Van Dorn's figures is that they do more than simply give you a typical wave height.
They reveal the statistical nature of a fully developed sea under a given wind, fetch, and duration, that is, a spectrum of heights with a well‐defined distribution often approximated by the Rayleigh distribution.
The underlying physics tells us that the energy transferred from wind to waves increases roughly with the square of the wind speed.
While Van Dorn's figures are derived under specific conditions (30 knots, 24 hours, 340-mile fetch), similar empirical relationships apply elsewhere.
With adjustments for local fetch, duration, water depth (which influences wave shoaling), and even currents, these relationships can be used to estimate wave statistics in other regions or storm conditions.
For example, modern wind–wave models like NOAA's Wavewatch III or SWAN for coastal regions use these principles to predict the entire wave spectrum for any given wind field.
The same physics that governs Van Dorn's example underlies all these models.
A stronger or longer-lasting wind (or a greater fetch) doesn't just increase the average wave height - it also broadens the distribution so that the probability of extreme waves (sometimes called rogue waves) increases.
So, we end up with a nonlinear relationship that tells us that even modest increases in wind speed can lead to disproportionately higher waves once the sea becomes fully developed.
Words by Luís MP | Founder of SurferToday.com
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