Key concepts

• The conventional short-term description of ocean waves requires statistical stationarity. A time record of actual ocean waves (the fluctuating sea-surface elevation as a function of time at one location) needs therefore to be as short as possible. However, characterising the waves with any reliability requires averaging over a duration that is as long as possible. The compromise at sea is a record length of 15--30 min. If the record is longer, it should be divided into such segments (possibly overlapping; each assumed to be stationary).

• The wave condition in a stationary record can be characterised with average wave parameters, such as the significant wave height and the significant wave period.

• The significant wave height is fairly well correlated with ‘the’ wave height as estimated visually by experienced observers. This is not true for the significant wave period.

• A more complete description of the wave condition is obtained by approximating the time record of the surface elevation as the sum of a large number of statistically independent, harmonic waves (wave components). This concept is called the random-phase/amplitude model.

• The random-phase/amplitude model leads to the concept of the one-dimensional variance density spectrum, which shows how the variance of the sea-surface elevation is distributed over the frequencies of the wave components that create the surface fluctuations.

• If the situation is stationary and the surface elevations are Gaussian distributed, the variance density spectrum provides a complete statistical description of the waves.

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