Key concepts

Short-term statistics

• The theory describing short-term statistical characteristics of wind waves is based on the assumption that the surface elevation is a stationary, Gaussian process.

• For such a process, Rice (1944, 1945) has given an analytical expression for the mean frequency of level crossing in terms of the variance density spectrum.

• With this expression it can be shown that, for waves with a narrow spectrum, the crest height and the wave height are Rayleigh distributed with the zeroth-order moment of the wave spectrum as the only parameter. Observations have shown that this is also the case for waves with a broader spectrum.

• The significant wave height is readily estimated from the spectrum as. This is typically 5%–10% larger than the value of estimated directly from measured time series.

• Observations show that, for wind-sea spectra, the significant wave period is typically 5% shorter than the peak period of the spectrum.

• The maximum individual wave height in a given duration (under stationary conditions) is a random variable, with a corresponding probability density function that can be estimated from the wave spectrum and the duration. In most storms, this maximum individual wave height is about twice the significant wave height.

• The mean length of a wave group, in terms of the number of waves, can be estimated from the width of the variance density spectrum.

Long-term statistics

• Long-term wave statistics (relating to dozens of years or more) can be obtained from observations or from computer simulations. Some theoretical support to analyse such observations and simulations is provided by the extreme-value theory.

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