Statistical description of wave parameters
Because of the random nature of natural waves, a statistical description of the waves is normally always used. The individual wave heights often follow the Rayleighdistribution. Statistical wave parameters are calculated based on this distribution. The most commonly used variables in coastal engineering are described below.
Contents
Most commonly used variables in coastal engineering
Significant wave height
The significant wave height, H_{s}, is the mean of the highest third of the waves in a timeseries of waves representing a certain sea state. This corresponds well with the average height of the highest waves in a wave group. H_{s} computed on the basis of a spectrum, is referred to as H_{m0}.
Mean wave period
The mean wave period, T_{m}, is the mean of all wave periods in a timeseries representing a certain sea state.
Peak wave period
The peak wave period, T_{p}, is the wave period with the highest energy. The analysis of the distribution of the wave energy as a function of wave frequency (period^{1}) for a timeseries of individual waves is referred to as a spectral analysis. Wind wave periods (frequencies) often follow the socalled JONSWAP and PiersonMoskowitz spectra. The peak wave period is extracted from the spectra. As a rule of thumb the following relation can be used: T_{p} ~ 5.3 H_{m0}^{1/2}.
Mean wave direction
The mean wave direction, θ_{m}, which is defined as the mean of all the individual wave directions in a timeseries representing a certain sea state.
Describing wave conditions
These parameters are often calculated from continuous or periodic timeseries of the surface elevations; typically the parameters are calculated once every one or three hours, whereby a new discrete timeseries of the statistical wave parameters is constructed. This timeseries is thereafter analysed statistically to arrive at a condensed description of the wave conditions as follows:
 Wave height distribution represented by H_{s} vs. percentage of exceedence. This often follows a Weilbulldistribution
 Directional distribution of the wave heights, which is often presented in the form of a wave rose
 Scatter diagram of T_{p} vs. H_{s}
Analyses of extreme wave conditions are performed on the basis of max. wave heights in single storm events or on the basis of annual max. wave heights. These analyses are often presented as exceedence probability vs. wave heights.
References
Further reading
 Mangor, Karsten. 2004. “Shoreline Management Guidelines”. DHI Water and Environment, 294pg.
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