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Convention for describing wave direction

Users should note that by convention the direction of waves (and hence also wave energy flux) is described as the direction the waves are moving towards.  This is opposite from the convention for wind direction which is defined as where the winds are coming from.  Thus a southwesterly wind blows from the southwest; the corresponding wind-sea moves towards the northeast and is a thus described as a northeasterly wind-sea.

Wave Height definitions

The wave height is the distance between trough and crest.  However, many waves co-exist at the surface of the ocean and their distribution is given by the 2D wave spectrum.  From this distribution, the significant wave height is defined as 4 times the square root of the integral over frequency and direction of the wave spectrum.  It can be shown to correspond to the average wave height of the one-third highest waves, commonly known as H_1/3.  The mean wave direction is the spectrally averaged propagation direction of the waves (weighted by amplitude).

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Other parameters are defined to characterise the sea state as prescribed by the wave spectrum.  In particular, the reciprocal of the frequency corresponding to the peak of the spectrum is the wave peak period.  Different mean periods are calculated by spectrally averaging the spectrum and similarly for mean wave direction (see IFS documentation part VII, chapter10).

Wind waves and Swell

Very often, the sea state is composed of different wave systems.  If there is any sufficient wind, there will always be a wave system associated with it, referred to to "wind-wave" or "wind-sea".  The part of the spectrum that is not associated with the local wind is normally called "swell".

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Fig2.2.1-4: A schematic example of the Wave Spectrum at a location off the Dutch coast associated with a long wave swell propagating from the northern North Sea and wind-sea propagating across the southern North Sea.  At a given time there will be a swell of relatively uniform frequency and direction, and a wind-sea of rather broader frequency and direction. A 2D plot of wave energy against frequency and direction is in the top right diagram.  For simplicity this is reduced to a 1D plot of wave energy against frequency.  These peak values of swell and wind-sea can be plotted in chart form.

Significant wave height

Based on theory of wave-wave interaction, the estimate of highest equivalent weight (H_max) is calculated from the wave spectrum. 

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Fig2.2.1-5: Wave Energy associated with a given frequency E(f) plotted against wave frequency (f).  The Equivalent Wave Height (EWH) associated with a given wave frequency is derived from the area under the curve for that frequency bin. The significant wave height H_s is derived from the total area beneath the curve.

Maximum wave height from forecasts and observations

Currently ECMWF output shows the expectation value of the maximum height of the envelope of waves (ρ).  However, buoy observations of sea elevation (η) tend to report the maximum wave height estimated from the zero crossing (H_max).  These values do not correspond exactly but differences are normally small.

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Fig2.2.1-6: Schematic showing difference between representation of maximum wave height.

The black line shows a record of sea surface elevation as measured by a buoy (η). The maximum crest height above zero-crossing is shown green.  The crest to trough height (H_max), is shown blue.

The forecast envelope of the varying sea surface wave crests is shown by the grey line (ρ). The maximum of the the envelope of crest heights is at a slightly different time and elevation.  The maximum envelope crest to trough height is taken as twice the maximum of the envelope above zero-crossing (shown red).