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Sea state

Sea state

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In oceanography
Oceanography , also called oceanology or marine science, is the branch of Earth science that studies the ocean...

, a sea state is the general condition of the free surface
Free surface
In physics, a free surface is the surface of a fluid that is subject to constant perpendicular normal stress and zero parallel shear stress,such as the boundary between two homogenous fluids,for example liquid water and the air in the Earth's atmosphere...

 on a large body of water—with respect to wind waves and swell
Swell (ocean)
A swell, in the context of an ocean, sea or lake, is a series surface gravity waves that is not generated by the local wind. Swell waves often have a long wavelength but this varies with the size of the water body, e.g. rarely more than 150 m in the Mediterranean, and from event to event, with...

—at a certain location and moment. A sea state is characterized by statistic
A statistic is a single measure of some attribute of a sample . It is calculated by applying a function to the values of the items comprising the sample which are known together as a set of data.More formally, statistical theory defines a statistic as a function of a sample where the function...

s, including the wave height
Significant wave height
In physical oceanography, the significant wave height is defined traditionally as the mean wave height of the highest third of the waves , but now usually defined as four times the standard deviation of the surface elevation...

, period, and power spectrum. The sea state varies with time, as the wind conditions or swell conditions change. The sea state can either be assessed by an experienced observer, like a trained mariner, or through instruments like weather buoy
Weather buoy
Weather buoys are instruments which collect weather and ocean data within the world's oceans, as well as aiding during emergency response to chemical spills, legal proceedings, and engineering design. Moored buoys have been in used since 1951, while drifting buoys have been used since 1979...

s, wave radar
Wave radar
Wind waves can be measured by several radar remote sensing techniques. Several instruments based on a variety of different concepts and techniques are available to the user and these are all often called wave radars...

 or remote sensing
Remote sensing
Remote sensing is the acquisition of information about an object or phenomenon, without making physical contact with the object. In modern usage, the term generally refers to the use of aerial sensor technologies to detect and classify objects on Earth by means of propagated signals Remote sensing...

In the context of spaceflight, a satellite is an object which has been placed into orbit by human endeavour. Such objects are sometimes called artificial satellites to distinguish them from natural satellites such as the Moon....


In case of buoy measurements, the statistics are determined for a time interval in which the sea state can be considered to be constant. This duration has to be much longer than the individual wave period, but smaller than the period in which the wind and swell conditions vary significantly. Typically, records of one hundred to thousand wave-periods are used to determine the wave statistics.

The large number of variables involved in creating the sea state cannot be quickly and easily summarized, so simpler scales are used to give an approximate but concise description of conditions for reporting in a ship's log or similar record.

World Meteorological Organization sea state code

The WMO sea state code largely adopts the 'wind sea' definition of the Douglas Sea Scale
Douglas Sea Scale
The Douglas Sea Scale is a scale which measures the height of the waves and also measures the swell of the sea. The scale is very simple to follow. The Douglas Sea Scale is expressed in one of 10 degrees.- The Scale :...

WMO Sea State Code Wave Height (meters) Characteristics
0 0 Calm (glassy)
1 0 to 0.1 Calm (rippled)
2 0.1 to 0.5 Smooth (wavelets)
3 0.5 to 1.25 Slight
4 1.25 to 2.5 Moderate
5 2.5 to 4 Rough
6 4 to 6 Very rough
7 6 to 9 High
8 9 to 14 Very high
9 Over 14 Phenomenal

Character of the sea swell
  0. None
Low 1. Short or average
2. Long
Moderate 3. Short
4. Average
5. Long
Heavy 6. Short
7. Average
8. Long
  9. Confused

Direction from which swell is coming should be recorded.
Confused swell should be recorded as "confused northeast," if coming from the direction of northeast.

Sea states in marine engineering

In engineering applications, sea states are often characterized by the following two parameters:
  • The significant wave height
    Significant wave height
    In physical oceanography, the significant wave height is defined traditionally as the mean wave height of the highest third of the waves , but now usually defined as four times the standard deviation of the surface elevation...

     H1/3 — the mean wave height
    Wave height
    In fluid dynamics, the wave height of a surface wave is the difference between the elevations of a crest and a neighbouring trough. Wave height is a term used by mariners, as well as in coastal, ocean and naval engineering....

     of the one third highest waves.
  • The mean wave period, T1.

The sea state is in addition to these two parameters (or variation of the two) also described by the wave spectrum  which is the product of a wave height spectrum and a wave direction spectrum . Some wave height spectra are listed below. The dimension of the wave spectrum is , and many interesting properties about the sea state can be found from the spectrum.

The relationship between the spectrum and the wave amplitude for a wave component is:

  • ITTC recommended spectrum for fully developed sea (ISSC spectrum/modified Pierson-Moskowitz spectrum):

  • ITTC recommended spectrum for limited fetch (JONSWAP spectrum)



An example function might be:

Thus the sea state is fully determined and can be recreated by the following function where is the wave elevation, is uniformly distributed between 0 and , and is randomly drawn from the directional distribution function

In addition to the short term wave statistics presented above, long term sea state statistics are often given as a joint frequency table of the significant wave height and the mean wave period. From the long and short term statistical distributions it is possible to find the extreme values expected in the operating life of a ship. A ship designer can find the most extreme sea states (extreme values of H1/3 and T1) from the joint frequency table, and from the wave spectrum the designer can find the most likely highest wave elevation in the most extreme sea states and predict the most likely highest loads on individual parts of the ship from the response amplitude operator
Response amplitude operator
In the field of ship design and design of other floating structures, a response amplitude operator is an engineering statistic, or set of such statistics, that are used to determine the likely behaviour of a ship when operating at sea...

s of the ship. Surviving the once in 100 years or once in 1000 years sea state is a normal demand for design of ships and offshore structures.