Significant wave height
Encyclopedia
In physical oceanography
, the significant wave height (Hs or SWH)
is defined traditionally as the mean wave height
(trough to crest
) of the highest third of the waves
(H1/3), but now usually defined as four times the standard deviation
of the surface elevation (or equivalently as four times the square root of the first moment of the wave spectrum). The symbol Hm0 is usually used for that latter definition. The significant wave height may thus
refer to Hm0 or H1/3, the difference in magnitude between the two definition is only a few percent.
during World War II. The significant wave height was intended to mathematically express the height estimated by a "trained observer". It is commonly used as a measure of the height of ocean waves.
, it is possible to encounter a wave that is much larger than the significant wave.
Generally, the statistical distribution of the individual wave heights is well approximated by a Rayleigh Distribution. For example, given that Hs = 10 meters, or 33 feet, statistically:
This implies that one might encounter a wave that is roughly double the significant wave height. However, in rapidly changing conditions, the disparity between the significant wave height and the largest individual waves might be even larger.
wave height, which is defined as square root of the average of the squares of all wave heights, is approximately equal to Hs divided by 2.
For example, according to the Irish Marine Institute:
stipulates that certain countries are responsible for providing weather forecasts for the world's oceans. These respective countries' meteorological offices are called Regional Specialized Meteorological Centers, or RSMCs. In their weather products, they give ocean wave height forecasts in significant wave height. In the United States, NOAA's National Weather Service
is the RSMC for a portion of the North Atlantic, and a portion of the North Pacific. The Ocean Prediction Center
and the Tropical Prediction Center's Tropical Analysis and Forecast Branch (TAFB) issue these forecasts.
RSMCs use wind-wave models
as tools to help predict the sea conditions. In the U.S., NOAA's WAVEWATCH III(R) model is used heavily.
Below is an example of a text forecast from the Ocean Prediction Center, where the term Seas represents Significant Wave Height.
Physical oceanography
Physical oceanography is the study of physical conditions and physical processes within the ocean, especially the motions and physical properties of ocean waters.Physical oceanography is one of several sub-domains into which oceanography is divided...
, the significant wave height (Hs or SWH)
is defined traditionally as 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....
(trough to crest
Crest (physics)
A crest is the point on a wave with the maximum value or upward displacement within a cycle. A trough is the opposite of a crest, so the minimum or lowest point in a cycle.-Interference:...
) of the highest third of the waves
Ocean surface wave
In fluid dynamics, wind waves or, more precisely, wind-generated waves are surface waves that occur on the free surface of oceans, seas, lakes, rivers, and canals or even on small puddles and ponds. They usually result from the wind blowing over a vast enough stretch of fluid surface. Waves in the...
(H1/3), but now usually defined as four times the standard deviation
Standard deviation
Standard deviation is a widely used measure of variability or diversity used in statistics and probability theory. It shows how much variation or "dispersion" there is from the average...
of the surface elevation (or equivalently as four times the square root of the first moment of the wave spectrum). The symbol Hm0 is usually used for that latter definition. The significant wave height may thus
refer to Hm0 or H1/3, the difference in magnitude between the two definition is only a few percent.
Origin and definition
The original definition resulted from work by the oceanographer Walter MunkWalter Munk
Walter Heinrich Munk is an American physical oceanographer. He is professor of geophysics emeritus and holds the Secretary of the Navy/Chief of Naval Operations Oceanography Chair at Scripps Institution of Oceanography in La Jolla, California.-Early life:Born in 1917 in Vienna, Austria-Hungary,...
during World War II. The significant wave height was intended to mathematically express the height estimated by a "trained observer". It is commonly used as a measure of the height of ocean waves.
Statistical distribution
Significant wave height, scientifically represented as Hs or Hsig, is one important level when considering the statistical distribution of ocean waves. The most common waves are less than that of Hs. This implies that encountering the significant wave is not frequent. However, statistically, when two significant waves come into phasePhase (waves)
Phase in waves is the fraction of a wave cycle which has elapsed relative to an arbitrary point.-Formula:The phase of an oscillation or wave refers to a sinusoidal function such as the following:...
, it is possible to encounter a wave that is much larger than the significant wave.
Generally, the statistical distribution of the individual wave heights is well approximated by a Rayleigh Distribution. For example, given that Hs = 10 meters, or 33 feet, statistically:
- 1 in 10 will be larger than 10.7 m (36 ft)
- 1 in 100 will be larger than 15.1 m (51 ft)
- 1 in 1000 will be larger than 18.6 m (62 ft)
This implies that one might encounter a wave that is roughly double the significant wave height. However, in rapidly changing conditions, the disparity between the significant wave height and the largest individual waves might be even larger.
Other statistics
Other statistical measures of the wave height are also widely used. The RMSRoot mean square
In mathematics, the root mean square , also known as the quadratic mean, is a statistical measure of the magnitude of a varying quantity. It is especially useful when variates are positive and negative, e.g., sinusoids...
wave height, which is defined as square root of the average of the squares of all wave heights, is approximately equal to Hs divided by 2.
For example, according to the Irish Marine Institute:
- "… at midnight on 9/12/2007 a record significant wave height was recorded of 17.2m at with a period of 14 seconds."
Weather forecasts
The World Meteorological OrganizationWorld Meteorological Organization
The World Meteorological Organization is an intergovernmental organization with a membership of 189 Member States and Territories. It originated from the International Meteorological Organization , which was founded in 1873...
stipulates that certain countries are responsible for providing weather forecasts for the world's oceans. These respective countries' meteorological offices are called Regional Specialized Meteorological Centers, or RSMCs. In their weather products, they give ocean wave height forecasts in significant wave height. In the United States, NOAA's National Weather Service
National Weather Service
The National Weather Service , once known as the Weather Bureau, is one of the six scientific agencies that make up the National Oceanic and Atmospheric Administration of the United States government...
is the RSMC for a portion of the North Atlantic, and a portion of the North Pacific. The Ocean Prediction Center
Ocean Prediction Center
The Ocean Prediction Center , established in 1995, is one of the National Centers for Environmental Prediction’s original six service centers. Until January 12, 2003, the name of the organization was the Marine Prediction Center. Its origins are traced back to the sinking of the RMS Titanic in...
and the Tropical Prediction Center's Tropical Analysis and Forecast Branch (TAFB) issue these forecasts.
RSMCs use wind-wave models
Wind wave model
In fluid dynamics, wind wave modeling describes the effort to depict the sea state and predict the evolution of the energy of wind waves using numerical techniques...
as tools to help predict the sea conditions. In the U.S., NOAA's WAVEWATCH III(R) model is used heavily.
Below is an example of a text forecast from the Ocean Prediction Center, where the term Seas represents Significant Wave Height.
Generalization to wave systems
A significant wave height is also defined similarly, from the wave spectrum, for the different systems that make up the sea. We then have a significant wave height for the wind-sea or for a particular swell.See also
- Sea stateSea stateIn oceanography, a sea state is the general condition of the free surface on a large body of water—with respect to wind waves and swell—at a certain location and moment. A sea state is characterized by statistics, including the wave height, period, and power spectrum. The sea state varies with...
- Rogue wave: a wave of over twice the significant wave height
- Ocean Prediction CenterOcean Prediction CenterThe Ocean Prediction Center , established in 1995, is one of the National Centers for Environmental Prediction’s original six service centers. Until January 12, 2003, the name of the organization was the Marine Prediction Center. Its origins are traced back to the sinking of the RMS Titanic in...