Inphysical oceanography, thesignificant wave height (SWH,HTSGW^[1] orH_s) is defined traditionally as the meanwave height (trough tocrest) of the highest third of thewaves (H_1/3). It is usually defined as four times thestandard deviation of the surface elevation – or equivalently as four times the square root of the zeroth-order moment (area) of thewave spectrum.^[2] The symbolH_m0 is usually used for that latter definition. The significant wave height (H_s) may thus refer toH_m0 orH_1/3; the difference in magnitude between the two definitions is only a few percent.SWH is used to characterizesea state, includingwinds andswell.

The original definition resulted from work by the oceanographerWalter Munk during World War II.^[3][4] 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.

Significant wave heightH_1/3, orH_s orH_sig, as determined in the time domain, directly from thetime series of the surface elevation, is defined as the average height of that one-third of theN measured waves having the greatest heights:^[5]$${\displaystyle H_{1/3}=\frac{1}{\frac{1}{3}N}\sum _{m=1}^{\frac{1}{3}N}{H}_m}$$ whereH_m represents the individual wave heights, sorted into descending order of height asm increases from 1 toN. Only the highest one-third is used, since this corresponds best with visual observations of experienced mariners, whose vision apparently focuses on the higher waves.^[5]

Significant wave heightH_m0, defined in thefrequency domain, is used both for measured andforecasted wavevariance spectra. Most easily, it is defined in terms of thevariancem₀ orstandard deviationσ_η of the surface elevation:^[6]$${\displaystyle H_{m_0}=4\sqrt{m_0}=4{\sigma }_{\eta },}$$ wherem₀, the zeroth-moment of the variance spectrum, is obtained byintegration of the variance spectrum. In case of a measurement, the standard deviationσ_η is the easiest and most accurate statistic to be used.

Significant wave height, scientifically represented asH_s orH_sig, is an important parameter for the statistical distribution of ocean waves. The most common waves are lower in height thanH_s, so significant waves do not occur constantly. In addition, many waves are higher than the significant wave.

Generally, the statistical distribution of the individual wave heights is well approximated by aRayleigh distribution.^[7] For example, given thatH_s is 10 metres (33 feet), statistically:

• 1 in 10 will be larger than 10.7 metres (35 ft)
• 1 in 100 will be larger than 15.1 metres (50 ft)
• 1 in 1000 will be larger than 18.6 metres (61 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 statistical measures of the wave height are also widely used. TheRMS wave height, which is defined as square root of the average of the squares of all wave heights, is approximately equal toH_s divided by 1.4.^[2][8]

For example, according to the Irish Marine Institute:^[9]

… at midnight on 9/12/2007 a record significant wave height was recorded of 17.2m at with [sic] a period of 14 seconds.

Although most measuring devices estimate the significant wave height from awave spectrum,satellite radar altimeters are unique in measuring directly the significant wave height thanks to the different time of return from wave crests and troughs within the area illuminated by the radar. The maximum ever measured wave height from a satellite is 20.1 metres (66 ft) during a North Atlantic storm in 2011.^[10]

TheWorld Meteorological Organization stipulates that certain countries are responsible for providing weather forecasts for the world's oceans. These respective countries' meteorological offices are calledRegional Specialized Meteorological Centers, or RSMCs. In their weather products, they give ocean wave height forecasts in significant wave height. In the United States, NOAA'sNational Weather Service is the RSMC for a portion of the North Atlantic, and a portion of the North Pacific. TheOcean Prediction Center and theTropical Prediction Center's Tropical Analysis and Forecast Branch (TAFB) issue these forecasts.

RSMCs usewind-wave models as tools to help predict the sea conditions. In the U.S.,NOAA's Wavewatch III model is used heavily.

Asignificant wave height is also defined similarly, from thewave spectrum, for the different systems that make up the sea. We then have asignificant wave height for the wind-sea or for a particular swell.

• Ocean Prediction Center
• Rogue wave – a wave of over twice the significant wave height
• Sea state

• Current global map of significant wave height and period
• NOAA Wavewatch III
• NWS Environmental Modeling Center
• Envirtech solid state payload for directional waves measurement

• Naval architecture
• Physical oceanography
• Shipbuilding
• Water waves

• Articles with short description
• Short description matches Wikidata
• Use dmy dates from February 2025