Significant wave height

{{Short description|Mean wave height of the highest third of the waves}} {{Use dmy dates|date=February 2025}}

In physical oceanography, the '''significant wave height''' ('''SWH''', '''HTSGW'''<ref>{{Cite web|url=https://earth.nullschool.net/about.html#waves|title=About earth :: A global map of wind, weather, and ocean conditions}}</ref> or ''H''_s) is defined traditionally as the mean ''wave height'' (trough to crest) of the highest third of the waves (''H''_1/3). It is usually defined as four times the standard deviation of the surface elevation – or equivalently as four times the square root of the zeroth-order moment (area) of the ''wave spectrum''.<ref name="Holthuijsen">{{Cite book | publisher = Cambridge University Press | isbn = 978-0-521-86028-4 | last = Holthuijsen | first = Leo H. | title = Waves in Oceanic And Coastal Waters | year = 2007 | page = 70 }}</ref> The symbol ''H''_m0 is usually used for that latter definition. The significant wave height (H_s) may thus refer to ''H''_m0 or ''H''_1/3; the difference in magnitude between the two definitions is only a few percent. SWH is used to characterize ''sea state'', including winds and swell.

==Origin and definition== The original definition resulted from work by the oceanographer Walter Munk during World War II.<ref>{{cite book |last=Denny |first=M.W. |url=https://archive.org/details/biologymechanics0000denn/page/76 |title=Biology and the Mechanics of Wave-swept Shores |publisher=Princeton University Press |year=1988 |isbn=0-691-08487-4 |location=Princeton, New Jersey |pages=76 |url-access=registration}}</ref><ref>{{cite book | last = Munk | first = W.H. | year = 1944 | title = Proposed uniform procedure for observing waves and interpreting instrument records | publisher = Wave Project at the Scripps Institution of Oceanography | location = La Jolla, California }}</ref> 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.

===Time domain definition=== Significant wave height ''H''_1/3, or ''H''_''s'' or ''H''_''sig'', as determined in the time domain, directly from the time series of the surface elevation, is defined as the average height of that one-third of the ''N'' measured waves having the greatest heights:<ref name=Holt_24_28>{{harvtxt|Holthuijsen|2007|pages=24–28}}</ref> <math display="block">H_{1/3} = \frac{1}{\frac13\,N}\, \sum_{m=1}^{\frac13\,N}\, H_m</math> where ''H''_m represents the individual wave heights, sorted into descending order of height as ''m'' increases from 1 to ''N''. 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.<ref name=Holt_24_28/>

===Frequency domain definition=== Significant wave height ''H''_m0, defined in the frequency domain, is used both for measured and forecasted wave variance spectra. Most easily, it is defined in terms of the variance ''m''₀ or standard deviation ''σ''_''η'' of the surface elevation:<ref>{{harvtxt|Holthuijsen|2007|page=70}}</ref> <math display="block">H_{m_0} = 4 \sqrt{m_0} = 4 \sigma_\eta, </math> where ''m''₀, the zeroth-moment of the variance spectrum, is obtained by integration of the variance spectrum. In case of a measurement, the standard deviation ''σ''_''η'' is the easiest and most accurate statistic to be used.

==Statistical distribution of the heights of individual waves== thumb|Statistical distribution of ocean wave heights Significant wave height, scientifically represented as ''H''_s or ''H''_sig, is an important parameter for the statistical distribution of ocean waves. The most common waves are lower in height than ''H''_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 a Rayleigh distribution.<ref>{{cite journal | last = Tayfun | first = Aziz | title = Narrow-band nonlinear sea waves | journal = Journal of Geophysical Research | volume = 85 | number= C3 | year = 1980 | pages=1543–1552 | doi=10.1029/jc085ic03p01548|bibcode = 1980JGR....85.1548T }}</ref> For example, given that ''H''_s is {{convert|10|m|ft|abbr=off}}, statistically:

* 1 in 10 will be larger than {{convert|10.7|m|ft}} * 1 in 100 will be larger than {{convert|15.1|m|ft}} * 1 in 1000 will be larger than {{convert|18.6|m|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 RMS wave height, which is defined as square root of the average of the squares of all wave heights, is approximately equal to ''H''_s divided by 1.4.<ref name="Holthuijsen"/><ref>{{Cite book | publisher = World Scientific | isbn = 978-981-02-0421-1 | last1 = Dean | first1 = Robert G. | first2 = Robert A. | last2 = Dalrymple | title = Water Wave Mechanics for Engineers and Scientists | year = 1991 | page = 193 }}</ref>

For example, according to the Irish Marine Institute:<ref>{{cite web | url = https://www.marine.ie/home/aboutus/newsroom/NewsArchive/2007/ResultsofWeatherBuoyReadings.htm | title = Report on Weather Buoy Readings During December Storm — 6th to 11th December | publisher = Irish Marine Institute | access-date = 2013-02-07 | url-status = dead | archive-url = https://web.archive.org/web/20131123045840/http://www.marine.ie/home/aboutus/newsroom/NewsArchive/2007/ResultsofWeatherBuoyReadings.htm | archive-date = 23 November 2013 | df = dmy-all }}</ref> {{bq|text=… at midnight on 9/12/2007 a record significant wave height was recorded of 17.2m at with {{sic}} a period of 14 seconds.}}

==Measurement== Although most measuring devices estimate the significant wave height from a wave 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 {{convert|20.1|m}} during a North Atlantic storm in 2011.<ref name="Quirin">{{Cite journal |doi = 10.1175/BAMS-D-11-00128.1|title = Phenomenal Sea States and Swell from a North Atlantic Storm in February 2011: A Comprehensive Analysis|year = 2012|last1 = Hanafin|first1 = Jennifer A.|last2 = Quilfen|first2 = Yves|last3 = Ardhuin|first3 = Fabrice|last4 = Sienkiewicz|first4 = Joseph|last5 = Queffeulou|first5 = Pierre|last6 = Obrebski|first6 = Mathias|last7 = Chapron|first7 = Bertrand|last8 = Reul|first8 = Nicolas|last9 = Collard|first9 = Fabrice|last10 = Corman|first10 = David|last11 = De Azevedo|first11 = Eduardo B.|last12 = Vandemark|first12 = Doug|last13 = Stutzmann|first13 = Eleonore|journal = Bulletin of the American Meteorological Society|volume = 93|issue = 12|pages = 1825–1832|bibcode = 2012BAMS...93.1825H|url = https://archimer.ifremer.fr/doc/00094/20538/|doi-access = free}}</ref>

==Weather forecasts== thumb|NOAA Wavewatch III model animation of significant wave height forecasts in the Pacific.

The World Meteorological Organization 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 model is used heavily.

==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 == * Ocean Prediction Center * Rogue wave{{snd}}a wave of over twice the significant wave height * Sea state

== Notes == {{reflist}}

== External links == *[https://earth.nullschool.net/#current/ocean/primary/waves/overlay=significant_wave_height/winkel3/ Current global map of significant wave height and period] *[https://polar.ncep.noaa.gov/waves/index2.shtml NOAA Wavewatch III] *[https://www.emc.ncep.noaa.gov/ NWS Environmental Modeling Center] *[http://www.envirtech.com/docs/DWSP-01%20Directional%20Wave%20%20Sensor%20Payload.pdf Envirtech solid state payload for directional waves measurement]

{{physical oceanography}}

Category:Naval architecture Category:Physical oceanography Category:Shipbuilding Category:Water waves