# Wave height

> Mediated Wiki article. Canonical URL: https://mediated.wiki/source/Wave_height
> Markdown URL: https://mediated.wiki/source/Wave_height.md
> Source: https://en.wikipedia.org/wiki/Wave_height
> Source revision: 1129149572
> License: Creative Commons Attribution-ShareAlike 4.0 International (https://creativecommons.org/licenses/by-sa/4.0/)

Difference between the elevations of a crest and a neighbouring trough

Wave characteristics

In [fluid dynamics](/source/Fluid_dynamics), the **wave height** of a [surface wave](/source/Ocean_surface_wave) is the difference between the [elevations](/source/Elevation) of a [crest](/source/Crest_(physics)) and a neighboring [trough](/source/Trough_(physics)).[1] *Wave height* is a term used by [mariners](/source/Sailor), as well as in [coastal](/source/Coastal_engineering), [ocean](/source/Offshore_construction) and [naval engineering](/source/Naval_engineering).

At sea, the term *[significant wave height](/source/Significant_wave_height)* is used as a means to introduce a well-defined and standardized [statistic](/source/Statistic) to denote the characteristic height of the [random](/source/Random) waves in a *[sea state](/source/Sea_state)*, including [wind sea](/source/Wind_wave) and [swell](/source/Swell_(ocean)). It is defined in such a way that it more or less corresponds to what a [mariner](/source/Sailor) observes when estimating visually the average wave height.

## Definitions

Depending on context, wave height may be defined in different ways:

- For a [sine wave](/source/Sine_wave), the wave height *H* is twice the [amplitude](/source/Amplitude) (i.e., the *[peak-to-peak amplitude](/source/Peak-to-peak_amplitude)*):[1] H = 2 a . {\displaystyle H=2a.}

- For a [periodic wave](/source/Periodic_function), it is simply the difference between the [maximum](/source/Maximum) and [minimum](/source/Minimum) of the surface elevation *z* = *η*(*x* – *c*p *t*):[1] H = max { η ( x − c p t ) } − min { η ( x − c p t ) } , {\displaystyle H=\max \left\{\eta (x\,-\,c_{p}\,t)\right\}-\min \left\{\eta (x-c_{p}\,t)\right\},} with *c*p the [phase speed](/source/Phase_speed) (or propagation speed) of the wave. The sine wave is a specific case of a periodic wave.

- In random waves at sea, when the surface elevations are measured with a [wave buoy](/source/Weather_buoy), the individual wave height *H*m of each individual wave—with an [integer](/source/Integer) label *m*, running from 1 to *N*, to denote its position in a sequence of *N* waves—is the difference in elevation between a wave crest and trough in that wave. For this to be possible, it is necessary to first split the measured [time series](/source/Time_series) of the surface elevation into individual waves. Commonly, an individual wave is denoted as the [time interval](/source/Time_interval) between two successive downward-crossings through the [average](/source/Average) surface elevation (upward crossings might also be used). Then the individual wave height of each wave is again the difference between maximum and minimum elevation in the time interval of the wave under consideration.[2]

### Significant wave height

This section is an excerpt from [Significant wave height](/source/Significant_wave_height).[[edit](https://en.wikipedia.org/w/index.php?title=Significant_wave_height&action=edit)]

In [physical oceanography](/source/Physical_oceanography), the [significant wave height](/source/Significant_wave_height) (SWH, HTSGW[3] or *H*s) is defined traditionally as the mean *wave height* ([trough](/source/Trough_(physics)) to [crest](/source/Crest_(physics))) of the highest third of the [waves](/source/Ocean_surface_wave) (*H*1/3). It is usually defined as four times the [standard deviation](/source/Standard_deviation) of the surface elevation – or equivalently as four times the square root of the zeroth-order moment ([area](/source/Area)) of the *[wave spectrum](/source/Wave_spectrum)*.[4] The symbol *H*m0 is usually used for that latter definition. The significant wave height (Hs) 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](/source/Sea_state)*, including [winds](/source/Wind) and [swell](/source/Swell_(ocean)).

### RMS wave height

Another wave-height statistic in common usage is the [root-mean-square](/source/Root-mean-square) (or RMS) wave height *H*rms, defined as:[2] H rms = 1 N ∑ m = 1 N H m 2 , {\displaystyle H_{\text{rms}}={\sqrt {{\frac {1}{N}}\sum _{m=1}^{N}H_{m}^{2}}},} with *H*m again denoting the individual wave heights in a certain [time series](/source/Time_series).

## See also

- [Sea state](/source/Sea_state)

- [Wind wave](/source/Wind_wave)

## Notes

1. ^ [***a***](#cite_ref-Kinsman_38_1-0) [***b***](#cite_ref-Kinsman_38_1-1) [***c***](#cite_ref-Kinsman_38_1-2) [Kinsman (1984](#CITEREFKinsman1984), p. 38)

1. ^ [***a***](#cite_ref-Holt_24_28_2-0) [***b***](#cite_ref-Holt_24_28_2-1) [Holthuijsen (2007](#CITEREFHolthuijsen2007), pp. 24–28)

1. **[^](#cite_ref-3)** ["About earth :: A global map of wind, weather, and ocean conditions"](https://earth.nullschool.net/about.html#waves).

1. **[^](#cite_ref-Significant_wave_height_Holthuijsen_4-0)** Holthuijsen, Leo H. (2007). *Waves in Oceanic And Coastal Waters*. Cambridge University Press. p. 70. [ISBN](/source/ISBN_(identifier)) [978-0-521-86028-4](https://en.wikipedia.org/wiki/Special:BookSources/978-0-521-86028-4).

## References

- Holthuijsen, Leo H. (2007), *Waves in Oceanic and Coastal Waters*, Cambridge University Press, [ISBN](/source/ISBN_(identifier)) [978-0-521-86028-4](https://en.wikipedia.org/wiki/Special:BookSources/978-0-521-86028-4), 387 pages.

- Kinsman, Blair (1984), *Wind waves: their generation and propagation on the ocean surface*, Dover Publications, [ISBN](/source/ISBN_(identifier)) [0-486-49511-6](https://en.wikipedia.org/wiki/Special:BookSources/0-486-49511-6), 704 pages.

- [Phillips, Owen M.](/source/Owen_Martin_Phillips) (1977), *The dynamics of the upper ocean* (2nd ed.), Cambridge University Press, [ISBN](/source/ISBN_(identifier)) [0-521-29801-6](https://en.wikipedia.org/wiki/Special:BookSources/0-521-29801-6), viii & 336 pages.

v t e Physical oceanography Waves Airy wave theory Ballantine scale Benjamin–Feir instability Boussinesq approximation Breaking wave Clapotis Cnoidal wave Cross sea Dispersion Edge wave Equatorial waves Gravity wave Green's law Infragravity wave Internal wave Iribarren number Kelvin wave Kinematic wave Longshore drift Luke's variational principle Miche criterion Mild-slope equation Radiation stress Rogue wave Draupner wave Rossby wave Rossby-gravity waves Sea state Seiche Significant wave height Soliton Stokes drift Stokes problem Stokes wave Swell Trochoidal wave Tsunami megatsunami Undertow Ursell number Wave action Wave base Wave height Wave nonlinearity Wave power Wave radar Wave setup Wave shoaling Wave turbulence Wave–current interaction Waves and shallow water one-dimensional Saint-Venant equations shallow water equations Wind fetch Wind setup Wind wave model Circulation Atmospheric circulation Baroclinity Boundary current Coriolis force Coriolis–Stokes force Craik–Leibovich vortex force Downwelling Eddy Ekman layer Ekman spiral Ekman transport El Niño–Southern Oscillation General circulation model Geochemical Ocean Sections Study Geostrophic current Global Ocean Data Analysis Project Gulf Stream Humboldt Current Hydrothermal circulation Langmuir circulation Longshore drift Loop Current Modular Ocean Model Ocean current Ocean dynamical thermostat Ocean dynamics Ocean gyre Overflow Princeton Ocean Model Rip current Subsurface ocean current Sverdrup balance Thermohaline circulation shutdown Upwelling Whirlpool Wind generated current World Ocean Circulation Experiment Tides Amphidromic point Earth tide Head of tide Internal tide Lunitidal interval Perigean spring tide Rip tide Rule of twelfths Slack tide Theory of tides Tidal bore Tidal force Tidal power Tidal race Tidal range Tidal resonance Tide gauge Tideline Landforms Abyssal fan Abyssal plain Atoll Bathymetric chart Carbonate platform Coastal geography Cold seep Continental margin Continental rise Continental shelf Contourite Guyot Hydrography Knoll Ocean bank Oceanic basin Oceanic plateau Oceanic trench Passive margin Seabed Seamount Submarine canyon Submarine volcano Plate tectonics Convergent boundary Divergent boundary Fracture zone Hydrothermal vent Marine geology Mid-ocean ridge Mohorovičić discontinuity Oceanic crust Outer trench swell Ridge push Seafloor spreading Slab pull Slab suction Slab window Subduction Transform fault Vine–Matthews–Morley hypothesis Volcanic arc Ocean zones Benthic Deep ocean water Deep sea Littoral Mesopelagic Oceanic Pelagic Photic Surf Swash Sea level Deep-ocean Assessment and Reporting of Tsunamis Global Sea Level Observing System North West Shelf Operational Oceanographic System Sea-level curve Sea level drop Sea level rise World Geodetic System Acoustics Deep scattering layer Ocean acoustic tomography Sofar bomb SOFAR channel Underwater acoustics Satellites Jason-1 OSTM/Jason-2 Jason-3 Related Acidification Argo Benthic lander Color of water DSV Alvin Marginal sea Marine energy Marine pollution Mooring National Oceanographic Data Center Ocean Explorations Observations Reanalysis Ocean surface topography Ocean temperature Ocean thermal energy conversion Oceanography Outline of oceanography Pelagic sediment Sea surface microlayer Sea surface temperature Seawater Science On a Sphere Stratification Thermocline Underwater glider Water column World Ocean Atlas Category Commons Oceans portal

---
Adapted from the Wikipedia article [Wave height](https://en.wikipedia.org/wiki/Wave_height) by Wikipedia contributors ([contributor history](https://en.wikipedia.org/wiki/Wave_height?action=history)). Available under [Creative Commons Attribution-ShareAlike 4.0 International](https://creativecommons.org/licenses/by-sa/4.0/). Changes may have been made.