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. These simulations consider atmospheric wind forcing, nonlinear wave interactions, and frictional dissipation, and they output statistics describing wave heights, periods, and propagation directions for regional seas or global oceans. Such wave hindcasts and wave forecasts are extremely important for commercial interests on the high seas.[1] For example, the shipping industry requires guidance for operational planning and tactical seakeeping purposes.[1]

For the specific case of predicting wind wave statistics on the ocean, the term ocean surface wave model is used.

Other applications, in particular coastal engineering, have led to the developments of wind wave models specifically designed for coastal applications.

NOAA Wavewatch III Sample Forecast
NOAA WAVEWATCH III (R) 120-hour Forecast for the North Atlantic

Historical overview

Early forecasts of the sea state were created manually based upon empirical relationships between the present state of the sea, the expected wind conditions, the fetch/duration, and the direction of the wave propagation.[2] Alternatively, the swell part of the state has been forecasted as early as 1920 using remote observations.[3]

During the 1950s and 1960s, much of the theoretical groundwork necessary for numerical descriptions of wave evolution was laid. For forecasting purposes, it was realized that the random nature of the sea state was best described by a spectral decomposition in which the energy of the waves was attributed to as many wave trains as necessary, each with a specific direction and period. This approach allowed to make combined forecasts of wind seas and swells. The first numerical model based on the spectral decomposition of the sea state was operated in 1956 by the French Weather Service, and focused on the North Atlantic.[4] The 1970s saw the first operational, hemispheric wave model: the spectral wave ocean model (SWOM) at the Fleet Numerical Oceanography Center.[5]

First generation wave models did not consider nonlinear wave interactions. Second generation models, available by the early 1980s, parameterized these interactions. They included the “coupled hybrid” and “coupled discrete” formulations.[6] Third generation models explicitly represent all the physics relevant for the development of the sea state in two dimensions. The wave modeling project (WAM), an international effort, led to the refinement of modern wave modeling techniques during the decade 1984-1994.[7] Improvements included two-way coupling between wind and waves, assimilation of satellite wave data, and medium-range operational forecasting.

Wind wave models are used in the context of a forecasting or hindcasting system. Differences in model results arise (with decreasing order of importance) from: differences in wind and sea ice forcing, differences in parameterizations of physical processes, the use of data assimilation and associated methods, and the numerical techniques used to solve the wave energy evolution equation.

General strategy


A wave model requires as initial conditions information describing the state of the sea. An analysis of the sea or ocean can be created through data assimilation, where observations such as buoy or satellite altimeter measurements are combined with a background guess from a previous forecast or climatology to create the best estimate of the ongoing conditions. In practice, many forecasting system rely only on the previous forecast, without any assimilation of observations.[8]

A more critical input is the "forcing" by wind fields: a time-varying map of wind speed and directions. The most common sources of errors in wave model results are the errors in the wind field. Ocean currents can also be important, in particular in western boundary currents such as the Gulf Stream, Kuroshio or Agulhas current, or in coastal areas where tidal currents are strong. Waves are also affected by sea ice and icebergs, and all operational global wave models take at least the sea ice into account.

Wave model current induced refraction
This figures show an example of the effects of currents on the wave heights. This example is adapted from scientific paper published in the Journal of Physical Oceanography (vol. 42, December 2012). The top panels show the tidal currents at 3 AM and 11 AM on 28 October 2008, off the West coast of France, around the island of Ouessant, which lies 20 km from the mainland. The bottom panel show the heights and directions of waves, computed with the numerical model WAVEWATCH III (R), using a triangular mesh with variable resolution. The strong currents south of Ouessant deflect the waves away from the measuring buoy at low tide.


The sea state is described as a spectrum; the sea surface can be decomposed into waves of varying frequencies using the principle of superposition. The waves are also separated by their direction of propagation. The model domain size can range from regional to the global ocean. Smaller domains can be nested within a global domain to provide higher resolution in a region of interest. The sea state evolves according to physical equations – based on a spectral representation of the conservation of wave action – which include: wave propagation / advection, refraction (by bathymetry and currents), shoaling, and a source function which allows for wave energy to be augmented or diminished. The source function has at least three terms: wind forcing, nonlinear transfer, and dissipation by whitecapping.[6] Wind data are typically provided from a separate atmospheric model from an operational weather forecasting center.

For intermediate water depths the effect of bottom friction should also be added.[9] At ocean scales, the dissipation of swells - without breaking - is a very important term.[10]


The output of a wind wave model is a description of the wave spectra, with amplitudes associated with each frequency and propagation direction. Results are typically summarized by the significant wave height, which is the average height of the one-third largest waves, and the period and propagation direction of the dominant wave.

Coupled models

Wind waves also act to modify atmospheric properties through frictional drag of near-surface winds and heat fluxes.[11] Two-way coupled models allow the wave activity to feed back upon the atmosphere. The European Centre for Medium-Range Weather Forecasts (ECMWF) coupled atmosphere-wave forecast system described below facilitates this through exchange of the Charnock parameter which controls the sea surface roughness. This allows the atmosphere to respond to changes in the surface roughness as the wind sea builds up or decays.



The operational wave forecasting systems at NOAA are based on the WAVEWATCH III (R) model.[12] This system has a global domain of approximately 50 km resolution, with nested regional domains for the northern hemisphere oceanic basins at approximately 18 km and approximately 7 km resolution. Physics includes wave field refraction, nonlinear resonant interactions, sub-grid representations of unresolved islands, and dynamically updated ice coverage. Wind data is provided from the GDAS data assimilation system for the GFS weather model. Up to 2008, the model was limited to regions outside the surf zone where the waves are not strongly impacted by shallow depths.[13]

The model can incorporate the effects of currents on waves from its early design by Hendrik Tolman in the 1990s, and is now extended for near shore applications.


The wave model WAM was the first so-called third generation prognostic wave model where the two-dimensional wave spectrum was allowed to evolve freely (up to a cut-off frequency) with no constraints on the spectral shape.[14] The model underwent a series of software updates from its inception in the late 1980s.[15] The last official release is Cycle 4.5, maintained by the German Helmholtz Zentrum, Geesthacht.[16]

ECMWF has incorporated WAM into its deterministic and ensemble forecasting system.,[17] known as the Integrated Forecast System (IFS). The model currently comprises 36 frequency bins and 36 propagation directions at an average spatial resolution of 25 km. The model has been coupled to the atmospheric component of IFS since 1998.[18][19]

Other models

Wind wave forecasts are issued regionally by Environment Canada.[20]

Regional wave predictions are also produced by universities, such as Texas A&M University’s use of the SWAN model (developed by Delft University of Technology) to forecast waves in the Gulf of Mexico.[21]

Another model, CCHE2D-COAST is a processes-based integrated model which is capable of simulating coastal processes in different coasts with complex shorelines such as irregular wave deformation from offshore to onshore, nearshore currents induced by radiation stresses, wave set-up, wave set-down, sediment transport, and seabed morphological changes.[22]

Other wind wave models include the U.S. Navy Standard Surf Model (NSSM).[23]


Comparison of the wave model forecasts with observations is essential for characterizing model deficiencies and identifying areas for improvement. In-situ observations are obtained from buoys, ships and oil platforms. Altimetry data from satellites, such as GEOSAT and TOPEX, can also be used to infer the characteristics of wind waves.

Hindcasts of wave models during extreme conditions also serves as a useful test bed for the models.[24]


A retrospective analysis, or reanalysis, combines all available observations with a physical model to describe the state of a system over a time period of decades. Wind waves are a part of both the NCEP Reanalysis[25] and the ERA-40 from the ECMWF.[26] Such resources permit the creation of monthly wave climatologies, and can track the variation of wave activity on interannual and multi-decadal time scales. During the northern hemisphere winter, the most intense wave activity is located in the central North Pacific south of the Aleutians, and in the central North Atlantic south of Iceland. During the southern hemisphere winter, intense wave activity circumscribes the pole at around 50°S, with 5 m significant wave heights typical in the southern Indian Ocean.[26]


  1. ^ a b Cox, Andrew T. & Vincent J. Cardone (2002). "20 Years Of Operational Forecasting At Oceanweather" (PDF). 7th International Workshop on Wave Hindcasting and Forecasting October 21–25, 2002, Banff, Alberta, Canada. Retrieved 2008-11-21.
  2. ^ Wittmann, Paul and Mike Clancy, "Thirty Years of Operational Ocean Wave Forecasting at Fleet Numerical Meteorology and Oceanography Center", Symposium on the 50th Anniversary of Operational Numerical Weather Prediction, 14–17 June 2004, University of Maryland
  3. ^ Robert Montagne, The swell forecasting service in Morocco (In French), 1922, Annales Hydrographiques, pp. 157-186. This paper describes the use of the method published by Gain in the same journal (1918) which combines a classification of North Atlantic Storms with the use of observations in Azores and Portugal to forecast the swells in Morocco.
  4. ^ Gelci, R., H. Cazalé, J. Vassal (1957) Sea state forecasting. The spectral method (In French), Bulletin d'information du Comité d'Océanographie et d'Etude des Côtes, Vol. 9 (1957), pp. 416-435.
  5. ^ "Wave Modeling", Oceanweather Inc
  6. ^ a b Komen, Gerbrand, "The Wave Modeling Group, a historical perspective"
  7. ^ G.J. Komen, L. Cavaleri, M. Donelan, K. Hasselmann, S. Hasselmann and P.A.E.M. Janssen, 1994. Dynamics and Modelling of Ocean Waves. Cambridge University Press, 532p.
  8. ^
  9. ^ Ardhuin, F.; O'Reilly, W. C.; Herbers, T. H. C.; Jessen, P. F. (2003). "Swell transformation across the continental shelf. part I: Attenuation and directional broadening". J. Phys. Oceanogr. 33 (9): 1921–1939. Bibcode:2003JPO....33.1921A. doi:10.1175/1520-0485(2003)033<1921:statcs>;2.
  10. ^ Ardhuin, F.; Chapron, B.; Collard, F. (2009). "Observation of swell dissipation across oceans". Geophys. Res. Lett. 36 (6): L06607. arXiv:0809.2497. Bibcode:2009GeoRL..36.6607A. doi:10.1029/2008GL037030.
  11. ^ Bender, L.C. (1996). "Modification of the Physics and Numerics in a Third-Generation Ocean Wave Model". Journal of Atmospheric and Oceanic Technology. 13 (3): 726–750. Bibcode:1996JAtOT..13..726B. doi:10.1175/1520-0426(1996)013<0726:motpan>;2.
  12. ^ Tolman, H. L., "WAVEWATCH III Model Description"
  13. ^ Tolman, 2002g: User manual and system documentation of WAVEWATCH-III version 2.22. NOAA / NWS / NCEP / MMAB Technical Note 222, 133 pp.
  14. ^ Komen, GJ and Cavaleri, L. and Donelan, M. and Hasselmann, K. and Hasselmann, S. and Janssen, P. et al, 1994: "Dynamics and Modelling of Ocean Waves", Cambridge, 534 pp
  15. ^ Hasselmann, S; Hasselmann, K; Janssen, P A E M; et al. (1988). "The WAM model - A third generation ocean wave prediction model". Journal of Physical Oceanography. 18 (12): 1775–1810. Bibcode:1988JPO....18.1775W. doi:10.1175/1520-0485(1988)018<1775:twmtgo>;2.
  16. ^ "Archived copy". Archived from the original on 2013-08-23. Retrieved 2012-03-22.CS1 maint: archived copy as title (link)
  17. ^ "The Ocean Wave Model" Archived 2008-06-03 at the Wayback Machine, European Centre for Medium-Range Weather Forecasts
  18. ^ Janssen, P. A. E. M., J. D. Doyle, J. Bidlot, B. Hansen, L. Isaksen and P. Viterbo, 2002: "Impact and feedback of ocean waves on the atmosphere", in Advances in Fluid Mechanics, Atmosphere-Ocean Interactions, Vol. I, WITpress, Ed. W.Perrie., pp 155-197
  19. ^ Janssen, P. A. E. M., 2004: The interaction of ocean waves and wind, Cambridge, 300 pages
  20. ^ "Operational Model Forecasts", Environment Canada
  21. ^ "Surf's Up: Professor Using Models To Predict Huge Waves", ScienceDaily, Feb. 23, 2005
  22. ^ "Archived copy". Archived from the original on 2016-03-04. Retrieved 2015-06-01.CS1 maint: archived copy as title (link)
  23. ^ "Validation Test Report for the Navy Standard Surf Model", US Naval Research Lab
  24. ^ Cardone, V.; Jensen, R.; Resio, D.; Swail, V.; Cox, A. (1996). "Evaluation of Contemporary Ocean Wave Models in Rare Extreme Events: The "Halloween Storm" of October 1991 and the "Storm of the Century" of March 1993". J. Atmos. Oceanic Technol. 13 (1): 198–230. Bibcode:1996JAtOT..13..198C. doi:10.1175/1520-0426(1996)013<0198:eocowm>;2.
  25. ^ Cox, A., V. Cardone, and V. Swail, "Evaluation Of NCEP-NCAR Reanalysis Project Marine Surface Wind Products For A Long Term North Atlantic Wave Hindcast"
  26. ^ a b Caires, S., A. Sterl, G. Burgers, and G. Komen, ERA-40, "Forty-year European Re-Analysis of the Global Atmosphere; Ocean wave product validation and analysis" Archived 2007-02-07 at the Wayback Machine

The ADCIRC model is a high-performance, cross-platform numerical ocean circulation model popular in simulating storm surge, tides, and coastal circulation problems.

Originally developed by Drs. Rick Luettich and Joannes Westerink,

the model is developed and maintained by a combination of academic, governmental, and corporate partners, including the University of North Carolina at Chapel Hill, the University of Notre Dame, and the US Army Corps of Engineers.

The ADCIRC system includes an independent multi-algorithmic wind forecast model and also has advanced coupling capabilities, allowing it to integrate effects from sediment transport, ice, waves, surface runoff, and baroclinicity.

Bahama Banks

The Bahama Banks are the submerged carbonate platforms that make up much of the Bahama Archipelago. The term is usually applied in referring to either the Great Bahama Bank around Andros Island, or the Little Bahama Bank of Grand Bahama Island and Great Abaco, which are the largest of the platforms, and the Cay Sal Bank north of Cuba. The islands of these banks are politically part of the Bahamas. Other banks are the three banks of the Turks and Caicos Islands, namely the Caicos Bank of the Caicos Islands, the bank of the Turks Islands, and wholly submerged Mouchoir Bank. Further southeast are the equally wholly submerged Silver Bank and Navidad Bank north of the Dominican Republic.

Carbonate platform

A carbonate platform is a sedimentary body which possesses topographic relief, and is composed of autochthonic calcareous deposits. Platform growth is mediated by sessile organisms whose skeletons build up the reef or by organisms (usually microbes) which induce carbonate precipitation through their metabolism. Therefore, carbonate platforms can not grow up everywhere: they are not present in places where limiting factors to the life of reef-building organisms exist. Such limiting factors are, among others: light, water temperature, transparency and pH-Value. For example, carbonate sedimentation along the Atlantic South American coasts takes place everywhere but at the mouth of the Amazon River, because of the intense turbidity of the water there. Spectacular examples of present-day carbonate platforms are the Bahama Banks under which the platform is roughly 8 km thick, the Yucatan Peninsula which is up to 2 km thick, the Florida platform, the platform on which the Great Barrier Reef is growing, and the Maldive atolls. All these carbonate platforms and their associated reefs are confined to tropical latitudes. Today's reefs are built mainly by scleractinian corals, but in the distant past other organisms, like archaeocyatha (during the Cambrian) or extinct cnidaria (tabulata and rugosa) were important reef builders.

Hendrik Tolman

Hendrik Lieuwe Tolman (born 16 January 1961 in Leeuwarden) is the original developer of the WAVEWATCH III (tm) wind wave model.He has been the branch chief for the Marine Modeling and Analysis Branch in the US National Weather Service of NOAA since 2007, having joined the branch in 1992.

Index of physics articles (W)

The index of physics articles is split into multiple pages due to its size.

To navigate by individual letter use the table of contents below.

List of submarine volcanoes

A list of active and extinct submarine volcanoes and seamounts located under the world's oceans. There are estimated to be 40,000 to 55,000 seamounts in the global oceans. Almost all are not well-mapped and many may not have been identified at all. Most are unnamed and unexplored. This list is therefore confined to seamounts that are notable enough to have been named and/or explored.


In offshore and coastal engineering, metocean refers to the syllabic abbreviation of meteorology and (physical) oceanography.

Model for Prediction Across Scales

The Model for Prediction Across Scales (MPAS) is a coupled Earth system modeling package that integrates atmospheric, oceanographic and cryospheric modeling on a variety of scales from the planetary to regional and mesoscale/microscale. It includes climate and weather modeling and simulations that were first used by researchers in 2013. The atmospheric components (MPAS-A) were led by the National Center for Atmospheric Research (NCAR)'s Earth System Laboratory (NESL) and the oceanographic components (MPAS-O) by the Climate, Ocean, and Sea Ice Modeling Group (COSIM) at Los Alamos National Laboratory (LANL). It has been used for real-time weather as well as seasonal forecasting of convection, tornadoes and tropical cyclones, among other uses. Its atmospheric modeling aspects are intended to use and complement rather than replace the Weather Research and Forecasting Model (WRF-ARW/NMM), the Global Forecast System (GFS) and the Community Earth System Model (CESM).

Oceanic plateau

An oceanic or submarine plateau is a large, relatively flat elevation that is higher than the surrounding relief with one or more relatively steep sides.There are 184 oceanic plateaus covering an area of 18,486,600 km2 (7,137,700 sq mi), or about 5.11% of the oceans. The South Pacific region around Australia and New Zealand contains the greatest number of oceanic plateaus (see map).

Oceanic plateaus produced by large igneous provinces are often associated with hotspots, mantle plumes, and volcanic islands — such as Iceland, Hawaii, Cape Verde, and Kerguelen. The three largest plateaus, the Caribbean, Ontong Java, and Mid-Pacific Mountains, are located on thermal swells. Other oceanic plateaus, however, are made of rifted continental crust, for example Falkland Plateau, Lord Howe Rise, and parts of Kerguelen, Seychelles, and Arctic ridges.

Plateaus formed by large igneous provinces were formed by the equivalent of continental flood basalts such as the Deccan Traps in India and the Snake River Plain in the United States.

In contrast to continental flood basalts, most igneous oceanic plateaus erupt through young and thin (6–7 km (3.7–4.3 mi)) mafic or ultra-mafic crust and are therefore uncontaminated by felsic crust and representative for their mantle sources.

These plateaus often rise 2–3 km (1.2–1.9 mi) above the surrounding ocean floor and are more buoyant than oceanic crust. They therefore tend to withstand subduction, more-so when thick and when reaching subduction zones shortly after their formations. As a consequence, they tend to "dock" to continental margins and be preserved as accreted terranes. Such terranes are often better preserved than the exposed parts of continental flood basalts and are therefore a better record of large-scale volcanic eruptions throughout Earth's history. This "docking" also means that oceanic plateaus are important contributors to the growth of continental crust. Their formations often had a dramatic impact on global climate, such as the most recent plateaus formed, the three, large, Cretaceous oceanic plateaus in the Pacific and Indian Ocean: Ontong Java, Kerguelen, and Caribbean.

Outline of oceanography

The following outline is provided as an overview of and introduction to Oceanography.

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. Others include biological, chemical and geological oceanography.

Physical oceanography may be subdivided into descriptive and dynamical physical oceanography.Descriptive physical oceanography seeks to research the ocean through observations and complex numerical models, which describe the fluid motions as precisely as possible.

Dynamical physical oceanography focuses primarily upon the processes that govern the motion of fluids with emphasis upon theoretical research and numerical models. These are part of the large field of Geophysical Fluid Dynamics (GFD) that is shared together with meteorology. GFD is a sub field of Fluid dynamics describing flows occurring on spatial and temporal scales that are greatly influenced by the Coriolis force.

Undersea mountain range

Undersea mountain ranges are mountain ranges that are mostly or entirely underwater, and specifically under the surface of an ocean. If originated from current tectonic forces, they are often referred to as a mid-ocean ridge. In contrast, if formed by past above-water volcanism, they are known as a seamount chain. The largest and best known undersea mountain range is a mid-ocean ridge, the Mid-Atlantic Ridge. It has been observed that, "similar to those on land, the undersea mountain ranges are the loci of frequent volcanic and earthquake activity".


WAM or Wam may refer to:

Wam, Pakistan, a village of Ziarat District

WAM (Emirates news agency), a news agency in the United Arab Emirates

WAM!, a cable television channel for children

Warren Abstract Machine, an abstract machine for the execution of Prolog

Web audience measurement, a tool that measures Internet usage in India

Web access management, a form of identity management

Weekender Records or Weekender Artist Management

Weisman Art Museum, in Minneapolis

Wet and messy fetishism

Wide area multilateration, a surveillance technology for air traffic management

Wireless asset monitoring system

Worcester Art Museum, in Worcester, Massachusetts

Wolfgang Amadeus Mozart (1756–1791), musician

WAM, a kind of wind wave model

Indian locomotive class WAM-4

Wave action (continuum mechanics)

In continuum mechanics, wave action refers to a conservable measure of the wave part of a motion. For small-amplitude and slowly varying waves, the wave action density is:

where is the intrinsic wave energy and is the intrinsic frequency of the slowly modulated waves – intrinsic here implying: as observed in a frame of reference moving with the mean velocity of the motion.

The action of a wave was introduced by Sturrock (1962) in the study of the (pseudo) energy and momentum of waves in plasmas. Whitham (1965) derived the conservation of wave action – identified as an adiabatic invariant – from an averaged Lagrangian description of slowly varying nonlinear wave trains in inhomogeneous media:

where is the wave-action density flux and is the divergence of . The description of waves in inhomogeneous and moving media was further elaborated by Bretherton & Garrett (1968) for the case of small-amplitude waves; they also called the quantity wave action (by which name it has been referred to subsequently). For small-amplitude waves the conservation of wave action becomes:

  using     and  

where is the group velocity and the mean velocity of the inhomogeneous moving medium. While the total energy (the sum of the energies of the mean motion and of the wave motion) is conserved for a non-dissipative system, the energy of the wave motion is not conserved, since in general there can be an exchange of energy with the mean motion. However, wave action is a quantity which is conserved for the wave-part of the motion.

The equation for the conservation of wave action is for instance used extensively in wind wave models to forecast sea states as needed by mariners, the offshore industry and for coastal defense. Also in plasma physics and acoustics the concept of wave action is used.

The derivation of an exact wave-action equation for more general wave motion – not limited to slowly modulated waves, small-amplitude waves or (non-dissipative) conservative systems – was provided and analysed by Andrews & McIntyre (1978) using the framework of the generalised Lagrangian mean for the separation of wave and mean motion.

Wave base

The wave base, in physical oceanography, is the maximum depth at which a water wave's passage causes significant water motion. For water depths deeper than the wave base, bottom sediments and the seafloor are no longer stirred by the wave motion above.

Wave model (disambiguation)

Wave model is a concept of language development in historical linguistics.

A wave model is a theoretical concept comparing a phenomenon of any type to any part of a physical wave.

Wave model can refer to:

Wind wave model, a mathematical model of sea waves

Density wave model, a mathematical model of a spiral galaxy

Kinematic wave model, an explanation of traffic flow

Wind-wave dissipation

Wind-wave dissipation or "swell dissipation" is process in which a wave generated via a weather system loses its mechanical energy transferred from the atmosphere via wind. Wind waves, as their name suggests, are generated by wind transferring energy from the atmosphere to the ocean's surface, capillary gravity waves play an essential role in this effect, "wind waves" or "swell" are also known as surface gravity waves.

Ocean zones
Sea level

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