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Ocean surface wave modeling describes the effort to depict the state and predict the evolution of the sea surface using numerical techniques. These simulations consider atmospheric wind forcing, nonlinear wave interactions, and frictional dissipation, and they output statistics describing wave amplitudes, periods, and propagation directions for regional seas or global oceans. Such forecasts are extremely important for commercial interests on the high seas.

Historical Overview
Early forecasts of the ocean 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. During the 1950s and 1960s, much of the theoretical groundwork necessary for numerical descriptions of wave evolution was laid. The 1970s saw the first operational, hemispheric wave model: the spectral wave ocean model (SWOM) at the Fleet Numerical Oceanography Center.

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. 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. Improvements included two-way coupling between wind and waves, assimilation of satellite wave data, and medium-range operational forecasting.

Input
A wave model requires as initial conditions information describing the current state of the sea. An analysis of the 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 current conditions.

Representation
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, which include wave propagation / advection, and a source function which allows for wave energy to be augmented or diminished. The source function has three terms: wind forcing, nonlinear transfer, and dissipation by whitecapping and bottom friction. Wind data are typically provided from a separate atmospheric model from an operational weather forecasting center.

Output
The output of an ocean surface 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
Ocean waves also act to modify atmospheric properties through frictional drag of near-surface winds and heat fluxes. Two-way coupled models allow the wave activity to feed back upon the atmosphere.

WAVEWATCH
The operational wave forecasting model at NOAA is the WAVEWATCH III. This model has a global domain of approximately 100 km resolution, with nested regional domains for the northern hemisphere oceanic basins at approximately 25 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. The model is limited to regions outside the surf zone where the waves are not strongly impacted by shallow depths.

Other Models
The ECMWF has incorporated the WAM wave model as part of its ensemble forecasting system. This model includes 30 frequency bins, 24 propagation directions, and an average spatial resolution of 40 km.

Ocean wave forecasts are issued regionally by Environment Canada.

Regional wave predictions are also produced by universities, such as Texas A&M University’s use of the SWAN model to forecast waves in the Gulf of Mexico.

Other ocean wave models include the Navy Standard Surf Model (NSSM).

The private sector is also active in producing ocean wave simulations and surf forecasts. For example, Oceanweather Inc. provides global operational forecasts and hindcasts of the sea state.

Validation
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 oceanic surface waves.

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

Reanalyses
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. Ocean surface waves are a part of both the NCEP Reanalysis and the ERA-40 from the ECMWF. 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.