Wave models depict sea heights, fetch areas, and swell propagation patterns for the oceans of the world. Input for the wave model is obtained from an atmospheric model. The NOAA Wave model (Wavewatch III) uses the AVN run of the MRF model as it's source. The FNMOC wave model uses the No-Gaps (NGP) atmospheric model. The wave models construct an estimate of sea heights, period and seas/swell headings over time using current and projected wind data from the atmospheric model. Remember, it's the interaction of wind on water that create waves, so it would seem logical to use the projected wind forecasts (over water) to predict the development of seas and eventually swells.

Of primarily interest to surf forecasters is the "00hr Hindcast" Sea height image (the first image depicting the height of seas). This image is derived from the Analysis image from the atmospheric model, which depicts the current state of the atmosphere and is constructed using confirmed wind observations from satellites, ground stations, buoys, weather balloons and a variety of other sources. That's right, it uses confirmed wind speed and direction data. The wave models take the confirmed wind data from the analysis image of the atmospheric model and use it to estimate the winds effect on open ocean waters, projecting seas heights, headings, and in some cases, swell propagation. This makes the "00hr Hindcast" image from a wave model the most accurate depiction of what actually happening on the oceans surface inside a storm that is outside the reach of buoys or the ERS-2 satellite.

NOAA Wavewatch III Wave Model from The Scripps Research Institute
In this example notice that high sea areas and associated swell vectors are displayed simultaneously. Seas are highest in the center of the fetch area and heading east.
Courtesy:  The Scripps Research Institute

Charts produced by wave models are fairly easy to read. There can be two charts produced for each forecast period: Sea Height and Swell Period. The Sea Height chart typically uses either color-coding or circles to indicate concentrations of similar sized seas. The "concentrations" represent the average height of the largest 1/3 of actual seas over a predefined time period. It is important to note that seas in these concentration areas can be higher over short time periods (3 or less hours) and individual waves much higher still. But for surf forecasting purposes, a 12-hour average sample seems to be sufficient, if not better, than a shorter time period because it smoothes out anomalous spikes. Sea heights are normally indicated in feet, but can be in meters (to convert meters to feet, multiply meters times 3.28).

The Sea Height chart also depicts the direction the sea is heading (which normally corresponds to the direction the wind is blowing). Sea heading is indicated by a barb or arrow that points in the direction the sea is moving and is commonly called a 'sea vector'. Though a good guide in the center of high seas and fetch areas, sea vectors can become less meaningful once the seas escape their source. In relatively clear waters, the sea vector can become heavily influenced by the direction of non-contributory surface winds in that area. For example, a solid long-period ground swell that is 1,000 nmiles away from it's source heading north might encounter a weak fetch area that is blowing south, completely contrary to the heading of the swell. The seas depiction of the wave model typically will indicate the swell vector in that area as heading southerly, influenced by the prevailing local winds and resulting short period wind waves, not north (the heading of the underlying long period swell). If you examine a wave model and a surface wind model (run for the same time period), the relationship between wind barbs and sea vector/arrow becomes apparent. This condition makes wave models that only produce a sea height chart less useful for tracking swells that have moved substantially away from their source.

The second image that can be produced by a wave model is the Swell Period chart. Period is indicated in seconds. Like the Sea Height chart, it use either color-coding or lines to indicate concentrations of swells and seas of equal period. The "concentrations" represent the average maximum period swell or sea present at a given location for a predefined time. An arrow is used to indicate the average heading of the swell for a specific location and is called a 'swell vector'. Note: Currently only the NOAA OMB Wavewatch III wave model produces a Swell Period chart. When viewing this image, the swell vectors (for the most part) are not influenced by local prevailing winds, but are driven purely by the heading of the underlying ground swell energy. As wind waves escape from under the influence of the storm that creates them, the shorter period/lesser energy wind waves fade while the longer period waves organize into sets based on their period. Waves of equal period join and travel together across the ocean. These waves become clearly visible on the Swell Period chart. They appear like a wall of water moving out from the storms center. The more energy and the grater the distance they travel, the more obvious they become. This is called a swell front. The leading edge of the front is composed of waves with periods typically greater than 16 seconds. Lesser period swells follow the leaders, in decreasing level of energy (e.g. 20 sec period swells followed by 17 sec period swells followed by 15 sec periods swells until the swell front dies.) The longer the storm was in-place and the greater the fetch area, the thicker the swell front will be. From a surfers perspective, thick swell fronts translate into a swell episode that will last a long time (several days rather than several hours).

The swell propagation algorithms in the Wavewatch III wave model also can track the swells as they migrate away from the storms that create them, managing to track up to 6 independent swells as they converge at predefined locations across the globe (buoys), providing the swell has a height of greater than about 6 inches. This is a very powerful tool for tracking swell migration.

NOAA Wavewatch III Wave Model from NOAA OMB
The first image displays sea heights. Notice several areas in the South Pacific with seas in the 7.0 meter range (23 ft). While these areas are interesting, they're not really high seas. The lower image displays swell periods and swell vectors. Notice the swellfront with period at 16-18 secs pushing northward from the South Pacific over the equator, while another swellfront is hitting North America with period at 15-17 secs. These were likely generated by strong wintertime Southern Hemisphere storms that have long since dissipated. The swell they produced pushes northward for days (and weeks) after the storm fades.
Image Courtesy: NOAA OMB 

The wave models provide an easy to read analysis and forecast of sea state conditions two times per day for 3 days (for the NOAA Suite) and one week (for the FNMOC Suite). The precaution about using wave models for swell prediction is doubly important. It's a model that uses a model to make a prediction. That is, the wave model uses an atmospheric model to determine the future state of the atmosphere, then makes a prediction of how the atmosphere will affect the water under it. So there's lot's of room for error.

Wave models do not perform well for smaller weather systems or systems where a high pressure gradient is present. Hurricanes are a good example. It seems the atmospheric models have difficulty accurately predicting the wind speeds in high gradient scenarios, which in-turn rapidly diminishes the wave models ability to accurately predict the sea heights the wind will produce. Rather, for hurricanes, surf forecasters develop their own rules based on experience and practice. And with the advent of the Wavewatch III wave model and it's Swell Period forecasts, the error factor starts rapidly compounding. Generally, Swell Period is a function of the height of the sea that produced it. If sea height is estimated low (lower than what is actually is), then swell period forecast will be low, which means the swell will travel faster than what the forecast predicts. This will result in the swell arriving earlier than what is forecast.

Regardless of these limitations, wave models do a remarkable job of predicting sea heights out to 2 days, with reasonable accuracy out to 3 days. If you view the wave model "00hr Hindcast" in conjunction with the combined ERS-2 and SSM/I wind field data maps, one can quickly confirm the location of active large fetch areas, the high seas associated with that fetch, wind speed, direction, and the heading of the largest seas. Though not a complete accurate picture due to variability of the initial data loaded into the wave model from the atmospheric models, these images are the single most important piece of data required by surf forecasters.

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