Imagine the following situation: You look at the predictions, and you find that 6-foot, 15-second swell is forecast to be arriving from the northwest sometime tomorrow. From experience, you know that is the perfect size, period and direction for your beach. The next day, you 'track' the swell by checking some wavebuoys just off the coast (wavebuoys give us real measurements of the waves, not a prediction). The swell has already hit the buoys, confirming what the models said" 6 foot, 15 seconds, straight from the northwest.
When the swell actually does arrive, there is something not quite right about it. There is no wind but the sea is mixed up and kind of choppy. In general, the swell lacks power and the waves aren't walling up the way they should. That's disappointing, especially since it was supposed to have been all-time.
Even the wavebuoy, which by all accounts cannot lie, also told us that the swell was all-time. It leaves you thinking that there must be more to it than the simple assumption that (a) the waves will be classic if the direction is right and the period is long, or (b) they'll be rubbish if the direction is wrong and the period is short.
The wavebuoy cannot lie, but what it can do is not tell us the whole story. That swell didn't turn out the way we thought it was going to, not because the information we were getting was incorrect, but because the information was not complete enough. Sometimes, the parameters given to us by the wave model predictions and the buoy measurements are not enough to distinguish between a clean 6-foot, 15-sec northwest swell and a messy one. The typical 'significant wave height', 'peak period' and 'mean direction' you see all the time are just statistical summaries of the state of the sea. Like averages, they are very useful and convenient but tend to hide a lot of information. In reality, the sea is actually made up of a combination of waves with different heights, periods and directions, all mixed up together, even in the cleanest groundswell. The way these different waves interact might not be distinguishable by just looking at those statistical summaries.
The reason why sometimes we need a bit more information is that we don't know how many different periods are mixed up together, and how many different directions. There might be a '15-second swell' where most of the waves are indeed very close to 15 s, or the waves are spread over wide range of periods from 5 s to 25 s. Likewise, there might be a 'north-westerly swell' where most of the waves are coming from very close to a north-westerly direction, or the waves are coming from a wide range of directions from west round to north.
A good way to illustrate the way the wave energy is distributed over all the different periods is to use a plot of wave energy versus period" a spectrum (see diagram). A spectrum can be thought of as a kind of statistical distribution of all the component waves that go to make up the wave field. Around the peak period, the wave energy is high, whereas, at longer and shorter periods, the energy gradually diminishes. The amount of wave energy at a particular period is governed by both the height and the abundance of waves around that period. For example, a peak period of 15 s (such as in the diagram) indicates more wave energy at that period than at any other, which, in turn means more and/or bigger waves with periods of around 15 s that at any other period.
Now, usually, the only thing that is quoted is peak period. But the peak period only tells us at what period there is most energy; it doesn't tell us anything about the distribution of energy at periods above or below that peak. For example, a broader and flatter curve (red) means the energy will be more spread out over the whole range of periods. Here, the sea will appear messy and confused because there are probably just as many big waves at short and long periods as there are at mid periods. In contrast, a narrow, pointed curve (blue) means all the energy is concentrated around the peak period and, therefore, the sea will only contain waves around a narrow range of periods. This gives us a purer, cleaner swell.
What is fundamental about the two curves in the graph is that, although one swell is very different from the other, they both have the same peak period (fifteen seconds). It is not just the peak period itself, but the energy either side of the peak (called the bandwidth) that makes a big difference to the quality of the surf.
If you are closer to the storm, then the swell is more likely to have a wider bandwidth. This is because all the different period waves that were generated inside the storm itself haven't propagated very far and, therefore, haven't separated out from each other. If you are further away from the storm centre, the swell will be more dispersed, and a narrower range of periods will be passing a given point at any given time.
In addition to the variation in period of all the waves making up the swell, there is also the variation in direction. If all the waves are arriving from a small range of directions then there is a narrow directional spread (and a clean, ruler-edged swell). In contrast, if there is a lot of variation in the direction of approach, then there is a wide directional spread (and a more mixed-up and peaky swell).
In wavebuoy reports and the outputs of wave-prediction models, a common way of summarising the direction is to use the direction from which there is most energy, called the peak direction. Sometimes, the mean or average direction is used, which is the average of all the directions put together. If you only have the peak or the mean direction, then it is impossible to know how much directional spread there is in the wave field.
Usually, swells that arrive from distant storms tend to have narrow directional spreads, and swells generated more locally tend to have wide directional spreads. At a particular observation point, swell can only be received from within the 'field of view' covered by the storm itself from the point of view of the observer. A storm thousands of miles from the observer will have a narrow 'field of view' with the swell arriving from only a narrow range of directions. In contrast, a storm that is practically on top of the observer will have a much wider 'field of view' allowing swell to arrive from many different directions at once.