a long train of swell waves at the cost of the energy losses and increased disorder affecting all the small breaking waves. The sorting of sand grain sizes, often seen on a beach, is a similar process (as is a lot of life). Dissipation The dissipation of swell energy is much stronger for short waves, which is why swells from distant storms are only long waves. The dissipation of waves with periods larger than 13 seconds is very weak but still significant at the scale of the Pacific Ocean. These long swells lose half of their energy over a distance that varies from over 20,000 km (half the distance round the globe) to just over 2,000 km. This variation was found to be a systematic function of the swell steepness: the ratio of the swell height to the wavelength. The reason for this behavior is still unclear, but it is possible that this dissipation is due to the friction at the air-sea interface. Swell dispersion and wave groups Swells are often created by storms thousands of nautical miles away from the shores where they break, and the propagation of the longest swells is primarily limited by shorelines. For example, swells generated in the Indian Ocean have been recorded in California after more than half a round-the-world trip. This distance allows the waves comprising the swells to be better sorted and free of chop as they travel toward the coast. Waves generated by storm winds have the same speed and will group together and travel with each other, while others moving at even a fraction of a meter per second slower will lag behind, ultimately arriving many hours later due to the distance covered. The time of propagation from the source t is proportional to the distance X divided by the wave period T. In deep water it is where g is the acceleration of gravity. For a storm located 10,000 km away, swells with a period T=15 s will arrive 10 days after the storm, followed by 14 s swells another 17 hours later, and so forth. The dispersed arrival of swells, starting with the longest period, with a reduction in the peak wave period over time, can be used to calculate the distance at which swells were generated. Whereas the sea state in the storm has a frequency spectrum with more or less the same shape (i.e. a well