Run-up is the height of a tsunami above sea level at the farthest point it reaches on the shore. This height may be considerably different from the height of the wave where it first hits the shore, and is commonly twice that of the height of the wave at the shore. Run-up heights of 30 feet (10 m) are fairly common for tsunamis, while heights of 150-300 feet (45-90 m) are rare, and heights greater than this in the range of 300-1,700 feet (90-525 m) are very rare, but have been observed in the past hundred years. Many things influence the run-up of tsunamis, including the size of the wave, the shape of the shoreline, the pro file of the water depth, diffraction, formation of edge waves that move along the coast, and other irregularities particular to individual areas. Some bays and other places along some shorelines may amplify the effects of waves that come in from a certain direction, making run-ups higher than average. These areas are called wave traps, and in many cases the incoming waves form a moving crest of breaking water, called a bore, that smashes into coastal areas with great force. Tsunami magnitudes are commonly reported using the maximum run-up height along a particular coastline.
When tsunamis approach the shore, the wave fronts pile up and the wave changes form from a sinusoidal wave to a solitary wave, with the entire wave form above sea level. These types of waves maintain their forms, and since the kinetic energy in the wave is evenly distributed throughout the wave, the waves lose very little energy as they approach the shore. steep coastlines may experience larger run-ups, since they have the least amount of energy dissipation. The shape and angles of cliffs along the beach can also amplify tsunami heights, in some cases tripling the height of the wave at the shore. Embayments that become narrower inland may amplify waves, and in some bays it may take two or even several tsunami crests for the amplification process to reach a maximum. Refraction effects can increase tsunami run-up around promontories where narrow strips of land jut out into the sea.
In some cases, tsunamis are refracted around the shores of islands, or both sides of bays, producing large edge waves that move parallel to shore. These edge waves must merge on the back sides of islands,
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Definition of tsunami run-up height. Note how this is higher than the wave height at the coast.
or in the ends of embayments, and in these locations particularly large run-ups have been recorded. Movement of edge waves around islands accounts for many of the large run-ups on the leeward sides of the Hawaiian Islands from the April 1, 1946, tsunami in Hilo, Hawaii, where many bays on the back sides of the islands experience run-ups almost as high as those facing the initial wave front. The 1992 Flores Island tsunami also saw many villages on the leeward sides (facing away from the wave front) of islands washed away by large tsunamis. These waves also formed by the waves being refracted around the islands, forming edge waves that combined to cause unusually large run-ups in specific locations. More than 2,000 people died when the 16-23-foot (5-7-m) waves washed into these villages on the back sides of the islands. Similarly, in a 1993 tsunami in Japan, the island of Okushiri focused the energy of a tsunami on the town of Hamatsumae lying behind the island. On July 12, a 100-foot (30-m) wave grew behind the island and washed into the town, killing 330 people.
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