What determines how destructive a tsunami will be near the origin and at a distant shore?

Tsunamis arrive at a coastline as a series of successive crests (high water levels) and troughs (low water levels) - usually occurring 10 to 45 minutes apart.  As they enter the shallow waters of coastlines, bays, or harbors, their speed decreases to about 50-60 km/h.   For example, in 15 m of water the speed of a tsunami will be only 45 km/h.  However 100 or more kilometers away, another tsunami wave travels in deep water towards the same shore at a much greater speed, and still behind it there is another wave, traveling at even greater speed.  

As the tsunami waves become compressed near the coast, the wavelength is shortened and the wave energy is directed upward - thus increasing their heights considerably.  Just as with ordinary surf, the energy of the tsunami waves must be contained in a smaller volume of water, so the waves grow in height.  Even though the wavelength shortens near the coast, a tsunami will typically have a wavelength in excess of ten kilometers when it comes ashore.   Depending on the water depth and the coastal configuration, the waves may undergo extensive refraction - another process that may converge their energy to particular areas on the shore and thus increase the heights even more.  Even if a tsunami wave may have been 1 meter of less in the deep ocean, it may grow into a huge 30-35 meter wave when it sweeps over the shore.  

Thus, tsunami waves may smash into the shore like a wall of water or move in as a fast moving flood or tide - carrying everything on their path.  Either way, the waves become a significant threat to life and property.   If the tsunami waves arrive at high tide, or if there are concurrent storm waves in the area, the effects will be cumulative and the inundation and destruction even greater.   The historic record shows that there have been many tsunamis that have struck the shores with devastating force, sometimes reaching heights of more than 30-50 meters.  For example, the 1946 tsunami generated by an earthquake off Unimak island in Alaska's Aleutian Islands, reached heights of more than 35 meters, which destroyed a reinforced concrete lighthouse and killed its occupants.  

Finally, the maximum height a tsunami reaches on shore is called the runup.  It is the vertical distance between the maximum height reached by the water on shore and the mean sea level surface.  Any tsunami runup over a meter is dangerous.  The flooding by individual waves will typically last from ten minutes to a half-hour, so the danger period can last for hours.  Tsunami runup at the point of impact will depend on how the energy is focused, the travel path of the tsunami waves, the coastal configuration, and the offshore topography.  

Effects on Islands
Small islands with steep slopes usually experience little runup - wave heights there are only slightly greater than on the open ocean.  This is the reason that islands with steep-sided fringing or barrier reefs are only at moderate risk from tsunamis.  

However, this is not the case for islands such as the Hawaiian or the Marquesas.  Both of these island chains do not have extensive barrier reefs and have broad bays exposed to the open ocean.  For example, Hilo Bay at the island of Hawaii and Tahauku Bay at Hiva Oa in the Marquesas are especially vulnerable.  The 1946 Aleutian tsunami resulted in runup, which exceeded 8 m at Hilo and 10 m at Tahauku; 59 people were killed in Hilo and two in Tahauku.  Similarly, any gap in a reef puts the adjacent shoreline at risk.  The local tsunami from the Suva earthquake of 1953 did little damage because of Fiji's extensive offshore reefs.  However, two villages on the island of Viti Levu, located on opposite gaps in the reef, were extensively damaged and five people were drowned.

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