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Impact of tsunami: runup and "run-in"

Attenuation laws for tsunami

Once a tsunami arrives at a coastline, the energy that has been carried by the waves from the source, perhaps across entire oceans, is finally largely liberated as kinetic and potential energy (although on steep coasts in particular a fraction may be reflected out to sea) as the water in the wave spreads over the coastal region.
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The TSUNAMI Initiative Gravestones flattened by run-in on Flores Island, Indonesia during 1992 Tsunami The TSUNAMI Initiative
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Gravestones flattened by run-in on Flores Island, Indonesia during 1992 Tsunami
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This movement of water onto the land is sometimes tranquil but is more commonly violent, with large breaking waves at or close to the shore converting into turbulent bores or surges of water. The extent of the region covered by this water varies according to the height and wavelength of the waves as they arrive in the nearshore region, and with the local topography.

On steep coastlines (ranging up to vertical coastal cliffs or artificial coastal defences) the extent of the region affected is best expressed in terms of runup, defined as the maximum height attained by the leading edge of the tsunami wave above a reference sea level, which is that which would normally occur at the time of tsunami impact. (Note that this definition therefore allows for tidal variations in sea level, although it does not allow for the rare case where a tsunami is superimposed upon a storm surge.) Maximum runup height H produced by a tsunami is often recorded and used as a measure of tsunami magnitude.

On more gently inclined coasts (with slopes of around 0.1 to 0.05 or less) and especially in more or less flat coastal areas, the extent of the area inundated by the tsunami is limited not by the maximum height that it can reach but rather by the dissipation of the wave by drag forces as it flows over the more or less rough surface of the land. In these regions it is more appropriate to consider the maximum width of the inundated zone or "run-in" as a measure of the scale of a tsunami event.

Factors controlling runup

A large number of experimental studies and observations of actual tsunami indicate that the principal factor controlling runup associated with any one wave in a tsunami wave train is the height H0 of the wave as it crosses the initial shoreline. If the wave is a non - breaking or tranquil wave then the eventual runup height is roughly equal to this initial height. However, if the wave is a breaking wave (typically, a bore or surge) it has a substantial amount of kinetic energy stored in the fast moving mass of water which will partly convert into an additional increment of runup height as it moves onto the land (that is to say, additional gravitational potential energy), and partly be dissipated through turbulence within the wave and drag at its base. Put another way, the momentum of the wave carries it further upslope. The size of the additional increment depends strongly on the inclination of the slope over which it is moving: for natural hillsides of around 20 degrees the runup height is commonly about twice the value of H0 whilst in the case of vertical cliffs or walls the runup height can be as much as 5 times H0. Thus, for example, a tsunami wave 10 m high impacting a 40 m high vertical cliff would still have sufficient mass and energy when it reached the top to cause severe damage to buildings on top of the cliff. Such a situation occurred at the Scotch Cap lighthouse and radio station in the 1 April 1946 Aleutian tsunami, where the tsunami surged up a steep cliff 115 feet high, demolishing the lighthouse partway up the cliff and severely damaging buildings on the flat ground at the top of the cliff.

Factors controlling the width of the inundated zone (inundation distance or "run-in")

On relatively flat - lying coastlines the extent of the zone inundated by tsunamis depends less upon the topography and more upon other properties of the terrain, principally the sizes, numbers and other characteristics of objects upon it which exert drag upon the base of surges or bores flowing rapidly across the landscape. These features are expressed in terms of a roughness coefficient that is related to the inundation distance or "run in" Xmax produced by a tsunami of given height H0 at the coast. For flat surfaces:

where H0 = wave height at coast and n = surface roughness coefficient

Values of n are thought to typically range from 0.015 to 0.07: it will be noted that this corresponds to a 40-fold range in Xmax. The following table shows typical values of n for different terrain types:

Mud flats, ice, open fields without crops0.0155700 m48.5 kilometres
Built - up areas (typical)0.0351050 m8.9 kilometres
Built - up areas (city centers with high rise buildings)0.03 100 m1 kilometre
Forests, jungle, rough lava flows0.07260 m2.2 kilometres

It should be noted that the roughness coefficient shows an effective decrease for waves that are large in relation to the sizes of the obstacles in their paths. For example, the large tsunamis (up to 35 m high at the coast) produced during the Krakatau eruption of 1883 penetrated up to 8 km into dense jungle, significantly further than predicted by the above relationship. This may however also reflect that the first tsunami wave in a series typically removes most of the obstructions in its path, reducing surface roughness for the later waves in the series.

It should however also be noted that shorter-period tsunami waves will not attain the maximum values of Xmax noted above since they will begin to retreat before the water inundates the full distance noted: this effect is complex and difficult to quantify, however.




© 2000 Natural Environment Research Council, Coventry University and University College London