# Calculating the threat of tsunami

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On 26 December 2004, an earthquake measuring 9.3 on the Richter scale created a tsunami that led to the deaths of over 289,000 people living in coastal villages in Asia and Africa. Scientists have made important advances towards predicting tsunami by combining mathematics, geology and physics.

The word 'tsunami' is Japanese, meaning 'harbour waves'. The Japanese know a lot about the destructive nature of these giant waves, having suffered from their effects for at least 1100 years. But the term 'harbour wave' is misleading, since tsunami don't just occur in harbours. Similarly, the popular term 'tidal wave' is inaccurate, since tsunami are not tidal (although the strength of their impact may be partly dependent on the tide level at the time of arrival). This scientific definition from the Department of Geophysics at the University of Washington, USA is perhaps more informative:

a tsunami is a wave train, or series of waves, generated in a body of water by an impulsive disturbance that vertically displaces the water column.

What causes a tsunami?

Tsunami are most often triggered by earthquakes (Box 1: What caused the Indian Ocean tsunami on 26 December 2004?), but they can also be produced by landslides, volcanic eruptions, explosions and the impact of meteorites or asteroids.

A tsunami is often invested with a great deal of energy by the earthquake or other disturbance that triggers it. This was illustrated graphically by the tsunami that hit Chile in 1868 and left ships stranded 3 kilometres inland. In southern New South Wales, tsunami of past ages are believed to have tossed boulders weighing up to 90 tonnes on to cliffs 30 metres high.

Wave energy

The energy in a wave is proportional to the length (the distance between two crests of the wave) and to the square of the height (the distance between the trough and the crest). This means that high-energy tsunami in the deep ocean may have a height of less than a metre but a wave length of up to 650 kilometres – in effect, its energy is spread out across the ocean. A tsunami with such a long wave length will lose energy quite slowly, so it is possible for it to travel vast distances and still wreak havoc when it hits a coast.

For example, an off-shore earthquake near Chile in 1960 sent waves of water speeding in all directions across the Pacific Ocean. The height of the waves was no more than a metre or so – making them indistinguishable in deep water from the general swell. The waves were travelling extremely fast and, just 22 hours later, a wave 6 metres high struck the coast of Japan on the other side of the ocean, killing about 200 people. The tsunami continued to reverberate around the Pacific for days, causing damage whenever it struck land.

When a tsunami hits shallow water

The energy in a wave is one factor that helps determine the damage a tsunami causes. When the wave hits shallow water, other factors that influence the destructive effect of a tsunami come into play – the velocity of the wave (which itself is influenced by the shape and depth of the sea bed) and its period. Period (T) is defined as the time interval between the passage of two successive crests past a given point. A wave's velocity (v) is calculated by dividing the distance between two crests of the wave (L) by T:

A tsunami grows in height as it approaches land. As the depth of the water decreases so too do wave length and wave velocity, but the energy invested in the wave train remains nearly constant. Because the energy in a wave is proportional to the length and to the square of the height, wave height increases as the seabed becomes shallower.

Many tsunami waves don't break as they hit land. They simply surge, flooding low-lying areas and rebounding off cliffs or hills - often causing as much or more damage as they recede back into the ocean.

Tsunami calculations are complicated

Calculating the velocity, wave height and destructive force of a tsunami for any stretch of coastline is complicated by several factors. For example, the shape of the sea bed can produce effects that might not be predicted by a simple wave equation. The presence of harbours and headlands also cause the waves to reflect, diffract and refract, changing their direction – indeed, some tsunami have been known to 'bend' around islands, eventually engulfing the coast on what was supposedly the protected side. Other complicating factors include the effect of backwash from one wave on the waves that follow and the exact nature of the disturbance that generated the tsunami in the first place.

Using maths to solve tsunami mysteries

In order to account for such complications in tsunami prediction, scientists use computer-based mathematical modelling techniques. One such technique has provided an answer to one of history's enduring mysteries – the demise of a civilisation on the island of Crete in the Aegean Sea (Box 2: The disappearance of an ancient civilisation). Elsewhere, mathematical modelling and an understanding of tsunami-causing events are used to predict the vulnerability of coastal areas to tsunami.

In Australia, for example, models predict that the northwest coast is most susceptible to tsunami. Other parts of Australia are also vulnerable, including the south and central coasts of New South Wales. In Queensland, the Great Barrier Reef may not provide absolute protection from tsunami originating in the Pacific – scientists claim to have found evidence of tsunami having come through gaps in the reef to deposit huge coral boulders.

Modelling tsunamis created by asteroids

Using computer modelling techniques that were developed to simulate the blast effects of nuclear weapons, scientists calculated recently that an asteroid measuring 4.8 kilometres in diameter landing in the mid-Atlantic would create a tsunami high enough to swamp the entire upper east coast of the USA. The city of New York, for example, would disappear. The chance of such an event is quite remote – Earth is likely to be struck by an asteroid of that size every 10 million years or so. But even an asteroid of about 400 metres in diameter could spawn waves approaching 100 metres in height.

Tsunami are rare events

To accurately assess tsunami risk, scientists need information on the likely occurrence and location of a tsunami-generating event, the expected magnitude of the event, the shape of the sea bed and the topography of the affected coastal area (Box 3: The warning system in the Pacific). Rarely is all this information available, complicating the identification of potentially vulnerable areas.

Nevertheless, as we collect more information, the identification of vulnerable regions using computer models should become increasingly accurate. This should assist town planning – for example, in vulnerable regions it may be necessary to restrict development on low-lying areas, or to build walls to protect dwellings from inundation.

To some extent, the danger posed by tsunami is increased by the fact that they are relatively rare events. Efforts made now to predict and guard against tsunami could turn the tide against this killer.

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Page updated February 2005.