How fast does a tsunami travel?
A tsunami is a series of waves caused by a sudden displacement of water, most often by an undersea earthquake, but also by landslides or volcanic eruptions. Its wavelength is huge, often over 100 miles, compared with the ocean depth, so it behaves as a shallow-water wave. Its speed depends only on the depth:
c = √(g × d)
where g = 9.81 m/s² and d is the depth of the water.
Example
Over 13,000 ft (about 4,000 m) of ocean:
- speed: √(9.81 × 3,962) ≈ 197 m/s, about 440 mph, as fast as a jet airliner;
- a coast 620 miles away is reached in about 1.4 hours;
- with a period of 20 minutes, the wavelength is about 147 miles;
- a 1.6 ft wave in deep water grows to about 7 ft in 33 ft of water near the shore.
Why tsunamis grow near the coast
As the water gets shallower, the wave slows down. The back of the wave catches up with the front, the wavelength shortens and the energy is compressed into less water, so the height increases. Green’s law estimates this shoaling:
H₂ = H₁ × (d₁ ÷ d₂)^(1/4)
This is a first approximation. Bays, harbors and the shape of the seafloor can amplify the wave much more, and the run-up on land can reach several times the wave height at the shore.
Warning signs
- A strong earthquake that makes it hard to stand, or a long rolling one, near the coast.
- A sudden drop in sea level, exposing the seabed, as the trough of the wave arrives first.
- A loud roar from the ocean.
If you notice any of these, move to high ground or inland immediately, without waiting for an official warning. Tsunami waves come in series for hours, and the first is often not the largest.
Warning systems
The Pacific Tsunami Warning Center and the National Tsunami Warning Center (NOAA) estimate arrival times with the same physics: they use detailed depth maps and solve for the travel time along each path. Deep-ocean pressure sensors (DART buoys) confirm whether a tsunami was generated.