How Is a Tsunami Different from an Ordinary Wave?
– You Can't Outwalk One
Think of the waves you see at the beach, rolling in and sliding back out. Many people assume a tsunami is just a bigger version of these. In fact the two are entirely different things, and they differ in speed and in the way the water moves. The idea that "if I see the sea pull back, I can run and still make it" falls apart once you do the maths on speed.
Everyday waves made by wind move only the water near the surface, up and down. A few metres down, the water hardly stirs. That is why a boat a little way out to sea is not bothered much by waves.
A tsunami is completely different. From the surface to the seabed, the whole column of water moves as one block. Even in a sea 4000 m deep, a tsunami sets the water near the bottom moving too.
This difference leads to a difference in speed. And a tsunami is far faster than you would imagine.
Thinking "I'll run once I see the water pull back" is dangerous. Let's check why, with some arithmetic.
The speed of an ordinary wave depends on its wavelength. A tsunami's depends on the depth. The deeper the water, the faster it travels.
In a deep ocean like the Pacific, it travels at about 700 km/h. Even in shallows near the shore, it is faster than a person can run.
"Seeing it and then fleeing" is not an option at these speeds. Let's take it step by step.
An ordinary wave is a "surface ripple"; a tsunami is "the water itself on the move"
When wind brushes the sea surface, the water moves in circles, up and down and back and forth. But this motion fades quickly with depth. It reaches down only about as far as the wavelength (the distance from one crest to the next). Ordinary waves have wavelengths of tens to hundreds of metres, so where the water is deeper than that, the seabed is barely affected.
A tsunami is different. Its wavelength is tens to hundreds of kilometres, orders of magnitude longer. Even next to the Pacific's average depth (around 4000 m), a tsunami's wavelength is far greater.
When the wavelength is much greater than the depth, the wave behaves not as a "ripple on the surface" but as a "movement of the whole column of water". This is called a shallow-water wave. Even the middle of the Pacific counts as "shallow water" for a tsunami.
A tsunami is the sea itself coming ashore.
Speed depends on depth, not wavelength
This is the key difference from ordinary waves. An ordinary wave in deep water travels faster the longer its wavelength. But for a tsunami, which acts as a shallow-water wave, speed has nothing to do with wavelength and depends on water depth alone.
Deeper means faster; shallower means slower. You can think of the sea's depth as a speedometer. A tsunami crossing the Pacific changes speed from place to place because the depth along its path changes.
And once you put real numbers into this formula, you see how unreal the speed is. The detailed calculation is in the fold-out section at the end, but the result is jetliner speed in the deep sea offshore, and faster than a person sprinting even in shallows near the shore.
Before a tsunami, the sea sometimes draws back from the shore first. But this does not always happen, and sometimes the first wave arrives with no warning at all.
Even if you did see the sea pull back, the numbers say that running for high ground from that moment would very likely be too late. Rather than "seeing it and then fleeing", it is considered vital to start evacuating the moment you feel shaking or a warning is issued.
Why does it grow taller near the shore?
Offshore, a tsunami is often only tens of centimetres to about 1 m high, and it is said that people on a ship may not even notice it. But as it nears land, its height keeps growing.
One reason is linked to the loss of speed. The amount of energy a tsunami carries does not change much. But when the water gets shallower and the wave slows, its height increases to keep that energy up (the detailed calculation is in the fold-out section).
On top of that, in landforms such as inlets and bays, waves converging from both sides concentrate at one point, and this is known to make them higher than simple calculations predict. That is why records of past large tsunamis show damage that was locally severe at the heads of bays.
Three things to remember right now
- If you feel strong or long shaking, go to high ground without waiting for a warningIf you are near the coast or a river and feel strong shaking, or weak shaking that goes on for a long time, that alone is your signal to evacuate. If a tsunami warning or major tsunami warning is issued, move to high ground immediately.
- Go on foot, higher and fartherEvacuating by car can cause traffic jams and make things more dangerous, it is said. Go on foot as a rule, and head for nearby high ground or an evacuation building, aiming for higher ground without hesitation.
- Never go back until the warning is liftedA tsunami does not always end after one wave; it can strike again and again. And the first wave is not always the biggest. Even if "it seems to have calmed down", do not decide for yourself to return. Stay on high ground until official word that it is lifted.
A tsunami can travel up a river from its mouth and reach far inland. In some places, "I'm far from the coast, so I'm safe" does not hold.
We recommend checking your local hazard map in advance for the areas expected to flood, including along rivers, and for evacuation sites.
Things you can check yourself (water and a model; no fire)
- Fill a large tray (or a washbowl) with water about 3–4 cm deep
- On one side of the bottom, sink a book or board to make an area about half as deep
- Press the opposite end once, gently, with your palm to make just one wave
- Follow with your eyes how fast the wave moves through the deep part and the shallow part
- You should see the wave slow down (and rise up) in the shallow part
Steps 4 and 5 are the heart of this observation. You can see with your own eyes that "when the depth changes, the wave's speed changes". This is a property of shallow-water waves that shows up even in a household tray, and real tsunamis are an extension of it. Do it outdoors or near a sink so spilled water doesn't matter.
Summary
A tsunami differs from an ordinary wave because not just the surface but the whole column of water down to the seabed moves together. Because of this, a tsunami's speed is set by water depth, not wavelength, and it is jet-fast offshore and faster than a person sprinting even near shore. There is almost no time left to "see it and then flee".
A tsunami is not just a big wave.
It is the sea itself in motion.
The idea seen here, that "the shallower the water, the slower the wave", is also why ordinary ocean waves always arrive parallel to the shore. We explain this in this article.
For those who want more – terms, numbers and links to textbooksFrom middle-school science to active research, each level is clearly marked
- Middle schoolCovered in middle-school science
- High schoolCovered in high-school "Basic Physics" and "Basic Earth Science"
- High school+High-school "Physics" and "Earth Science", or extension and sidebar material in textbooks
- UniversitySpecialist university content (physical oceanography) not taught in high school
- ResearchTopics researchers are still investigating, not taught even at university as settled
Middle schoolTerms: words around tsunamis
- Wavelength: the distance from one crest to the next.
- Shallow-water wave: a wave whose wavelength is much greater than the water depth, so the whole column of water moves. The tsunami in this article is one.
- Run-up: a tsunami moving up over land or a river.
- Tsunami warning / major tsunami warning: warnings issued by the Japan Meteorological Agency according to the expected tsunami height.
- Hazard map: a map showing areas expected to flood and evacuation sites. Local governments produce and publish them.
High schoolChecking with a formula: is a tsunami really faster than you can run?
The article said "speed is set by depth". Here we use that formula to work out the actual speed.
speed = √(gravitational acceleration × water depth)
| Speed | Unit is m/s |
| Gravitational acceleration | 9.8 m/s² |
| Water depth | Unit is m |
| √ | Square root (the number that gives this value when squared) |
This is the formula for the speed of a shallow-water wave, and it has nothing to do with wavelength or wave height. Only water depth appears in it. That is why the conclusion, "the deeper, the faster", differs from our sense of how ordinary waves behave.
| Average depth of the Pacific | Take about 4000 m |
| Work out the bracket | 9.8 × 4000 ＝ 39200 |
| Find its square root | 198 × 198 ＝ 39204, so about 198 |
| Speed | About 198 m/s |
| Convert to km/h | 198 × 3.6 ≒ 713 km/h |
About 713 km/h. That is close to the cruising speed of a jet airliner (roughly 800–900 km/h). This speed is why a tsunami crossing the Pacific can reach the far shore in only about half a day.
| Shallow sea near the coast | Take a depth of 10 m |
| Work out the bracket | 9.8 × 10 ＝ 98 |
| Find its square root | 9.9 × 9.9 ≒ 98, so about 9.9 |
| Speed | About 9.9 m/s |
| Convert to km/h | 9.9 × 3.6 ≒ 35.6 km/h |
A depth of 10 m is already very close to the beach. Even so, it is 35.6 km/h.
A person's top running speed is roughly 20–25 km/h for a short sprint, and slower if you keep running for long. Even a tsunami that has reached the shallows beats a person's all-out sprint.
This calculation is why "seeing the water pull back and then running" doesn't work. By the time you see it, you can no longer outrun it.
* Real depths vary greatly from place to place, and the seabed's shape also changes the speed. This is a calculation to get the order of magnitude.
A commonly used approximation is that the amount of energy a wave carries stays roughly constant as the depth changes. The result is a relationship in which height makes up for lost speed.
height ratio ≈ (original depth ÷ new depth) to the power of 1/4
| Offshore depth | 4000 m |
| Depth near the shore | 10 m |
| Depth ratio | 4000 ÷ 10 ＝ 400 |
| Square root of 400 | 20 × 20 ＝ 400, so 20 |
| Square root of 20 (＝ fourth root of 400) | 4.47 × 4.47 ≒ 20, so about 4.47 |
| By what factor does the height grow? | About 4.5 times |
A tsunami 50 cm high offshore would grow, by this simple calculation alone, to more than 2 m. And this is a rough guide that assumes a flat coast. In reality, the shape of inlets and bays is known to amplify it much further.
* This relationship is a simplification that assumes a smoothly varying seabed. Real coastlines and seabed shapes are more complex, and in some places the wave grows higher than the simple calculation gives, in others it is held lower.
High school+Ordinary waves set their speed the opposite way from tsunamis
For ordinary wind waves in deep water (where the water is well deeper than the wavelength), speed is set by wavelength and barely depends on depth. Waves with longer wavelengths travel faster.
A tsunami (a shallow-water wave), on the other hand, has a speed set by depth alone, independent of wavelength. The two formulas differ in form and in what they depend on. Though both are called "waves", they are different physical phenomena underneath.
This difference comes from how deep the water's motion reaches. In an ordinary wave, the motion reaches only about half a wavelength down, and deeper water takes no part. In a tsunami, the wavelength is far greater than the depth, so all the water down to the seabed joins in the motion. This difference in "how much water moves" is the root of the difference in how speed is set.
UniversityOffshore observation determines how accurate warnings are
A tsunami's height depends on many factors, including the location and size of the quake and the shape of the seabed. Predicting the exact height from the limited information available just after it starts is not easy.
So pressure gauges on the seabed and GPS-based sea-surface observations are used to detect a tsunami directly as it travels. These data are used to update the first forecast and issue more accurate information.
However, there is also a time lag between an offshore observation point and land, so a delay between observing and announcing is unavoidable. As calculations ② and ③ show, the tsunami itself is so fast that this delay translates directly into less time to evacuate.
ResearchWhat is still unclear
- Predicting in advance, precisely, how much a tsunami will be amplified in an inlet or bay is still a hard problem. Complex coastlines and seabed shapes interact, and simulation accuracy keeps being improved, but fully reproducing every real terrain is not easy.
- Methods to predict tsunami height instantly and accurately from an earthquake's size are still developing. Uncertainty remains, especially with the limited data available just after the event.
- For tsunamis caused by undersea landslides or volcanic activity, prediction and warning systems are said to be less well developed than for earthquake tsunamis. Estimating the path and size from the source poses different difficulties than for earthquakes.
- Research from psychology and the social sciences on turning "early evacuation" into real behaviour also continues. Even with accurate physical predictions, whether they lead to actual evacuation is another question, it is said.
The basic formula for a tsunami's speed has been known for over 100 years. Even so, it is still not easy to say in advance exactly where and how high a tsunami will get. A simple formula does not mean an easy prediction.
Links to textbooks (by level)
| Level | Subject / unit | Where in this article |
|---|---|---|
| Middle school | Science: properties of waves / earthquakes and tsunamis | Wavelength, basic properties of tsunamis |
| High school | Basic Physics: properties of waves | Calculation with speed ＝ √(gh) |
| High school | Basic Earth Science: oceans and tsunamis | How tsunami warnings work, principles of evacuation |
| High school+ | Physics: wave motion | Deep-water and shallow-water waves set speed differently |
| University | Physical oceanography, geophysics | Offshore observation and warning updates, how amplification works |
| Research | Tsunami science (unsolved) | Predicting amplification in bays, landslide tsunamis, evacuation behaviour |
| – | Disaster prevention | Principles of evacuation, hazard maps, danger along rivers |
- Explanatory materials on tsunami warnings and advisories and on how tsunamis form, from the Japan Meteorological Agency (気象庁).
- Guidelines and reports on tsunami evacuation from the Cabinet Office (内閣府), Disaster Management.
- Satake, K., Tsunamis (a research overview of tsunami physics, in Encyclopedia of Solid Earth Geophysics).
- Explanatory materials on developing tsunami hazard maps, from the Ministry of Land, Infrastructure, Transport and Tourism (国土交通省) and the Japan Meteorological Agency (気象庁).
- Synolakis, C. E. & Bernard, E. N., Tsunami science before and beyond Boxing Day 2004, Philosophical Transactions of the Royal Society A 364, 2006.
* The speed and height figures are representative guides using average water depths. They vary greatly with the actual sea area and terrain.
* This article is a general-audience science explainer. In a tsunami, follow the warnings and advisories issued by the Japan Meteorological Agency and the instructions of your local government and community evacuation plan. The figures given are guides to help you understand how it works; the actual speed and height of a real tsunami vary greatly with terrain and conditions.