# Why do tsunami waves begin with the water flowing away from shore?

A sign of a tsunami is that the water rushes away from the shore, then comes back to higher levels. It seems that waves should be both + and - polarized and that some tsunamis should go in the opposite direction. That is the first indication of them would be that the water begins rising. However, other than situations very close to the source, it seems that the wave always begins with the water drawing away from the coast.

For example, the wikipedia article on tsunamis states that:

In the 2004 Indian Ocean tsunami drawback was not reported on the African coast or any other eastern coasts it reached. This was because the wave moved downwards on the eastern side of the fault line and upwards on the western side. The western pulse hit coastal Africa and other western areas.

The above is widely repeated. However, when you search the scientific literature, you find that this is not the case:

Proc. IASPEI General Assembly 2009, Cape Town, South Africa., Hermann M. Fritza, Jose C. Borrerob, "Somalia Field Survey after the December 2004 Indian Ocean Tsunami":

The Italian-speaking vice council, Mahad X. Said, standing at the waterfront outside the mosque upon the arrival of the tsunami (Figure 10a), gave a very detailed description of the initial wave sequence. At first, a 100-m drawback was noticed, followed by a first wave flooding the beach. Next, the water withdrew again by 900 m before the second wave partially flooded the town. Finally, the water withdrew again by 1,300 m offshore before the third and most powerful wave washed through the town. These drawbacks correspond to 0.5-m, 4-m, and 6-m depths. The detailed eyewitness account of the numerous drawbacks is founded on the locations of the offshore pillars.

So is there a physical reason why tsunamis, perhaps over longer distances, tend to be oriented so that the first effect is a withdrawal of the water?

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Are you sure tsunamis actually do this? Do you know for sure that there aren't many tsunami where they high water comes first? –  Mark Eichenlaub Mar 12 '11 at 0:15
No, I am not. But it appears in the news repeatedly. In fact, the wikipedia article writes: "If the first part of a tsunami to reach land is a trough—called a drawback—rather than a wave crest, the water along the shoreline recedes dramatically, exposing normally submerged areas." Which implies that it can go either way. –  Carl Brannen Mar 12 '11 at 0:19
Ah, here it is: "In the 2004 Indian Ocean tsunami drawback was not reported on the African coast or any other eastern coasts it reached. This was because the wave moved downwards on the eastern side of the fault line and upwards on the western side. The western pulse hit coastal Africa and other western areas." en.wikipedia.org/wiki/Tsunami –  Carl Brannen Mar 12 '11 at 0:20

Water waves are rather complicated, and the differential equations which describe them are call Boussenesq equations. A tsunami is not a transverse wave. It is a pressure wave with a longitudinal mode. It also travels very fast at about 700km/hr. What happens is that this travels as a pressure wave in the open ocean, but when it reaches a continental shelf the wave is reflected partially upwards. This has the effect of converting it into a transverse wave as water moving along is now pushed upwards. This is a very nonlinear process and nontrivial to model. This pushing up of the water does initially cause water at the shore to recede outwards. The wave which seconds later reaches shore is much more slow moving, and a lot of that wave energy is converted into the towering wave front that sweeps in.

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This is the best technical explanation I've seen, but note the wikipedia statement: "In the 2004 Indian Ocean tsunami drawback was not reported on the African coast or any other eastern coasts it reached. "This was because the wave moved downwards on the eastern side of the fault line and upwards on the western side. The western pulse hit coastal Africa and other western areas." en.wikipedia.org/wiki/Tsunami I'm not sure what to believe. I may try to get more information about the Africa tsunami. –  Carl Brannen Mar 12 '11 at 2:23
I'm accepting this as the answer as I did find an example with the 2004 tsunami arrived in Africa with a withdrawal. –  Carl Brannen Mar 16 '11 at 2:24
This isn't seen in small-scale wave tank experiments and is therefore hard to believe. Is there even a simulation on the web showing significant recession from a positive pressure source like you describe? I like the simpler answer from Carlos more (it is surprising that most earthquakes would lower the ocean floor, but I guess it would make sense that the earth tends to stabilize into a more compact form). –  bobuhito Oct 14 '13 at 17:13
If the analogy of a tightly held string carrying tension suits here, wouldn't the force vector point inwards on both end nodes under a transverse vibration? –  Renae Lider Apr 4 at 19:18

The positive or negative elevation of the leading wave is related to what happened to the ocean floor during the earthquake. If the seabed was raised, a crest should lead the tsunami; if it was lowered then a trough leads.

In the 2004 Sumatra tsunami, a piece of seabed of about 1000 km x 100 km went down a few meters. Another strip, located to the west of the first and with roughly the same size, went up. Because of this, the wave moving east (towards Thailand) was led by a trough. The one moving west, which reached Sri Lanka, India and Africa, was led by a crest.

This is seen in the simulation of that tsunami shown below (by Kenji Satake, of the Active Fault Research Center in Tsukuba, Japan). In the red areas the water surface is higher than normal, and in the blue ones it is lower.

A similar animation, with some data added, is at http://es.ucsc.edu/~ward/indo.mov

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I had a look on the linked animation too, but neither seems to take into account the nearing the shore situation. The colors are the same on the front whereas we know that as it goes up the incline to land the water goes higher and higher. It can go up 20meters on highly inclined slopes. This means it is drawing up water, and depleting the water up the incline before it breaks, imo. Even a trough up the incline should grow in height, depleting the water ahead. –  anna v Mar 12 '11 at 9:48

I will simplify the question. When large waves come towards the beach there is always an undertow. Has an "overtow" been seen before the undertow?

My explanation while watching waves was that the waves break gathering mass on an incline. Growing in height they draw water symmetrically, but there is less water ahead, because of the incline, than behind, and the water is sucked up by the wave crest before it arrives. I expect the same mechanism to hold for the much longer wavelength tsunami wave.

I guess data from high rocky shores might be enlightening. When I visited Japan I went on tour up the east coast from Tokyo and was impressed that there were no beach facilities and the beaches looked like garbage dumps. I was told this was because of the tsunamis.Long beaches ending up in precipices of land overlooking them.

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Dear Carl, the recession of the sea level is an inevitable consequence of the mass conservation: the extra water in the tsunami has to come from somewhere. It comes from both sides - from the region in front of the wave as well as behind the wave.

So if the sea level is most elevated somewhere, it must obviously be lowered at both sides, too.

Imagine that you have a wave packet given by the function $$f(x) = \exp(-ax^2) \cos (kx)$$ The maximum absolute value of $f(x)$ is at $x=0$, right? That's the tsunami. However, it's inevitable that the second highest absolute value which can still be seen is at the pair of the nearby local minima. The two maxima at even higher values of $|x|$ are already pretty much negligible.

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why not just multiply that wave packet by -1? –  Mark Eichenlaub Mar 11 '11 at 21:53
Oh I see. That is the real question. –  Luboš Motl Mar 11 '11 at 22:20
I don't see (or think) that the wave train has to have a negative phase at the leading edge. Nor is the location of which wave is the highest fixed. Obviously if you see a strong negative phase, you should expect a positive phase to come within a few minutes (i.e. head for higher ground), but I see no reason that the wavetrain has to begin with a large enough negative phase to be able to count on it. –  Omega Centauri Mar 11 '11 at 22:40
@Omega Centauri; Yeah, this is exactly what bothers me. One possible explanation is something like "earthquakes always reduce the gravitational potential of the earth and therefore correspond to an initial reduction in altitude, hence the first wave is negatively oriented." But I don't quite buy it. By the way, this is something I used to think about while hanging around with the other grad students at Newport Beach, CA. I always had my escape planned. (Funny, the rest of the grad students didn't seem to think about tsunamis while at the beach.) –  Carl Brannen Mar 11 '11 at 23:40
I think that Lubos is right nevertheless. There are two phenomenons on vastly different scale. I observed the surf at a very shallow beach in Lanzarote some months ago, and the effect as descibed by Lubos was there. –  Georg Mar 12 '11 at 13:06

It is a matter of conservation of mass. In order to raise the water a certain height, the extra mass of the water has to come from somewhere. That somewhere is the area directly ahead of the wave. So in the end the average height of the water does not change. Lower the level by 1 meter for 10 meters, and you have enough to make 10 meter wave with 1 meter width.

clarification: This effect travels at the speed of sound underwater, whereas the surface waves travel at a lesser speed, thus the dip precedes the rise.

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This answer does not address the question at all. -1 –  Mark Eichenlaub Mar 12 '11 at 0:05
It does when I add the clarification you see above now. –  ja72 Mar 12 '11 at 0:25
Okay, well it address the topic now, so I removed the down vote. Nonetheless I don't think the issue is very clear. Why not just reverse the argument? In order to lower the water a certain height, the extra mass has to go somewhere... –  Mark Eichenlaub Mar 12 '11 at 0:46