Dear Sameera! Since tsunami is a long surface water wave, it has the speed V=(gD)^(1/2). Since g=9.81 m/s2, in the case of D=40 cm, we get V=2 m/s. For D=1 m, we get V=3 m/s. This is the speed with which the whole volume of water flows. Can a person stand in this flow or not? One can try in a mountain river. I guess one cannot do it if V=5 m/s, but perhaps at V=1 m/s this is not difficult. So V=2 m/s, corresponding to wave height 40 cm, might indeed be critical for many people. But this border is likely to be fuzzy (humans are different), so that both 30 cm and 50 cm might be correct answers.

Another question: whether it is dangerous to fall down? I  guess not if water depth is only 30 cm, but might be for somebody if it is 50 cm. All depends also if this is sandy beach or stones. Finally, some tsunami are turbulent, and for a given speed turbulence is more dangerous. However, it propagates at less distance inside because of friction.

To summarize, I think that tsunami less than 30 cm high are not of much danger, apart from children and in rough terrain, while above 1 meter could be dangerous for all.

The final issue is where this height is observed. If approaching tsunami is 30 cm high where the water depth is 10 meters, it can increase its height substantially before reaching the shore. You can look at my attached paper. It is rather mathematical, but I also provide coefficient of amplification of a solitary tsunami wave on the shelf in a Table. https://www.researchgate.net/publication/275581998_Evolution_of_long_nonlinear_waves_on_shelves

P.S. I am not a person who studied human safety. I just know the physics of tsunami waves.

Conference Paper Evolution of long nonlinear waves on shelves

Dear Sameera, 

Seems strange discussing this through ResearchGate. Anyway, please find attached one of our recent papers which summarises this quite well. Basically, the Port and Harbours Research Institute (PARI) did this, and basically tied a rope to the top of their 1:1 tsunami wave flume, and took turns throwing tsunamis at themselves (apparently many in PARI went through this...). Relevant paragraphs of our paper are below. I can confirm through my own "experiments" while trying to measure wave set-up that anything above the knee is very dangerous and while likely make you fall to the water and be dragged away, though we were not measuring wave velocity in this "experiment". Anyway, if you have any doubt we can always discuss in person. 

A large-sized water flume experiment in Japan found that

a 60-year-old man did not experience any strong feelings

of fear when he walked against a water flow as high as his

crotch with speeds of up to 0.8ms􀀀1 (Suga et al., 1995).

However, he felt intense fear when the flow reached a height

of 1m or a velocity of 1ms􀀀1, which effectively prevented

him from walking without a supporting rope. Nishihata et

al. (2005) confirmed through the same type of experiments

that the maximum inundation depth at which adult males and

females (aged from 21 to 59) can safely evacuate is 0.7m or

less. Takagi et al. (2016b) also found that the family members

featured in a video taken during the storm surge caused

by Typhoon Haiyan which hit the Philippines in 2013 could

cross a flooded street because the flow speed and depth were

both not too large, 0.6ms􀀀1 and 0.6 m, respectively.

Wright et al. (2010) propose a depth–velocity product of

1.0m2 s􀀀1 as the general safe limit for pedestrians through

a comprehensive study undertaken by a project for the New

South Wales (NSW) State Emergency Service (SES). However,

a plot of the relationship between human’s instability

and flow regime appears to be scattered by multiple factors

such as surface material; subject actions – either standing or

moving –, experience and training, clothing and footwear and

physical attributes, including muscular development and/or

other disabilities; and the definition of stability limit (i.e.

feeling unsafe or complete loss of footing) (Cox et al., 2010).

Jonkman and Penning-Rowsell (2008) also emphasize that

friction instability appears to occur earlier than moment instability

(toppling) for the combination of shallow depth and

high velocities. Thus, the depth–velocity product criterion

suggested by Wright et al. (2010) could become optimistic

for some adverse conditions. For example, regarding physical

differences between an adult and a child, Cox et al. (2010)

suggests that for children with a height and mass product of

between 25 and 50 (m kg), low hazard exists for low hazard exists for flow values

of a depth–velocity product < 0.4m2 s􀀀1.

Dear Miguel, you provide some interesting facts that can be useful for an assessment of tsunami impact. Mostly I agree with that "a plot of the relationship between human’s instability and flow regime appears to be scattered by multiple factors”. That is true that both depth and velocity have a negative impact. But I think that those factors have to be considered separately. A person who can swim can easily survive with slowly moving high wave. A falling person in a flow of only 0.5 m depth with 2 m/s can die if stones are also moving or his head strikes over some hard object (like a wall). Unexpectedness and darkness is another factor of risk. Many people are caught by tsunami during sleeping, and if it is strong enough to destroy a house, consequences can be very severe.

Dear Sameera, you should not listen to an advice not to ask such questions on RG. It is still a place, where one can get a consultancy of values from $1 to $1000 for free. There are some altruists. Also, people not working in consultancy often have no idea about value of their advice. And many are driven by a desire of growth of their RG scores, despite the fact that score still has no correlation with salary. (A joke, but perhaps with some truth inside).

I do not know what your reason to ask this question was. If it was pure curiosity, I guess that you got enough. If you are participating in a research project on that and have some extra money, I would recommend a natural experiment with people behavior in a river. If I would be in such situation and would not get sufficient information after reading literature, I would do the following.

Suppose you have several rivers with flow (0.5, 1, 1.5, 2, 3, 4 m/sec) and different depths: 0.3, 0.5, 0.7, 1 meter, etc. Also one river usually has an increasing depth and velocity with the distance from its shore.

You have to think first about what is safety. There should be some threshold criterium. Is it 1% of people injured? Is it 1% of people dead? Maybe 3%? 5%? 10%?

If you have 10-30-100 volunteers, they go into unknown stream of water and move till the threshold, where they can no longer move or fall down. We have 3-dimensional (or even more) variety here: depth H, speed of flow V, and bottom structure (sand, small stones, large stones, etc). Then we can find empirically the shape of critical pattern (a curve in H-V space for a given bottom), where x% of people can no longer control (fall down). After that you can map tsunami height with river speed using the formula that I have suggested in my previous post, V=\sqrt(g D).

P.S. I participated 3 times in EGU conferences: http://egu2016.eu/ . They have a session on tsunami within Natural Hazards block. Mostly people came from geophysics, but there is a lot of useful information also on tsunami impact.

It depends on many factors and not only the height of the wave if one can keep standing or not. There are reports of tsunamis which occured as water rising slowly rather than being a wave that comes towards the land. Factors that can make a huge difference is the topography of the coast, if there are mangroves, reefs that take out energy, if debris is floating in the water that can hit you, etc, etc. Most important I gained the impression when making interveiws with people who were caught in tsunamis in Samoa (2009) and Solomon Islands (2007) is the speed of the waves and debris load.

The force on your legs depends in addition to heigth on velocity of the tsunami flow. According to US tsunami load code ASCE 7-16 drag force /one leg will be

Fd = C/2*density*b*h*U^2, Where C=1,2(round), density 1000 kg/m^3, b about 0,1 m, h=0,3 or 0,5 m and flow velocity about 10 m/s in stong tsunami third wave and about 3 m/s in first wave of the tsunami.

Drag force per one leg will be with velocity 10 m/s Fd= 3 kN (50 cm) and 1,8 kN (30 cm). With 3 m/s you will survive.

Recommendation to run onshore after first tsunami wave.

It all depends on the speed of the wave.