Ionospheric airglow signature of tsunami waves confirmed

From the University of Illinois, something quite interesting, long speculated on, now confirmed.

Tsunami airglow signature could lead to early detection system

Airglow waves captured by the Illinois imaging system over Hawaii. The red line represents the location of the ocean-level tsunami at the time of the image.

Researchers at the University of Illinois have become the first to record an airglow signature in the upper atmosphere produced by a tsunami using a camera system based in Maui, Hawaii.

The signature, caused by the March 11 earthquake that devastated Japan, was observed in an airglow layer 250 kilometers above the earthā€™s surface. It preceded the tsunami by one hour, suggesting that the technology could be used as an early-warning system in the future. The findings were recently published in the peer-reviewed Geophysical Research Letters.

The observation confirms a theory developed in the 1970s that the signature of tsunamis could be observed in the upper atmosphere, specifically the ionosphere. But until now, it had only been demonstrated using radio signals broadcast by satellites.

ā€œImaging the response using the airglow is much more difficult because the window of opportunity for making the observations is so narrow, and had never been achieved before,ā€ said Jonathan Makela, an associate professor of electrical and computer engineering and researcher in the Coordinated Science Laboratory. ā€œOur camera happened to be in the right place at the right time.ā€

Tsunamis can generate appreciable wave amplitudes in the upper atmosphere ā€“ in this case, the airglow layer. As a tsunami moves across the ocean, it produces atmospheric gravity waves forced by centimeter-level surface undulations. The amplitude of the waves can reach several kilometers where the neutral atmosphere coexists with the plasma in the ionosphere, causing perturbations that can be imaged.

On the night of the tsunami, conditions above Hawaii for viewing the airglow signature were optimal. It was approaching dawn (nearly 2:00 a.m. local time) with no sun, moon or clouds obstructing the view of the night sky.

Along with graduate student Thomas Gehrels, Makela analyzed the images and was able to isolate specific wave periods and orientations. In collaboration with researchers at the Institut de Physique du Globe de Paris, CEA-DAM-DIF in France, Instituto Nacional de Pesquisais Espaciais (INPE) in Brazil, Cornell University in Ithaca, NY, and NOVELTIS in France, the researchers found that the wave properties matched those in the ocean-level tsunami measurements, confirming that the pattern originated from the tsunami.Ā  The team also cross-checked their data against theoretical models and measurements made using GPS receivers.

Makela believes that camera systems could be a significant aid in creating an early warning system for tsunamis. Currently, scientists rely on ocean-based buoys and models to track and predict the path of a tsunami. Previous upper atmospheric measurements of the tsunami signature relied on GPS measurements, which are limited by the number of data points that can be obtained, making it difficult to create an image. It would take more than 1,000 GPS receivers to capture comparable data to that of one camera system. In addition, some areas, such as Hawaii, donā€™t have enough landmass to accumulate the number of GPS units it would take to image horizon to horizon.

In contrast, one camera can image the entire sky.Ā  However, the sun, moon and clouds can limit the utility of camera measurements from the ground. By flying a camera system on a geo-stationary satellite in space, scientists would be able to avoid these limitations while simultaneously imaging a much larger region of the earth.

To create a reliable system, Makela says that scientists would have to develop algorithms that could analyze and filter data in real-time. And the best solution would also include a network of ground-based cameras and GPS receivers working with the satellite-based system to combine the individual strengths of each measurement technique.

ā€œThis is a reminder of how interconnected our environment it,ā€ Makela said.Ā  ā€œThis technique provides a powerful new tool to study the coupling of the ocean and atmosphere and how tsunamis propagate across the open ocean.ā€

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bushbunny
July 14, 2011 10:59 pm

Maybe they can link the full moon with king tides too?

Rabe
July 14, 2011 11:18 pm

Measurements by GPS receivers? Placed ones? Moving ones? Are they joking? Measuring time differences against what? Location differences against what? Just like to know.

tallbloke
July 14, 2011 11:23 pm

If the Tsunami is the cause of the ripple in the ionosphere, how can it be used to predict the tsunami? Maybe I missed something.

Editor
July 14, 2011 11:35 pm

tallbloke – the paper says “It preceded the tsunami by one hour“. Presumably it means it preceded the tsunami reaching the coast by one hour. That would still be very useful, because (I’m guessing) tsunamis can’t always be detected at source.

July 14, 2011 11:36 pm

It began one hour before the quake/tsunami.
There’s clearly “more to know” about the sequencing and mechanisms!

July 15, 2011 12:19 am

I wonder if it is a tsunami effect, or the ionospheric airglow is caused by strong geomagnetic oscillations that are often (but not always) associated with the large earthquakes.

Hector Pascal
July 15, 2011 12:25 am

“It preceded the tsunami by one hour”. In Hawaii, not Japan. People on the Tohoku coast started evacuating directly after the earthquake. No warning was needed. Those who couldn’t evacuate in time, drowned. Hawaii had plenty of warning from direct measurement, not looking at the sky.
Interesting stuff, but not very helpful.

Bob in Castlemaine
July 15, 2011 12:31 am

Nowadays we are, quite legitimately, sceptical about findings originating from government funded research with any, even remote, connection to “climate science”. But I think it is appropriate to reserve judgment in this instance. If this line of research proves capable of improving tsunami warning capability there is the potential to save many, many lives.

July 15, 2011 12:44 am

If this is a ripple effect of the sea water ion content being moved rapidly enough to generate air glow by induction into the ionosphere, there will be a low frequency wave pulse that was able to extend its influence far enough ahead to alert wild animals as it passes through an hour ahead.
Then it should be possible to monitor the wave lengths that are generated, just like seismic wave patterns, and by comparison quantify the effects to expect from the Tsunami quake combo.

charles nelson
July 15, 2011 1:34 am

Wow…I love stuff like this.

Roger Knights
July 15, 2011 2:04 am

Something like the proposed monitoring system would have been helpful in the aftermath of the big Indonesian quake. The tsunami-alert center in Hawaii wasn’t sure the quake had generated a tsunami, so it didn’t issue an alert until it was too late for most.

Gary Mount
July 15, 2011 2:08 am

Careful reading of the article finds…
“a camera system based in Maui, Hawaii”
and…
“It preceded the tsunami by one hour”
Means, not the creation of the tsunami, but of it hitting Hawaii, and detecting that event 1 hour before it hit by detecting the signature in the airglow layer, by the camera at the location of interest and concern.
One use of this technology could be for early warning for locations with poor communications with the rest of the world. But is there such a place left in the world? At least a backup or secondary line of defence.

Steve C
July 15, 2011 2:22 am

I note that the researchers refer to “The signature, caused by the March 11 earthquake …”.
Hmm, I wonder. Is it in fact a matter of (a) tectonic forces causing flexing piezoelectric rocks to generate regions of ionisation in the adjacent atmosphere, with the observed airglow effect, or might it be (b) incoming EM energy from the sun causing incidental ionisation at the same time as it flexes the piezoelectric rocks and triggers the quake?
Given Piers Corbyn’s apparent ability to forecast periods of higher earthquake activity by studying the sun and the Earth’s neighbourhood, (b) makes a lot of sense to me: there’s a lot more energy floating about outside our atmosphere than inside it. Has anyone investigated this possibility? Obviously, I’m not discounting effects from any other interactions (like the centimetre-scale ripples on the sea surface), but which way does the energy actually flow as the quake starts?

David
July 15, 2011 2:27 am

“As a tsunami moves across the ocean, it produces atmospheric gravity waves forced by centimeter-level surface undulations. The amplitude of the waves can reach several kilometers…”
I am guessing the gravity waves travel faster then the ocean wave?

Dr T G Watkins
July 15, 2011 2:29 am

If the air glow preceded the tsunami by one hour how can the signature be caused by atmos. gravity waves in turn produced by cm. level undulations in the sea?
The signature must precede the earthquake if their prose is accurate.
Earthquake Lights as a possible cause of the ionosphere phenomenon??

Steve T
July 15, 2011 2:52 am

Surely what is being detected is like a “shock wave” travelling one hour ahead of the tsunami (not to confuse the tsunami(wall of water) with the cause of the tsunami. The warning time will depend on the distance the tsunami has to travel, if more than an hour away, some notice of it’s arrival will be possible.
So if the tsunami originates four hours away there will be three hours warning approx.
This is not something that will predict a tsunami occuring but will give notice of it”s arrival.

July 15, 2011 3:42 am

Science maybe coming to terms with reality, the inter connect between the sun the moon and the planets is profound, throw in the the rest of the Universe bombarding us and it becomes more complex. That a quite sun has been noted in history with increased volcanism and Earth tremors shows we are very effected. That strange lights are seen in the sky when Earth quakes occur is historic also. That the upper atmosphere glows is no surprise, the harmonic reverberations in the Earth and the magnetic field when volcanoes erupt and Earth quakes occur are governed by the same equations that are used to trigger atomic weapons. No surprise at all, let us hope that the information can be used to save lives, if they delve deep enough they will also be able to predict volcanic eruptions accurately and the reciprocal Earth quakes. This stuff has been known for decades yet science has had its head in the sand pretending their theories are totally correct like climate science.

Cementafriend
July 15, 2011 3:47 am

I wonder if they got their idea from this http://arxiv.org/ftp/arxiv/papers/1105/1105.2841.pdf by Ouzounov et al which uses a lot of satellite information.

Gary Mount
July 15, 2011 4:10 am

Steve T says: …
“So if the tsunami originates four hours away there will be three hours warning approx.”
If the tsunami travelled at 800 km/h from Japan, it would have taken about 8 hours. The tsunami was detected in Hawaii (or would have been) by the method in this article 1 hour before it hit, 7 hours after the event (the quake). Your math doesn’t add up.

July 15, 2011 4:11 am

Hmmm…reminds me of a song by Rush from G/P – “Distant Early Warning”

July 15, 2011 4:12 am

Hmmmā€¦reminds me of a song by Rush from P/G ā€“ ā€œDistant Early Warningā€
Sorry – fixed

TBear (Warm Cave in Cold-as-Snow-Sydney)
July 15, 2011 4:22 am

Ok, the Bear is not the sharpest cue in this particular rack, but this article fails make any sense.
Even if gravity waves travel at the same speed, C, of electromagnetic radiation generally (and we don’t know that they do, as we don’t actually know what causes gravity, so far as the Bear knows) isn’t the supposed measuring of an electromagnetic artefact of a mechanical wave disturbance (the actual tsunami) a rather indirect way of doing things?
And how could it `precede’ the actual wave? Seems like time travel is required.
Or have I been breathing in too much of that carbon gas?

July 15, 2011 5:14 am

Steve C says:
July 15, 2011 at 2:22 am
I think you got right idea.
http://www.vukcevic.talktalk.net/gms.htm

Ian W
July 15, 2011 5:21 am

Seems there is a lot of confusion that is unnecessary here.
A tsunami wave is not only in the ocean but also in the atmosphere all the way up to the ionosphere and above.
A camera on Maui is looking toward the ionosphere on the horizon and picks up the disturbance of the atmospheric gravity wave caused by the tsunami which is directly below that disturbance. The slant range to the disturbance in the ionosphere will be considerable, but depends on the level of the ionized layer being disturbed and seen by the camera.
The tsunami will take around an hour to reach the camera position from the time the ionospheric disturbance caused by the atmospheric gravity wave is first visible on the horizon.
From a satellite the tsunami in the atmosphere will be visible directly above the tsunami in the ocean as the tsunami is a wave propagating in the ocean and the atmosphere.

Enneagram
July 15, 2011 6:06 am

@M.A.Vukcevic says:
July 15, 2011 at 12:19 am
You are right, it seems the other way around.

Enneagram
July 15, 2011 6:12 am

Airglow?…donĀ“t they know the word “plasma”?

Olen
July 15, 2011 6:27 am

Using a satellite is a good idea, when not checking on tidal waves maybe it could spy on China. Kind of a return favor for their spying on us.

Steve T
July 15, 2011 6:38 am

Gary Mount says:
July 15, 2011 at 4:10 am
Steve T says: ā€¦
Gary, sorry if I wasn’t clear. My four hours / three hours was meant as an example of when any warning could be given not a calculation of the recent tsunami.
I was trying to say what Ian W has said at 5.21 but didn’t explain it anything like as clearly. In theory (cameras in the right places etc) the beginnings of a tsunami can be detected by this method about one hour after it has commenced, thus giving time to warn anyone more than an hour “downstream”.

July 15, 2011 7:53 am

Certainly a method for imaging the whole wavefront structure of tsunamis while still in mid ocean would be useful .

Crispin in Waterloo
July 15, 2011 8:52 am

tallbloke says:
If the Tsunami is the cause of the ripple in the ionosphere, how can it be used to predict the tsunami? Maybe I missed something.
+++++++
I agree with Gary above. It happened to be visible from the impact point 1 hour before contact. That is helpful, but the satellite-borne system will see the tsunami the whole time as it travels from the source. That should provide anything up to 24 hours notice on the other side of the Pacific.
Surely the same system could be used to spot earthquakes as well? They should be visible before ground stations receive the vibrations conducted through the Earth.

July 15, 2011 9:04 am

Tbear;
Just verbal confusion; these gravity waves are those travelling in the ocean and atmosphere, not through space from colliding neutron stars, etc., if any. Compressed gas, e.g., is a bit heavier, and tugs on nearby gas, and so it goes. šŸ˜‰

Ged
July 15, 2011 9:25 am

@TBear,
This is a meteorological “gravity wave”, which is not a “wave of gravity”. It refers to occilations of the atmosphere due to the influence of gravity on density differentials in the atmosphere. This has nothing to do with gravity itself. See: https://secure.wikimedia.org/wikipedia/en/wiki/Gravity_wave
The hypothesized “gravity causing wave” in theoretical physics is called a “gravitational wave”, technically. And yes, it has never been detected or proven, despite many sophisticated detectors looking for evidence of such. Doesn’t seem “gravitational waves” exist.

Dave Springer
July 15, 2011 9:29 am


The problem is tracking a tsunami wave through deep water. Even though the wave is massive when it’s thousands of meters from top to bottom there is hardly any indication of it on the surface. If I read this report right the mass of the water involved is large enough to change local gravity by a hair which in turn causes some very faint glow in the ionosphere as the wave passes underneath and with a sensitive-enough camera with an unobstructed view the light from the glow can be imaged. By that means the wave velocity can be determined and by extension a forecast made of when and where it will reach shore.

Ray
July 15, 2011 11:18 am

It seems that they prefer to delay such discovery by going through the peer revision process and get a paper. Let’s just hope their publishing decision won’t cause the lost of lives due to a delay in the implementation of such technology.

Mac the Knife
July 15, 2011 11:43 am

“As a tsunami moves across the ocean, it produces atmospheric gravity waves forced by centimeter-level surface undulations.”
Q: The gravity waves are a result of the ‘centimeters level surface undulations’ that are the physical manifestation of the entire water column being raised and lowered? It is the raising and lowering of the total mass of the entire column of water, that causes the graviity waves, even though the surface manifestation is only a few inches high?
“The amplitude of the waves can reach several kilometers where the neutral atmosphere coexists with the plasma in the ionosphere, causing perturbations that can be imaged.”
Q: The mass of the large column of water raised a few inches sheds a gravity wave that causes an equivalent mass shift of atmosphere at the edge of the ionosphere? That is the source of the ‘amplification’, i.e.; The mass of the water shifted causes a corresponding shift of an equivalent mass of atmosphere, at the ionosphere level, producing large atmospheric phenomena that can be easily photographed/resolved?

July 15, 2011 11:48 am

Based on the press release, probably a really beneficial discovery. I’ll celebrate when the study is replicated without false positives. The press release raises a few very small flags: (1) They were looking for something they ‘knew’ was there. (2) Part of their cross-checking was done against theoretical models. (3) No mention of error analysis. (4) Signal strengths are unstated in the abstract. If on the cutting edge of detectability, that is a situation historically prone to subjective error. The abstract looks good, though; I’m just mildly skeptical and would like to see the full paper.

July 15, 2011 12:00 pm

Ray says: “It seems that they prefer to delay such discovery by going through the peer revision process and get a paper. Letā€™s just hope their publishing decision wonā€™t cause the lost of lives due to a delay in the implementation of such technology.”
That’s the way it’s done in legitimate science, Ray. Most people who comment here are not in favor of panicky response to new discoveries, since much of the time, those discoveries prove false, even outside of Climatology. It isn’t science until it’s replicated, and there are other methods of initiating tsunami warnings. Criticism regarding peer review isn’t warranted at this late stage.

July 15, 2011 12:49 pm

Did I miss something here?
If you can measure a tiny tsunami with this technique, then the normal Lunar tides must cause huge ripples in the atmosphere. Why no mention of them?
.

stephen richards
July 15, 2011 1:53 pm

I did see many reports of piezo-electric discharges caused by earthquakes being reported by aircraft some 20 years ago and these effects were giving a reasonable amout of time for evac etc but this abstracts lacks sufficient detail to make any form of judgement at all. It’s too crude an abstract to be useful but that may be intended in order to persuade you to buy the paper.

July 15, 2011 2:21 pm

Ralph says:
July 15, 2011 at 12:49 pm
“Did I miss something here?”
These huge ripples in the atmosphere have been known about for years, the connection to the lunar tidal effects have been ignored, blocked from consideration due to an unwarranted fear of
“Astrology” an ancient study of supposed effects from the interactions of the Earth with its neighbors in the solar system.
Now that satellites can measure and define the changes in solar wind speed and density, and can visualize the flows in the atmosphere that are the lunar tidal effects, the fear of “Astrology” coming back to life again needs to be suppressed, so that humans can be seen as the drivers and controllers of all things. The politicians and scientists derive there power and funding from that misunderstanding of causation and need to focus it through themselves, to control people and funds.
Leroux, Marcel (1993). The Mobile Polar High: a new concept explaining present mechanisms of meridional air-mass and energy exchanges and global propagation of palaeoclimatic changes. Global and Planetary Change 7, 69-93.
http://ddata.over-blog.com/xxxyyy/2/32/25/79/Leroux-Global-and-Planetary-Change-1993.pdf
Under stood quite well the dynamics of these large blobs of polar air masses that make up the polar side component of the lunar atmospheric tidal bulges, but never saw the connection or suppressed it due to the huge amount of resistance he would get from being tagged as an astrologer. Research into the timing and strength of the arrival of lunar declinational tidal bulges gives the data needed to successfully do long range weather forecasting, past 5 – 10 days.
The definition of the “natural variability” of the weather is in effect the sum of the sun/lunar interactions with the inner planets and sun, by tidal and gravitational harmonic interlocking over billions of years, being electromagnetically influenced by the outer planets to give rise to the sunspot cycles and CME activity levels, that further drive longer term “natural variations” that run the climate cycles from 60 year periods to 179 year periods.
Once these “natural cyclic patterns of variability” are accounted for there is little left for Trace gas GHG influences to be “behind the wheel” so in fear of the loss of control of the public at large these subjects are Taboo, even here.
http://tallbloke.wordpress.com/2011/07/03/richard-holle-getting-the-study-of-cycles-back-into-weather-forecasting/
Some of us are not afraid of the unknown and like to study it in our spare time.
http://research.aerology.com/project-progress/map-detail/

kuhnkat
July 15, 2011 3:24 pm

Please note that the warning period was based on the LOCATION OF THE CAMERA!!! If the camera had been closer to Japan the warning period could have been longer with appropriate conditions.

kuhnkat
July 15, 2011 3:41 pm

Richard Holle,
I think you need to collaborate with Piers Corbyn who appears to use similar metrics.
http://www.weatheraction.com/

July 15, 2011 4:40 pm

kuhnkat says:
July 15, 2011 at 3:41 pm
I have offered to share all data and the updated code when it is available, my daughter thinks we need to set up a server with all of the tabled data, code in an open source format, and instructions on how to use it.
Piers is dependent upon subscribers for his funds, protecting his method is his financial security I would not want to interfere with his efforts, but as I have no income from my efforts, I can give it all away so others can benefit from my efforts even after I am gone.
*The wisdom of old age, mellowed by attending funerals, sweetens with time, CAGW greed not so much.*

Gary Pearse
July 15, 2011 4:51 pm

Certainly interesting but it would have been nice to have a explanation of what is happening understandable to civilians.

July 15, 2011 5:16 pm

Ralph says on July 15, 2011 at 12:49 pm
Did I miss something here?
If you can measure a tiny tsunami with this technique, then the normal Lunar tides must cause huge ripples in the atmosphere. Why no mention of them?

Perhaps it is a ‘rate’ thing: dz/dt (where ‘z’ is the vertical axis normal to the ‘surface’ of the local earth); higher rates producing more ‘airglow’.
It would seem that the rate-of-change for Lunar tides is much lower, thereby producing an imperceptible airglow …
.

sky
July 15, 2011 5:25 pm

Interesting as the connection of tsunamis to ionosphereic airglow may be, the impracticalities of using that, it as an early warning system are immense. The basic problem with tsunamis is not the lack of information about the physical features, as some here suggest, but the fact that bureaucrats and the public do not react to events intelligently.
Once a tsunami is generated, detection via satellite altimetry or the network of DART preesure gauges and buoys is rather foolproof technology. The arrival time from the source area to any location is readily determined from the phase velocity c=sqrt(gh) of long gravity waves. As the catasrophic Indonesian tsdunami a few years ago demonstrated , however, the Pacific Tsunami Warning Center cancelled its alert after the determination that there was negligible propagation into that ocean. The idea ofof warning their Indian Ocean colleagues that they should be on alert after a Richter 9 quake on a tsunamigenic dipslip fault seems not to haver occurred to these civil servants. And when Indian Met Institute employees were alerted by more circumspect scientists, thier attitude was on of “it’s not my bailiwick to issue warnings.” Thus many tens of thousands of lives that could have been saved by a few hours notice beyond Indonesia were forefeited to bureaucratic inertia.

savethesharks
July 15, 2011 9:59 pm

sky says:
July 15, 2011 at 5:25 pm
The basic problem with tsunamis is not the lack of information about the physical features, as some here suggest, but the fact that bureaucrats and the public do not react to events intelligently.
…Many tens of thousands of lives that could have been saved by a few hours notice beyond Indonesia were forefeited to bureaucratic inertia.
=========================
Extremely well said.
Chris
Norfolk, VA, USA

tallbloke
July 16, 2011 2:05 am

Thanks everyone for helping me out on this.
Richard Holle says:
July 15, 2011 at 2:21 pm

Good comment Richard, I just said something imilar over at Judy Curry’s blog:
Our investigations over at the talkshop find a complex set of mutually reinforcing/diminishing cycles around 11, 22, 45, 55-60, 75 and ~200-220 years among shorter and longer periods. These are evidenced by rising beach ridges, arctic ocean surface temperature variation, periodicities in the C14 and 10Be proxies. They all relate to well known interactions in planetary orbital cycles and when they are combined, they successfully replicate the Lean TSI proxy from before the Maunder Minimum. They also coincide with changes in Earthā€™s length of day and this is the real story behind natural variations. They have as principle drivers gravity and electro-magnetism. Orbital mechanics and solar activity can account for Earthā€™s climatic variation. Changes in atmospheric Co2 levels are a minor secondary effect some distance down the chain of causation.
———————————-
The 75 year cycle shows up in Arctic sst’s and is Lunar in origin. I should also have mentioned the 18.6 year lunar cycle and it’s harmonics, which beats with the ~36 year period which relates to solar motion driven by the planets en masse.
The 179 year cycle you mention is not a fixed period cycle, and it doesn’t show up as a peak in the C14 or 10Be records. There is a ‘wandering period’ effect of the gas giants though which varies between ~160 and ~180 years, and it shows up as reinforcement/lengthening of de Vries cycle effects and Gleissberg cycle effects. Analysis of this reveals why Theodor Landscheidt was one solar cycle out in his 1988 prediction of a solar slowdown starting at solar cycle 23.
We are getting closer to nailing all this down and I’m starting to write a summary paper for the blog linking to the individual posts covering the various cycle periods.

Hector Pascal
July 16, 2011 2:41 am

FWIW, the tsunami in Miyako City (Iwate) went to 40.5 metres.
http://headlines.yahoo.co.jp/hl?a=20110716-00000041-mai-soci.view-000
Residents had 12-13 minutes evacuation time between the earthquake and the tsunami arrival.

TBear (Warm Cave in Cold-as-Snow-Sydney)
July 16, 2011 3:33 am

The Bear’s questions have been answered. Thnx.
Interesting how these threads usually end up getting to the point ….

July 16, 2011 4:27 am
Brad1007
July 28, 2011 2:18 am

Waves often propogate ahead of a low level wave in the lower atmosphere, so used as an extra aid in detection prior to Tsunami arrival is feasible.

Brad1007
July 28, 2011 2:26 am

CORRECTION:
Waves at altitude caused by a low level wave/density current, often propogate ahead wtith time, so using upper level waves, caused by a Tsunami, as an extra aid in detection prior to Tsunami arrival is feasible.