Categories
Extreme weather Natural phenomena

Tsunami measurements

This blog-post dives into the measurements of the 2011 11’th March Tsunami from the ‘Great Sendai Earthquake’. The Great Sendai Earthquake, caused a loss of lives in the order of 20.000 and insurmountable amounts of economic damages.

Tsunami measurements from NDBC buoys

Lets focus on measuring the Tsunami itself. We do this to try and understand how the tsunami spread across the globe. To investigate this we will have a look into some wave buoy measurements from the National Data Buoy Center in short, NDBC.

The NDBC wave buoy measurement equipment, are located at different distances from the earthquake epicenter across the Pacific Ocean. Figure 1, showcases all buoy measurement locations of the NDBC Tsunami program within the pacific ocean. These buoys are specifically designed for Tsunami detection purposes.

Screen dumb of NDBC-buoy locations across the pacific ocean with stations where no-data is available, recent data and historical data.
Figure 1: NDBC NOAA wave buoy locations with historic, recent and decommissioned stations.

The water depth and distances vary with thousands of kilometers between the buoy observation stations. However we will see that measuring a tsunami is still possible even across the vastness of the pacific ocean.

Related read: What caused this catastrophic event? How do we mitigate future catastrophes?

Measurements from the (National Data Buoy Center) NDBC buoys – (North Oceanic and Atmospheric Administration) – NOAA

Measurements are extremely valuable for understanding the natural world in general and in particular the oceans dynamics.

Although the vastness and shear scale of the oceans makes such a task almost implausible we still try and measure wave heights, wind speeds and current speeds by placing buoys out at sea.

Buoy data and placements

The NDBC-buoys are located offshore and for this exercise we will specifically look into buoys 43451, 21418 and 21413 which was in place during the March 11’th 2011 Tsunami. The driving mechanism behind the Tsunami was the “Great Sendai Earthquake”. We can see the Earthquake epicenter and aftershock locations in Figure 2.

Related read: Top ten misconceptions about earthquakes, Top ten misconceptions about tsunamis

In order to showcase the differences in measured surface elevations between the NDBC-buoys. I have created Figures 3-8 where measurements are shown and GIS (Geographical Information System)-figures are created of the buoy locations in question. Here we can see that the measurements of the Tsunami are occurring at different times across the pacific ocean.

Earthquake epicenters. GIS- (Geographical Information System) image of the magnitude 8.9 earthquake nearby Sendai. Measurements of aftershocks and epicenter of earthquake is shown with red circles.
Figure 2: Epicenter of the magnitude 8.9 Earthquake “Great Sendai Earthquake” prior to the Tsunami hitting shores of Japan among other locations.
Tsunami measurement at NDBC-bouy 43451. Data show the initial disturbance of the wave profile.
Figure 3: NDBC Buoy 43451 de-trended measured surface elevations across the Tsunami event where the high-frequent disturbance is clearly available.
Tsunami measurement at NDBC-bouy 21418. Data show the initial disturbance of the wave profile due to the measured Tsunami.
Figure 4: NDBC Buoy 21418 de-trended measured surface elevations across the Tsunami event where the high-frequent disturbance is clearly available.
Tsunami measurement at NDBC-bouy 21413. Data show the initial disturbance of the wave profile due to the measured Tsunami.
Figure 5: NDBC buoy 21413 de-trended measured surface elevations across the Tsunami event where the high-frequent disturbance is clearly available.
Tsunami measurement at all relevant NDBC-bouys showcasing the differences in time between measured Tsunami signals. Data show the initial disturbance of the wave profile due to the measured Tsunami at different time-stamps enabling the calculation of a wave-train celerity.
Figure 6: All NDBC buoy measurements of the Tsunami from the “Great Sendai Earthquake” on 11’th of march 2011. Each have been individually de-trended.
GIS-Figure of the location of buoy measuring center NDBC buoy 21418 and NDBC buoy 21413. Terrain and bathymetric data are all showcased with blue and terrain colored maps following the GEBCO bathymetries.
Figure 7: NDBC-buoys across the western part of the pacific ocean with locations of buoys 21418, 21413 and the epicenter of the Great Sendai Earthquake. Terrain heights and water depths are displayed following GEBCO and google-maps imprinting
GIS-Figure of the location of buoy measuring center NDBC buoy 43412. Terrain and bathymetric data are all showcased with blue and terrain colored maps following the GEBCO bathymetries.
Figure 8: NDBC-buoy across the eastern part of the pacific ocean with locations of buoys 21418, 21413 and the epicenter of the Great Sendai Earthquake. Terrain heights and water depths are displayed following GEBCO and google-maps imprinting

Tsunami wave celerity

The Figures above show that there are differences in the Tsunami surface elevations. The Tsunami wave disturbance develops and travel across the globe changing underway.

We can calculate the average wave celerity using the time difference of the measured wave disturbance between individual buoys. The arrival time of the wave at the eastern NDBC buoy 43412 is approximately 30 hours after the first measured signal. See Figures 7 and 8 for locations.

The approximate distance between NDBC buoy 21418 and 43412 is 15.000 km’s. Using this approximate distance together with the time difference of 30 hours and we get that the celerity of the Tsunami wave is approximately 500 km/hr!

In conclusion, the Tsunami moves with approximately 500 km/hr across the deep ocean of the Pacific. That is faster than a racing formula 1 car!

lets now try and examine the wave-shape of the Tsunami itself.

Tsunamis – Single or multiple waves?

Lets investigate Figures 3-6 more in-depth. In all figures, we can see that the initial wave disturbance comprises of multiple individual waves with different frequencies. Each of these waves travel independently and exchange energy with one-another. For instance, Figure 6 show individual wave buoy signals plotted together. In order to process the wave buoy data to reach the above signals we do the following steps:

  • Firstly, we download the individual raw wave data.
  • Secondly, we preprocess the data series removing unwanted data.
  • Thirdly, we detrend the data removing mean water depths from the equation.
  • Finally, we plot the results against each other with date-stamps.
  • In conclusion we can now investigate the Tsunami wave amplitude individually.

We can see that the large amplitude in buoys 21418 and 21413 are smoothed out in buoy 43412. This confirms the hypothesis that the wave dispersion relation transforms energy from bound high frequency harmonics towards carrier low frequency harmonics resulting in the smoothing out the of wave signal across distance.

Tsunami wave trains

In reality, Tsunamis consist of a plethora of waves with different amplitudes, frequencies and directions, all interacting resulting in what we call a Tsunami. When we think of an individual Tsunami wave, in reality we think of a wave-train of multiple waves with different frequencies, amplitudes and directions whose sum and difference make up the Tsunami.

In linear wave theory, we assume that these individual waves are all travelling independent of one-another, resulting in a wave-train of motion where the net wave train moves at speeds different from the individual frequencies.

This agrees with the above measured wave celerity as the individual tsunami wave-train moves with 500 km/hr while the incoming individual Tsunami wave frequency only travels of few tens of kilometers an hour.

Tsunami amplitude

Lastly lets look into the tsunami wave amplitude. We have now concluded that the Tsunami wave consists of a train of individual waves whose frequencies and directions all interact. We have also concluded that the wave-train travels across the ocean with approximately 500 km/hr whenever the water depth is large O(4000 m’s). The last interesting piece of the puzzle is the most feared one, the Tsunami amplitude.

We can see that the amplitudes out in the deep sea are O(1/10 m’s) above figures and small compared to the amplitudes experienced near the shore O(10 m’s). Now one may wonder why are there so large differences in the observed wave amplitude between the deep and shallow ocean?

Why are Tsunamis wave heights increasing at shorelines?

The answer lies in the dynamical nature of wave shoaling. As waves near the shore, the wave-energy transforms from the sub-harmonic space into the super-harmonics. Shoaling causes the wave to slow down and transform increasing the wave amplitudes of the incoming wave until breaking occurs. Check out this blogpost explaining shoaling in detail.

The wave period of the Tsunami wave endures throughout the breaking causing the water to keep rushing in over shores, low breakwaters damaging infrastructure and potentially people.

Conclusion

In this blogpost we have examined the measurements of the 11’th March 2011 Tsunami caused by the Great Sendai Earthquake.

We have looked into the placements of NDBC buoys along with measured amplitudes of the Tsunami.

We have estimated the wave celerity at deep water O(4000 m’s) to be 500 km/hr, faster than a racing formula 1 car.

We have explained in short details why wave heights at nearshore is substantially different from the deep water measurements.

References

https://www.ndbc.noaa.gov/

https://www.britannica.com/event/Japan-earthquake-and-tsunami-of-2011

https://www.sciencelearn.org.nz/resources/596-tsunami-shoaling

Categories
Natural phenomena

Kelvin-Helmholtz instability

In this blogpost we try and explore a fundamental phenomena called the Kelvin-Helmholtz instability and exemplify it with a paperweight toy.

What is the Kelvin-Helmholtz instability

First of all, lets try and understand what is the Kelvin-Helmholtz instability. The Kelvin-Helmholtz instability is not a person with a mental health issue, rather it is the naturally occurring instabilities which develop when two fluids of opposite nature try and pass each other.

Video 1: Numerical solution of the Kelvin-Helmholtz instabilities utilizing Discontinous Galerkin methods for interface fluid-dynamics simulations.

These instabilities play an important role in everything from the development of clouds, hurricanes, tornadoes and wind gusts down to mixing of saline sea-water, temperatures and development of waves.

What is the role of viscosity

Swirls and vortices are needing to be dissipated by internal frictional forces on scales not visible for the human eye. This is where the viscos part of the equations come into play.

Viscosity is the internal resistance of fluids mixing arising from natural phenomena such as Kelvin-Helmholtz instabilities. The more viscos fluids resist mixing and visa versa.

Related Read: how do one measure the viscosity of fluids? The Buckingham-Pi Theorem

Toy world example

The Kelvin-Helmholtz instability is explained through large-scale phenomena above, such as the creation of clouds. However, the phenomena appears on all scales including more tangible scales such as paperweights.

By injecting a dense fluid with dye and filling up the container with water, it is possible to create the illusion of a drifting ship within the ocean. See Gallery 1.

By tilting the resulting mixture of colored (dense fluid) and lighter (water) it is possible to create a turbulent seas which then creates waves inside the container.

This creation of waves is also caused by the Kelvin-Helmholtz instability within the fluid interfaces. The viscosity and top floating pressure of fluid helps to stabilize the system after a short while. The result is an interactive toy boat paperweight bouncing around in disturbed seas.

How do I get my own toy?

In order to buy the paperweight toy follow the amazon link below, I also get some affiliate commissions so not only do you get an amazing toy, you are also helping the site out directly.

I have chosen four different variations of the conceptually same toy. The unifying characteristic is that all of them are showcasing the same fun natural phenomena. The toys vary in expression from the titanic and an iceberg, Dinosaur and volcano, Penguins surfing and a surfer with a shark.

Conclusion

In this blogpost we have explored the naturally occurring phenomena that is the Kelvin-Helmholtz instability. Furthermore we have exemplified it with a toy paperweight.

Categories
Extreme weather Natural phenomena

Tsunamis. The what, when and where.

Tsunamis are violent phenomena happening across the globe as a bi-result of external stressors. In this blogpost we will dive into some key aspects of tsunamis.

It’s important to understand the nature of tsunamis as these effect the lives of millions of people across the globe. They are violent and causes huge loss of life, economic and social damage in the millions.

Tsunamis the what

Tsunamis are natural phenomena occurring as a result of huge displacements of water. Equally they are caused by natural external pressures such as landslides, earthquakes and volcanic eruptions.

To describe them imagine a huge wave of water rushing in, that keeps coming as time passes. As a matter of fact this causes massive flooding as a result with devastating forces impacting structures, flood gates, towns, roads, trees and houses alike.

The Great Sendai Earthquake Tsunami

To understand how devastating the events of tsunamis can be, lets try and examine one recent catastrophic event: the Tsunami of 11’th of March 2011, caused by the Great Sendai Earthquake.

In the video below, you can see the entire video of the 11’th of march 2011 tsunami hitting and overtopping the flood barriers. It is clearly seen how the water keeps rushing in over the flood barriers even after the first hit. This event was catastrophic and resulted in the loss of lives amounting to 20.000 lives lost.

Video 1: Tsunami hitting the town of Miyako of Japan.

Numerical wave models WAM – Wave watch III – NOAA

To model a Tsunamis impact, one can use a numerical weather prediction tool which is a wave-modelling tool. Multiple wave-modelling suites exists which all have differences in treatment of source-sink terms. The wave-watch III model is a numerical wave model which have been utilized for creating a wave map.

A wave amplitude map showcases differences in wave attenuation across the entirety of the pacific ocean. Here a valid source term describes that the tsunami source arises from the earthquake epicenter. NOAA have released a map showcasing numerical results of wave attenuation across the entire pacific, see Figure 1.

Figure 1: Map prepared by the U.S. National Oceanic and Atmospheric Administration depicting the tsunami wave height model for the Pacific Ocean following the March 11, 2011, earthquake off Sendai, Japan.

Other theoretical frameworks exists for describing and prediction of wave models. The main ones are MIKE – models (State-of-the-art), DELFT and WAM.

Theoretical wave theories

Important to realize is that there exist multiple theoretical frameworks to try and understand the propagation of tsunamis. To highlight a few of the most wide-spread theoretical wave methodologies are as follows: Cnoidal, Linear (Airy wave theory), 2’nd and higher order (Stokes waves), Stream function wave theory and Boussinesq wave theory. Consider this blogpost which goes into the differences and similarities of the different wave theories.

Wave measurements of the Tsunami

Theoretical considerations for describing the propagation of wave energy is important. At the same time they can’t stand alone and as a result we need measurements of the surface displacements as these are more valuable when trying to understand Tsunamis. Luckily, there exists measurements freely available for users to download.

The NDBC system, allows users to download real-time and historic data. By looking at historic quality controlled measurements we can understand what the tsunami amplitude at sea is. This allows us to answer questions such as what are tsunami amplitudes at sea? Where do they arise from? How fast are tsunamis moving?

Tsunamis the when

Tsunamis are caused by underwater eruptions, landslide displacements and volcanic eruptions to mention a few of the important ones.

History shows that tsunamis happens as a result of undersea earthquakes displacing large masses of water developing a wave train with large amplitudes. Legends have it that the Krakatoa Eruption caused mayor destructions and a worldwide tsunami travelling across the world causing havoc.

Tsunamis the where

When trying to understand Tsunamis and where they might be potential dangers there are certain rules of thump to follow.

Firstly, in order to be a potential hazard area, a considerable amount of water needs to be present.

Secondly, when water are present some of the potential sources of tsunamis need to be present. This can include subduction zones caused by the continental plate tectonics, earth hotspots with volcanic activities and large terrain variations with potential rock-slides or icebergs melting and cracking causing tsunami events.

Related read: How do we measure Tsunamis?

Thirdly, people need to reside in shores connecting these waters and especially nearby the epicenters of earthquakes are a significant potential hazard area.

To conclude, there are multiple factors which need to be present before a significant risk of tsunamis however in certain places, this causes quite large burdens for societies at large.

Concluding remarks

Tsunamis are unpredictable in nature and violent catastrophes causing large problems for the nearby societies. They are difficult to effectively mitigate and require long term investments in due time whenever peace is sufficient. They can be described as a huge volume of water which keeps rushing inland and the combination of high amplitude and long period makes the wave increasingly dangerous.

The unpredictability arises from the underlying natural phenomena driving these catastrophic events. Methodologies exist with geophysical sounders listening to the rumbling of the earth allowing early warning of incoming earthquakes which may cause tsunamis. Another example of early warning signs is the receding coastline immediately before the wave arises on shore.

The locations of tsunamis require quite a few preconditions before posing a threat to society. Firstly, there needs to be a significant amount of water present. Secondly, underlying driving mechanisms such as earthquakes, volcanic eruptions and rock slides need to be present. Thirdly, people need to reside and live in the neighborhood. All of these conditions are rarely met, luckily since they are one of natures most devastating events.

Related read: What kind of investments are needed to ensure that accidents and loss of lives are minimized?, What are the common misconceptions about Tsunamis

References

Tsunami video hitting the Japanese town of Miyako on March 11’th 2011 – https://www.youtube.com/watch?v=86ThCibkHQw&ab_channel=Rachid82UK*
Wave-height map of tsunami from NOAA –https://www.britannica.com/event/Japan-earthquake-and-tsunami-of-2011

NOAA Wave Watch III –https://polar.ncep.noaa.gov/waves/wavewatch/