Unit 5 Tsunami Propagation

1 Introduction to
2 Tsunamis of
   the Past
3 Plate Tectonics
4 Tsunami Generation
5 Tsunami Propagation
6 Tsunami Inundation
7 Tsunami Aftermath
   and Response

5.1 Tsunami Propagation

Essential Question:
Which factors affect how tsunamis travel, or propagate?

Enduring Understanding:
Understanding and modeling how tsunami waves travel helps in the prediction of tsunami travel times, allowing for warnings and evacuations.


When considering how tsunami waves propagate, or travel across the ocean, it is important to understand wave behavior. Before discussing tsunami waves, this unit defines what a wave is and describes wave characteristics. Comparing wind-generated waves and tsunami waves is useful for understanding the force, scope and potential danger of large tsunamis.

Using data from past tsunami events and known wave characteristics, scientists have developed models for calculating tsunami travel times to deliver warnings to communities that may be impacted by a tsunami. These models make use of complex data based on the size and location of an earthquake, the depth of the ocean as determined by bathymetric measurements, the distance to a given location, the shape of the coastline in impact zones, and past run-up heights.

Tsunami warning center scientists have developed models to predict the tsunami travel times for certain high risk locations. When an earthquake of magnitude 7.5 or higher is generated along a coastal area, warning centers may be able to warn communities of an impending tsunami and give a time estimate of when the first wave will arrive.

Image: Great Wave off Kanagawa, by Hokusai, color woodblock print first published between 1826 and 1833.

Hawaiian translation

5.2 Waves

Waves are a disturbance that propagates, or travels, through space and time transferring energy from one point to another. Waves can be electromagnetic or mechanical. The basic parts of any type of wave are the same, although waves differ in their characteristics.

Wave vocabulary

Electromagnetic Waves

Electromagnetic waves are able to travel through a vacuum, like space. The electromagnetic spectrum classifies waves by wavelength and includes radio waves, visible light, x-rays, and gamma rays.

Mechanical Waves

Mechanical waves must travel through a solid, liquid, or gas medium. Waves lose energy as they travel through these mediums.

5.3 Equilibruim and Disturbance

The state of equilibrium is the state when a system is in balance. A disturbance moves the system out of equilibrium. All systems try to return to equilibrium after a disturbance.
Gravity is the force that attempts to restore water molecules to equilibrium when they are disturbed by wave energy.

The equilibrium of ocean water is disturbed by the gravity of the moon and sun, which produce the tides. Other disturbances include tsunami triggers, wind and human and animal activity.

There are four basic types of water waves: tides, seiches, wind-generated waves, and tsunamis waves.


Tides are the rise and fall of sea level caused by the combined gravitational pull of the moon and sun.


A seiche is a standing or stationary wave oscillating in an enclosed body of water such as a bay, lake or reservoir often caused by an earthquake, wind or tsunami. A seiche looks like waves sloshing back and forth from one end of a bay to another. Two propagating waves traveling in opposite directions combine to form the standing wave.

Wind Waves

Most ocean waves are generated by wind. As the wind blows across the surface of the water, it pushes on the surface of the water forming waves. Wind can create waves of different sizes, from small capillary or ripple waves, to larger swells. Strong winds and storms can produce chops and swells. Wavelengths vary from centimeters to 30 meters high (100 feet).

As the wind blows on the surface, the energy of the wave reaches a certain known depth into the water, the depth of influence, equal to one half of the wavelength. The motion of the water particles decreases as depth increases, until the depth of influence is reached.

In deep water, wind waves cause water particles to move in a circular motion. A common misconception is that wind waves propel a boat or object forward on the surface of the water. Because water particles return to the same approximate position as the energy passes through, an object on a wave does not move forward with the wave energy, but returns to the same general area.

As wind-generated waves approach a shoreline, and the depth of the water decreases, the height and amplitude of the wave increases until the wave breaks due to gravity, forming the waves surfers know and love.

swell waves illustration

Tsunami Waves

Tsunami waves differ from wind-generated waves and should never be surfed. When tsunamis are produced, the water displaced by an earthquake, landslide, or volcanic activity generates waves that travel in all directions through the entire water column, from the bottom of the ocean to the top.

The energy of tsunami waves is much greater than most wind-generated waves. Some tsunamis may be barely noticeable in size, while others generate powerful waves that can devastate coastal areas.

Tsunamis are characterized by very long wavelengths that travel across the open ocean very quickly. The speed of tsunami waves depends on the depth of the ocean and gravity: the deeper the ocean, the faster the waves travel, sometimes as fast as 890 kilometers per hour (~550 mph) or about the same speed as a jet airplane.  

Tsunami waves are also characterized by having small amplitudes, so that on the open ocean a tsunami might go unnoticed by a ship that experiences nothing more than a gentle rise and fall.

The equation used to calculate the speed of a tsunami wave is = √(gravity*depth). As gravity remains constant at 9.8 m/s2, the only variable that changes is depth. Bathymetric mapping, or the study and measurement of undersea features and ocean depth, is an ongoing process that leads to better understanding of tsunami wave propagation.

In the Open Ocean versus Close to Shore

Waves behave differently in the open ocean than close to shore due mostly to the change in depth, but also due to the shape of the seafloor and landforms.

In the open ocean, tsunamis can have a wavelength of 200 kilometers, much longer than the 100-meter wavelength of wind waves. Because of their large wavelengths, longer than the ocean is deep, tsunami waves behave like shallow water waves, and the water molecules move in an oval pattern as the wave passes through the water.

Illustration: tsunami in open water vs close to shoreBecause the speed of tsunamis is related to ocean depth, when the wave moves to shallow water, the wavelength decreases and the wave compresses and grows in height. The wave height can increase up to and above 30 meters (100 feet), and the wave slows down to around 20 to 45 mph. Even though the tsunami wave slows down in shallow water, the amount of energy in the waves remains the same and will still outpace a human runner.


Wave speed is a function of ocean depth. As a tsunami wave approaches shore (shallow water), it slows down. The energy is compressed and wave heights can increase significantly.

Eyewitness Descriptions of Tsunami Waves and Other Phenomena from Moloka‘i

Attesting to Hawai‘i’s vulnerability when it comes to tsunamis generated from Alaska’s Aleutian trench, eyewitnesses from the 1946, 1957, and 1964 tsunamis share descriptions of events, of the waves, of animal behavior and other phenomena.

Click to download a pdf with eyewitness accounts

5.4 Bathymetry

Bathymetric Map of the Ocean


 The History of Bathymetric Mapping

NOAA image NOAA image

Early depth measurements were taken by tossing a weighted rope over the side of a ship. Credit: NOAA

Humans have lived near water for thousands of years and have always had estimates of coastal water depths. It wasn’t until larger ocean-going vessels began exploring deeper waters that standardized bathymetric measurement became necessary. Early measurements made by navies, explorers and fishers consisted of using a measured rope tied to a heavy weight. The weighted rope was tossed over the side of a ship, and the sailors would take a measurement or “depth sounding.” This early form of bathymetry was limited to a single depth at single point, leaving much of the ocean floor a mystery.

Modern bathymetric maps are produced by incorporating much more data, often displayed graphically. Several technologies are used in gathering bathymetric data:

  1. In sonar mapping, devices mounted to ships send out focused sound waves. The amount of time it takes the sound wave to return is calculated into distance. This method produces detailed maps of the ocean floor but is time intensive. The U. S. Naval Research Laboratory report in 2000 estimated it would take 200 ship-years to fully map ocean depths exceeding 500 meters, meaning it would take one ship 200 years or 200 ships one year to accomplish this goal. With current ship and resource levels, the Naval Research Laboratory estimates it will take 20 to 30 years to fully map the deep-ocean floor.
  1. Satellites use radar by detecting slight variations of surface water caused by the gravity of large undersea landmasses such as mountains or trenches. This method is useful for quickly mapping large sections of the ocean but is limited to structures larger than 10 kilometers in area.
  2. Aircraft mounted light detection and ranging (LIDAR) technology is employed to measure depth in clear shallow water. LIDAR operates in a similar fashion as radar but emits light from a laser rather than microwaves to measure the distance to an object.

Bathymetry is essential for understanding tsunami wave behavior. As a tsunami wave moves the entire water column, the speed of the wave is determined by the depth and topography of the ocean floor.

LIDAR illustration

LIDAR, used to measure depth in clear shallow water, emits light from a laser to measure the distance to an object. Credit: USGS

Image: Contemporary methods of depth measurements give a clearer picture of ocean floor features than in the past but are time-intensive. Credit: NOAA

Contemporary methods of depth measurement give a clearer picture of ocean floor features than in the past but are time-intensive. Credit: NOAA

Bathymetry from lead line to sonar

Single and multibeam sonar measurements collect depth data based on how long it takes for a sound wave, or echo, to return to the source. Credit: USGS

Sounding the Depths

5.5 Wave Behavior

Waves change when they reach the end of a medium, travel across different media, or interact with other waves and barriers, such as coastlines, bays, reefs and other landforms. The physical environment, undersea and above-sea landforms, influences tsunami waves. Four types of wave behavior include reflection, refraction, diffraction and interference.


The shape of a coastline affects how waves behave and how the waves are reflected, or bounced back. Whether the coastline is straight or a curved bay will influence reflection. In addition, waves interact as reflection influences incoming waves.

The Law of Reflection:

The arrow, or incident ray, indicates the direction of wave energy and is called the angle of incidence (θi). When the wave strikes the barrier, it reflects, or bounces off, in such a way that the angle of reflection (θr) and angle of incidence (θi) are the same.

The Law of Reflection states that the angle of incidence (θi) equals the angle of reflection (θr), where θ means angle, i means incidence and r means reflection.

Reflection off of Curved Surfaces:

If the barrier is in the shape of a parabola, such as a bay, then the waves will reflect and converge at a single point called a focal point.

Illustration: The law of reflection
Illustration: Reflection off of Curved Surfaces


Illustration: Refraction of Waves

As waves move across different media, their behavior changes. When tsunami waves with a wavelength much greater than the water depth transition from deep water to shallow water, wave speed and wavelength decrease, and wave height increases.





As waves refract, the direction of wave energy changes as well as the wavelength and speed.


Diffraction occurs when waves bend and change direction as they travel around a barrier or go through openings. Diffraction is most obvious when the wavelength is greater than the obstacle. As wavelength increases, the degree of diffraction increases. This is why even the leeward side of islands experience tsunami waves.



Diffraction occurs when waves bend and change direction as they travel around a barrier.


When two waves interact, a new wave forms with different properties. As waves interfere with each other or superimpose, amplitudes add together and create new patterns.



As waves interfere with each other or superimpose, amplitudes add together and create new patterns.

Wave Propagation, Kuril Island Tsunami, November 15, 2006

A magnitude 8.1 underwater earthquake near the Kuril Islands in Russia on November 15, 2006 triggered a tsunami that propagated across the ocean affecting coastlines around the Pacific Basin. Tsunami wave behavior is visible in the animations as the tsunami propagates and interacts with ocean floor features and coastlines.

The tsunami radiation pattern is indicated with color-coded information about the maximum wave height at different locations throughout the Pacific Ocean.

A timer and moving yellow squares indicate time elapsed since time of the earthquake, providing an estimate of tsunami arrival time at different locations.

Actual data from DART buoys (white or blue line) is compared with researched model data (red line). DART (Deep-ocean Assessment and Reporting of Tsunamis), real-time tsunami monitoring systems developed by the Pacific Marine Environmental Laboratory (NOAA), are positioned throughout the ocean.

5.6 Models

Scientific models are widely used in science to help researchers visualize and understand the complex systems and interactions of Earth. Models are symbolic representations of reality that are less expensive and safer to test than running a full-sized experiment. They present multiple “what if?” scenarios that allow researchers to test several variables at once.

Models are limited to the variables that are included and are by definition not as complex as the actual system they are representing. Models should be viewed as hypotheses and can be tested against real-world observational data.

Examples of Models

Non-scientists often interact with models as types of forecasting such as weather reports, hurricane path estimates and tsunami warnings.

Models are often used in engineering or construction. For example, the Boeing 747 jet airliner was the first commercial aircraft designed and completely modeled on a computer before construction. The digital model allowed engineers to experiment with design changes and investigate the placement of electronics or hydraulics without the cost and time of building physical prototypes. Currently, production of cars, buildings, and city infrastructure are digitally modeled to aid in refining the final physical product.

Conceptual Models

Another example of a model is a conceptual model. These models assist in understanding complex systems but do not involve complex mathematics or have the ability to forecast or predict. A way to think about conceptual models is to think of a simple box and arrow diagram. These models are often used to describe Earth’s water or carbon cycles.






Conceptual models, like this graphic representation of the water cycle, help us visualize complex processes.
Credit: NASA

Numerical Models

Numerical models perform complex calculations that take different natural processes into account. For example, Tsunami Travel Time maps are models that represent data visually and display the estimated time a tsunami wave takes to travel from the source outward through the ocean. Variables such as sea floor depth and undersea topography are used to calculate tsunami wave velocity using the equation v=√gd, where v = speed or velocity of the wave, g = acceleration due to gravity and d = depth of the ocean. Once the velocity of a wave is determined, the simple equation of T=d*r, in which T = time, d = distance and r = rate, is used to determine how long it will take for a tsunami wave to arrive at a particular location.

If the ocean floor were uniformly flat with a consistent depth (no land to alter wave length), it would be simple to estimate how long it would take tsunami waves to travel to a specific location. The actual ocean floor is much more complex and models take these factors into account. TTT maps show a clear relationship between the depth of the ocean and the speed of a tsunami.

The MOST (Method of Splitting Tsunami) Model

The MOST model, successfully and thoroughly tested, is a numerical model that simulates three tsunami processes: earthquake, propagation across the ocean, and inundation. Animations have been used to model historical tsunamis, but the main objective is to forecast wave arrival time, wave height and inundation area immediately after a tsunami event.

The NOAA video of the February 27, 2010 tsunami generated just off the coast of Chile shows how fast the tsunami traveled across the ocean. Observed wave amplitude is compared to the modeled. Yellow squares indicate DART buoys that gather observational tsunami data. Wave behavior is represented graphically as the tsunami encounters barriers.

5.7 Review

Take the following practice quiz to review content covered in Unit 5.

  1. What is tsunami propagation?

  1. What is a wave?
    A disturbance that travels through space and time, transferring energy from one point to another.

  1. How is wavelength measured?

  1. Tsunami waves are characterized by very long wavelengths, small amplitudes and fast travel times. In what other significant way do tsunami waves differ from wind-generated waves?

  1. When tsunami waves pass below objects floating in deep water, what happens?

  1. The shape of the ocean floor influences the propagation of tsunami waves by causing the waves to change velocity and wavelength and hence to be refracted or bent. What data do tsunami researchers use to help predict the time it takes a tsunami to travel from its source to areas of impact?

  1. When a wave is reflected from a surface, what is the angle of reflection?

  1. What happens when two waves meet?

  1. Scientists build models to visualize and understand the complex interactions of Earth's systems. Tsunami Travel Time (TTT) maps are models that represent data visually and display the estimated time tsunami waves take to travel from the source outward through the ocean. Which variables do these models take into account?

  1. Method of Splitting Tsunami (MOST) numerical model animations have been used to model historical tsunamis, but the main objective is to forecast wave arrival times, wave heights and inundation areas immediately after a tsunami generation and prior to impact. Which tsunami processes does the MOST model simulate?