A tsunami is a series of waves generated by a large, sudden displacement of water, usually caused by a powerful underwater earthquake, volcanic eruption, or massive landslide. The destructive power of this natural phenomenon is associated with its height, but the actual measurement is highly variable. The common perception of a towering wave crest in the open ocean is often misleading, as the wave’s characteristics change dramatically as it approaches the coast.
The Critical Difference Between Wave Height and Run-Up
Understanding the true height of a tsunami requires distinguishing between two measurements: wave height and run-up. Wave height refers to the vertical distance of the water surface relative to the normal sea level at the time of measurement. In the open ocean, tsunami wave height is typically very small, often less than one meter, which is why ships rarely notice them passing underneath.
The run-up represents the destructive potential of the wave on land. This measurement is the maximum vertical height above the standard sea level that the water reaches on the shore. As the water surges inland, it flows up hillsides and terrain, and the highest point of this inundation is the run-up. This figure is most frequently cited when reporting the maximum heights achieved by a major tsunami event.
A large tsunami might have a near-shore wave height of 10 meters, but the water can flow much higher up a steep slope, resulting in a greater run-up. The run-up is a measurement taken after the event, based on the highest water marks, debris lines, or scour marks left on structures and vegetation. The distinction is meaningful because the destructive force is tied to the volume and speed of the water at the coast, not a massive wave crest in the deep ocean.
How Water Depth Transforms Tsunami Height
The physical process that converts a nearly imperceptible open-ocean wave into a destructive coastal surge is known as shoaling. In the deep ocean, where depths can exceed 4,000 meters, a tsunami travels at speeds over 800 kilometers per hour, similar to a jet airplane. The wave’s energy is distributed throughout the entire water column, resulting in low height and an extremely long wavelength that can span hundreds of kilometers.
As the tsunami approaches the continental shelf and water depth decreases, shoaling begins. The shallower seabed creates drag, causing the wave to slow dramatically, sometimes to 30 to 50 kilometers per hour. The principle of energy conservation dictates that as the wave’s speed decreases, its energy must be compressed and forced upward.
This upward energy transfer causes the wave height to increase rapidly, a phenomenon described by Green’s Law. What was a swift, low swell in the deep ocean transforms into a slower, taller wave as it reaches the coastline. This mechanical explanation accounts for why a tsunami less than one meter high offshore can grow to multiple meters in height as it interacts with the shallow waters near the shore.
Local Geography and Extreme Heights
While shoaling is responsible for the overall increase in height, the final run-up heights are determined by the specific contours of the local geography. Coastal features such as V-shaped bays, narrow harbors, and fjords can channel and focus the incoming water, concentrating the wave’s energy. This funnelling effect forces the water higher than it would rise on a straight coastline, often leading to localized destruction.
The most extreme example of geographical amplification is the 1958 Lituya Bay event in Alaska, which produced the highest run-up ever recorded at 524 meters (1,720 feet). This was a megatsunami triggered by a massive rockslide into the narrow inlet, not a typical seismic tsunami. This event demonstrates the potential for localized geographic features to amplify a wave far beyond what a typical earthquake-generated tsunami achieves.
For tsunamis caused by tectonic activity, run-up heights are formidable but lower than the Lituya Bay event. The 2011 Tohoku tsunami in Japan reached a maximum run-up of 40.5 meters (133 feet) in areas of the Iwate Prefecture, amplified by the coastline’s steep topography. The 2004 Indian Ocean tsunami reached run-up heights of up to 30 meters (100 feet) in localized areas near the source. These examples confirm that the combination of shoaling and coastal topography determines how high the destructive water ultimately reaches.