How can a tsunami cross an ocean almost unnoticed, then suddenly become a wall of water near shore?

How can a tsunami cross an entire ocean almost unnoticed, then turn into a wall of water near shore? The trick is that the wave is huge in length, but tiny in height out at sea, so ships often barely notice it.^[10][11]

Offshore, the wave energy is spread through the whole water column, and tsunami speed depends on water depth. In deep water they can race at jet-plane speeds, yet still stay only about a meter high.^[11][15]

As the tsunami reaches shallow water, the seabed slows the front of the wave first. The energy has nowhere to go but up, so the wave bunches, shortens in wavelength, and grows taller through shoaling.^[7][9]

That is why a barely visible swell offshore can become several meters high near land, and in some places appear as a rising tide, breaking waves, or a bore. Coast shape and seafloor relief can amplify it even more.^[7][4][25]