What effect does slowing down in speed have on the height of tsunami waves close to shore?

The effect of the slowing of a tsunami close to shore is that the wave increases in height. It becomes a lot taller! The trick to getting this in perspective is in understanding that as the wave travels across the water, it stretches out. As it is now longer while en route across the open ocean, it isn't as tall. In fact, it is possible to be on a ship in the middle of a deep ocean as a tsunami passes and not really notice anything alarming because the wave is so elongated. As it reaches shore, the leading edge of the wave begins to slow up in the shallower water. This results in a "bunching up" of the water and the wave can then rise to a frightening - and destructive - height just as it comes ashore. To expand a little: Ordinary ocean waves are movements only of the top layers of water, and if you were diving a few meters below the surface, you would not feel the effects of even rather strong waves. Tsunamis, however, involve the movement of truly huge amounts of water amounting to the entire "column" of water from the ocean floor to the surface. This is another way to see why the above explanation increases tsunami height. We're not talking about bigger and bigger "Surfing" waves, but a huge volume of water crowding up on itself as it moves over the rising ocean floor.