Why do tsunami waves grow taller near shore?

In deep ocean, tsunami waves travel incredibly fast (400-500 mph) but are barely noticeable—typically just 1-6 feet tall! As the wave enters shallow water, physics requires it to slow down. The wave speed follows: Speed = √(gravity × depth)

But the wave's energy must be conserved! As speed decreases, energy converts to height. This amplification follows: Height ratio = (depth ratio)^0.25. This is called "shoaling."

How coastal slope matters:

• Gentle slopes: Energy spreads out over distance (8-15 ft typical)
• Moderate slopes: Standard physics amplification (20-30 ft typical)
• Steep slopes: Energy compresses dramatically (50-80+ ft possible)