What happens to the water depth as the Tsunami waves approach the coast ?

As a tsunami wave approaches the coast, it transitions from the deep ocean to shallow water. The water depth decreases significantly as the wave moves over the continental slope and toward the shoreline [c1][c3]. This reduction in depth triggers the 'shoaling effect.' Because the speed of a tsunami is proportional to the square root of the water depth, the wave slows down as the depth decreases [c3][t1]. To conserve energy flux, the decrease in speed and wavelength is compensated by a dramatic increase in wave amplitude or height [c1][t4]. Consequently, while the water depth decreases, the wave itself grows from an imperceptible ripple in the deep ocean into a towering wall of water near the coast [c3][t6]. This process explains why tsunamis are most destructive at the shoreline despite being nearly invisible to ships in deep water [c1][t3].

Sources

1. [1] Physical Geography by PMF IAS, Manjunath Thamminidi, PMF IAS (1st ed.) > Chapter 15: Tsunami > Normal Waves vs Tsunami Waves > p. 193
2. [2] Physical Geography by PMF IAS, Manjunath Thamminidi, PMF IAS (1st ed.) > Chapter 15: Tsunami > Propagation of The Waves > p. 191
3. [3] https://www.usgs.gov/centers/pcmsc/life-tsunami