Complex sentence: Also tsunamis shoal (change their height) in accord with this law, as they propagate through the ocean and up the continental shelf (governed by refraction and diffraction); very close to the coast nonlinear effects become important and Green's law no longer applies.
Split into simpler sentences: Also tsunamis shoal (change their height) in accord with this law, as they propagate--governed by refraction and diffraction--through the ocean and up the continental shelf. Very close to the coast nonlinear effects become important and Green's law no longer applies.