OK...dragging out fragments from my old brain...

Wouldn't the appearance and performance of the wave depend on several factors? Tsunamis are very long waves, so if the crest, trough or somewhere in between arrives onshore, this should influence the wave. In some cases, if the trough arrives, water goes OUT to sea and then comes rushing back. I would also guess that shoreline topography and sea depth might be involved. In many of the Sumatran photos (from Thailand, as I recall) showed a rush of water that just kept coming on and on...

Good points made here. I just watched a thing on TV about Rogue Waves..and these guys can apparently get to 100 feet with a stunningly steep crest.