The best explanation I’ve heard is the ‘height’ is how far above see level the wave stops.
so you have a large volume of water moving forward. Lets use a block of wood as our ‘water’.
The water on the bottom is moving along the ground and getting slowed down by friction. Lets use sandpaper as the ground. The force of the water moving along the ground slowly removes some of the force of the water, the sand paper removing some of the wood. The further it goes, the less force is left. Eventually the force dissipates and everything flows back to the ocean. The distance inland that it travelled, including how high it rose, is the ‘elevation’ you were referring to.
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