Hi,
How to animate terrain?
For example, in frame 1, I set some height offset and then in frame 100 I increase the height offset. 
So that the terrain moves higher.
How to make this?

Benny

You cannot animate a terrain. You would need a prop in the shape of a terrain.

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Ok.
How about water? Can you animate the level of water?

Unfortunately not with the built-in water.

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You can level the water with some limitation.
Water prop does not have timeline transform track so the key would be hidden and you have to add the flag in project track to note where the level key is.

So if you uncheck Transform Gizmo (and Snap to Grid if checked) in Preferences you may rise/lower water prop level by hitting W and use mouse scroll wheel.

Thanks, 4u2ges. Learning something every day..:unsure:

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For animated terrain beyond XYZ scaling of a prop, you can import an Alembic file. If you use Motion Director to animate your characters, they will follow the animated terrain surface as it moves.

Wow!  Very cool.