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Is it even possible? How much water would it take? Does the whole earth need to be flooded to reach that height?

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No it isn't possible. 7000 feet is 2133 metres. That water level would cover almost all the land mass of the globe, except for the highest mountains, like the Himalayas, the Andes etc. It would need at least twice the current volume of water in the ocean. Total melting of all icecaps would add less than 2% of the volume of water required.

There might be limited local circumstances where you could wash a boat up several hundred metres up a hillside. There have been historical tsunamis that when channeled into narrow inlets have created waves of 500 metres, but the topography required to do this would only be found in very specific locations, very close to the coast. Larger tsunami waves have occurred in the geological past from volcanic events, major landslides or asteroid impacts, but it is unlikely that any event has occurred since mankind started building boats, that was large enough to create a 2000 metre wave, and that hasn't left clear geological evidence.

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