The arctic ice sheet floats. Greenland is an island and Antarctica a continent, both of them surrounded by a little floating ice.

Melting that ice shifts a km-deep layer of ice from a fixed position above nearby sea level to being part of the liquid ocean. This means that it doesn't exert any gravitational pull on the ocean nearby, so the water-covered part of the globe becomes a little bit more spherical. Not much more spherical: The article says 30-50m on the coast of Greenland, which is a very small fraction of the earth's radius.

The 30-50m column of water is distributed elsewhere.

Replying to myself, this implies that near Greenland, the gravitational effect of the ice cap should be ~30 times as big as the moon's (which causes a tide of a little over a meter). Which doesn't seem horribly implausible.

The moon causes a rise of about 54cm, and the sun around 28cm.

from the wikipedia entry for tides.

https://en.wikipedia.org/wiki/Tide#Amplitude_and_cycle_time

An amplitude of 54cm is about a meter peak-to-peak.

Parent is writing about Antarctica, the ice sheet is not floating but would be replaced by air which is a lot less dense.

And the land rising effect is certainly there, its well known from our norther hemisphere where satellite measurements have tracked for quite a while now how i.e northern Europe still rises in comparison to the southern parts due to the not being covered by the ice age glaciers anymore.

I don't think the comparison with the surrounding land mass is relevant here. The landmass might have a much larger effect than the ice, but the landmass will not melt. While my mental image considers the water to envelop the world as a sphere, I actually have no idea how large the differences in the distance from the core to the water surface is in different parts of the world.

> I actually have no idea how large the differences in the distance from the core to the water surface is in different parts of the world

Taking the core to be a point, the distance to the sea's surface would depend on factors such as

* The earth’s variation from a pure sphere (6,378.137 km (3,963.191 mi) at the Equator and 6,356.752 km (3,949.903 mi) at the poles) [0, 1]

* The local depth of the sea (up to 10,984 metres for the Mariana Trench [2])

* Tidal effects [3]

[0] https://en.wikipedia.org/wiki/Spheroid

[1] https://en.wikipedia.org/wiki/Figure_of_the_Earth

[2] https://en.wikipedia.org/wiki/Mariana_Trench

[3] https://en.wikipedia.org/wiki/Tide

And, I suppose, the centripetal force caused by the rotation. But maybe that is the whole reason for earth being a spheroid?

And correct me if I'm wrong, but the local depth of the sea should not matter, as water would fill the depth before the levels stabilized. But perhaps the local volume of the water affects the size of the effects of tidal forces and local land mass.

Mostly related to your line of inquiry, the point on land that is furthest from the center of the Earth is Mount Chimborazo in Ecuador.[1] It is located one degree south of the equator and is very tall to begin with.

[1] https://oceanservice.noaa.gov/facts/highestpoint.html