This question on Maths SE asked how we might calculate the effect on sea level if all the world's ice (ie including the whole Antarctic ice sheet) were to melt. I posted an answer containing calculations suggesting - and this came as a surprise to me - that the rise in sea level would be up to about 40 metres more at high northern than at high southern latitudes. The key qualitative assumptions underlying this conclusion are:
- Most of the world's ice is in the Antarctic ice sheet.
- The melting of all the world's ice and spread of the resulting liquid water across the oceans would result in a shift in the earth's centre of gravity. Given 1 above, the shift would be towards the north.
- The shift in the earth's centre of gravity would not significantly affect the position of the earth's land masses and ocean bed which in this context can be regarded as a solid mass around which the ocean water would position itself.
- The distribution of liquid water across the world's oceans, though affected by other factors, is largely determined by the gravitational force pulling it towards the earth's centre of gravity. Hence a northward shift in the centre of gravity would pull a slightly larger proportion of the ocean water to the northern hemisphere.
Are these assumptions broadly correct?