SCHWEIGER: “Melting sea ice has no impact on sea level rise because it’s already floating in the ocean.”
Like a glass of ice water. As it warms, the ice in the glass melts, but the total volume of water does not change. However, melting sea ice does contribute to climate change. That’s because white sea ice reflects the sun. So when it melts, the dark open ocean now absorbs sunlight and heats up, raising global temperatures, which in turn cause glaciers and ice sheets on land to melt further. Globally, sea levels have risen four to eight inches since the last century and will continue to rise as the ice melts, putting coastal communities worldwide at risk.
http://www.yaleclimateconnections.org/2014/11/loss-of-land-i...
Take two situations:
1. A mass of sea water is replaced by the same mass of fresh water. Sea levels/volume would increase as the average density would be lowered. (this is not the case)
2. A volume of fresh water is added to the ocean. Then V_total = V_ocean + V_freshwater.
However, your correction itself isn't strictly correct. Melting sea ic can change sea levels by changing the density of the water in the ocean. Also, by melting it changes the amount of sunlight that is reflected. The increase in sunlight reaching the oceans will cause thermal expansion of the water.