If the ice cap melts, how much of it will end up in the oceans an how much will evaporate into the atmosphere as water vapor? If the earth and atmosphere is warmer, the air can hold more water vapor, no?
A real model would account for evaporation, yes. I think most would run off, the heat of vaporization for water is large compared to heat of fusion.
Once I had the ice cap math in a spreadsheet, I calculated how much energy it would take to deliberately melt all that ice. Assume we had it in a pot, or ran electric heating wires through the ice cap, how much energy?
Assume the ice is homogeneous and all at the same temperature and same specific heat, how much energy to get the calculated mass from -5 C to 0 C, then add in the phase change energy, then to go from 0 to 1C, was what I did (specific heat changes after the phase change). I won’t do it again here, it’s simple enough to replicate.
I got a very large number, something like twenty nuke plants running full bore for 20 years, to industrially melt the Greenland Ice Cap. It no longer seemed feasible to melt it by raising “global temperature” by a degree or two for twenty years.