Thermal intake of melting ice as compared to thermal capacity of earth

[Willber Force]

Though this topic mentions climate change, I don't think it really is about it that, strongly anyway. I've just joined and noticed a ban on climate change discussions before posing this one, I don't think this is one, but if it is, I suppose the beast must have one of it's many heads chopped off. I'm just dumbfounded that it had to come to that, if anything, that's what I've got from this.

Back a few years ago there was a question climate change people were asking, which was, why there was more cooling than expected? One thing that came to mind right away was how melting water took in more heat than just its thermal capacity (I think I'm saying that right) and if it was capable of accounting for it and how strongly if any.

I don't know if anyone here is capable of easily answering that question, I do better with mechanical and electrical systems. I've made various starts into doing a back of the envelope calculation which I though would be as easy as thermal capacity of atmosphere, plus top meter of earth, plus oceans compared to amount of heat absorbed by the volume of ice that melted and degraded. But I couldn't make it to a start of an answer. I would think people involved in this would have those kinds of numbers around, but I didn't have any luck finding them on any of the occasions I've tried.

Anyway, it's getting late. Sorry if this is a stupid question, just something I've been wondering about for far too long.

 

[mfb]

Melting the complete ice sheet of Greenland would just need as much energy as the Earth receives in 2 months, and the ice is certainly not melting within that timescale.

Values used: 2 850 000km^3 of ice https://en.wikipedia.org/wiki/Greenland_ice_sheet
334kJ/kg enthalpy of fusion https://en.wikipedia.org/wiki/Enthalpy_of_fusion
WolframAlpha

I'm not sure about the topic, I'll see if we allow that.