# Does the ice melt faster when breaks free from larger sheet and drops into Antarctic Ocean waters?

My question is, when Ice is intact with the large sheet and exposed only to air, it melts at some pace. But does it melt faster or slower when the big piece breaks free from the sheet and drops into the water ? Why?

Well, it depends upon the temperature of the water and the temperature of the land supporting the ice. However, land is usually transferring heat by conduction, while water can also transfer heat by convection, so it should melt faster in the ocean generally. Also, the salt in sea water depresses the freezing point.

Have a look at this paper from NASA.

The principle cause of ice sheet breakup is the relatively warm ocean undercutting the edge of the sheet. The overhanging ice then fractures off and falls into the ocean.

To uderstand why the small pieces melt faster consider that melting occurs mainly at the edges of the piece of ice (presumably the water flow is turbulent there so mixing is fast) so the larger the perimeter of the iceberg the faster the melting. Suppose we model the berg as a disk or radius $r$ and depth $d$, then the mass of the berg is:

$$m = \rho \pi r^2 d$$

and the length of the perimeter $\ell$ is:

$$\ell = 2\pi r$$

So the ratio of the perimeter to the mass, $R$, is:

$$R = \frac{2}{\rho r d}$$

If we assume the total melting rate is proportional to the perimeter then we get a melting rate:

$$\dot{m} \propto \frac{1}{r}$$

So the rate of melting is inversely proportional to the berg size. In other words smaller bergs melt faster than larger ones.

The usual caveats apply: there are assumptions made in this calculation that are only approximately true. There will be melting from the bottom of the berg, and the thickness of the berg will change with time. However the calculation gives the basic idea.