This magical bottom-only melt arises because "Ice conducts heat better than water", and so it will conduct the atmospheric energy through to the water under the ice, allowing the ice to melt from the bottom, but not the top. This is drivel. Heat cannot of itself pass from one body to a hotter body. i.e. if the ice is conducting heat downwards, then the top of the ice is hotter than the bottom, so the top will melt first.
Commenting in this discussion, this is my understanding of the situation.
Hyperion is technically correct - this situation is possible under some circumstances.
The quote above is correct that the top will be 'hotter' than the bottom, because that is where the heat is coming from.
However, it is incorrect in claiming that means the top will always melt first. The reason is the presence of salt at the bottom, but not at the top, which lowers the melting point at the bottom.
E.g the top will melt at 0 degrees C if there's no salt, but the bottom may melt at -1.8 degrees C at a reasonable salinity for sea water.
So the situation of bottom melt in Arctic sea ice with heat carried from a dry top is theoretically possible.
In practice, on the other hand, I suspect that such a scenario is presumably unlikely to make a big contribution to the overall melt.
The reason is that
the thermal conductivity of ice is not all that good: it's around 2.2 W/(mK). So there is going to be a non-negligible temperature gradient in order to carry a non-negligible flow of heat down through the ice.
Consider this scenario, chosen to be a type of threshold case:
1 meter thick ice
0 degrees at the top
-1.8 degrees at the bottom
With both top and bottom at the threshold temperature for melting.
Linearizing for simplicity, the thermal gradient is 1.8 degrees/meter.
This implies a heat flow of ~2.2 W/(m.K) x 1.8 K/m = 4 W/m^2
The heat of melting of ice is 334 kJ/kg (same reference as above).
So rate of melting is ~4 J/(s.m^2) x / (334,000 J/kg x 900 kg/m^3) ~ 1.3e-8 m/s
(presuming a density of 900 J/kg)
A month is ~pi x 10^7s / 12 (using a useful mnemonic for approximate number of seconds in a year)
So that rate of melting would be 1.3e-8 m/s x pi x 10^7 / 12 ~ 3.5e-2 m/month = 3.5 cm/month.
So this threshold situation would be a bottom melt rate of only 3 or 4 cm per month.
If the bottom melt rate is:
a) Above this, then the top will be wet;
b) Below this, then the top can be dry even when the bottom is melting from heat carried downwards.
This is obviously a simplified situation - it is not rigorous - and is for ice that is 1 meter thick.
(If the ice is thinner\thicker then the melt rate can be more\less, in approximately inverse proportion to the thickness.)
But it illustrates the general point that ice dry at the top cannot be carrying much heat down to be melting the bottom.
SUMMARY:
Consider a situation for the Arctic sea ice where the heat to melt ice is coming from above. Then:
1) Bottom melt can only be fast, or even moderately fast, if the top is wet; and
2) The maximum bottom melt rate where a dry top is even possible (where the heat comes from above, & holding to some sort of long term equilibrium) is only of order a few cm/month.
So bottom melt with a dry top but still using heat arriving through the ice and from the top, while physically possible, is likely not the dominant scenario for Arctic sea ice.