It will not have escaped your notice in recent days that the freezing of a puddle of water on the road begins with the formation of a layer of ice on top. And yet, if you care to think about it, this is odd. Let me take you slowly through the freezing process.
Most materials expand when they are heated, and shrink as they are cooled; water, to a limited extent, is no exception. What ought to happen, therefore, is that as the temperature of the air falls on a frosty night and cools the top of a pool of water, the coldness should make the surface water denser, and therefore heavier for a given volume, than the warmer layers beneath - and this cold water ought to sink. The coldest water, therefore, ought always to be at the bottom, and the puddle should freeze from the bottom up.
But water has a strange, indeed unique, property. If water is cooled, it shrinks in volume only until the temperature reaches 4 degrees, and then it begins to expand again. To put it another way, water is at its densest and heaviest at 4 degrees.
As its temperature falls further towards the freezing point, it becomes lighter for a given volume, a fact which has important consequences for our freezing puddle. When, on a freezing night, the top layer of a pool becomes colder than 4 degrees, it begins to become lighter rather than heavier with decreasing temperature, and therefore does not sink; at temperatures approaching the freezing point the coldest water stays on top, and freezing, therefore, starts at the surface of the pond.
Given sufficient time with sub-zero air temperatures, the layer of ice becomes thicker, but not as quickly as one might think. As in the case of any substance changing from the liquid into the solid state, energy is released in the form of "latent heat" when water changes into ice. A layer of ice already on the water serves as an efficient insulator to prevent the dissipation of this heat, and delays any further freezing.
The thicker the layer of ice on the pond, the better the insulation it provides, and the more the process of freezing underneath is slowed down. As a first approximation, the thickness of ice increases with the square root of time; if the first millimetre of ice forms in one hour, it will take four hours for the thickness to reach 2 mm, and nine hours before the ice is 3 mm thick - assuming, of course, that the air temperature above remains at the same sub-zero level.