Most people have never given much thought to how an icicle grows. I suppose that's because most of us have filled the ice trays with water, tucked them into the freezer and in a short time have ice. Water plus cold air gives ice cubes, right? Well yes, but it's much more complex than that. In fact, the process has not been well understood until recently.
A lot of ice that formed in north Florida yesterday started as rain. That was because the air aloft was warmer than the air at the surface, which was below freezing. If the precipitation fell as snow or ice it would have to melt first before icicles could form.
Once the water contacts a frozen surface or an environment of freezing air, the water will freeze on an object. That forms the base of the icicle or the icicle root. Then as successive sheets of water flow over the root, the warm water gives its heat to the surrounding layer of air in contact with the forming icicle and can then cool and freeze.
This transference of heat is the same principle Grandma used in winter to protect the food stored in the "root cellar" (if you lived up north in farm country). She would put a pan of water on the floor, which would freeze and give its heat to the air which would keep the veggies warm.
So as the air heats around the icicle it rises like a hot air balloon. This puts a thicker layer of warmed air near the top of the icicle. So as successive sheets of water fall down the icicle to freeze they are able to do so faster at the tip, where the air is cooler. Thus the icicle forms a long pencil like structure.
But that's just the beginning. The process is much more complex with different areas of the icicle growing at different rates and air getting caught up in the process, and temperature differences causing fractures. Temperature and growth rates influence the crystal formation of the freezing water and rings and ridges form in these marvels of natures engineering.
In the end, the complex physics is found to be described nicely by the math that describes the formation of those rock stalactites found in underground caves. The process are different but the math can be transferred by changing a few numbers here and there.
So the next time you are visiting the frozen north take a moment to appreciate those frozen marvels; the icicle.