Graphs revisited; Ice puzzles revisited.

First, an answer: this graph...

is a windchill graph. The coloured regions are the onset of frostbite in exposed people. :) NOAA has a nicer version here.

Avery chimmed in on the question about the ice, and raised potentially good points. I knew that the explanation that I'd got when I was younger had considerable doubt cast on it, and caveated my post appropriately. Or, maybe not enough! But, luckily, I'm in fine company, as my incorrect answer is repeated in various textbooks. Here's the most correct answer, as we understand it today, from ScienceNOW, the news arm of the Journal Science:

Ice has always been a slippery subject. As simple as an ice cube may seem, scientists have long been baffled about why its surface is so slick. But an upcoming paper in Surface Science may give researchers a firmer grasp of ice's surface subtleties by hinting that its outermost molecules behave like a liquid.

That would give the surface layer drastically different properties from those of the bulk of the crystal, says Gabor Somorjai, a surface chemist at the Lawrence Berkeley National Laboratory. The liquidlike layer could explain, for instance, why it is more fun to skate on ice than on concrete. According to Somorjai's colleague, Michel van Hove, the popular conception that ice's slipperiness comes from pressure-induced melting is wrong. "It doesn't work out," says van Hove. "You put data into the formula, and there's not enough pressure." The slippery layer, he says, is there to start, even at very low temperatures.

Somorjai and van Hove discovered this layer when they probed the surface of thin layers of ice with low-energy electron diffraction, a technique that uses electrons to determine the surface structure of a crystal in the same way as x-ray diffraction reveals the crystal structure of a solid. The researchers expected to see the scattering signature of the first three layers of ice molecules, but they only saw two. After determining that the invisible top layer did, indeed, exist, the researchers hypothesized that its water molecules were vibrating three or four times faster than those in the lower layers--blurring its diffraction pattern to invisibility. Although the water molecules are bound in the lattice like a solid, says Somorjai, "the vibrational amplitude is like a liquid."

Besides making ice slippery, says Somorjai, the liquidlike layer could help explain how ice crystals in the upper atmosphere help catalyze the chemical reactions that deplete ozone. The finding, says Steve George, a chemist at the University of Colorado, "illustrates how we don't understand the simplest things we know about."