An accumulation of ice on the surfaces of an airplane in flight can be ridiculously dangerous, so a lot of science has gone into analyzing the causes and effects. It's known, for example, that large droplets of supercooled water are likely to cause clear icing that covers a large area of the wing, while small droplets are more likely to freeze with entrained air and cause wacky shapes to form around the leading edges of the wing. This is called rime icing. Either way, or both (there's nothing to say you can't get a mixture of both types at once) airplane performance is affected. For starters the airplane will fly more slowly, climb less rapidly, and burn more fuel to get to destination. That alone could kill you, and that's just for starters. This post isn't about the effects of icing, though. This paragraph is just here for people who otherwise wouldn't know why anyone cared about the stuff in the paragraphs coming up.
Some aircraft are certified for operation in known ice, that is to be flown in conditions that are known and expected to cause ice to accrete on aircraft. There's a possibility that definition will cause an argument, because I see that the FAA and NTSB have contradicted themselves a little on this. In Canada there is a much lesser density of PIREPs to airspace and a lot fewer airports of escape, so the conservative definition is the only one that makes sense to me. For flight into known ice, the airframe and the airplane deicing and/or anti-icing systems have to be shown to tolerate conditions conducive to moderate amounts of clear or rime icing. NASA (the first A stands for aeronautics, so not all their research is in outer space) tells me the model for the former is called intermittent maximum and represents "liquid water between 1.1-2.9 g/m3 with drop sizes 15-50 microns in diameter over a 2.6 nm encounter," while the latter model is continuous maximum and represents "liquid water between 0.2-0.8 g/m3 with drop sizes 15-40 microns in diameter over a 17.4 nm encounter."
So first of all: less that three grams of liquid water per cubic metre doesn't seem like very much. A gram of water is a millilitre, about the capacity of the plastic screw cap on a pop bottle. A cubic metre is a fair chunk of space, like the storage capacity of one of those IKEA Expedit room dividers everyone has, the 16-box kind, with two more boxes stacked on top. You wouldn't even notice three millilitres of water in one of those, what with all the scented candles and old copies of Aviation Safety Newsletter stacked inside. I know clouds are stereotypically fluffy and insubstantial, but I would have thought they had a lot more water density than that. So huh, clouds are way drier than I thought.
Secondly, why "over a 2.6 nm/17.4 nm encounter"? At first I assumed that was translated from metric, but 2.6 nm is 4.8152 km and 17.4 nm is 32.2248 km. It turns out that they are 2.99 and 20.0 statute miles, respectively. So three miles and twenty miles. Who the heck does science in grams per cubic metre over statute miles? That's crazier than Canadians measuring our room temperature in celsius and our oven temperatures in Fahrenheit. It's even crazier than having to figure out whether something like pumpkin or peanut butter is a solid or a liquid before converting an American recipe. (Seriously, if the recipe says to use a ten-ounce jar of peanut butter, I never know if I'm supposed to weigh it or measure it volumetrically, because the Americans have the same name for two different units, one for solid things by weight, and one for liquid things by volume. Like the TSA, the recipes expect me to just know what they consider a liquid. Take tuna, for example. I was once told that canned tuna ... I'm getting off topic here. But while I'm here, what the heck is a "stick of butter". Who buys their butter in sticks?) It's even crazier than Aviatrix trying to cook from American recipes.
The certification standards are based on data collection flights performed in the 1940s. If you plot all the possible atmospheric scenarios on a graph with liquid water content on the y-axis and droplet size on the x-axis, the area that is considered safe to operate in is bounded by the x-axis, the y-axis and a curve that approximates a line of negative slope. You may now be asking yourself, does Aviatrix get off on writing sentences like that, or is she just too lazy to draw a graph and show you? The answer is that I get off on knowing that many of my readers can parse that sentence just fine, and I'm too lazy to copy someone else's graph. If there's lots of water you can only tolerate small drops, but if there's not that much water the drops can be bigger. The logical conclusion is that if there's no water at all you are allowed drops of infinite size and that you may fly through a tank completely filled with supercooled water if the drops are infinitely small. That's why I said it was a curve. Presumably the axes are asymptotes. Oh yeah, talk graphing to me, Aviatrix.
One could argue that changes in aircraft design since might have changed the validity of those results, but subsequent work in other types and in wind tunnels should be enough to keep the standard valid. Here's a little bit about how the certification is done these days: flying around seeking out the standard conditions for certification, plus using computer models to determine what shape ice would form on the aircraft, and then sending test pilots out to fly with those globs glued on the plane. I guess when they first did tests to determine what an airplane should be able to handle, they flew through convective cloud for three miles and through stratus for twenty miles and then quantified the conditions they had flown through. They probably did it in ounces per bushel or pop caps per IKEA bookshelf, and it's only been converted to grams per cubic metre for the modern day. Beats me how they determined all that, anyway in the days before the laser equipment they have now.
While trying to find the history of the certification standard I get bogged down in documents on the history of the legal "if supercooled water hangs in the sky and there's no airframe there to accrete it, is it known icing?" debate. This PDF seems like a pretty definitive document about the controversy. Given that many of the people arguing that it's not known icing until they take off and know it's there were doing so as the pilot of record at accident tribunals, I'm sticking to my assessment that if conditions known to produce ice are there, it's known icing.