Minor Differences, Beautiful Effect

That photo was from a snow squall that passed through New York two weeks ago. While I generally like snow and really wished that we’d got some actual accumulation on the ground, the aftermath was quite beautiful. Trees were covered in snow, parked cars had a thin layer, and any exposed soil had a light dusting, all contrasting with the bare sidewalks and roadbeds.

There’s no great mystery here. Snowflakes melt rapidly if they are exposed to above-freezing temperatures. The air temperature had dropped that day from above freezing down to right around freezing as the squall passed. Wood doesn’t have a lot of thermal mass and the trees are all in their winter slumber, with minimal internal activity. So the temperature of the tree branches dropped more or less in parallel to the air, allowing snow build up.

Soil has more thermal mass than wood, so its temperature was higher. As the snow cooled the top of the soil by hitting and melting, eventually the temperature got down enough so some snow stuck. Concrete has a lot of thermal mass and so it stayed too warm for any snow to collect. And the steel of car roofs quickly cooled.

The thing is, we’re talking about very small differences in temperature. The difference between the tree branches and sidewalk was less than ten degrees, probably less than five degrees. But because that narrow range included the freezing point for water, there were markedly and visibly different results.

The point – as much as there as one other than posting that striking photo – is that nonlinear effects can surprise us. If the difference in temperature were between ten below freezing and five below, the difference in snow buildup would be small. If the temperature difference were between five above freezing and ten above, there would be no snow difference because there would be no buildup at all. This kind of surprise, with a big difference in one set of conditions, bracketed by small differences in similar conditions, has been behind a lot of engineering failures over the years. I prefer the snow.

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