When the Frost is on the Treetops
It starts as a mere powdering of white on the birch branches, a film on the windshield. As clear, windless weather continues in the valley bottoms, some of the minute flecks of ice begin to outgrow their brethren, growing into tiny plates ridged with the lines of uneven growth. After a week or two, branches and snow alike are covered with plates jutting out like the wings of fingernail-sized butterflies. Then the sun returns, warming the delicate hoarfrost into evaporation during the day; or wind or snow knocks the tiny plates from the branches.
Hoarfrost is most common in the interior of Alaska, where the necessary clear, windless conditions are most common. Like air pollution, its formation is dependent on thermal radiation, so heavy hoarfrost may warn of poor air quality. But the inversions responsible are of much smaller scale than the ones we measure with weather balloons or towers.
Consider a twig on a cloudless night. Like anything else at temperatures above absolute zero, it radiates energy in the thermal infrared. Air is not as good a radiator as the twig, so it cannot return as much energy as the twig is losing. The twig cools. If the air contains enough water vapor that it is anywhere close to saturation, the twig is likely to become cooler than the dew point, and water will begin to condense on the twig. In winter, that water will freeze. Once there is ice on the twig, the water in the air will freeze directly onto the ice crystals on the twig. Those crystals whose initial growth is aimed outward will be in a position to radiate and cool most efficiently, and will also trap water before it gets closer to the center of the crystal mass. Thus they will continue to grow fastest.
Of course this process is not confined to twigs. The snow surface behaves in the same way, and it may even have an additional water source from the warmer snow deeper in the snow pack. So when frost is forming on trees and bushes, there are usually tiny blades of frost growing out from the snow surface as well. They just take a little more looking for.
Since the whole process depends on radiative energy loss, sheltered areas such as the snow under a spruce tree will have very little frost formation compared with exposed areas. The same is true of dew, which forms by the same process at warmer temperatures. Of course if there is an extra moisture source, such as leakage of warm, moist air from a house, hot springs, or artificial open water such as a cooling pond, hoar frost can form almost anywhere.
We don't know everything about hoar frost. For instance, during a frost episode at Fairbanks, there is often a distinct line along the hills with frost below the line and bare branches above it. It shouldn't be directly due to the inversion, because frost growth is actually faster at warmer temperatures if the relative humidity is the same. And the temperature difference between twigs and the air should if anything be greater on exposed hilltops. I have always assumed that the line showed the elevation above which the wind was strong enough to knock the crystals off the branches, or perhaps even to warm the branches enough that frost could not form. Another, less likely possibility is that the air is drier near the hilltops. Does anyone who lives near this frost line have some helpful observations?
