Radiation frost

Why does frost form on a clear, still night but not under cloud, when the air temperature is the same?

Two nights, both with a minimum air temperature of plus 3 degrees. On the clear, still one the lawn is white by dawn and the courgettes are dead; on the overcast one nothing happens. Worse, the first case looks impossible: water freezes at zero, the thermometer never went below three, and yet there is ice. Either the thermometer is wrong, or something is being measured that is not the thing that froze. Which is it?

It is the second, and the clue is in where the thermometer sits. By convention, air temperature is measured in a shaded, ventilated screen at somewhere between 1.25 and 2 metres above the ground. Nobody measures at grass height. So ask whether the grass could be colder than the air a metre and a half above it, and if so, why.

Every surface radiates energy continuously, in the infrared, at a rate set by its temperature. By day the sun more than makes up the loss. After sunset the loss continues with nothing coming in from that direction — but the ground is not radiating into nothing. It is radiating at the sky, and the sky radiates back.

How much back? That depends entirely on what is up there. Water vapour, carbon dioxide and cloud droplets all absorb and re-emit infrared. A cloud base is effectively opaque in the infrared and sits at roughly the temperature of the air around it, so it returns nearly as much as it receives, and the ground's net loss becomes small. A clear sky is a different proposition: the radiation escapes upward through thinning, colder and colder air, and much of it, in the wavelengths where the atmosphere is transparent, reaches space. The effective temperature of a clear, dry sky can be tens of degrees below the air temperature at the surface.

So on a clear night the ground is losing energy fast and gaining little. It cools. And here is the step that resolves the paradox: the ground cools the air touching it, rather than the reverse. A thin layer at the surface chills below the air above it, and because cold air is dense it stays put. The result is an inversion — coldest at the ground, warming upward — and the screen at a metre and a half is reading the wrong end of it. A gap of three or four degrees between grass and screen on a good radiation night is routine.

Now, why does the stillness matter? Because wind mixes. Even a light breeze drags warmer air from above down onto the surface and carries the chilled air away, so the inversion never establishes and the surface stays close to the screen reading. Clear and calm are two separate requirements, and either one alone spares you.

The surface itself matters too: bare, damp, firm soil conducts heat up from below through the night, while loose tilled soil, mulch or long grass insulates the surface from that reservoir and lets it radiate itself far colder. Frost appears on the grass and the car roof before the path.

Which is exactly what tells us how to fight it. If the problem is an inversion, break it: orchard wind machines and, historically, helicopters do nothing but drag warmer air from ten or fifteen metres up down onto the crop — useless when a cold air mass has simply arrived, since then there is no warm layer to fetch.

The other method looks like madness. Growers turn sprinklers on the crop and let it ice over. But freezing water releases energy — the latent heat of fusion, about 334 kilojoules per kilogram — and as long as liquid water keeps arriving and keeps freezing, that release holds the ice-and-water mixture at zero. Zero is survivable for most buds; minus four is not. The catch is that it must run continuously until the ice thaws: stop early and evaporation from the wet surface, which costs far more energy than freezing releases, drives the temperature down faster than doing nothing at all.

The core correction is that "air temperature" is not one number. There is a steep vertical gradient near the surface on a radiation night, and the standard measurement sits deliberately above it. So a forecast minimum of plus 2 is a genuine frost warning, not a reassurance — which is why agricultural services issue separate grass-minimum forecasts.

A second refinement: two quite different things are called frost. What has been described here is radiation frost, made locally on a calm clear night, and it is the kind fans and sprinklers can beat. An advection freeze is the arrival of a cold air mass, usually with wind, in which the whole column is below freezing; there is no inversion to mix down and no local remedy. Cloud and wind are protective against the first and irrelevant to the second.

One simplification worth naming: the sky's effective radiating temperature is not a single figure. It depends on humidity, cloud height and thickness, and on how much of the sky is covered, so the clean two-way split below summarises a continuous quantity.

• Why cold air drains downhill into hollows overnight, and how frost pockets form in otherwise safe terrain.
• What sets the atmospheric window — the wavelengths in which the ground's radiation escapes to space rather than being returned.

Every term the collection defines is gathered in the glossary.