Sources of data: a military base about 30 miles, a PWS about three miles and my RadioShack thermometer.
0400-0700 hrs. All three recorded temperature 42°F. The PWS and the military base recorded dew point at 32°F and humidity in the mid 60s. Alitiude 4200ft. Wind calm.
The temperature of the air is not the temperature of the roof. The roof temperature dropped below 32 because the roof radiated heat during the night to the night sky.
You’ll see this often with frost on cars. Cars that are exposed to the night sky will have frost in the morning, those under a carport will not. Both will be exposed to the same ambient air temperature, but the car out in the open will cool more than the car under cover.
Likewise, gardeners know to cover delicate plants even if the air temperature is not getting down to zero (Celsius), because the “grass temperature” is usually several degrees below the air temperature on a clear cool night. Air temperature is measured at a standard height (usually 5ft IIRC) above ground level, to minimise the effect of this radiation cooling on the reading.
It’s about the heat flow. There are three fundamental ways of transferring heat: Conduction (direct contact), Convection (contact with a fluid) and radiation (electromagnetic waves).
Crops can experience frost even though the ambient air temperature is above freezing if the heat loss due to radiation (cloudless night) is greater than the convective heat gain from the air.
To add to this, the temperature of the night sky is basically the temperature of outer space, about -270 C. Your roof is much much warmer than this, so it radiates its heat out to space, but space radiates very little back to the roof. So the roof cools off lower than the air temperature.
Orchards and vineyards are frequently located in areas conducive to nocturnal winds. Moving the warmer air over the plants keeps them from frosting.
In some places large fans are used to warm crops at night to prevent frost. Smoke producing smudge pots are sometimes used to create a haze that reduces radiant cooling.
I don’t think the OP was talking about frost remaining on roofs as the temperature rose to 42F, but about frost forming when the temperature only *fell *to 42F.
I’ve never seen frost on the ground or on exposed surfaces with an air temperature of 42F. The air temp at which this begins to occur has always been about 35-36F in my experience.
Last Monday, I woke to find frost on rooves and the grass even though my outside thermometer read about 4.5 degrees Celsius. Thanks for this discussion which has shown me that my thermometer may not be broken after all.