There is a horticultural rule of thumb that says if the surface temperature in your garden is below 5C at 10:m there is danger of frost.

There is a horticultural rule of thumb that says if the surface temperature in your garden is below 5C at 10:00 p.m there is danger of frost. In the absence of wind and assuming that the radiative cooling occurs all below 100m (i.e. the temperature at 100m remains constant), what does this rule of thumb tell you about an average overnight radiative cooling rate(in Wm^-2)? In other words, what is the average cooling rate that will dip the surface temperature to 0C at 6:00a.m. ? You can assume that the temperature increases linearly from the surface to 100 mm at any given time. what would threshold temperature be if the lowest 100m were well-mixed by surface winds throughout the night ?