Frost Point Calculator

The frost point is the temperature at which a sample of air reaches saturation with respect to a flat ice surface, as distinct from the dew point, which references supercooled liquid water. Below 0 degrees C these are not the same number. Molecules in the hexagonal ice lattice are held by a more rigid hydrogen bond network than molecules in liquid water, so fewer escape per unit time and the saturation vapor pressure over ice is lower. Since the ice curve lies below the water curve, a given vapor pressure saturates against ice at a warmer temperature, meaning the frost point always exceeds the dew point below freezing. The calculation here takes vapor pressure from the dew point via the Magnus form, then inverts the Buck 1981 ice equation with its coefficients 6.1115 hPa, 22.452, and 272.55 degrees C. The gap between the two curves is small but consequential. It peaks near minus 12 degrees C, where ice saturation pressure runs roughly 10 percent below water saturation, and this is precisely the temperature band where mixed-phase clouds produce most mid-latitude precipitation. Practical thresholds follow from the same physics: air saturated with respect to water at minus 12 degrees C is supersaturated by about 10 percent with respect to ice, which drives vapor deposition onto crystals. The main caveat is reference ambiguity. Most surface stations report relative humidity against liquid water even below freezing, so a reading of 92 percent can still correspond to ice supersaturation, and any cold-weather moisture analysis must state which reference it uses.

The distinction between saturation over water and over ice was established experimentally in the nineteenth century, but its meteorological significance was not appreciated until the 1930s. Alfred Wegener had noted in 1911 that ice and water could not both be in equilibrium with the same vapor. Tor Bergeron developed the argument into a precipitation mechanism, presenting it at the International Union of Geodesy and Geophysics assembly in Lisbon in 1935: in a cloud containing both ice crystals and supercooled droplets, the environment is at water saturation and therefore supersaturated over ice, so crystals grow while droplets evaporate. Walter Findeisen extended and quantified the process in 1938, and it is now known as the Bergeron-Findeisen mechanism. Measurement advanced in parallel. The chilled mirror principle descends from John Frederic Daniell's hygrometer of 1820, adapted so the mirror is cooled until frost rather than dew is detected optically, reaching accuracies near 0.1 degrees C. For the very dry stratosphere, balloon-borne cryogenic frost point hygrometers developed at the NOAA laboratories in Boulder, Colorado, have sustained a water vapor record since the 1980s at frost points down to about minus 90 degrees C. On the formulation side, the Goff-Gratch equations of the 1940s were the long-standing reference before Arden Buck published his simpler and comparably accurate water and ice expressions in 1981.