The dew point, or dew-point temperature, is the temperature at which dew, or condensation, forms as you cool a gas. Where the condensate is ice, this is known as the frost point.
The relative humidity is the ratio of the amount of water vapour, e, in the air to the amount of water vapour, es, that would be in the air if saturated at the same temperature and pressure. It can be expressed
relative humidity (in %) = e/es × 100 (Equation 1)
Unfortunately, there is no simple, direct formula for converting between dew point and relative humidity. Conversions between these two parameters must be carried out via the intermediate step of evaluating both the actual vapour pressure of water and the saturation vapour pressure at the prevailing temperature.
Vapour pressure can be calculated using the Magnus formula. This states that at a temperature t (in °C), the saturation vapour pressure ew(t), in pascals (Pa), over liquid water, is
ln ew(t) = ln 611.2 + (17.62 t)/(243.12+t) (Equation 2)
For information, 100 Pa = 1 millibar (mbar)
For the range -45 °C to +60 °C, values given by this equation have an uncertainty of < ±0.6 % of value, at the 95% confidence level.
Over ice, ei(t) is
ln ei(t) = ln 611.2 + (22.46 t)/(272.62+t) (Equation 3)
For the range -65 °C to +0.01 °C, values given by this equation have an uncertainty of < ±1.0 % of value, at the 95% confidence level.
This is a more accurate but complex alternative formula for vapour pressure (in pascals) from dew point (in kelvin) for water:
ln ew(T) = -6096.9385 T-1 + 21.2409642 - 2.711193×10-2 T + 1.673952×10-5 T2 + 2.433502 ln T (Equation 4)
and for ice:
ln ei(T) = -6024.5282 T-1 + 29.32707 + 1.0613868×10-2 T - 1.3198825×10-5 T2 - 0.49382577 ln T (Equation 5)
(Formulae due to Sonntag, 1990, updated from formulae given by Wexler, 1976 and 1977.)
The uncertainties associated with these equations are:
at the 95% confidence level.
The accuracy of these calculations depends slightly on the pressure and temperature of the gas concerned. For air near room temperature and atmospheric pressure, the water vapour enhancement factor affects the result by approximately 0.5 % of value.
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