Dew Point - Calculating The Dew Point

Calculating The Dew Point

See also: Psychrometric chart

A well-known approximation used to calculate the dew point, Tdp, given just the actual ("dry bulb") air temperature, T and relative humidity (in percent), RH, is the Magnus formula:

\begin{align} \gamma(T,R\!H)&=\ln\left(\frac{R\!H}{100}\exp\!\!\left(\frac{bT}{c+T}\right)\right)=\ln\left(\frac{R\!H}{100}\right)+\frac{bT}{c+T};\\ T_{dp}&= \frac{c\gamma(T,R\!H)}{b-\gamma(T,R\!H)};\end{align}

The more complete formulation and origin of this approximation involves the interrelated saturated water vapor pressure (in units of millibar, which is also hPa) at T, Ps(T), and the actual water vapor pressure (also in units of millibar), Pa(T), which can be either found with RH or approximated with the barometric pressure (in millibar units), BPmb, and "wet-bulb" temperature, Tw is:

\begin{align} P_s(T)& = \frac{100}{R\!H}P_\text{a}(T) = a\exp\!\!\left(\frac{bT}{c+T}\right);\\ P_\text{a}(T) & = \frac{R\!H}{100}P_s(T)=a\exp(\gamma(T,R\!H)),\\ &\approx P_s(T_\text{w}) - B\!P_\text{mb} 0.00066 \left\left(T-T_\text{w}\right);\\ T_\text{dp} & = \frac{c\ln(P_\text{a}(T)/a)}{b-\ln(P_\text{a}(T)/a)};\end{align}

For greater accuracy, Ps(T) (and, therefore, γ(T,RH)) can be enhanced, using part of the Bögel modification, also known as the Arden Buck equation, which adds a fourth, d constant:

\begin{align}P_{s:m}(T)&=a\exp\!\!\bigg(\left(b-\frac{T}{d}\right)\left(\frac{T}{c+T}\right)\bigg);\\ \gamma_m(T,R\!H)&=\ln\Bigg(\frac{R\!H}{100}\exp\!\! \bigg(\left(b-\frac{T}{d}\right)\left(\frac{T}{c+T}\right)\bigg) \Bigg);\\ T_{dp}&= \frac{c\gamma_m(T,R\!H)}{b-\gamma_m(T,R\!H)};\end{align}
(where )

There are several different constant sets in use, the ones used in NOAA's presentation are taken from a 1980 paper by David Bolton in the Monthly Weather Review:

These valuations provide a minimum accuracy of 0.1%, for

-30°C ≤ T ≤ +35°C;
1% < RH < 100%;

Also noteworthy is the Sonntag1990,

Another common set of values originates from the 1974 Psychrometry and Psychrometric Charts, as presented by Paroscientific,

Also, in the Journal of Applied Meteorology and Climatology, Arden Buck presents several different valuation sets, with different minimum accuracies for different temperature ranges. Two particular sets provide a range of -40°C → +50°C between the two, with even greater minimum accuracy than all of the other, above sets (maximum error at given |C°| extreme):

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