Description
Calculate the temperature (deg. K) of saturated air at pressure p (in mb) and with mixing ratio w (in g/kg). The vapor pressure e is calculated using Note 2 of the Herzegh memo. The formula for the temperature was derived from Note 6 by substituting a two term Taylor series expansion for the ln(T_3/T) term and solving for T.
Formula
$$
e = \frac {pw} {1000 \epsilon + w} \\
T_{3} = 273.15 \\
A = 5.0065 \\
B = 19.83923 \\
E_{3} = 6.1078 \\
t_{mr} = \frac {T_{3}A} {A - B + \sqrt{B^{2} + 2Aln(\frac {E_{3}} {e})}}
$$
Source
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