# Vapor pressure deficit

# Definition

The vapor pressure deficit \(\Delta{e}\) is the difference between saturation \(e_s\) and actual vapor pressure \(e_a\)

# Formula

The vapor pressure deficit \(\Delta{e}\) [kPa] can be calculated using temperature and relative humidity as follows (cf. Allen et al. 1998):\[\Delta{e}=e_s-e_a\]

with

\[e_s=0.6108\cdot e^{\frac{17.27\cdot{T}}{T+237.3}}\]

and

\[e_a=e_s\cdot{\dfrac{H}{100}}\]

where \(T\) is temperature [°C] and \(H\) [%] relative humidity.

However, using mean air temperature as above results in a lower estimate of \(e_s\), thus in a lower vapor pressure deficit. It would therefore be more appropriate to use, if available, maximal and minimum temperature for calculating \(e_s\), as follows (Allen et al. 1998):

\[e_s=\dfrac{1}{2}\bigg({0.6108\cdot e^{ \frac{17.27\cdot{T_{max}}}{T_{max}+237.3}}+0.6108\cdot e^{\frac{17.27\cdot{T_{min}}}{T_{min}+237.3}}}\bigg)\]

where \(T_{max}\) is maximal temperature [°C] and \(T_{min}\) minimal temperature [°C].

NB: The conversion between kiloPascals and millimeters of mercury is as follows: 1 [kPa] = 7.500616827042 [mmHg]

# Reference

Allen et al. (1998)