# 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)