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)