Vapor pressure deficit


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


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



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



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]


Allen et al. (1998)


Variable Description Unit
\(T\) air temperature °C
\(T_{dew}\) dew point temperature °C
\(H\) air humidity %
\(P\) rainfall mm
\(U\) windspeed m/s
\(w\) days since last rain
(or rain above threshold)
\(rr\) days with consecutive rain d
\(\Delta t\) time increment d
\(\Delta{e}\) vapor pressure deficit kPa
\(e_s\) saturation vapor pressure kPa
\(e_a\) actual vapor pressure kPa
\(p_{atm}\) atmospheric pressure kPa
\( PET\) potential evapotranspiration mm/d
\(r\) soil water reserve mm
\(r_s\) surface water reserve mm
\(EMC\) equilibrium moisture content %
\(DF\) drought factor -
\(N\) daylight hours hr
\(D\) weighted 24-hr average moisture condition hr
\(\omega\) sunset hour angle rad
\(\delta\) solar declination rad
\(\varphi\) latitude rad
\(Cc\) cloud cover Okta
\(J\) day of the year (1..365/366) -
\(I\) heat index -
\(R_n\) net radiation MJ⋅m-2⋅d-1
\(R_a\) daily extraterrestrial radiation MJ⋅m-2⋅d-1
\(R_s\) solar radiation MJ⋅m-2⋅d-1
\(R_{so}\) clear-sky solar radiation MJ⋅m-2⋅d-1
\(R_{ns}\) net shortwave radiation MJ⋅m-2⋅d-1
\(R_{nl}\) net longwave radiation MJ⋅m-2⋅d-1
\(\lambda\) latent heat of vaporization MJ/kg
\(z\) elevation m a.s.l.
\(d_r\) inverse relative distance Earth-Sun -
\(\alpha\) albedo or canopy reflection coefficient -
\(\Delta\) slope of the saturation vapor pressure curve kPa/°C
\(Cc\) cloud cover eights
\(ROS\) rate of spread m/h
\(RSF\) rate of spread factor -
\(WF\) wind factor -
\(WRF\) water reserve factor -
\(FH\) false relative humidity -
\(FAF\) fuel availability factor -
\(PC\) phenological coefficient -

Suffix Description
\(-\) mean / daily value
\(_{max}\) maximum value
\(_{min}\) minimum value
\(_{12}\) value at 12:00
\(_{13}\) value at 13:00
\(_{15}\) value at 15:00
\(_{m}\) montly value
\(_{y}\) yearly value
\(_{f/a}\) value at fuel-atmosphere interface
\(_{dur}\) duration
\(_{soil}\) value at soil level

Constant Description
\(e\) Euler's number
\(\gamma\)psychrometric constant
\(G_{SC}\)solar constant
\(\sigma\)Stefan-Bolzmann constant