Evapotranspiration

The calculation of evapotranspiration requires daily potential evapotranspiration. Actual evapotranspiration is energy-limited or water-limited, respectively. The evapotranspiration processes sequentially subtract from available PET (\(PET_{res}\)).

Evaporation from interception storage

Evaporation from interception storage \(EVAP_{int}\) (mm \(\Delta t^{-1}\)):

\[\begin{split}EVAP_{int}=\left\{\begin{array}{lr} S_{int} & PET_{res} > S_{int} \\ PET_{res} & PET_{res} \leq S_{int} \end{array}\right.\end{split}\]

Soil evaporation

Soil evaporation \(EVAP_{soil}\) (mm \(\Delta t^{-1}\)) implemented with Stage I-Stage II approach (Or et al., 2013). Threshold between Stage I and Stage II is defined by readily evaporable water \(S_{rew}\). Within Stage I capillary flow connects to soil surface (i.e. constant evaporation rate) whereas within Stage II capillary flow collapses (i.e. vapour diffusion rate).

\[EVAP=PET_{res} \cdot c_{evap}\]

with

\[\begin{split}c_{evap}=\begin{cases} 1 - \frac{f_{ground-cover}}{max(f_{ground-cover})} & EVAP_{d} \leq S_{rew} \\ 1 - \frac{f_{ground-cover}}{max(f_{ground-cover})} \cdot \frac{S_{tew} - EVAP_{d}}{S_{tew} - S_{rew}} & S_{rew} < EVAP_{d} \leq S_{tew} \\ 0 & EVAP_{d} > S_{tew} \end{cases}\end{split}\]

where \(EVAP_{d}\) is the cumulated soil evaporation since last rainfall (mm) and \(S_{tew}\) is the total evaporable water (mm)

\[S_{tew}=(\theta_{fc} - 0.5 \cdot \theta_{pwp}) \cdot z_{evap}\]

\[\begin{split}S_{rew}=\left\{\begin{array}{lr} 0.02 & \theta_{pwp} < 0.02\\ \frac{\theta_{pwp}}{0.24}& \theta_{pwp} \geq 0.02 \& \theta_{pwp} \leq 0.24\\ 0.24 & \theta_{pwp} > 0.24 \end{array}\right.\end{split}\]

\[z_{evap}=\frac{S_{rew}}{0.24} \cdot z_{evap-max}\]

where \(z_{evap-max}\) is the maximum length of soil capillaries connected to the soil surface (mm; \(z_{evap-max}=150\))

Transpiration

Transpiration \(TRANSP\) (mm \(\Delta t^{-1}\)) with seasonally-variant transpiration coefficients \(c_{transp}\) and water stress coeffcient of transpiration \(c_{ws}\):

\[TRANSP=PET_{res} \cdot c_{transp}\]

with

\[\begin{split}c_{transp}=\left\{\begin{array}{lr} \frac{f_{ground-cover}}{max(f_{ground-cover})} & c_{ws} \geq 1 \\ \frac{f_{ground-cover}}{max(f_{ground-cover})} \cdot c_{ws} & c_{ws} < 1 \end{array}\right.\end{split}\]

\[c_{ws}=\frac{\theta - \theta_{pwp}}{f_{pwt} \cdot \theta_{fc} - \theta_{pwp}}\]

where \(f_{pwt}\) is the fraction of plant water stress (-; \(f_{pwt}=0.75\))