Growing degree day GDD at time step t (°C day^{-1}):
GDD = \begin{cases}
TA_{ceil} - TA_{base} & \frac{(TA_{max}+TA_{min})}{2} > TA_{ceil} \\
\frac{(TA_{max}+TA_{min})}{2}]-TA_{base} & TA_{base} \leq \frac{(TA_{max}+TA_{min})}{2} \leq TA_{ceil} \\
TA_{base} & \frac{(TA_{max}+TA_{min})}{2} < TA_{base}
\end{cases}
where TA_{max} is the daily maximum air temperature (°C), TA_{min} is the daily minimum air temperature (°C), TA_{base} is the lower threshold of crop growth (°C) and TA_{ceil} is the upper threshold of crop growth (°C).
Time since growth (i.e sum of growing degree day) t_{grow} (°C day^{-1}):
t_{grow}=\sum_{t=t_{sowing}}^{t_{harvesting}} GDD_t
Time since decay (i.e sum of growing degree day) t_{grow} (°C day^{-1}):
t_{decay}=\sum_{t=t_{0-decay}}^{t_{harvesting}} GDD_t
Coefficient of crop water stress c_{ws} (-):
c_{ws}=\begin{cases}
1 & \theta>\theta_{ws} \\
\frac{\theta-\theta_{pwp}}{\theta_{ws}-\theta_{pwp}} & \theta_{pwp} \leq \theta \leq \theta_{ws}
\end{cases}
Growth of crop canopy:
CC = \begin{cases}
CC_0 \cdot e^{c_{ccg} \cdot c_{ws} \cdot t_{grow}} & CC < CC_{max} / 2 \\
CC_{max} - (CC_{max} - CC_0) \cdot e^{-(c_{ccg} \cdot c_{ws} \cdot t_{grow})} & CC \geq CC_{max} / 2 \\
\end{cases}
where CC is the fraction of ground covered by crop canopy (-) at time step t, CC_0 is the initial fraction of ground covered by crop canopy (-), CC_{max} is the the maximum fraction of ground covered by crop canopy (-), c_{ccg} is the coefficient of crop canopy growth (-) and t_{grow} is the time since crop growth (°C day^{-1}).
Decay of crop canopy:
CC=CC_{max} \cdot [1-0.05(e^{\frac{c_{ccd}}{CC_{max}} \cdot t_{decay}} - 1)]
where c_{ccd} is the coefficient of crop canopy decay (-) and t_{decay} is the time since crop decay (°C day^{-1}).
Crop root growth:
z_{root}=z_{root-max}-(z_{root-max}-z_{root-0}) * e^{c_{crg} \cdot c_{ws} \cdot t_{grow}}
where z_{root} is the crop root depth (m) at time step t, z_{root-0} is the initial crop root depth (m), z_{root-max} is the the maximum crop root depth (m) and c_{crg} is the coefficient of crop root growth (-).
Crop transpiration TRANSP_{crop} at time step t (mm \Delta t^{-1}):
TRANSP_{crop}=PET_{res} * k_{cb} * c_{ws}
k_{cb}=k_{cb-min} + CC \cdot (k_{cb-mid} - k_{cb-min})
where k_{cb} is the basal crop coeffcient (-), k_{cb-min} is the minimum basal crop coeffcient (-) and k_{cb-mid} is the the basal crop coeffcient at full canopy development (-).