Crop phenology

Growing degree day \(GDD\) at time step \(t\) (\(°C day^{-1}\)):

\[\begin{split}GDD = \begin{cases} TA_{ceil} - TA_{base} & \frac{(TA_{max}+TA_{min})}{2} > TA_{ceil} \\ \frac{(TA_{max}+TA_{min})}{2}]-TA_{base} & TA_{base} \leq \frac{(TA_{max}+TA_{min})}{2} \leq TA_{ceil} \\ TA_{base} & \frac{(TA_{max}+TA_{min})}{2} < TA_{base} \end{cases}\end{split}\]

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 \(c_{ws}\) (-):

\[\begin{split}c_{ws}=\begin{cases} 1 & \theta>\theta_{ws} \\ \frac{\theta-\theta_{pwp}}{\theta_{ws}-\theta_{pwp}} & \theta_{pwp} \leq \theta \leq \theta_{ws} \end{cases}\end{split}\]

Growth of crop canopy:

\[\begin{split}CC = \begin{cases} CC_0 \cdot e^{c_{ccg} \cdot c_{ws} \cdot t_{grow}} & CC < CC_{max} / 2 \\ CC_{max} - (CC_{max} - CC_0) \cdot e^{-(c_{ccg} \cdot c_{ws} \cdot t_{grow})} & CC \geq CC_{max} / 2 \\ \end{cases}\end{split}\]

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 (-).