Ontogenesis

The plant development is simulated using the principle of heat summation. The effective temperature is limited by a minimum temperature, which is referred to as base temperature. Suitable soil moisture is required for the emergence of the seeds, which is at least 30% of the available water. Ponding at the soil surface would hinder seed emergence. If soil moisture is ideal, the topsoil layer’s temperature will be used for heat summation.

\[DD_{0, t} = DD_{0,t-1} + (T_{S10} - T_{B0}) \cdot \Delta t\]

\(DD_{0, t}\) Actual temperature sum in developmental stage 0 \([^{\circ} C \, d]\)
\(DD_{0, t-1}\) Yesterday’s temperature sum in developmental stage 0 \([^{\circ} C \, d]\)
\(T_{S10}\) Soil temperature in 0–10 cm depth \([^{\circ} C]\)
\(T_{B0}\) Base temperature developmental stage 0 \([^{\circ} C]\)
\(\Delta t\) Time step \([d]\)

As soon as the crop-specific temperature sum for seed emergence is reached, the following developmental stage is initiated. From this time on the daily mean temperature will be summed up. Stress factors drought and N deficiency accelerate the summation, while vernalisation and day length factors decelerate it:

\[DD_{n,t} = DD_{n,t-1} + (T_{av} - T_{Bn}) \cdot b_s \cdot b_v \cdot b_D \cdot \Delta t\]

\(DD_{n,t}\) Actual temperature sum in developmental stage \(n\) \([^{\circ} C \, d]\)
\(DD_{n,t-1}\) Yesterday’s temperature sum in developmental stage \(n\) \([^{\circ} C \, d]\)
\(T_{av}\) Daily mean air temperature in 2 m height \([^{\circ} C]\)
\(T_{Bn}\) Base temperature developmental stage n \([^{\circ} C]\)
\(b_s\) Acceleration factor environmental stress
\(b_v\) Vernalisation factor
\(b_D\) Day length factor
\(\Delta t\) Time step \([d]\)

where

\[b_s = max( 1 + ( 1 - \zeta_W)^2, 1 + (1-\zeta_N)^2 )\]

\(b_s\) Acceleration factor environmental stress
\(\zeta_w\) Stress factor drought
\(\zeta_N\) Stress factor N deficiency

Satisfaction of the crop’s vernalisation requirement is considered as follows:

\[b_V = \begin{cases} \frac{(d_V - d_{VT})}{(d_{VR} - d_{VT})} & d_{VT} \geq 1 \\ 1 & d_{VT}<1 \end{cases}\]

Figure 1: Effective vernalisation in relation to the daily mean air temperature.

\(b_V\) Vernalisation factor
\(d_V\) Current number of vernalisation days \([d]\)
\(d_{VT}\) Vernalisation threshold \([^{\circ} C \, d]\)
\(d_{VR}\) Crop-specific vernalisation requirement \([^{\circ} C \, d]\)

where

\[d_V = d_{V-1} + b_{V_{eff}} \cdot \Delta t\]

\(d_V\) Current number of vernalisation days \([d]\)
\(d_{V-1}\) Number of vernalisation days until yesterday \([d]\)
\(b_{V_{eff}}\) Effective vernalisation
\(\Delta t\) Time step \([d]\)

and

\[d_{VT} = min( d_{VR}, 9 ) - 1\]

\(d_{VT}\) Vernalisation threshold \([^{\circ} C \, d]\)
\(d_{VR}\) Crop-specific vernalisation requirement \([^{\circ} C \, d]\)

The vernalisation factor is always positive.

Day length is considered in relation to a crop-specific base day length and to the crop’s day length requirement:

\[b_D = \frac{N_{photo} - N_{basis}}{N_{req} - N_{basis}}\]

\(b_D\) Day length factor
\(N_{photo}\) Photoperiodic day length \([h]\)
\(N_{basis}\) Crop-specific base day length \([h]\)
\(N_{req}\) Crop-specific day length requirement \([h]\)