## 2 Materials and Methods
### Model Overview  
A schematic overview of the model is presented in Figure 2. All the simulated components and related equations of the flowchart are described in the following sections. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Site**} & \multirow{2}{*}{**Year**} & \multicolumn{2}{c}{**Recorded**} & \multicolumn{2}{c}{**Observed**} & \multicolumn{2}{c}{**Simulated**} \\ \cline{3-8}  & & **Sowing Date** & **Y (t/ha)** & **B (t/ha)** & **GS 61** & **Y (t/ha)** & **B (t/ha)** & **GS 61** \\ \hline \multirow{3}{*}{Crossnacrevey} & 2013 & 8-November & 15.8 & 19.2 & 25-June & 11.6 & 19.9 & 14-June \\  & 2014 & 29-October & 10.7 & 19 & 16-June & 9.6 & 18.7 & 9-June \\  & 2015 & 4-December & 11.9 & 22.5 & 30-June & 10.9 & 21.5 & 28-June \\ \hline \multirow{3}{*}{Carlow} & 2013 & 25-October & 10.7 & 18 & 19-June & 15.2 & 25.8 & 7-June \\  & 2014 & 14-October & 12.1 & 25.5 & 11-June & 10.7 & 21.1 & 21-June \\  & 2015 & 14-October & 13 & 22.6 & 13-June & 13.1 & 25.1 & 12-June \\ \hline \multirow{3}{*}{[PERSON]} & 2013 & 23-October & 15 & 22.5 & 18-June & 15.7 & 26.6 & 31-May \\  & 2014 & 15-October & 13.4 & 25.9 & 10-June & 15.4 & 27.5 & 8-June \\ \cline{1-1}  & 2015 & 6-November & 13.2 & 24 & 14-June & 14.8 & 24.7 & 4-June \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Observed yield (Y), biomass (B), sowing dates and date of growth stage 61 (GS61) for the selected WW study sites and years and model estimated yield, biomass and GS61. The model framework used in this work was originally developed by [13] and was initially tested for WW. The original model is based on the Monteith light use efficiency (LUE) theory [46] and its relationship to biomass. Within the model, biomass is separated into leaf and non-leaf components using a partitioning function and specific leaf area is used to simulate crop growth. Grain yield is simulated using a rate of grain-filling parameter. The model simulates GAI, biomass, and yield on a daily time step, consistent with the driving meteorological inputs. The basic equations for simulating crop biomass and yield are shown in Equations (1)-(5). Equation (4a,c) shows the temperature stress function. \[\Delta\mathrm{DAM}=\mathrm{APAR}\;\times\mathrm{ELUE}\;\times\;\mathrm{F_{T}(T_ {a})}\times\mathrm{WST} \tag{1}\]  
where, DAM is the daily accumulated biomass, APAR is the Absorbed photosynthetically active radiation computed as a product of the global radiation, climatic efficiency parameter and the fractional absorbed photosynthetic active radiation (FAPAR), calculated using [PERSON]'s law. Equations (2) and (3) show the calculations for APAR and the use of Beer's law. \(\mathrm{F_{T}(T_{a})}\) is a temperature stress function (Equation (4a-4c), \(T_{a}\) is the mean air temperature, and WST is the water stress coefficient (Equation (11)) computed from the soil-water balance module. WST is not in the basic version of the SAFY model, it is added here to take water stress into account when estimating crop biomass. \[\mathrm{APAR}=\mathrm{R_{g}}\times\in_{c}\times\mathrm{FAPAR} \tag{2}\]  
where, \(\mathrm{R_{g}}\) is the global radiation in \(\mathrm{Mj.m^{-2}}\) and \(\mathrm{\epsilon_{c}}\) is a climatic efficiency parameter. \[\mathrm{FAPAR}=1-\;\mathrm{e^{-k_{ext}\times GAI}} \tag{3}\]  
where, \(k_{ext}\) is the light extinction coefficient. \[\mathrm{F_{T}(T_{a})}=1-\left[\frac{\mathrm{T_{opt}}-\;T_{a}}{\mathrm{T_{opt} }-\;T_{min}}\right]^{\beta}\;,\;\mathrm{if}\;T_{min}<\;T_{a}<\;T_{opt} \tag{4a}\]  
Figure 2: Model Overview—Simulated fluxes are highlighted in bold. \[\mathrm{F_{T}(T_{a})}=1-\left[\frac{T_{opt}-\ T_{a}}{T_{opt}-\ T_{max}}\right]^{ \beta}\,\ \mathrm{if\ T_{max}>\ T_{a}>\ T_{opt}} \tag{4b}\]  
\[\mathrm{F_{T}(T_{a})}=0,\ \mathrm{if\ T_{a}<\ T_{min}\ or\ T_{a}>\ T_{max}} \tag{4c}\]  
where, \(T_{opt}\) is the optimal temperature for the crop, \(T_{min}\) and \(T_{max}\) are the minimum and maximum temperature thresholds beyond which crop growth ceases. \(T_{a}\) is the mean air temperature and \(\beta\) is the degree of the polynomial.