# Leaf area expansion



## Actual leaf area (daily increase)


At emergence (Fig. \@ref(fig:PhenologWheatModule)), an initial leaf
area is specified for each plant by `initial_tpla`, with a
default value of 200 mm\textsuperscript{2} plant\textsuperscript{-1}. 

During the tiller formation phase (Fig. \@ref(fig:PhenologWheatModule)),
the daily increase in leaf area index ($\Delta\text{LAI}_{d}$) is
the minimum between `stressed` leaf
area index ($\Delta\text{LAI}_{d,\,s}$) and the carbon-limited leaf
area index ($\Delta\text{LAI}_{d,\,c}$). 


\begin{equation}

\Delta\text{LAI}_{d}=\min(\Delta\text{LAI}_{d,\,s},\;\Delta\text{LAI}_{d,\,c})

\end{equation}




##  Stressed leaf area


During the tiller formation phase, the `stressed` daily increase
in leaf area ($\Delta LAI_{d,s}$) is calculated as the potential
increase in LAI reduced by environmental factors.

\begin{equation}

\Delta\text{LAI}_{d,\,s}=\Delta\text{LAI}_{d,\,p}\times\min(f_{w,\;expan},\,f_{N,\,expan},\,f_{P,\,expan}) (\#eq:StressLeafArea)

\end{equation}

where $f_{N,\,expan}$, $f_{p,\,expan}$ and $f_{w,\,expan}$ are
the nitrogen, phosphorus and soil water stress factors concerning
canopy expansion, respectively (Equation \@ref(eq:NStressLeafExpansion),
 Section @ref(Phosphorus-stress) and Equation \@ref(eq:WaterStressLeafExpansion)).

The potential daily increase of leaf area ($\Delta\text{LAI}_{d,\,p}$)
is calculated by the potential daily increase in leaf number and leaf
size. 


\begin{equation}

\Delta\text{LAI}_{d,\,p}=\Delta N_{d,\,p}\times L_{n}\times D_{p}

\end{equation}

where $\Delta N_{d,\,p}$ is the potential increase in leaf number
(for the whole plant), $D_{p}$ is the plant population, and $L_{n}$
is the potential leaf area for leaves of the `current` node (this
corresponds to the new potential leaf area produced by the different
tillers in the real world) and depends on the node number on the main
and unique stem considered by APSIM-Wheat.

\begin{equation}

L_{n}=h_{ls}(n_{d}+n_{0})

\end{equation}

where $n_{0}$ is the growing leaf number in the sheath (`node_no_correction`
in wheat.xml) and equals to 2 as default value. The function $h_{ls}(n_{d})$
is defined by parameters `x_node_no` and `y_leaf_size`
in wheat.xml and linearly interpolated by APSIM (Fig. \@ref(fig:wdLeafSizeByNode)).


```{r wdLeafSizeByNode,fig.cap='Leaf area per node ($L_{n}$) in regards to the main stem node number $n_{0} + n_{d}$.' }  

p <- wdVisXY(wheat_xml, 
		"x_node_no", "y_leaf_size ",
		xlab = "Main stem node number",
		ylab = expression(paste("Potential leaf area per node", ~"("*mm^2*")")))
print(p)

```



## Carbon-limited leaf area


Leaf area related to carbon production is calculated by the increase
in leaf dry weight ($\Delta Q_{leaf}$ Equation \@ref(eq:actualBiomassProduction))
and the maximum specific leaf area ($\text{SLA}_{max}$), which is
related to leaf area index (LAI).


\begin{equation}

\Delta\text{LAI}_{d,\,c}=\Delta Q_{leaf}\times\text{SLA}_{max}

\end{equation}


\begin{equation}

\text{SLA}_{max}=h_{SLA}(\text{LAI})

\end{equation}

This function is defined by parameters `x_lai` and `y_sla_max`
in wheat.xml and linearly interpolated by APSIM (Fig. \@ref(fig:wdSLA)).


```{r wdSLA,fig.cap='Relationship between maximum specific leaf area and leaf area index.' }  

p <- wdVisXY(wheat_xml, 
		"x_lai", "y_sla_max",
		xlab = expression(paste("Leaf area index", ~"("*mm^2*" "*mm^{-2}*")")),
		ylab = expression(paste("Maximum specific leaf area", ~"("*mm^2*" "*g^{-1}*")")))
print(p)

```