Sapling biomass for trees : \\

\begin{equation}
\alpha_{tree} = 1
\end{equation}

\begin{equation}
SAPL_{leaf} =  \left( \frac {4 \cdot k_{allom1} \cdot \left( \dfrac{4 \cdot r_{hs:s} \cdot SLA }{\pi .k_{la:sa}}\right)^{0.8} }{SLA} \right)^5
\end{equation}

\begin{equation}
SAPL_{sapabove} = 0.5 \cdot P \cdot \frac{SAPL_{leaf}}{\left( \dfrac
  {k_{la:sa}}{SLA} \right) } \cdot k_{allom2} \cdot \left(
  \sqrt{4.\frac{r_{hs:s}}{\pi} \frac{SAPL_{leaf}}{ \left( \dfrac {k_{la:sa}}{SLA} \right) }} \right) ^{k_{allom3}} 
\end{equation}

\begin{equation}
SAPL_{sapbelow} = SAPL_{sapabove}
\end{equation}


\begin{equation}
SAPL_{heartabove} = 2.SAPL_{sapabove}
\end{equation}

\begin{equation}
SAPL_{heartbelow} = 2.SAPL_{sapbelow}
\end{equation}

\begin{equation}
SAPL_{root} = 0.1 \cdot \frac{1}{\alpha_{tree}} \cdot SAPL_{leaf} 
\end{equation}

\begin{equation}
SAPL_{fruit} = 0.3 \cdot SAPL_{leaf} 
\end{equation}

\begin{equation}
SAPL_{reserve} = 
\begin{cases}
5 \cdot SAPL_{leaf} & \text{if PFT not evergreen} \\
0 & \text{if PFT evergreen}
\end{cases} %\]
\end{equation}

where : \\
\begin{itemize}
 \item  $k_{allom1}= 100$; \quad $ k_{allom2} = 40$; \quad  $k_{allom3}= 0.5$.
 \item  $r_{hs:s}$ is the ratio between the sum of the mass of sapwood and heartwood over sapwood.
 \item  $k_{la:sa} = 8000 $
 \item  $P = 200000$ is the pipe density. 
\end{itemize}



