# Competition for light

FTC's competition for light is modelled through the FTC light extinction module. The PAR at 0.75 m height at the centre of the simulation pixel is calculated using the general light model, considering only interception of the adult trees. This PAR level is assumed representative of the entire FTC space (0-1.30 m height).

The light level at height \textit{w} in the FTC simulation space is:

(30)       ${\displaystyle PAR(w)=<{\hat {I}}_{ATot}>e^{-k\cdot LAAb(w)}}$

(31)       ${\displaystyle LAAb(w)=\sum _{i}\int _{\,w}^{\,1.30}LAFTC_{i}(h)dh}$

where LAAb(w) is the leaf area above w, and LAFTCi}(h) is the function describing the vertical leaf area distribution of the ith FTC, obtained from empirical relationships. The APAR of a FTC is modelled as:

(32)       ${\displaystyle APAR_{i}=fAPAR<{\hat {I}}_{ATot}>\int _{\,0}^{\,1.30}LAFTC_{i}(w)\cdot e^{-k\cdot LAAb\left(w\right)}d(w)}$

For computational simplicity, the vertical space between 0 and 1.30 m is divided in m-units, then Equations 31 and 32 become:

(33)       ${\displaystyle LAAb_{j}=\sum _{i}\sum _{l=j+1}^{m}LAFTC_{il}}$

(34)       ${\displaystyle APAR_{i}=fAPAR<{\hat {I}}_{ATot}>\sum _{j}\left(LAFTC_{ij}\cdot e^{-k\cdot LAAb_{j}}\right)}$

where LAFTC is the 2-D matrix of the leaf area distribution over the FTC's and over the vertical space, obtained through the function:

(35)       ${\displaystyle LAFTC_{ij}=\int _{\,a}^{\,b}LAFTC_{i}(h)dh\qquad {\rm {where}}\qquad a=\left(j-1\right){\frac {1.30}{m}};\,\,\,b=j{\frac {1.30}{m}}}$

Figure 6: STELLA® model of the growth of an FTC cohort: competition between cohorts and with adult trees is mediated by absorbed photosynthetically active radiation (APAR, determined by competition for light) and by the gas exchange factor (determined by competition for water).