Canopy profile

The leaf area density (LAD), \(a(z)\) [m\(^2\) m\(^{-3}\)], at height \(z\) are given by a beta distribution as

\[\begin{equation} a(z) = \left(\frac{L}{h_c}\right) \left( \frac{ (z/h_c)^{p-1} (1 - (z/h_c)^{q-1})}{B(p,q)}\right) \end{equation}\]

where \(p\) and \(q\) are the shape function of the beta distribution, \(B(p,q)\) is a normalization constant, \(h_c\) is the canopy height. The total leaf area index (LAI),\(L\) [m\(^2\) m\(^{-2}\)] and the cumulative leaf area index, \(L(z)\) [m\(^2\) m\(^{-2}\)], from the top of the canopy is given as

\[\begin{align} L &=& \int_0^{h_c} a(z) dz \\ L(z) &=& \int_z^{h_c} a(z) dz \end{align}\]

The stem area density (SAD) is also similarly modeled by a beta distribution. The plant area density (PAD) is the sum of LAD and SAD.