The subscript \(i\) refers to optical sensor rings (\(i=1,\dots,5\)), and the subscript \(j\) refers to observational pairs (\(j=1,\dots,N_{obs}\)). \(B_{ij}\) is the \(j^{th}\) below-canopy observation, \(i^{th}\) ring, and \(A_{ij}\) is its corresponding above canopy reading.
\(L_j\) is the leaf area index calculated for an individual A/B pair :
\[L_j=2\sum_{i=1}^5 K_{ij}W_i\]\(K_{ij}\) is the contact value for the pair (reported with label CNTCT).
\[K_{ij} =-\frac{\operatorname{Ln}{\frac{B_{ij}}{A_{ij}}}}{S_i}\]:::{.card title = “Preamble variables”} * SMP: sample size (\(N_{obs}\)) * SEL: standard error of the leaf area index value * SEM: standard error of the mean tilt angle * DIFN: Diffuse non-interceptance (D) is the fraction of sky radiation that will penetrate the canopy, averaged over the hemisphere :::
The weighting factors for LAI and DIFN work out to be (when no rings are masked):
| \(\theta_i\) | \(d\theta_i\) | \(W_i\) | \(W'_i\) |
|---|---|---|---|
| 7 | 12.2 | 0.041 | 0.033 |
| 23 | 12.2 | 0.131 | 0.097 |
| 38 | 11.8 | 0.201 | 0.127 |
| 53 | 13.2 | 0.290 | 0.141 |
| 68 | 13.2 | 0.337 | 0.102 |