Calculating untrimmed biomass
Two calculations were required to calculate the dry biomass of the untrimmed part (i.e. that still standing): one for the small branches accompanied with leaves and twigs and the other for the large branches. The untrimmed biomass is the sum of the two results:
B untrimmed dry = B untrimmed dry branch + B dry section
Each section i of the large branches was considered as a cylinder of volume (Smalian’s formula):
Vi =π/8 Li (D21i + D22i)
Where Vi is the volume of section i, Li its length, and D1i and D2i are the diameters of the two extremities of section i. The dry biomass of the large branches is the product of mean wood density and the total volume of the large branches:
\begin{equation} \text{B\ }\text{dry\ section}\ =\ R\ \times\sum_{i}\text{Vi}\nonumber \\ \end{equation}
Where the sum corresponds to all the sections in the large branches, and where mean wood density is calculated by:
\begin{equation} R\ =\ \frac{B_{\text{\ dry\ wood}}^{\text{aliquot}}}{\text{V\ }_{\text{fresh\ wood}}^{\text{aliquot}}}\nonumber \\ \end{equation}
The dry biomass of small untrimmed branches, twigs and leaves was calculated from the regression model developed between the basal diameter of the trimmed branches and biomass of trimmed branches, twigs and leaves. This model is established by following the same procedure as for the development of an allometric model. Power type equations were used:
B dry branch = a + bDc
Where a, b and c are model parameters and D branch basal diameter. Using a model of this type, the dry biomass of the untrimmed branches and their components (twigs and leaves) is:
B untrimmed dry branch=\({\sum_{j}{(a\ +\ bD}}_{j}^{c}\) )
Where the sum is all the untrimmed small branches and their components and Dj is the basal diameter of the branch j (Picard et al ., 2012).