This report is the result of the use of the python package bgc_md, as means to translate published models to a common language. The underlying yaml file was created by Verónika Ceballos-Núñez (Orcid ID: 0000-0002-0046-1160) on .
The model depicted in this document considers carbon allocation with a process based approach. It was originally described by Haverd et al. (2016).
| Name | Description | Unit |
|---|---|---|
| \(C_{L}\) | Leaf biomass | \(molC\cdot m^{-2}\) |
| \(C_{R}\) | Fine roots biomass | \(molC\cdot m^{-2}\) |
| \(C_{stem}\) | Trunk and coarse roots | \(molC\cdot m^{-2}\) |
| Name | Description |
|---|---|
| \(\alpha_{L}\) | carbon allocation coefficient, Heaviside step function that depends on C_L and C_R |
| \(\alpha_{R}\) | carbon allocation coefficient, Heaviside step function that depends on C_L and C_R |
| \(\alpha_{stem}\) | carbon allocation coefficient, Heaviside step function that depends on C_L and C_R |
| Name | Description | Unit |
|---|---|---|
| \(k_{L}\) | First-order rate constant | \(day^{-1}\) |
| \(k_{R}\) | First-order rate constant | \(day^{-1}\) |
| \(m_{stem}\) | Stem biomass turnover | \(molC\cdot m^{-2}\cdot day^{-1}\) |
| Name | Description | Expression |
|---|---|---|
| \(x\) | vector of states for vegetation | \(x=\left[\begin{matrix}C_{L}\\C_{R}\\C_{stem}\end{matrix}\right]\) |
| \(u\) | scalar function of photosynthetic inputs | \(u=F_{Cgrowth}\) |
| \(\beta\) | vector of partitioning coefficients of photosynthetically fixed carbon | \(\beta=\left[\begin{matrix}\alpha_{L}\\\alpha_{R}\\\alpha_{stem}\end{matrix}\right]\) |
| \(B\) | matrix of cycling rates | \(B=\left[\begin{matrix}- k_{L} -\frac{m_{stem}}{C_{stem}} & 0 & 0\\0 & - k_{R} -\frac{m_{stem}}{C_{stem}} & 0\\0 & 0 & - m_{stem}\end{matrix}\right]\) |
| \(f_{v}\) | the righthandside of the ode | \(f_{v}=u\beta + B x\) |
\(C_{L}: F_{Cgrowth}\cdot\alpha_{L}\)
\(C_{R}: F_{Cgrowth}\cdot\alpha_{R}\)
\(C_{stem}: F_{Cgrowth}\cdot\alpha_{stem}\)
\(C_{L}: \frac{C_{L}\cdot\left(C_{stem}\cdot k_{L} + m_{stem}\right)}{C_{stem}}\)
\(C_{R}: \frac{C_{R}\cdot\left(C_{stem}\cdot k_{R} + m_{stem}\right)}{C_{stem}}\)
\(C_{stem}: C_{stem}\cdot m_{stem}\)
\(C_L = \frac{F_{Cgrowth}^{2}\cdot\alpha_{L}\cdot\alpha_{stem}}{F_{Cgrowth}\cdot\alpha_{stem}\cdot k_{L} + m_{stem}^{2}}\)
\(C_R = \frac{F_{Cgrowth}^{2}\cdot\alpha_{R}\cdot\alpha_{stem}}{F_{Cgrowth}\cdot\alpha_{stem}\cdot k_{R} + m_{stem}^{2}}\)
\(C_stem = \frac{F_{Cgrowth}\cdot\alpha_{stem}}{m_{stem}}\)
Haverd, V., Smith, B., Raupach, M., Briggs, P., Nieradzik, L., Beringer, J., … Cleverly, J. (2016). Coupling carbon allocation with leaf and root phenology predicts treegrass partitioning along a savanna rainfall gradient. Biogeosciences, 13(3), 761–779. http://doi.org/10.5194/bg-13-761-2016