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 29/7/2015.
The model depicted in this document considers carbon allocation with a process based approach. It was originally described by King (1993).
forest
| Abbreviation | Source |
|---|---|
| Chosen based on the performance of Pinus radiata at Puruki, New Zeland | King (1993) |
| Name | Description | Unit |
|---|---|---|
| \(F\) | Foliage dry mass | \(kgC\cdot m^{-2}\) |
| \(R\) | Fine roots dry mass | \(kgC\cdot m^{-2}\) |
| \(W\) | Woody tissue dry mass | \(kgC\cdot m^{-2}\) |
| Name | Description | Expression | Unit |
|---|---|---|---|
| \(k\) | Radiation extinction coefficient of canopy | - | - |
| \(\Phi_{0}\) | Incident PAR | - | \(MJ\cdot m\cdot ^{-2}\cdot year^{-1}\) |
| \(\omega\) | Specific leaf area | - | \(m\cdot ^2\cdot kg^{-1}\) |
| \(\Phi\) | Annual photosynthetically active radiation (PAR) intercepted by the canopy | \(\Phi=\Phi_{0}\cdot\left(1 - e^{- F\cdot k\cdot\omega}\right)\) | \(MJ\cdot m\cdot ^{-2}\cdot year^{-1}\) |
| \(\epsilon\) | Light utilization coefficient | - | \(kg\cdot MJ^{-1}\) |
| \(G\) | Rate of biomass production per unit ground area | \(G=\Phi\cdot\epsilon\) | \(kg\cdot m^{-2}\cdot year^{-1}\) |
| Name | Description | Expression |
|---|---|---|
| \(\eta_{f}\) | Fraction of biomass production partitioned to leaves | - |
| \(\eta_{r}\) | Fraction of biomass production partitioned to roots | - |
| \(\eta_{w}\) | Fraction of biomass production partitioned to wood | \(\eta_{w}=-\eta_{f} -\eta_{r} + 1\) |
| Name | Description | Unit |
|---|---|---|
| \(\gamma_{f}\) | Senescence rate per unit foliage biomass | \(kg^{-1}\) |
| \(\gamma_{r}\) | Senescence rate per unit fine roots biomass | \(kg^{-1}\) |
| Name | Description | Expression |
|---|---|---|
| \(x\) | vector of states for vegetation | \(x=\left[\begin{matrix}F\\R\\W\end{matrix}\right]\) |
| \(u\) | scalar function of photosynthetic inputs | \(u=G\) |
| \(b\) | vector of partitioning coefficients of photosynthetically fixed carbon | \(b=\left[\begin{matrix}\eta_{f}\\\eta_{r}\\\eta_{w}\end{matrix}\right]\) |
| \(A\) | matrix of turnover (cycling) rates | \(A=\left[\begin{matrix}-\gamma_{f} & 0 & 0\\0 & -\gamma_{r} & 0\\0 & 0 & 0\end{matrix}\right]\) |
| \(f_{v}\) | the righthandside of the ode | \(f_{v}=u b + A x\) |
\(F: \Phi_{0}\cdot\epsilon\cdot\eta_{f}\cdot\left(1 - e^{- F\cdot k\cdot\omega}\right)\)
\(R: \Phi_{0}\cdot\epsilon\cdot\eta_{r}\cdot\left(1 - e^{- F\cdot k\cdot\omega}\right)\)
\(W: \Phi_{0}\cdot\epsilon\cdot\left(1 - e^{- F\cdot k\cdot\omega}\right)\cdot\left(-\eta_{f} -\eta_{r} + 1\right)\)
\(F: F\cdot\gamma_{f}\)
\(R: R\cdot\gamma_{r}\)
\(F = 0\)
\(R = 0\)
\(W = W\)
King, D. A. (1993). A model analysis of the influence of root and foliage allocation on forest production and competition between trees. Tree Physiology, 12(2), 119–135. http://doi.org/10.1093/treephys/12.2.119