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 Gu et al. (2010).
forest
| Name | Description | Unit |
|---|---|---|
| \(C_{S}\) | Carbon in stem | - |
| \(C_{R}\) | Carbon in root | - |
| \(C_{L}\) | Carbon in leaf | - |
| Name | Description | Unit |
|---|---|---|
| \(t\) | time step | \(year\) |
| \(NPP\) | Net Primary Production | - |
| \(L\) | Scalar light availability | - |
| \(W\) | Scalar water availability | - |
| Name | Description | Expression |
|---|---|---|
| \(N_{ava}\) | effect of nitrogen availability on carbon allocation | - |
| Name | Description | Expression |
|---|---|---|
| \(\Omega\) | Sensitivity of allocation to changes in resources availability. If =0, partitioning is determined by constant allocation fractions. | - |
| \(\epsilon_{S}\) | Parameter relative to vegetation type | - |
| \(\epsilon_{R}\) | Parameter relative to vegetation type | - |
| \(\epsilon_{L}\) | Parameter relative to vegetation type | \(\epsilon_{L}=-\epsilon_{R} -\epsilon_{S} + 1\) |
| \(a_{S}\) | Allocation fraction to stem | \(a_{S}=\frac{\Omega\cdot\left(- L - 0.5\cdot N_{ava} + 1.5\right) +\epsilon_{S}}{\Omega\cdot\left(- L - N_{ava} - W + 3\right) + 1}\) |
| \(a_{R}\) | Allocation fraction to root | \(a_{R}=\frac{\Omega\cdot\left(- 0.5\cdot N_{ava} - W + 1.5\right) +\epsilon_{R}}{\Omega\cdot\left(- L - N_{ava} - W + 3\right) + 1}\) |
| \(a_{L}\) | Allocation fraction to leaf | \(a_{L}=\frac{\epsilon_{L}}{\Omega\cdot\left(- L - N_{ava} - W + 3\right) + 1}\) |
| Name | Description | Unit |
|---|---|---|
| \(\gamma_{S}\) | Stem turnover rate | \(years\) |
| \(\gamma_{R}\) | Root turnover rate | \(years\) |
| \(\gamma_{L}\) | Stem turnover rate | \(years\) |
| Name | Description | Expression |
|---|---|---|
| \(x\) | vector of states for vegetation | \(x=\left[\begin{matrix}C_{S}\\C_{R}\\C_{L}\end{matrix}\right]\) |
| \(u\) | scalar function of photosynthetic inputs | \(u=NPP\) |
| \(b\) | vector of partitioning coefficients of photosynthetically fixed carbon | \(b=\left[\begin{matrix}a_{S}\\a_{R}\\a_{L}\end{matrix}\right]\) |
| \(A\) | matrix of cycling rates | \(A=\left[\begin{matrix}-\gamma_{S} & 0 & 0\\0 & -\gamma_{R} & 0\\0 & 0 & -\gamma_{L}\end{matrix}\right]\) |
| \(f_{v}\) | the righthandside of the ode | \(f_{v}=u b + A x\) |
\(C_{S}: \frac{NPP\cdot\left(\Omega\cdot\left(- L - 0.5\cdot N_{ava} + 1.5\right) +\epsilon_{S}\right)}{\Omega\cdot\left(- L - N_{ava} - W + 3\right) + 1}\)
\(C_{R}: \frac{NPP\cdot\left(\Omega\cdot\left(- 0.5\cdot N_{ava} - W + 1.5\right) +\epsilon_{R}\right)}{\Omega\cdot\left(- L - N_{ava} - W + 3\right) + 1}\)
\(C_{L}: \frac{NPP\cdot\left(-\epsilon_{R} -\epsilon_{S} + 1\right)}{\Omega\cdot\left(- L - N_{ava} - W + 3\right) + 1}\)
\(C_{S}: C_{S}\cdot\gamma_{S}\)
\(C_{R}: C_{R}\cdot\gamma_{R}\)
\(C_{L}: C_{L}\cdot\gamma_{L}\)
\(C_S = \frac{0.5\cdot NPP\cdot\left(2.0\cdot L\cdot\Omega + N_{ava}\cdot\Omega - 3.0\cdot\Omega - 2.0\cdot\epsilon_{S}\right)}{\gamma_{S}\cdot\left(L\cdot\Omega + N_{ava}\cdot\Omega +\Omega\cdot W - 3.0\cdot\Omega - 1.0\right)}\)
\(C_R = \frac{0.5\cdot NPP\cdot\left(N_{ava}\cdot\Omega + 2.0\cdot\Omega\cdot W - 3.0\cdot\Omega - 2.0\cdot\epsilon_{R}\right)}{\gamma_{R}\cdot\left(L\cdot\Omega + N_{ava}\cdot\Omega +\Omega\cdot W - 3.0\cdot\Omega - 1.0\right)}\)
\(C_L = \frac{NPP\cdot\left(\epsilon_{R} +\epsilon_{S} - 1.0\right)}{\gamma_{L}\cdot\left(L\cdot\Omega + N_{ava}\cdot\Omega +\Omega\cdot W - 3.0\cdot\Omega - 1.0\right)}\)
Gu, F., Zhang, Y., Tao, B., Wang, Q., Yu, G., Zhang, L., & Li, K. (2010). Modeling the effects of nitrogen deposition on carbon budget in two temperate forests. Ecological Complexity, 7(2), 139–148. http://doi.org/10.1016/j.ecocom.2010.04.002