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 Pavlick, Drewry, Bohn, Reu, & Kleidon (2013).
global
| Name | Description | Unit |
|---|---|---|
| \(C_{A}\) | Carbon in stored assimilates | \(gC\cdot m^{-2}\) |
| \(C_{L}\) | Carbon in leaves | \(gC\cdot m^{-2}\) |
| \(C_{R}\) | Carbon in fine roots | \(gC\cdot m^{-2}\) |
| \(C_{WL}\) | Carbon in aboveground wood (branches and stems) | \(gC\cdot m^{-2}\) |
| \(C_{WR}\) | Carbon in belowground wood (coarse roots) | \(gC\cdot m^{-2}\) |
| \(C_{S}\) | Carbon in seeds (reproductive tisses) | \(gC\cdot m^{-2}\) |
| Name | Description | Unit |
|---|---|---|
| \(C_{RES S}\) | Growth respiration coefficient | \(gC\cdot gC^{-1}\) |
| \(C_{RES L}\) | Growth respiration coefficient | \(gC\cdot gC^{-1}\) |
| \(C_{RES R}\) | Growth respiration coefficient | \(gC\cdot gC^{-1}\) |
| \(C_{RES WL}\) | Growth respiration coefficient | \(gC\cdot gC^{-1}\) |
| \(C_{RES WR}\) | Growth respiration coefficient | \(gC\cdot gC^{-1}\) |
| Name | Description | Expression | Unit |
|---|---|---|---|
| \(A_{S}\) | Allocation fraction to seeds | \(A_{S}=\frac{f_{SEED}\cdot t_{5}}{t_{5} + t_{6} + t_{7} + t_{8}}\) | - |
| \(A_{L}\) | Allocation fraction to leaves | \(A_{L}=\frac{f_{GROW}\cdot t_{6}\cdot\left(1 - t_{9}\right)}{t_{5} + t_{6} + t_{7} + t_{8}}\) | - |
| \(A_{R}\) | Allocation fraction to fine roots | \(A_{R}=\frac{f_{GROW}\cdot t_{7}\cdot\left(1 - t_{10}\right)}{t_{5} + t_{6} + t_{7} + t_{8}}\) | - |
| \(A_{WL}\) | Allocation fraction to aboveground wood | \(A_{WL}=\frac{f_{GROW}\cdot f_{VEG}\cdot t_{6}\cdot t_{9}}{t_{5} + t_{6} + t_{7} + t_{8}}\) | - |
| \(A_{WR}\) | Allocation fraction to belowground wood | \(A_{WR}=\frac{f_{GROW}\cdot f_{VEG}\cdot t_{10}\cdot t_{7}}{t_{5} + t_{6} + t_{7} + t_{8}}\) | - |
| \(\tau_{S}\) | Seeds turnover rate | - | \(days\) |
| \(\tau_{L}\) | Stem turnover rate | - | \(days\) |
| \(\tau_{R}\) | Fine roots turnover rate | - | \(days\) |
| \(\tau_{WL}\) | Aboveground wood turnover rate | - | \(days\) |
| \(\tau_{WR}\) | Belowground wood turnover rate | - | \(days\) |
| Name | Description | Expression |
|---|---|---|
| \(x\) | vector of states for vegetation | \(x=\left[\begin{matrix}C_{A}\\C_{S}\\C_{L}\\C_{R}\\C_{WL}\\C_{WR}\end{matrix}\right]\) |
| \(u\) | scalar function of photosynthetic inputs | \(u=NPP\) |
| \(b\) | vector of partitioning coefficients of photosynthetically fixed carbon | \(b=\left[\begin{matrix}1\\0\\0\\0\\0\\0\end{matrix}\right]\) |
| \(A\) | matrix of cycling rates | \(A=\left[\begin{matrix}- A_{L}\cdot\left(1 - C_{RES L}\right) - A_{R}\cdot\left(1 - C_{RES R}\right) - A_{S}\cdot\left(1 - C_{RES S}\right) - A_{WL}\cdot\left(1 - C_{RES WL}\right) - A_{WR}\cdot\left(1 - C_{RES WR}\right) &\frac{f_{GERM}\cdot\gamma_{GERM}}{\max\left(k_{GERM}, p\right)} & 0 & 0 & 0 & 0\\A_{S}\cdot\left(1 - C_{RES S}\right) & -\frac{f_{GERM}\cdot\gamma_{GERM}}{\max\left(k_{GERM}, p\right)} -\frac{1}{\tau_{S}} & 0 & 0 & 0 & 0\\A_{L}\cdot\left(1 - C_{RES L}\right) & 0 & -\frac{1}{\tau_{L}} & 0 & 0 & 0\\A_{R}\cdot\left(1 - C_{RES R}\right) & 0 & 0 & -\frac{1}{\tau_{R}} & 0 & 0\\A_{WL}\cdot\left(1 - C_{RES WL}\right) & 0 & 0 & 0 & -\frac{1}{\tau_{WL}} & 0\\A_{WR}\cdot\left(1 - C_{RES WR}\right) & 0 & 0 & 0 & 0 & -\frac{1}{\tau_{WR}}\end{matrix}\right]\) |
| \(f_{v}\) | the righthandside of the ode | \(f_{v}=u b + A x\) |
\(C_{A}: GPP - RES_{a}\)
\(C_{S}: \frac{C_{S}}{\tau_{S}}\)
\(C_{L}: \frac{C_{L}}{\tau_{L}}\)
\(C_{R}: \frac{C_{R}}{\tau_{R}}\)
\(C_{WL}: \frac{C_{WL}}{\tau_{WL}}\)
\(C_{WR}: \frac{C_{WR}}{\tau_{WR}}\)
\(C_{A} \rightarrow C_{S}: -\frac{C_{A}\cdot f_{SEED}\cdot t_{5}\cdot\left(C_{RES S} - 1\right)}{t_{5} + t_{6} + t_{7} + t_{8}}\)
\(C_{A} \rightarrow C_{L}: \frac{C_{A}\cdot f_{GROW}\cdot t_{6}\cdot\left(C_{RES L} - 1\right)\cdot\left(t_{9} - 1\right)}{t_{5} + t_{6} + t_{7} + t_{8}}\)
\(C_{A} \rightarrow C_{R}: \frac{C_{A}\cdot f_{GROW}\cdot t_{7}\cdot\left(C_{RES R} - 1\right)\cdot\left(t_{10} - 1\right)}{t_{5} + t_{6} + t_{7} + t_{8}}\)
\(C_{A} \rightarrow C_{WL}: \frac{C_{A}\cdot f_{GROW}\cdot t_{6}\cdot t_{9}\cdot\left(1 - e^{0.5\cdot C_{L}\cdot SLA}\right)\cdot\left(C_{RES WL} - 1\right)\cdot e^{- 0.5\cdot C_{L}\cdot SLA}}{t_{5} + t_{6} + t_{7} + t_{8}}\)
\(C_{A} \rightarrow C_{WR}: \frac{C_{A}\cdot f_{GROW}\cdot t_{10}\cdot t_{7}\cdot\left(1 - e^{0.5\cdot C_{L}\cdot SLA}\right)\cdot\left(C_{RES WR} - 1\right)\cdot e^{- 0.5\cdot C_{L}\cdot SLA}}{t_{5} + t_{6} + t_{7} + t_{8}}\)
\(C_{S} \rightarrow C_{A}: \frac{10^{\frac{4}{t_{4}^{4}}}\cdot C_{S}\cdot f_{GERM}}{\max\left(k_{GERM}, p\right)}\)
Pavlick, R., Drewry, D. T., Bohn, K., Reu, B., & Kleidon, A. (2013). The jena diversity-dynamic global vegetation model (jedi-dgvm): A diverse approach to representing terrestrial biogeography and biogeochemistry based on plant functional trade-offs. Biogeosciences, 10(6), 4137–4177. http://doi.org/10.5194/bg-10-4137-2013