General Overview
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 3/5/2018.
About the model
The model depicted in this document considers carbon allocation with a process based approach. It was originally described by Arora & Boer (2005).
Space Scale
regional
state_variables
| \(C_{leaf}\) |
Amount of carbon for the leaf |
\(kgC\cdot m^{-2}\) |
| \(C_{stem}\) |
Amount of carbon for the stem |
\(kgC\cdot m^{-2}\) |
| \(C_{roots}\) |
Amount of carbon for the root |
\(kgC\cdot m^{-2}\) |
additional_variables
| \(k_{leaf}\) |
|
- |
| \(cn_{leaf}\) |
|
- |
| \(k_{stem}\) |
|
- |
| \(cn_{stem}\) |
|
- |
| \(k_{roots}\) |
|
- |
| \(cn_{roots}\) |
|
- |
| \(gt\) |
Function of Q_10 and temperature |
- |
| \(teta\) |
|
- |
photosynthetic_parameters
| \(t\) |
time step |
\(year\) |
| \(GPP\) |
Carbon gain via photosynthesis (Gross Primary Productivity, GPP) |
\(KgC\cdot m^{−2}\cdot yr^{−1}\) |
| \(NPP\) |
Net primary Productivity (NPP) |
\(KgC\cdot m^{−2}\cdot yr^{−1}\) |
respiration
| \(R_{leaf}\) |
Leaf respiration |
\(R_{leaf}=\frac{C_{leaf}\cdot gt\cdot k_{leaf}\cdot teta}{cn_{leaf}}\) |
| \(R_{stem}\) |
Stem respiration |
\(R_{stem}=\frac{C_{stem}\cdot gt\cdot k_{stem}\cdot teta}{cn_{stem}}\) |
| \(R_{roots}\) |
Roots respiration |
\(R_{roots}=\frac{C_{roots}\cdot gt\cdot k_{roots}\cdot teta}{cn_{roots}}\) |
partitioning
| \(Allo_{fact stem}\) |
|
- |
- |
| \(Allo_{fact roots}\) |
|
- |
- |
| \(Allo_{fact leaf}\) |
|
\(Allo_{fact leaf}=- Allo_{fact roots} - Allo_{fact stem} + 1\) |
- |
| \(a_{L}\) |
Parameter introduced by the author of this entry in order to summarize equations on the paper. |
\(a_{L}=\begin{cases} Allo_{fact leaf}\cdot GPP - R_{leaf} &\text{for}\: NPP < 0\\Allo_{fact leaf}\cdot NPP &\text{for}\: NPP > 0\end{cases}\) |
- |
| \(a_{S}\) |
Parameter introduced by the author of this entry in order to summarize equations on the paper. |
\(a_{S}=\begin{cases} Allo_{fact stem}\cdot GPP - R_{stem} &\text{for}\: NPP < 0\\Allo_{fact stem}\cdot NPP &\text{for}\: NPP > 0\end{cases}\) |
- |
| \(a_{R}\) |
Parameter introduced by the author of this entry in order to summarize equations on the paper. |
\(a_{R}=\begin{cases} Allo_{fact roots}\cdot GPP - R_{roots} &\text{for}\: NPP < 0\\Allo_{fact roots}\cdot NPP &\text{for}\: NPP > 0\end{cases}\) |
- |
litter
| \(Y_{leaf}\) |
Litter production |
\(year\) |
| \(Y_{stem}\) |
Litter production |
\(year\) |
| \(Y_{roots}\) |
Litter production |
\(year\) |
components
| \(x\) |
vector of states for vegetation |
\(x=\left[\begin{matrix}C_{leaf}\\C_{stem}\\C_{roots}\end{matrix}\right]\) |
| \(u\) |
Vector of functions of photosynthetic inputs |
\(u=\left[\begin{matrix}a_{L}\\a_{S}\\a_{R}\end{matrix}\right]\) |
| \(A\) |
matrix of cycling rates |
\(A=\left[\begin{matrix}-\frac{1}{Y_{leaf}} & 0 & 0\\0 & -\frac{1}{Y_{stem}} & 0\\0 & 0 & -\frac{1}{Y_{roots}}\end{matrix}\right]\) |
| \(f_{v}\) |
the righthandside of the ode |
\(f_{v}=A x + u\) |
Pool model representation
Figure 1: Pool model representation
\(C_{leaf}: \begin{cases} -\frac{C_{leaf}\cdot gt\cdot k_{leaf}\cdot teta}{cn_{leaf}} + GPP\cdot\left(- Allo_{fact roots} - Allo_{fact stem} + 1\right) &\text{for}\: NPP < 0\\NPP\cdot\left(- Allo_{fact roots} - Allo_{fact stem} + 1\right) &\text{for}\: NPP > 0\end{cases}\)
\(C_{stem}: \begin{cases} Allo_{fact stem}\cdot GPP -\frac{C_{stem}\cdot gt\cdot k_{stem}\cdot teta}{cn_{stem}} &\text{for}\: NPP < 0\\Allo_{fact stem}\cdot NPP &\text{for}\: NPP > 0\end{cases}\)
\(C_{roots}: \begin{cases} Allo_{fact roots}\cdot GPP -\frac{C_{roots}\cdot gt\cdot k_{roots}\cdot teta}{cn_{roots}} &\text{for}\: NPP < 0\\Allo_{fact roots}\cdot NPP &\text{for}\: NPP > 0\end{cases}\)
Output fluxes
\(C_{leaf}: \frac{C_{leaf}}{Y_{leaf}}\)
\(C_{stem}: \frac{C_{stem}}{Y_{stem}}\)
\(C_{roots}: \frac{C_{roots}}{Y_{roots}}\)
References