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 21/1/2016.
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
global
Available parameter values
Information on given parameter sets
| Original dataset of the publication |
Eastern US and Germany, cold broadleaf deciduous |
Arora & Boer (2005) |
state_variables
| \(C_{L}\) |
Amount of carbon for the leaf |
\(kgC\cdot m^{-2}\) |
| \(C_{S}\) |
Amount of carbon for the stem |
\(kgC\cdot m^{-2}\) |
| \(C_{R}\) |
Amount of carbon for the root |
\(kgC\cdot m^{-2}\) |
photosynthetic_parameters
| \(G\) |
Carbon gain via photosynthesis (Gross Primary Productivity, GPP) |
- |
| \(N\) |
Net primary Productivity (NPP) |
\(N=G - R_{gL} - R_{gR} - R_{gS} - R_{mL} - R_{mR} - R_{mS}\) |
| \(LAI\) |
Leaf Area Index |
- |
| \(k_{n}\) |
PFT-dependent light extinction coefficient |
- |
| \(L\) |
Light availability (scalar index between 0 and 1) |
\(L=e^{- LAI\cdot k_{n}}\) |
water_availability
| \(\theta_{i}\) |
Volumetric soil moisture content |
- |
| \(\theta_{field}\) |
Field capacity |
- |
| \(\theta_{wilt}\) |
Wilting point |
- |
| \(W_{i}\) |
Availability of water in soil layer i. Weighted by the fraction of roots present in each soil layer |
\(W_{i}=\max\left(0,\min\left(1,\frac{\theta_{i} -\theta_{wilt}}{\theta_{field} -\theta_{wilt}}\right)\right)\) |
| \(W\) |
Averaged soil water availability index |
- |
respiration_fluxes
| \(t\) |
time step |
\(year\) |
| \(R_{gL}\) |
Growth respiration flux for the leaves |
- |
| \(R_{mL}\) |
Maintenance respiration flux for the leaves |
- |
| \(R_{gS}\) |
Growth respiration flux for the stem |
- |
| \(R_{mS}\) |
Maintenance respiration flux for the stem |
- |
| \(R_{gR}\) |
Growth respiration flux for the root |
- |
| \(R_{mR}\) |
Maintenance respiration flux for the root |
- |
| \(R_{hD}\) |
Heterotrophic respiration from litter (debris) |
- |
| \(R_{hH}\) |
Heterotrophic respiration from soil carbon (humus) |
- |
allocation_fractions
| \(\epsilon_{L}\) |
PFT-dependent parameter for leaf |
- |
| \(\epsilon_{S}\) |
PFT-dependent parameter for stem |
- |
| \(\epsilon_{R}\) |
PFT-dependent parameter for root |
\(\epsilon_{R}=-\epsilon_{L} -\epsilon_{S} + 1\) |
| \(\omega\) |
PFT-dependent parameter |
- |
| \(a_{S}\) |
Stem allocation fraction |
\(a_{S}=\frac{\epsilon_{S} +\omega\cdot\left(1 - L\right)}{\omega\cdot\left(- L - W + 2\right) + 1}\) |
| \(a_{R}\) |
Root allocation fration |
\(a_{R}=\frac{\epsilon_{R} +\omega\cdot\left(1 - W\right)}{\omega\cdot\left(- L - W + 2\right) + 1}\) |
| \(a_{L}\) |
Leaf allocation fraction |
\(a_{L}=- a_{R} - a_{S} + 1\) |
allocation_coefficients
| \(A_{S}\) |
Amount of carbon allocated to the stem |
\(A_{S}=\begin{cases} G\cdot a_{S} &\text{for}\: N < 0\\N\cdot a_{S} + R_{gS} + R_{mS} &\text{for}\: N > 0\end{cases}\) |
| \(A_{R}\) |
Amount of carbon allocated to the root |
\(A_{R}=\begin{cases} G\cdot a_{R} &\text{for}\: N < 0\\N\cdot a_{R} + R_{gR} + R_{mR} &\text{otherwise}\end{cases}\) |
temperature
| \(T_{air}\) |
Temperature of the air |
\(°C\) |
| \(T_{cold}\) |
Cold temperature threshold for a PFT below which leaf loss begins to occur |
\(°C\) |
| \(b_{T}\) |
Parameter that describes sensitivity of leaf loss to temp. below the T\(_{cold}\) |
- |
| \(\beta_{T}\) |
Temperature measure (varies between 0 and 1) |
- |
litter_fluxes
| \(D_{L}\) |
Litter loss from the leaves |
\(D_{L}=C_{L}\cdot\left(\gamma_{N} +\gamma_{T} +\gamma_{W}\right)\) |
| \(D_{S}\) |
Litter loss from the stem |
\(D_{S}=C_{S}\cdot\gamma_{S}\) |
| \(D_{R}\) |
Litter loss from the root |
\(D_{R}=C_{R}\cdot\gamma_{R}\) |
components
| \(x\) |
vector of states for vegetation |
\(x=\left[\begin{matrix}C_{L}\\C_{S}\\C_{R}\end{matrix}\right]\) |
| \(u\) |
Vector of functions of photosynthetic inputs |
\(u=\left[\begin{matrix}G - R_{mL}\\a_{S}\\a_{R}\end{matrix}\right]\) |
| \(A\) |
matrix of cycling rates |
\(A=\left[\begin{matrix}-\gamma_{N} -\gamma_{T} -\gamma_{W} & 0 & 0\\0 & - R_{gS} - R_{mS} -\gamma_{S} & 0\\0 & 0 & - R_{gR} - R_{mR} -\gamma_{R}\end{matrix}\right]\) |
| \(f_{v}\) |
the righthandside of the ode |
\(f_{v}=A x + u\) |
Pool model representation
Figure 1: Pool model representation
\(C_{L}: G - R_{mL}\)
\(C_{S}: \frac{\epsilon_{S} +\omega\cdot\left(1 - e^{- LAI\cdot k_{n}}\right)}{\omega\cdot\left(- W + 2 - e^{- LAI\cdot k_{n}}\right) + 1}\)
\(C_{R}: \frac{-\epsilon_{L} -\epsilon_{S} +\omega\cdot\left(1 - W\right) + 1}{\omega\cdot\left(- W + 2 - e^{- LAI\cdot k_{n}}\right) + 1}\)
Output fluxes
\(C_{L}: C_{L}\cdot\left(\gamma_{N} +\gamma_{Tmax}\cdot\left(1 -\beta_{T}\right)^{b_{T}} +\gamma_{W}\right)\)
\(C_{S}: C_{S}\cdot\left(R_{gS} + R_{mS} +\gamma_{S}\right)\)
\(C_{R}: C_{R}\cdot\left(R_{gR} + R_{mR} +\gamma_{R}\right)\)
\(C_L = \frac{G - R_{mL}}{\gamma_{N} +\gamma_{Tmax}\cdot\left(1 -\beta_{T}\right)^{b_{T}} +\gamma_{W}}\)
\(C_S = \frac{-\epsilon_{S}\cdot e^{LAI\cdot k_{n}} -\omega\cdot e^{LAI\cdot k_{n}} +\omega}{R_{gS}\cdot W\cdot\omega\cdot e^{LAI\cdot k_{n}} - 2\cdot R_{gS}\cdot\omega\cdot e^{LAI\cdot k_{n}} + R_{gS}\cdot\omega - R_{gS}\cdot e^{LAI\cdot k_{n}} + R_{mS}\cdot W\cdot\omega\cdot e^{LAI\cdot k_{n}} - 2\cdot R_{mS}\cdot\omega\cdot e^{LAI\cdot k_{n}} + R_{mS}\cdot\omega - R_{mS}\cdot e^{LAI\cdot k_{n}} + W\cdot\gamma_{S}\cdot\omega\cdot e^{LAI\cdot k_{n}} - 2\cdot\gamma_{S}\cdot\omega\cdot e^{LAI\cdot k_{n}} +\gamma_{S}\cdot\omega -\gamma_{S}\cdot e^{LAI\cdot k_{n}}}\)
\(C_R = \frac{\left(W\cdot\omega +\epsilon_{L} +\epsilon_{S} -\omega - 1\right)\cdot e^{LAI\cdot k_{n}}}{R_{gR}\cdot W\cdot\omega\cdot e^{LAI\cdot k_{n}} - 2\cdot R_{gR}\cdot\omega\cdot e^{LAI\cdot k_{n}} + R_{gR}\cdot\omega - R_{gR}\cdot e^{LAI\cdot k_{n}} + R_{mR}\cdot W\cdot\omega\cdot e^{LAI\cdot k_{n}} - 2\cdot R_{mR}\cdot\omega\cdot e^{LAI\cdot k_{n}} + R_{mR}\cdot\omega - R_{mR}\cdot e^{LAI\cdot k_{n}} + W\cdot\gamma_{R}\cdot\omega\cdot e^{LAI\cdot k_{n}} - 2\cdot\gamma_{R}\cdot\omega\cdot e^{LAI\cdot k_{n}} +\gamma_{R}\cdot\omega -\gamma_{R}\cdot e^{LAI\cdot k_{n}}}\)
References