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 14/3/2016.
The model depicted in this document considers carbon allocation with a process based approach. It was originally described by Wang, Law, & Pak (2010).
global
| Abbreviation | Source |
|---|---|
| Evergreen needle leaf forest | Wang et al. (2010) |
| Evergreen broadleaf forest | @Wang2010Biogeosciences |
| Deciduous needle leaf forest | Wang et al. (2010) |
| Deciduous broadleaf forest | @Wang2010Biogeosciences |
| Mixed forest | Wang et al. (2010) |
| Shrub land (open and close shrubland) | Wang et al. (2010) |
| Woddy savannah | Wang et al. (2010) |
| Savannah | Wang et al. (2010) |
| Grassland | Wang et al. (2010) |
| Crop land (cropland mosaic was aggregated into this term) | Wang et al. (2010) |
| Barren or sparse vegetation | Wang et al. (2010) |
| Name | Description |
|---|---|
| \(C_{leaf}\) | Plant (carbon) pool Leaf |
| \(C_{root}\) | Plant (carbon) pool Root |
| \(C_{wood}\) | Plant (carbon) pool Wood |
| Name | Description | Expression | Unit |
|---|---|---|---|
| \(\Delta_{t}\) | Time step of model integration | - | \(d\) |
| \(N_{min}\) | Amount of mineral N in soil | - | \(gN\cdot m^{-2}\) |
| \(P_{lab}\) | Amount of labile P in soil | - | \(gP\cdot m^{-2}\) |
| \(F_{nupmin}\) | Minimum amount of N uptake required to sustain a given NPP | - | - |
| \(F_{pupmin}\) | Minimum amount of P uptake required to sustain a given NPP | - | - |
| \(x_{nup}\) | Nitrogen uptake limitation on NPP | \(x_{nup}=\min\left(1,\frac{N_{min}}{\Delta_{t}\cdot F_{nupmin}}\right)\) | - |
| \(x_{pup}\) | Phosphorus uptake limitation on NPP | \(x_{pup}=\min\left(1,\frac{P_{lab}}{\Delta_{t}\cdot F_{pupmin}}\right)\) | - |
| \(x_{npup}\) | Nutrient uptake limiting factor | \(x_{npup}=\min\left(x_{nup}, x_{pup}\right)\) | - |
| \(n_{leaf}\) | N:C ratio of leaf biomass | - | \(gN/gC\) |
| \(p_{leaf}\) | P:C ratio of leaf biomass | - | \(gP/gC\) |
| \(k_{n}\) | Empirical constant | - | \(gN\cdot (gC)^{-1}\) |
| \(k_{p}\) | Empirical constant | - | \(gP\cdot (gC)^{-1}\) |
| \(x_{nleaf}\) | \(x_{nleaf}=\frac{n_{leaf}}{k_{n} + n_{leaf}}\) | - | |
| \(x_{pleaf}\) | \(x_{pleaf}=\frac{p_{leaf}}{k_{p} + p_{leaf}}\) | - | |
| \(x_{npleaf}\) | Nutrient concentration limiting factor | \(x_{npleaf}=\min\left(x_{nleaf}, x_{pleaf}\right)\) | - |
| \(F_{cmax}\) | Nutrient unlimited NPP | - | \(gC\cdot m^{-2}\cdot d^{-1}\) |
| \(F_{c}\) | Net Primary Productivity (flux) | \(F_{c}=F_{cmax}\cdot x_{npleaf}\cdot x_{npup}\) | \(gC\cdot m^{-2}\cdot d^{-1}\) |
| Name | Description |
|---|---|
| \(a_{leaf}\) | Fraction of NPP allocated to plant pool Leaf |
| \(a_{root}\) | Fraction of NPP allocated to plant pool Root |
| \(a_{wood}\) | Fraction of NPP allocated to plant pool Wood |
| Name | Description | Expression | Unit |
|---|---|---|---|
| \(x\) | vector of states for vegetation | \(x=\left[\begin{matrix}C_{leaf}\\C_{root}\\C_{wood}\end{matrix}\right]\) | - |
| \(u\) | scalar function of photosynthetic inputs | \(u=F_{c}\) | - |
| \(b\) | vector of partitioning coefficients of photosynthetically fixed carbon | \(b=\left[\begin{matrix}a_{leaf}\\a_{root}\\a_{wood}\end{matrix}\right]\) | - |
| \(A\) | matrix of turnover (cycling) rates | \(A=\left[\begin{matrix}-\mu_{leaf} & 0 & 0\\0 & -\mu_{root} & 0\\0 & 0 & -\mu_{wood}\end{matrix}\right]\) | - |
| \(f_{v}\) | the righthandside of the ode | \(f_{v}=u b + A x\) | \(gC\cdot m^{-2}\cdot d^{-1}\) |
\(C_{leaf}: F_{cmax}\cdot a_{leaf}\cdot\min\left(\frac{n_{leaf}}{k_{n} + n_{leaf}},\frac{p_{leaf}}{k_{p} + p_{leaf}}\right)\cdot\min\left(1,\frac{N_{min}}{\Delta_{t}\cdot F_{nupmin}},\frac{P_{lab}}{\Delta_{t}\cdot F_{pupmin}}\right)\)
\(C_{root}: F_{cmax}\cdot a_{root}\cdot\min\left(\frac{n_{leaf}}{k_{n} + n_{leaf}},\frac{p_{leaf}}{k_{p} + p_{leaf}}\right)\cdot\min\left(1,\frac{N_{min}}{\Delta_{t}\cdot F_{nupmin}},\frac{P_{lab}}{\Delta_{t}\cdot F_{pupmin}}\right)\)
\(C_{wood}: F_{cmax}\cdot a_{wood}\cdot\min\left(\frac{n_{leaf}}{k_{n} + n_{leaf}},\frac{p_{leaf}}{k_{p} + p_{leaf}}\right)\cdot\min\left(1,\frac{N_{min}}{\Delta_{t}\cdot F_{nupmin}},\frac{P_{lab}}{\Delta_{t}\cdot F_{pupmin}}\right)\)
\(C_{leaf}: C_{leaf}\cdot\mu_{leaf}\)
\(C_{root}: C_{root}\cdot\mu_{root}\)
\(C_{wood}: C_{wood}\cdot\mu_{wood}\)
\(C_leaf = \frac{F_{cmax}\cdot a_{leaf}\cdot\min\left(\frac{n_{leaf}}{k_{n} + n_{leaf}},\frac{p_{leaf}}{k_{p} + p_{leaf}}\right)\cdot\min\left(1,\frac{N_{min}}{\Delta_{t}\cdot F_{nupmin}},\frac{P_{lab}}{\Delta_{t}\cdot F_{pupmin}}\right)}{\mu_{leaf}}\)
\(C_root = \frac{F_{cmax}\cdot a_{root}\cdot\min\left(\frac{n_{leaf}}{k_{n} + n_{leaf}},\frac{p_{leaf}}{k_{p} + p_{leaf}}\right)\cdot\min\left(1,\frac{N_{min}}{\Delta_{t}\cdot F_{nupmin}},\frac{P_{lab}}{\Delta_{t}\cdot F_{pupmin}}\right)}{\mu_{root}}\)
\(C_wood = \frac{F_{cmax}\cdot a_{wood}\cdot\min\left(\frac{n_{leaf}}{k_{n} + n_{leaf}},\frac{p_{leaf}}{k_{p} + p_{leaf}}\right)\cdot\min\left(1,\frac{N_{min}}{\Delta_{t}\cdot F_{nupmin}},\frac{P_{lab}}{\Delta_{t}\cdot F_{pupmin}}\right)}{\mu_{wood}}\)
Wang, Y. P., Law, R. M., & Pak, B. (2010). A global model of carbon, nitrogen and phosphorus cycles for the terrestrial biosphere. Biogeosciences, 7(7), 2261–2282. http://doi.org/10.5194/bg-7-2261-2010