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 16/9/2016.
The model depicted in this document considers carbon allocation with a process based approach. It was originally described by Williams, Schwarz, Law, Irvine, & Kurpius (2005).
Deciduous forest, Phenology
All C fixed during a day is either released -autotrophic respiration (Ra)- or allocated to tissue pools (C_f, C_w, C_r), R_a is not directly temperature sensitive, Phenology -> Timing of leaf out controlled by simple growing degree day model, and leaf-fall by a min. temperature threshold., Maximum amount of C that can be allocated to leaves is limited by the parameter C_fmax, All C losses are via mineralization (no dissolved losses)
deciduous forest
| Abbreviation | Description | Source |
|---|---|---|
| param_vals | NPP value was given per year. p14, p15 and p16 values not given in publication | Williams et al. (2005) |
| Abbreviation | Description | Source |
|---|---|---|
| init_vals | C_lab values not provided in publication | Williams et al. (2005) |
| Name | Description | Unit |
|---|---|---|
| \(C_{f}\) | Foliar C mass | \(gC\cdot m^{-2}\) |
| \(C_{lab}\) | Labile C mass | \(gC\cdot m^{-2}\) |
| \(C_{w}\) | Wood C mass | \(gC\cdot m^{-2}\) |
| \(C_{r}\) | Fine root C mass | \(gC\cdot m^{-2}\) |
| Name | Description | Unit |
|---|---|---|
| \(NPP\) | \(gC\cdot m^{-2}\cdot day^{-1}\) |
| Name | Description | Unit |
|---|---|---|
| \(p_{2}\) | Fraction of GPP respired | - |
| \(p_{16}\) | Fraction of labile transfers respired | \(day^{-1}\) |
| Name | Description |
|---|---|
| \(p_{3}\) | Fraction of NPP partitioned to foliage |
| \(p_{4}\) | Fraction of NPP partitioned to roots |
| Name | Description | Unit |
|---|---|---|
| \(p_{5}\) | Turnover rate of foliage | \(day^{-1}\) |
| \(p_{6}\) | Turnover rate of wood | \(day^{-1}\) |
| \(p_{7}\) | Turnover rate of roots | \(day^{-1}\) |
| \(p_{14}\) | Fraction of leaf loss transferred to litter | - |
| \(p_{15}\) | Turnover rate of labile carbon | \(day^{-1}\) |
| Name | Description | Expression | Unit |
|---|---|---|---|
| \(t\) | time | - | \(day\) |
| \(p_{10}\) | Parameter in exponential term of temperature dependent rate parameter | - | - |
| \(mint\) | Dayly minimum temperature | - | - |
| \(maxt\) | Dayly maximum temperature | - | - |
| \(T_{rate}\) | Temperature sensitive rate parameter | \(T_{rate}=0.5\cdot e^{0.5\cdot p_{10}\cdot\left(maxt + mint\right)}\) | - |
| \(multtl\) | Turnover of labile C (0 = off, 1 = On) | - | - |
| \(multtf\) | Turnover of foliage C (0 = off, 1 = On) | - | - |
| Name | Description | Expression |
|---|---|---|
| \(x\) | vector of states of vegetation | \(x=\left[\begin{matrix}C_{f}\\C_{lab}\\C_{w}\\C_{r}\end{matrix}\right]\) |
| \(u\) | scalar function of photosynthetic inputs | \(u=NPP\) |
| \(b\) | vector of partitioning coefficients of photosynthetically fixed carbon | \(b=\left[\begin{matrix}multtl\cdot p_{3}\\0\\1 - p_{4}\\p_{4}\end{matrix}\right]\) |
| \(A\) | matrix of cycling rates | \(A=\left[\begin{matrix}- T_{rate}\cdot multtf\cdot p_{16}\cdot p_{5}\cdot\left(1 - p_{14}\right) - T_{rate}\cdot multtf\cdot p_{5}\cdot\left(1 - p_{14}\right)\cdot\left(1 - p_{16}\right) - multtf\cdot p_{14}\cdot p_{5} & T_{rate}\cdot multtl\cdot p_{15}\cdot\left(1 - p_{16}\right) & 0 & 0\\T_{rate}\cdot multtf\cdot p_{5}\cdot\left(1 - p_{14}\right)\cdot\left(1 - p_{16}\right) & - T_{rate}\cdot multtl\cdot p_{15}\cdot p_{16} - T_{rate}\cdot multtl\cdot p_{15}\cdot\left(1 - p_{16}\right) & 0 & 0\\0 & 0 & - p_{6} & 0\\0 & 0 & 0 & - p_{7}\end{matrix}\right]\) |
| \(f_{v}\) | the right hand side of the ode | \(f_{v}=u b + A x\) |
\(C_{f}: NPP\cdot multtl\cdot p_{3}\)
\(C_{w}: NPP\cdot\left(1 - p_{4}\right)\)
\(C_{r}: NPP\cdot p_{4}\)
\(C_{f}: C_{f}\cdot multtf\cdot p_{5}\cdot\left(p_{14} - 0.5\cdot p_{16}\cdot\left(p_{14} - 1\right)\cdot e^{0.5\cdot p_{10}\cdot\left(maxt + mint\right)}\right)\)
\(C_{lab}: 0.5\cdot C_{lab}\cdot multtl\cdot p_{15}\cdot p_{16}\cdot e^{0.5\cdot p_{10}\cdot\left(maxt + mint\right)}\)
\(C_{w}: C_{w}\cdot p_{6}\)
\(C_{r}: C_{r}\cdot p_{7}\)
\(C_{f} \rightarrow C_{lab}: 0.5\cdot C_{f}\cdot multtf\cdot p_{5}\cdot\left(p_{14} - 1\right)\cdot\left(p_{16} - 1\right)\cdot e^{0.5\cdot p_{10}\cdot\left(maxt + mint\right)}\)
\(C_{lab} \rightarrow C_{f}: - 0.5\cdot C_{lab}\cdot multtl\cdot p_{15}\cdot\left(p_{16} - 1\right)\cdot e^{0.5\cdot p_{10}\cdot\left(maxt + mint\right)}\)
\(C_f = \frac{2.0\cdot NPP\cdot multtl\cdot p_{3}\cdot e^{0.5\cdot p_{10}\cdot\left(maxt + mint\right)}}{multtf\cdot p_{5}\cdot\left(\left(p_{16} - 1.0\right)\cdot\left(p_{14}\cdot p_{16} - p_{14} - p_{16} + 1.0\right)\cdot e^{p_{10}\cdot\left(maxt + mint\right)} +\left(- p_{14}\cdot e^{0.5\cdot p_{10}\cdot\left(maxt + mint\right)} + 2.0\cdot p_{14} + e^{0.5\cdot p_{10}\cdot\left(maxt + mint\right)}\right)\cdot e^{0.5\cdot p_{10}\cdot\left(maxt + mint\right)}\right)}\)
\(C_lab = \frac{2.0\cdot NPP\cdot p_{3}\cdot\left(p_{14}\cdot p_{16} - p_{14} - p_{16} + 1.0\right)\cdot e^{0.5\cdot p_{10}\cdot\left(maxt + mint\right)}}{p_{15}\cdot\left(\left(p_{16} - 1.0\right)\cdot\left(p_{14}\cdot p_{16} - p_{14} - p_{16} + 1.0\right)\cdot e^{p_{10}\cdot\left(maxt + mint\right)} +\left(- p_{14}\cdot e^{0.5\cdot p_{10}\cdot\left(maxt + mint\right)} + 2.0\cdot p_{14} + e^{0.5\cdot p_{10}\cdot\left(maxt + mint\right)}\right)\cdot e^{0.5\cdot p_{10}\cdot\left(maxt + mint\right)}\right)}\)
\(C_w = -\frac{NPP\cdot\left(p_{4} - 1.0\right)}{p_{6}}\)
\(C_r = \frac{NPP\cdot p_{4}}{p_{7}}\)
Williams, M., Schwarz, P. A., Law, B. E., Irvine, J., & Kurpius, M. R. (2005). An improved analysis of forest carbon dynamics using data assimilation. Global Change Biology, 11(1), 89–105. http://doi.org/10.1111/j.1365-2486.2004.00891.x