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 29/3/2016.
The model depicted in this document considers carbon allocation with a process based approach. It was originally described by Thomas & Williams (2014).
global
| Name | Description |
|---|---|
| \(C_{leaf}\) | Carbon in foliage |
| \(C_{wood}\) | Carbon in wood |
| \(C_{root}\) | Carbon in roots |
| \(C_{labile}\) | Labile carbon |
| \(C_{bud}\) | Bud carbon |
| \(C_{labileRa}\) | Maintenance respiration pool |
| Name | Description | Expression | Unit |
|---|---|---|---|
| \(GPP\) | Photosynthesis; based on ACM model (see article for description) | - | \(gC\cdot day^{-1}\) |
| Name | Description | Unit |
|---|---|---|
| \(Ra_{growth}\) | Growth respiration that occurs when tissue is allocated; a constant fraction of carbon allocated to tissue | \(gC\cdot m^{-2}\cdot day^{-1}\) |
| \(Ra_{excess}\) | Respiration that occurs when labile C exceeds a maximum labile C store; used for N fixation | \(gC\cdot m^{-2}\cdot day^{-1}\) |
| \(Ra_{main}\) | Respiration of living tissues; a function of N content and temperature | \(gC\cdot m^{-2}\cdot day^{-1}\) |
| Name | Description | Unit |
|---|---|---|
| \(a_{budC2leaf}\) | Allocation from bud C pool to leaf C | \(gC\cdot m^{-2}\cdot day^{-1}\) |
| \(a_{woodC}\) | Allocation from labile C to wood C | \(gC\cdot m^{-2}\cdot day^{-1}\) |
| \(a_{rootC}\) | Allocation from labile C to root C | \(gC\cdot m^{-2}\cdot day^{-1}\) |
| \(a_{budC2Ramain}\) | Allocation of bud C pool to maintenance respiration pool when maintain respiration pool reaches zero; represents forgoing future leaf C to prevent carbon starvation. | \(gC\cdot m^{-2}\cdot day^{-1}\) |
| \(a_{budC}\) | Allocation of labile C to bud C; a fraction of the potential maximum leaf C | \(gC\cdot m^{-2}\cdot day^{-1}\) |
| \(a_{Ramain}\) | Allocation of labile C to future maintenance respiration; helps prevent carbon starvation during periods of negative NPP | \(gC\cdot m^{-2}\cdot day^{-1}\) |
| \(a_{labileRamain}\) | Allocation of labile C to respiration of living tissues | \(gC\cdot m^{-2}\cdot day^{-1}\) |
| Name | Description | Expression | Unit |
|---|---|---|---|
| \(\tau_{leaf}\) | Turnover of leaf (C and N) | - | \(day^{-1}\) |
| \(\tau_{wood}\) | Turnover of wood (C and N) | - | \(day^{-1}\) |
| \(\tau_{root}\) | Turnover of root (C and N) | - | \(day^{-1}\) |
| \(t_{leafC}\) | Turnover of leaf C to litter C; constant over year in humid tropics; seasonal otherwise | \(t_{leafC}=C_{leaf}\cdot\tau_{leaf}\) | \(gC\cdot m^{-2}\cdot day^{-1}\) |
| \(t_{woodC}\) | Turnover of wood C to CWDC pool; occurs throughout year | \(t_{woodC}=C_{wood}\cdot\tau_{wood}\) | \(gC\cdot m^{-2}\cdot day^{-1}\) |
| \(t_{rootC}\) | Turnover of root C to litter C; occurs throughout year | \(t_{rootC}=C_{root}\cdot\tau_{root}\) | \(gC\cdot m^{-2}\cdot day^{-1}\) |
| Name | Description | Expression |
|---|---|---|
| \(x\) | vector of states (C\(_{i}\)) for vegetation | \(x=\left[\begin{matrix}C_{labile}\\C_{bud}\\C_{leaf}\\C_{wood}\\C_{root}\\C_{labileRa}\end{matrix}\right]\) |
| \(u\) | scalar function of photosynthetic inputs | \(u=GPP\) |
| \(b\) | vector of partitioning coefficients of photosynthetically fixed carbon | \(b=\left[\begin{matrix}1\\0\\0\\0\\0\\0\end{matrix}\right]\) |
| \(A_{x}\) | matrix of cycling rates | \(A_{x}=\left[\begin{matrix}\frac{- Ra_{excess} - Ra_{growth} - a_{budC} - a_{labileRamain} - a_{rootC} - a_{woodC}}{C_{labile}} & 0 & 0 & 0 & 0 & 0\\\frac{a_{budC}}{C_{labile}} &\frac{- a_{budC2Ramain} - a_{budC2leaf}}{C_{bud}} & 0 & 0 & 0 & 0\\0 &\frac{a_{budC2leaf}}{C_{bud}} & -\tau_{leaf} & 0 & 0 & 0\\\frac{a_{woodC}}{C_{labile}} & 0 & 0 & -\tau_{wood} & 0 & 0\\\frac{a_{rootC}}{C_{labile}} & 0 & 0 & 0 & -\tau_{root} & 0\\\frac{a_{labileRamain}}{C_{labile}} &\frac{a_{budC2Ramain}}{C_{bud}} & 0 & 0 & 0 & -\frac{Ra_{main}}{C_{labileRa}}\end{matrix}\right]\) |
| \(f_{v}\) | the righthandside of the ode | \(f_{v}=u b + A_{x} x\) |
\(C_{labile}: GPP\)
\(C_{labile}: Ra_{excess} + Ra_{growth}\)
\(C_{leaf}: C_{leaf}\cdot\tau_{leaf}\)
\(C_{wood}: C_{wood}\cdot\tau_{wood}\)
\(C_{root}: C_{root}\cdot\tau_{root}\)
\(C_{labileRa}: Ra_{main}\)
\(C_{labile} \rightarrow C_{bud}: a_{budC}\)
\(C_{labile} \rightarrow C_{wood}: a_{woodC}\)
\(C_{labile} \rightarrow C_{root}: a_{rootC}\)
\(C_{labile} \rightarrow C_{labileRa}: a_{labileRamain}\)
\(C_{bud} \rightarrow C_{leaf}: a_{budC2leaf}\)
\(C_{bud} \rightarrow C_{labileRa}: a_{budC2Ramain}\)
\(C_labile = C_{labile}\)
\(C_bud = C_{bud}\)
\(C_leaf = \frac{a_{budC2leaf}}{\tau_{leaf}}\)
\(C_wood = \frac{a_{woodC}}{\tau_{wood}}\)
\(C_root = \frac{a_{rootC}}{\tau_{root}}\)
\(C_labileRa = C_{labileRa}\)
Thomas, R. Q., & Williams, M. (2014). A model using marginal efficiency of investment to analyze carbon and nitrogen interactions in terrestrial ecosystems (ACONITE version 1). Geoscientific Model Development, 7(5), 2015–2037. http://doi.org/10.5194/gmd-7-2015-2014