This report is the result of the use of the Python 3.4 package Sympy (for symbolic mathematics), as means to translate published models to a common language. It was created by Verónika Ceballos-Núñez (Orcid ID: 0000-0002-0046-1160) on 29/3/2016, and was last modified on lm.
The model depicted in this document considers carbon allocation with a process based approach. It was originally described by Thomas & Williams (2014).
National Science Foundation Awards AGS-1020767 and EF-1048481
global
The following table contains the available information regarding this section:
| Name | Description |
|---|---|
| \(C_{leaf}\) | Carbon in foliage |
| \(C_{wood}\) | Carbon in wood |
| \(C_{root}\) | Carbon in roots |
| \(C_{labile}\) | - |
| \(C_{bud}\) | - |
| \(C_{labileRa}\) | - |
| \(N_{leaf}\) | - |
| \(N_{wood}\) | - |
| \(N_{root}\) | - |
| \(N_{labile}\) | - |
| \(N_{bud}\) | - |
The following table contains the available information regarding this section:
| Name | Description | Type | Units |
|---|---|---|---|
| \(GPP\) | Photosynthesis; based on ACM model (see article for description) | variable | \(gC\cdot day^{-1}\) |
The following table contains the available information regarding this section:
| Name | Description | Type | Units |
|---|---|---|---|
| \(a_{budC2leaf}\) | Allocation from bud C pool to leaf C | variable | \(gC\cdot m^{-2}\cdot day^{-1}\) |
| \(a_{woodC}\) | Allocation from labile C to wood C | variable | \(gC\cdot m^{-2}\cdot day^{-1}\) |
| \(a_{rootC}\) | Allocation from labile C to root C | variable | \(gC\cdot m^{-2}\cdot day^{-1}\) |
| \(a_{budC2Ramain}\) | Allocation of bud C pool to maintenance respiration pool when maintain respiration pool reaches zero; represents forgoing future leaf C to prevent carbon starvation. | variable | \(gC\cdot m^{-2}\cdot day^{-1}\) |
| \(a_{budC}\) | Allocation of labile C to bud C; a fraction of the potential maximum leaf C | variable | \(gC\cdot m^{-2}\cdot day^{-1}\) |
| \(a_{Ramain}\) | Allocation of labile C to future maintenance respiration; helps prevent carbon starvation during periods of negative NPP | variable | \(gC\cdot m^{-2}\cdot day^{-1}\) |
| \(a_{budN2leaf}\) | Allocation from bud N pool to leaf C (???); bud N is set in previous year | variable | \(gN\cdot m^{-2}\cdot day^{-1}\) |
| \(a_{budN2Ramain}\) | When bud C is used for maintenance respiration (a\(_budC2Ramain\) > 0), bud N is returned to the labile N pool | variable | \(gN\cdot m^{-2}\cdot day^{-1}\) |
| \(a_{budN}\) | Allocation of labile N to bud N; in seasonal environments it occurs in year prior to being displayed as leaf N | variable | \(gN\cdot m^{-2}\cdot day^{-1}\) |
| \(a_{woodN}\) | Allocation from labile N to wood N | variable | \(gN\cdot m^{-2}\cdot day^{-1}\) |
| \(a_{rootN}\) | Allocation from labile N to root N (???) | variable | \(gN\cdot m^{-2}\cdot day^{-1}\) |
| \(a_{labileRamain}\) | Allocation of labile C to respiration of living tissues | variable | \(gC\cdot m^{-2}\cdot day^{-1}\) |
The following table contains the available information regarding this section:
| Name | Description | doi | Type | Units |
|---|---|---|---|---|
| \(U_{NH4}\) | Uptake of NH\(_4^+\) from mineral soil NH\(_4^+\) | \(\frac{10.1007}{BF_{00015315}}\) | variable | \(gN\cdot m^{-2}\cdot day^{-1}\) |
| \(U_{NO3}\) | Uptake of NO\(_3^-\) from mineral soil NO\(_3^-\) | \(\frac{10.1007}{BF_{00015315}}\) | variable | \(gN\cdot m^{-2}\cdot day^{-1}\) |
| \(U_{Nfix}\) | Fixation of N from N\(_2\); function of Ra\(_excess\) flux, temperature, N demand, and C cost | - | variable | \(gN\cdot m^{-2}\cdot day^{-1}\) |
The following table contains the available information regarding this section:
| Name | Description | Expressions | Type | Units |
|---|---|---|---|---|
| \(\tau_{wood}\) | Turnover of wood (C and N) | - | parameter | \(day^{-1}\) |
| \(\tau_{root}\) | Turnover of root (C and N) | - | parameter | \(day^{-1}\) |
| \(t_{leafC}\) | Turnover of leaf C to litter C; constant over year in humid tropics; seasonal otherwise | - | variable | \(gC\cdot m^{-2}\cdot day^{-1}\) |
| \(t_{woodC}\) | Turnover of wood C to CWDC pool; occurs throughout year | \(t_{woodC}=C_{wood}\,\tau_{wood}\) | variable | \(gC\cdot m^{-2}\cdot day^{-1}\) |
| \(t_{rootC}\) | Turnover of root C to litter C; occurs throughout year | \(t_{rootC}=C_{root}\,\tau_{root}\) | variable | \(gC\cdot m^{-2}\cdot day^{-1}\) |
| \(t_{retransN}\) | Reabsorption of N from leaves to labile N | - | - | \(gN\cdot m^{-2}\cdot day^{-1}\) |
| \(t_{leafN}\) | Turnover of leaf N to litter N; constant over year in humid tropics; seasonal otherwise | - | variable | \(gN\cdot m^{-2}\cdot day^{-1}\) |
| \(t_{woodN}\) | Turnover of wood N to CWDN pool; occurs throughout year | \(t_{woodN}=N_{wood}\,\tau_{wood}\) | variable | \(gN\cdot m^{-2}\cdot day^{-1}\) |
| \(t_{rootN}\) | Turnover of root N to litter N; occurs throughout year | \(t_{rootN}=N_{root}\,\tau_{root}\) | variable | \(gN\cdot m^{-2}\cdot day^{-1}\) |
The following table contains the available information regarding this section:
| Name | Description | Type | Units |
|---|---|---|---|
| \(Ra_{growth}\) | Growth respiration that occurs when tissue is allocated; a constant fraction of carbon allocated to tissue | variable | \(gC\cdot m^{-2}\cdot day^{-1}\) |
| \(Ra_{excess}\) | Respiration that occurs when labile C exceeds a maximum labile C store; used for N fixation | variable | \(gC\cdot m^{-2}\cdot day^{-1}\) |
| \(Ra_{main}\) | Respiration of living tissues; a function of N content and temperature | variable | \(gC\cdot m^{-2}\cdot day^{-1}\) |
The following table contains the available information regarding this section:
| Name | Description | Expressions |
|---|---|---|
| \(x\) | vector of states (C\(_i\)) for vegetation | \(x=\left[\begin{matrix}C_{leaf}\\C_{wood}\\C_{root}\\C_{labile}\\C_{bud}\\C_{labileRa}\\N_{leaf}\\N_{wood}\\N_{root}\\N_{labile}\\N_{bud}\end{matrix}\right]\) |
| \(I\) | vector of fluxes into pool (C\(_i\)) | \(I=\left[\begin{matrix}a_{budC2leaf}\\a_{woodC}\\a_{rootC}\\GPP\\a_{budC}\\a_{budC2Ramain} + a_{labileRamain}\\a_{budN2leaf}\\a_{woodN}\\a_{rootN}\\U_{NH4} + U_{NO3} + U_{Nfix} + a_{budN2Ramain} + t_{retransN}\\a_{budN2leaf}\end{matrix}\right]\) |
| \(O\) | vector of fluxes out of pool (C\(_i\)) | \(O=\left[\begin{matrix}- t_{leafC}\\- t_{woodC}\\- t_{rootC}\\- a_{budC} - a_{rootC} - a_{woodC}\\- a_{budC2leaf}\\0\\- t_{leafN} - t_{retransN}\\- t_{woodN}\\- t_{rootN}\\- a_{budN} - a_{rootN} - a_{woodN}\\0\end{matrix}\right]\) |
| \(R\) | vector of respiration fluxes of pool (C\(_i\)) | \(R=\left[\begin{matrix}0\\0\\0\\- Ra_{excess} - Ra_{growth} - a_{labileRamain}\\- a_{budC2Ramain}\\- Ra_{main}\\0\\0\\0\\0\\- a_{budN2Ramain}\end{matrix}\right]\) |
| \(f_{v}\) | the righthandside of the ode | \(f_{v}=I+O+R\) |
\(\left[\begin{matrix}a_{budC2leaf} - t_{leafC}\\- C_{wood}\cdot\tau_{wood} + a_{woodC}\\- C_{root}\cdot\tau_{root} + a_{rootC}\\GPP - Ra_{excess} - Ra_{growth} - a_{budC} - a_{labileRamain} - a_{rootC} - a_{woodC}\\a_{budC} - a_{budC2Ramain} - a_{budC2leaf}\\- Ra_{main} + a_{budC2Ramain} + a_{labileRamain}\\a_{budN2leaf} - t_{leafN} - t_{retransN}\\- N_{wood}\cdot\tau_{wood} + a_{woodN}\\- N_{root}\cdot\tau_{root} + a_{rootN}\\U_{NH4} + U_{NO3} + U_{Nfix} - a_{budN} + a_{budN2Ramain} - a_{rootN} - a_{woodN} + t_{retransN}\\- a_{budN2Ramain} + a_{budN2leaf}\end{matrix}\right]\)
\(\left[\begin{array}{ccccccccccc}0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\0 & -\tau_{wood} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\0 & 0 & -\tau_{root} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\0 & 0 & 0 & 0 & 0 & 0 & 0 & -\tau_{wood} & 0 & 0 & 0\\0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -\tau_{root} & 0 & 0\\0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\end{array}\right]\)
\(C_{leaf} = C_{leaf}\)
\(C_{wood} = \frac{a_{woodC}}{\tau_{wood}}\)
\(C_{root} = \frac{a_{rootC}}{\tau_{root}}\)
\(C_{labile} = C_{labile}\)
\(C_{bud} = C_{bud}\)
\(C_{labileRa} = C_{labileRa}\)
\(N_{leaf} = N_{leaf}\)
\(N_{wood} = \frac{a_{woodN}}{\tau_{wood}}\)
\(N_{root} = \frac{a_{rootN}}{\tau_{root}}\)
\(N_{labile} = N_{labile}\)
\(N_{bud} = N_{bud}\)
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