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 17/7/2015, 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 C. S. C. Potter & Randerson (1993).
This paper presents a modeling approach aimed at seasonal resolution of global climatic and edaphic controls on patterns of terrestrial ecosystem production and soil microbial respiration. We use satellite imagery (Advanced Very High Resolution Radiometer and International Satellite Cloud Climatology Project solar radiation), along with historical climate (monthly temperature and precipitation) and soil attributes (texture, C and N contents) from global (1°) data sets as model inputs. The Carnegie-Ames-Stanford approach (CASA) Biosphere model runs on a monthly time interval to simulate seasonal patterns in net plant carbon fixation, biomass and nutrient allocation, litterfall, soil nitrogen mineralization, and microbial CO\(_2\) production. The model estimate of global terrestrial net primary production is 48 Pg C yr\(^{-1}\) with a maximum light use efficiency of 0.39 g C MJ\(^{-1}\) PAR. Over 70% of terrestrial net production takes place between 30°N and 30°S latitude. Seasonal variations in atmospheric CO\(_2\) concentrations from three stations in the Geophysical Monitoring for Climate Change Flask Sampling Network correlate significantly with estimated net ecosystem production values by latitude. -from Authors
global
| Abbreviation | Source |
|---|---|
| Original dataset of the publication | C. S. C. Potter & Randerson (1993) |
| Tundra | C. S. Potter (1999) |
| High-latitude forest | C. S. Potter (1999) |
| Boreal coniferous forest | C. S. Potter (1999) |
| Temperate grassland | C. S. Potter (1999) |
| Mixed coniferous forest | C. S. Potter (1999) |
| Temperate deciduous forest | C. S. Potter (1999) |
| Desert and bare ground | C. S. Potter (1999) |
| Semi-arid shrubland | C. S. Potter (1999) |
| Savanna and woody grassland | C. S. Potter (1999) |
| Tropical evergreen rain forest | C. S. Potter (1999) |
The following table contains the available information regarding this section:
| Name | Description |
|---|---|
| \(C_{f}\) | Carbon in foliage |
| \(C_{r}\) | Carbon in roots |
| \(C_{w}\) | Carbon in woody tissue |
The following table contains the available information regarding this section:
| Name | Description | Expressions | Type | Values Original dataset of the publication |
Tundra | High-latitude forest | Boreal coniferous forest | Temperate grassland | Mixed coniferous forest | Temperate deciduous forest | Desert and bare ground | Semi-arid shrubland | Savanna and woody grassland | Tropical evergreen rain forest |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| \(SOL\) | Total solar radiation (SOL(x,t)) | - | variable | - | - | - | - | - | - | - | - | - | - | - |
| \(FPAR\) | Fraction of incoming PAR intercerpted by green vegetation (FPAR(x,t)) | - | variable | - | - | - | - | - | - | - | - | - | - | - |
| \(IPAR\) | Intercepted photosynthetically active radiation(IPAR(x,t)). The factor of 0.5 accounts for the fact that approx. half of SOL is in PAR waveband (0.4-0.7 \(\mu\)m) | \(IPAR=0.5\,SOL\,FPAR\) | variable | - | - | - | - | - | - | - | - | - | - | - |
| \(\epsilon\) | PAR use efficiency (\(\epsilon(x,t)\)). Function that depends on effects of temperature and water stress | - | variable | - | - | - | - | - | - | - | - | - | - | - |
| \(NPP\) | New production of plant biomass (NPP(x,t)) at a grid cell (\(x\)) in month \(t\) | \(NPP=IPAR\,\epsilon\) | variable | - | - | - | - | - | - | - | - | - | - | - |
The following table contains the available information regarding this section:
| Name | Description | Type | Values Original dataset of the publication |
Tundra | High-latitude forest | Boreal coniferous forest | Temperate grassland | Mixed coniferous forest | Temperate deciduous forest | Desert and bare ground | Semi-arid shrubland | Savanna and woody grassland | Tropical evergreen rain forest |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| \(\alpha_{f}\) | Proportional allocation constant of available carbon allocated to foliage | parameter | \(\frac{1}{3}\) | \(0.25\) | \(0.3\) | \(0.25\) | \(0.45\) | \(0.25\) | \(0.3\) | \(0.25\) | \(0.25\) | \(0.3\) | \(0.25\) |
| \(\alpha_{r}\) | Proportional allocation constant of available carbon allocated to roots | parameter | \(\frac{1}{3}\) | \(0.25\) | \(0.25\) | \(0.25\) | \(0.55\) | \(0.25\) | \(0.25\) | \(0.25\) | \(0.25\) | \(0.25\) | \(0.25\) |
| \(\alpha_{w}\) | Proportional allocation constant of available carbon allocated to wood | parameter | \(\frac{1}{3}\) | \(0.5\) | \(0.45\) | \(0.5\) | - | \(0.5\) | \(0.45\) | \(0.5\) | \(0.5\) | \(0.45\) | \(0.5\) |
The following table contains the available information regarding this section:
| Name | Description | Type | Units | Values Original dataset of the publication |
Tundra | High-latitude forest | Boreal coniferous forest | Temperate grassland | Mixed coniferous forest | Temperate deciduous forest | Desert and bare ground | Semi-arid shrubland | Savanna and woody grassland | Tropical evergreen rain forest |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| \(\tau_{f}\) | Residence time of carbon in foliage | parameter | \(years\) | - | \(1.5\) | \(1\) | \(2.5\) | \(1.5\) | \(1.5\) | \(1\) | \(1.5\) | \(1.5\) | \(1\) | \(1.5\) |
| \(\tau_{r}\) | Residence time of carbon in roots | parameter | \(years\) | - | \(3\) | \(3\) | \(3\) | \(5\) | \(3\) | \(3\) | \(3\) | \(3\) | \(5\) | \(2\) |
| \(\tau_{w}\) | Residence time of carbon in wood | parameter | \(years\) | - | \(50\) | \(50\) | \(50\) | - | \(40\) | \(40\) | \(50\) | \(50\) | \(25\) | \(25\) |
The following table contains the available information regarding this section:
| Name | Description | Expressions |
|---|---|---|
| \(x\) | vector of states for vegetation | \(x=\left[\begin{matrix}C_{f}\\C_{r}\\C_{w}\end{matrix}\right]\) |
| \(u\) | scalar function of photosynthetic inputs | \(u=NPP\) |
| \(b\) | vector of partitioning coefficients of photosynthetically fixed carbon | \(b=\left[\begin{matrix}\alpha_{f}\\\alpha_{r}\\\alpha_{w}\end{matrix}\right]\) |
| \(A\) | matrix of turnover (cycling) rates | \(A=\left[\begin{matrix}-\tau_{f} & 0 & 0\\0 & -\tau_{r} & 0\\0 & 0 & -\tau_{w}\end{matrix}\right]\) |
| \(f_{v}\) | the righthandside of the ode | \(f_{v}=u\,b+A\,x\) |
| Flux description | |
|---|---|
 Figure 1: Pool model representation |
Input fluxes\(C_{f}: 0.5\cdot FPAR\cdot SOL\cdot\alpha_{f}\cdot\epsilon\) Output fluxes\(C_{f}: C_{f}\cdot\tau_{f}\)\(C_{r}: C_{r}\cdot\tau_{r}\) \(C_{w}: C_{w}\cdot\tau_{w}\) |
\(\left[\begin{matrix}- C_{f}\cdot\tau_{f} + 0.5\cdot FPAR\cdot SOL\cdot\alpha_{f}\cdot\epsilon\\- C_{r}\cdot\tau_{r} + 0.5\cdot FPAR\cdot SOL\cdot\alpha_{r}\cdot\epsilon\\- C_{w}\cdot\tau_{w} + 0.5\cdot FPAR\cdot SOL\cdot\alpha_{w}\cdot\epsilon\end{matrix}\right]\)
\(\left[\begin{matrix}-\tau_{f} & 0 & 0\\0 & -\tau_{r} & 0\\0 & 0 & -\tau_{w}\end{matrix}\right]\)
\(C_{f} = \frac{0.5}{\tau_{f}}\cdot FPAR\cdot SOL\cdot\alpha_{f}\cdot\epsilon\)
\(C_{r} = \frac{0.5}{\tau_{r}}\cdot FPAR\cdot SOL\cdot\alpha_{r}\cdot\epsilon\)
\(C_{w} = \frac{0.5}{\tau_{w}}\cdot FPAR\cdot SOL\cdot\alpha_{w}\cdot\epsilon\)
\(C_f: \frac{0.166666666666667}{\tau_{f}}\cdot FPAR\cdot SOL\cdot\epsilon\), \(C_r: \frac{0.166666666666667}{\tau_{r}}\cdot FPAR\cdot SOL\cdot\epsilon\), \(C_w: \frac{0.166666666666667}{\tau_{w}}\cdot FPAR\cdot SOL\cdot\epsilon\)
\(\lambda_{1}: -\tau_{w}\)
\(\lambda_{2}: -\tau_{r}\)
\(\lambda_{3}: -\tau_{f}\)
\(C_f: 0.0833333333333333\cdot FPAR\cdot SOL\cdot\epsilon\), \(C_r: 0.0416666666666667\cdot FPAR\cdot SOL\cdot\epsilon\), \(C_w: 0.005\cdot FPAR\cdot SOL\cdot\epsilon\)
\(\lambda_{1}: -1.500\)
\(\lambda_{2}: -3.000\)
\(\lambda_{3}: -50.000\)
\(C_f: 0.15\cdot FPAR\cdot SOL\cdot\epsilon\), \(C_r: 0.0416666666666667\cdot FPAR\cdot SOL\cdot\epsilon\), \(C_w: 0.0045\cdot FPAR\cdot SOL\cdot\epsilon\)
\(\lambda_{1}: -50.000\)
\(\lambda_{2}: -3.000\)
\(\lambda_{3}: -1.000\)
\(C_f: 0.05\cdot FPAR\cdot SOL\cdot\epsilon\), \(C_r: 0.0416666666666667\cdot FPAR\cdot SOL\cdot\epsilon\), \(C_w: 0.005\cdot FPAR\cdot SOL\cdot\epsilon\)
\(\lambda_{1}: -3.000\)
\(\lambda_{2}: -50.000\)
\(\lambda_{3}: -2.500\)
\(C_f: 0.15\cdot FPAR\cdot SOL\cdot\epsilon\), \(C_r: 0.055\cdot FPAR\cdot SOL\cdot\epsilon\), \(C_w: \frac{0.5}{\tau_{w}}\cdot FPAR\cdot SOL\cdot\alpha_{w}\cdot\epsilon\)
\(\lambda_{1}: -\tau_{w}\)
\(\lambda_{2}: -5.0\)
\(\lambda_{3}: -1.5\)
\(C_f: 0.0833333333333333\cdot FPAR\cdot SOL\cdot\epsilon\), \(C_r: 0.0416666666666667\cdot FPAR\cdot SOL\cdot\epsilon\), \(C_w: 0.00625\cdot FPAR\cdot SOL\cdot\epsilon\)
\(\lambda_{1}: -40.000\)
\(\lambda_{2}: -1.500\)
\(\lambda_{3}: -3.000\)
\(C_f: 0.15\cdot FPAR\cdot SOL\cdot\epsilon\), \(C_r: 0.0416666666666667\cdot FPAR\cdot SOL\cdot\epsilon\), \(C_w: 0.005625\cdot FPAR\cdot SOL\cdot\epsilon\)
\(\lambda_{1}: -40.000\)
\(\lambda_{2}: -3.000\)
\(\lambda_{3}: -1.000\)
\(C_f: 0.0833333333333333\cdot FPAR\cdot SOL\cdot\epsilon\), \(C_r: 0.0416666666666667\cdot FPAR\cdot SOL\cdot\epsilon\), \(C_w: 0.005\cdot FPAR\cdot SOL\cdot\epsilon\)
\(\lambda_{1}: -1.500\)
\(\lambda_{2}: -3.000\)
\(\lambda_{3}: -50.000\)
\(C_f: 0.0833333333333333\cdot FPAR\cdot SOL\cdot\epsilon\), \(C_r: 0.0416666666666667\cdot FPAR\cdot SOL\cdot\epsilon\), \(C_w: 0.005\cdot FPAR\cdot SOL\cdot\epsilon\)
\(\lambda_{1}: -1.500\)
\(\lambda_{2}: -3.000\)
\(\lambda_{3}: -50.000\)
\(C_f: 0.15\cdot FPAR\cdot SOL\cdot\epsilon\), \(C_r: 0.025\cdot FPAR\cdot SOL\cdot\epsilon\), \(C_w: 0.009\cdot FPAR\cdot SOL\cdot\epsilon\)
\(\lambda_{1}: -5.000\)
\(\lambda_{2}: -1.000\)
\(\lambda_{3}: -25.000\)
\(C_f: 0.0833333333333333\cdot FPAR\cdot SOL\cdot\epsilon\), \(C_r: 0.0625\cdot FPAR\cdot SOL\cdot\epsilon\), \(C_w: 0.01\cdot FPAR\cdot SOL\cdot\epsilon\)
\(\lambda_{1}: -1.500\)
\(\lambda_{2}: -2.000\)
\(\lambda_{3}: -25.000\)
Potter, C. S. (1999). Terrestrial biomass and the effects of deforestation on the global carbon cycle satellite observations. BioScience, 49(10), 769–778. http://doi.org/10.2307/1313568
Potter, C. S. C., & Randerson, J. (1993). Terrestrial ecosystem production: A process model based on global satellite and surface data. Global Biogeochemical Cycles, 7(4), 811–841. http://doi.org/10.1029/93GB02725