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 S. W. Running & Coughlan (1988).
An ecosystem process model is described that calculates the carbon, water and nitrogen cycles through a forest ecosystem. The model, FOREST-BGC, treats canopy interception and evaporation, transpiration, photosynthesis, growth and maintenance respiration, carbon allocation above and below-ground, litterfall, decomposition and nitrogen mineralization. The model uses leaf area index (LAI) to quantify the forest structure important for energy and mass exchange, and this represents a key simplification for regional scale applications. FOREST-BGC requires daily incoming short-wave radiation, air temperature, dew point, and precipitation as driving variables. The model was used to simulate the annual hydrologic balance and net primary production of a hypothetical forest stand in seven contrasting environments across North America for the year 1984. Hydrologic partitioning ranged from 14/86/0% for evaporation, transpiration and outflow, respectively, in Fairbanks, AK (annual precipitation of 313 mm) to 10/27/66% in Jacksonville, FL (annual ppt of 1244 mm), and these balances changed as LAI was increased from 3 to 9 in successive simulations. Net primary production (npp) ranged from 0.0 t C ha-1 year-1 at Tucson, AZ, to 14.1 t C ha-1 year-1 at Knoxville, TN and corresponded reasonably with observed values at each site. The sensitivity of ecosystem processes to varying LAI in different climates was substantial, and underscores the utility of parameterizing this model at regional scales in the future with forest LAI measurements derived from satellite imagery. ?? 1988.
site
| Abbreviation | Source |
|---|---|
| Original dataset of the publication | S. W. Running & Coughlan (1988) |
| Additional set 1 | Hunt Jr, Martin, & Running (1991) |
| Additional set 2 | Korol, Running, Milner, & Hunt (1991) |
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 | Type | Values Original dataset of the publication |
Additional set 1 | Additional set 2 |
|---|---|---|---|---|
| \(\eta_{f}\) | parameter | \(\frac{1}{4}\) | \(\frac{1}{5}\) | \(\frac{12}{25}\) |
| \(\eta_{r}\) | parameter | \(\frac{2}{5}\) | \(\frac{11}{20}\) | \(\frac{37}{100}\) |
| \(\eta_{w}\) | parameter | \(\frac{7}{20}\) | \(\frac{1}{4}\) | \(\frac{3}{20}\) |
The following table contains the available information regarding this section:
| Name | Entry Author Orcid | Type | Values Original dataset of the publication |
Additional set 1 | Additional set 2 |
|---|---|---|---|---|---|
| \(\gamma_{f}\) | 0000-0002-0046-1160 | parameter | \(\frac{33}{100}\) | - | - |
| \(\gamma_{r}\) | 0000-0002-0046-1160 | parameter | \(\frac{2}{5}\) | \(\frac{3}{4}\) | \(\frac{3}{4}\) |
| \(\gamma_{w}\) | 0000-0002-0046-1160 | parameter | \(0\) | - | - |
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 | - |
| \(b\) | vector of partitioning coefficients of photosynthetically fixed carbon | \(b=\left[\begin{matrix}\eta_{f}\\\eta_{r}\\\eta_{w}\end{matrix}\right]\) |
| \(A\) | matrix of turnover (cycling) rates | \(A=\left[\begin{matrix}-\gamma_{f} & 0 & 0\\0 & -\gamma_{r} & 0\\0 & 0 & -\gamma_{w}\end{matrix}\right]\) |
| \(f_{v}\) | the righthandside of the ode | \(f_{v}=u\,b+A\,x\) |
| Flux description | |
|---|---|
 Figure 1: Pool model representation |
Input fluxes\(C_{f}: \eta_{f}\cdot u\) Output fluxes\(C_{f}: C_{f}\cdot\gamma_{f}\)\(C_{r}: C_{r}\cdot\gamma_{r}\) \(C_{w}: C_{w}\cdot\gamma_{w}\) |
\(\left[\begin{matrix}- C_{f}\cdot\gamma_{f} +\eta_{f}\cdot u\\- C_{r}\cdot\gamma_{r} +\eta_{r}\cdot u\\- C_{w}\cdot\gamma_{w} +\eta_{w}\cdot u\end{matrix}\right]\)
\(\left[\begin{matrix}-\gamma_{f} & 0 & 0\\0 & -\gamma_{r} & 0\\0 & 0 & -\gamma_{w}\end{matrix}\right]\)
\(C_{f} = \frac{\eta_{f}}{\gamma_{f}}\cdot u\)
\(C_{r} = \frac{\eta_{r}}{\gamma_{r}}\cdot u\)
\(C_{w} = \frac{\eta_{w}}{\gamma_{w}}\cdot u\)
\(C_f: \frac{25}{33}\cdot u\), \(C_r: u\), \(C_w: C_{w}\)
\(\lambda_{1}: 0.000\)
\(\lambda_{2}: -0.400\)
\(\lambda_{3}: -0.330\)
\(C_f: \frac{u}{5\cdot\gamma_{f}}\), \(C_r: \frac{11}{15}\cdot u\), \(C_w: \frac{u}{4\cdot\gamma_{w}}\)
\(\lambda_{1}: -\gamma_{w}\)
\(\lambda_{2}: -0.75\)
\(\lambda_{3}: -\gamma_{f}\)
\(C_f: \frac{12\cdot u}{25\cdot\gamma_{f}}\), \(C_r: \frac{37}{75}\cdot u\), \(C_w: \frac{3\cdot u}{20\cdot\gamma_{w}}\)
\(\lambda_{1}: -\gamma_{w}\)
\(\lambda_{2}: -0.75\)
\(\lambda_{3}: -\gamma_{f}\)
Hunt Jr, E. R., Martin, F. C., & Running, S. W. (1991). Simulating the effects of climatic variation on stem carbon accumulation of a ponderosa pine stand: Comparison with annual growth increment data. Tree Physiology, 9(1_2), 161–171. http://doi.org/10.1093/treephys/9.1-2.161
Korol, R. L., Running, S. W., Milner, K. S., & Hunt, E. R. (1991). TESTING a mECHANISTIC cARBON bALANCE mODEL aGAINST oBSERVED tREE gROWTH. Canadian Journal of Forest Research-Revue Canadienne De Recherche Forestiere, 21(7), 1098–1105. http://doi.org/10.1139/x91-151
Running, S. W., & Coughlan, J. C. (1988). A general model of forest ecosystem processes for regional applications i. hydrologic balance, canopy gas exchange and primary production processes. Ecological Modelling, 42(2), 125–154. http://doi.org/10.1016/0304-3800(88)90112-3