This report presents a general overview of the model Emanuel1981 , which is part of the Biogeochemistry Model Database BGC-MD. The underlying yaml file entry that contains all the information of the model was created by Carlos A. Sierra (Orcid ID: 0000-0003-0009-4169) on 12/9/2016. The entry was processed by the python package bgc-md to produce symbolic output.
The model was originally described by Emanuel, Killough, & Olson (1981).
| Name | Description |
|---|---|
| \(x_{1}\) | Non-woody tree parts |
| \(x_{2}\) | Woody tree parts |
| \(x_{3}\) | Ground vegetation |
| \(x_{4}\) | Detritus/Decomposers |
| \(x_{5}\) | Active soil carbon |
| Name | Description | Expression |
|---|---|---|
| \(x\) | vector of state variables | \(x=\left[\begin{matrix}x_{1}\\x_{2}\\x_{3}\\x_{4}\\x_{5}\end{matrix}\right]\) |
| \(u\) | vector of photosynthetically fixed carbon | \(u=\left[\begin{matrix}I_{1}\\0\\I_{3}\\0\\0\end{matrix}\right]\) |
| \(B\) | matrix of cycling rates | \(B=\left[\begin{matrix}- F_{1} & 0 & 0 & 0 & 0\\F_{21} & - F_{2} & 0 & 0 & 0\\0 & 0 & - F_{3} & 0 & 0\\F_{41} & F_{42} & F_{43} & - F_{4} & 0\\0 & F_{52} & F_{53} & F_{54} & - F_{5}\end{matrix}\right]\) |
| \(f_{v}\) | the righthandside of the ode | \(f_{v}=B x + u\) |
\(x_{1}: I_{1}\)
\(x_{3}: I_{3}\)
\(x_{1}: x_{1}\cdot\left(F_{1} - F_{21} - F_{41}\right)\)
\(x_{2}: x_{2}\cdot\left(F_{2} - F_{42} - F_{52}\right)\)
\(x_{3}: x_{3}\cdot\left(F_{3} - F_{43} - F_{53}\right)\)
\(x_{4}: x_{4}\cdot\left(F_{4} - F_{54}\right)\)
\(x_{5}: F_{5}\cdot x_{5}\)
\(x_{1} \rightarrow x_{2}: F_{21}\cdot x_{1}\)
\(x_{1} \rightarrow x_{4}: F_{41}\cdot x_{1}\)
\(x_{2} \rightarrow x_{4}: F_{42}\cdot x_{2}\)
\(x_{2} \rightarrow x_{5}: F_{52}\cdot x_{2}\)
\(x_{3} \rightarrow x_{4}: F_{43}\cdot x_{3}\)
\(x_{3} \rightarrow x_{5}: F_{53}\cdot x_{3}\)
\(x_{4} \rightarrow x_{5}: F_{54}\cdot x_{4}\)
\(x_1 = \frac{I_{1}}{F_{1}}\)
\(x_2 = \frac{F_{21}\cdot I_{1}}{F_{1}\cdot F_{2}}\)
\(x_3 = \frac{I_{3}}{F_{3}}\)
\(x_4 = \frac{1}{F_{1}\cdot F_{2}\cdot F_{3}\cdot F_{4}}\cdot\left(F_{1}\cdot F_{2}\cdot F_{43}\cdot I_{3} + F_{3}\cdot I_{1}\cdot\left(F_{2}\cdot F_{41} + F_{21}\cdot F_{42}\right)\right)\)
\(x_5 = \frac{1}{F_{1}\cdot F_{2}\cdot F_{3}\cdot F_{4}\cdot F_{5}}\cdot\left(F_{1}\cdot F_{2}\cdot I_{3}\cdot\left(F_{4}\cdot F_{53} + F_{43}\cdot F_{54}\right) + F_{3}\cdot I_{1}\cdot\left(F_{2}\cdot F_{41}\cdot F_{54} + F_{21}\cdot F_{4}\cdot F_{52} + F_{21}\cdot F_{42}\cdot F_{54}\right)\right)\)
Emanuel, W. R., Killough, G. G., & Olson, J. S. (1981). Modelling the circulation of carbon in the world’s terrestrial ecosystems. In B. Bolin (Ed.), Carbon cycle modelling (pp. 335–353). John Wiley and Sons.