This report presents a general overview of the model CASA (9 pools) , 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 Holger Metzler (Orcid ID: 0000-0002-8239-1601) on 18/01/2018. The entry was processed by the python package bgc-md to produce symbolic output.
The model was originally described by Rasmussen et al. (2016).
| Name | Description | Unit |
|---|---|---|
| \(x_{1}\) | Leaves | \(Pg C\) |
| \(x_{2}\) | Roots | \(Pg C\) |
| \(x_{3}\) | Wood | \(Pg C\) |
| \(x_{4}\) | Litter 1 | \(Pg C\) |
| \(x_{5}\) | Litter 2 | \(Pg C\) |
| \(x_{6}\) | Litter 3 | \(Pg C\) |
| \(x_{7}\) | Soil 1 | \(Pg C\) |
| \(x_{8}\) | Soil 2 | \(Pg C\) |
| \(x_{9}\) | Soil 3 | \(Pg C\) |
| Name | Description | Expression |
|---|---|---|
| \(C\) | carbon content | \(C=\left[\begin{matrix}x_{1}\\x_{2}\\x_{3}\\x_{4}\\x_{5}\\x_{6}\\x_{7}\\x_{8}\\x_{9}\end{matrix}\right]\) |
| \(s\) | input vector | \(s=\left[\begin{matrix}s_{1}\\s_{2}\\s_{3}\\0\\0\\0\\0\\0\\0\end{matrix}\right]\) |
| \(\xi\) | environmental effects multiplier, not for all pools | \(\xi=\xi_{b}^{0.1\cdot T_{s} - 1.5}\) |
| \(B\) | Matrix of cycling and transfer rates | \(B=\left[\begin{matrix}- b_{11} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\0 & - b_{22} & 0 & 0 & 0 & 0 & 0 & 0 & 0\\0 & 0 & - b_{33} & 0 & 0 & 0 & 0 & 0 & 0\\b_{41} & b_{42} & 0 & - b_{44}\cdot\xi & 0 & 0 & 0 & 0 & 0\\b_{51} & b_{52} & 0 & 0 & - b_{55}\cdot\xi & 0 & 0 & 0 & 0\\0 & 0 & b_{63} & 0 & 0 & - b_{66}\cdot\xi & 0 & 0 & 0\\0 & 0 & 0 & b_{74}\cdot\xi & b_{75}\cdot\xi & b_{76}\cdot\xi & - b_{77}\cdot\xi & b_{78}\cdot\xi & b_{79}\cdot\xi\\0 & 0 & 0 & 0 & b_{85}\cdot\xi & b_{86}\cdot\xi & b_{87}\cdot\xi & - b_{88}\cdot\xi & b_{89}\cdot\xi\\0 & 0 & 0 & 0 & 0 & 0 & b_{97}\cdot\xi & b_{98}\cdot\xi & - b_{99}\cdot\xi\end{matrix}\right]\) |
| \(f_{s}\) | the right hand side of the ode | \(f_{s}=B C + s\) |
\(x_{1}: \alpha\cdot f_{i}\cdot s_{0}\cdot\left(\frac{7.5\cdot\rho\cdot\left(284 +\frac{1715\cdot e^{0.0305\cdot t}}{e^{0.0305\cdot t} + 1714}\right)\cdot\left(1.68\cdot T_{s0} +\frac{1.68\cdot\sigma}{\log{\left (2\right )}}\cdot\log{\left (\frac{284}{285} +\frac{343\cdot e^{0.0305\cdot t}}{57\cdot e^{0.0305\cdot t} + 97698}\right )} + 0.012\cdot\left(T_{s0} +\frac{\sigma}{\log{\left (2\right )}}\cdot\log{\left (\frac{284}{285} +\frac{343\cdot e^{0.0305\cdot t}}{57\cdot e^{0.0305\cdot t} + 97698}\right )} - 25\right)^{2} + 0.700000000000003\right)\cdot\log{\left (\frac{284}{285} +\frac{343\cdot e^{0.0305\cdot t}}{57\cdot e^{0.0305\cdot t} + 97698}\right )}}{\left(- 1.68\cdot T_{s0} +\rho\cdot\left(284 +\frac{1715\cdot e^{0.0305\cdot t}}{e^{0.0305\cdot t} + 1714}\right) -\frac{1.68\cdot\sigma}{\log{\left (2\right )}}\cdot\log{\left (\frac{284}{285} +\frac{343\cdot e^{0.0305\cdot t}}{57\cdot e^{0.0305\cdot t} + 97698}\right )} - 0.012\cdot\left(T_{s0} +\frac{\sigma}{\log{\left (2\right )}}\cdot\log{\left (\frac{284}{285} +\frac{343\cdot e^{0.0305\cdot t}}{57\cdot e^{0.0305\cdot t} + 97698}\right )} - 25\right)^{2} - 0.700000000000003\right)\cdot\left(3.36\cdot T_{s0} +\rho\cdot\left(284 +\frac{1715\cdot e^{0.0305\cdot t}}{e^{0.0305\cdot t} + 1714}\right) +\frac{3.36\cdot\sigma}{\log{\left (2\right )}}\cdot\log{\left (\frac{284}{285} +\frac{343\cdot e^{0.0305\cdot t}}{57\cdot e^{0.0305\cdot t} + 97698}\right )} + 0.024\cdot\left(T_{s0} +\frac{\sigma}{\log{\left (2\right )}}\cdot\log{\left (\frac{284}{285} +\frac{343\cdot e^{0.0305\cdot t}}{57\cdot e^{0.0305\cdot t} + 97698}\right )} - 25\right)^{2} + 1.40000000000001\right)} + 1\right)\)
\(x_{2}: \alpha\cdot f_{i}\cdot s_{0}\cdot\left(\frac{7.5\cdot\rho\cdot\left(284 +\frac{1715\cdot e^{0.0305\cdot t}}{e^{0.0305\cdot t} + 1714}\right)\cdot\left(1.68\cdot T_{s0} +\frac{1.68\cdot\sigma}{\log{\left (2\right )}}\cdot\log{\left (\frac{284}{285} +\frac{343\cdot e^{0.0305\cdot t}}{57\cdot e^{0.0305\cdot t} + 97698}\right )} + 0.012\cdot\left(T_{s0} +\frac{\sigma}{\log{\left (2\right )}}\cdot\log{\left (\frac{284}{285} +\frac{343\cdot e^{0.0305\cdot t}}{57\cdot e^{0.0305\cdot t} + 97698}\right )} - 25\right)^{2} + 0.700000000000003\right)\cdot\log{\left (\frac{284}{285} +\frac{343\cdot e^{0.0305\cdot t}}{57\cdot e^{0.0305\cdot t} + 97698}\right )}}{\left(- 1.68\cdot T_{s0} +\rho\cdot\left(284 +\frac{1715\cdot e^{0.0305\cdot t}}{e^{0.0305\cdot t} + 1714}\right) -\frac{1.68\cdot\sigma}{\log{\left (2\right )}}\cdot\log{\left (\frac{284}{285} +\frac{343\cdot e^{0.0305\cdot t}}{57\cdot e^{0.0305\cdot t} + 97698}\right )} - 0.012\cdot\left(T_{s0} +\frac{\sigma}{\log{\left (2\right )}}\cdot\log{\left (\frac{284}{285} +\frac{343\cdot e^{0.0305\cdot t}}{57\cdot e^{0.0305\cdot t} + 97698}\right )} - 25\right)^{2} - 0.700000000000003\right)\cdot\left(3.36\cdot T_{s0} +\rho\cdot\left(284 +\frac{1715\cdot e^{0.0305\cdot t}}{e^{0.0305\cdot t} + 1714}\right) +\frac{3.36\cdot\sigma}{\log{\left (2\right )}}\cdot\log{\left (\frac{284}{285} +\frac{343\cdot e^{0.0305\cdot t}}{57\cdot e^{0.0305\cdot t} + 97698}\right )} + 0.024\cdot\left(T_{s0} +\frac{\sigma}{\log{\left (2\right )}}\cdot\log{\left (\frac{284}{285} +\frac{343\cdot e^{0.0305\cdot t}}{57\cdot e^{0.0305\cdot t} + 97698}\right )} - 25\right)^{2} + 1.40000000000001\right)} + 1\right)\)
\(x_{3}: \alpha\cdot f_{i}\cdot s_{0}\cdot\left(\frac{7.5\cdot\rho\cdot\left(284 +\frac{1715\cdot e^{0.0305\cdot t}}{e^{0.0305\cdot t} + 1714}\right)\cdot\left(1.68\cdot T_{s0} +\frac{1.68\cdot\sigma}{\log{\left (2\right )}}\cdot\log{\left (\frac{284}{285} +\frac{343\cdot e^{0.0305\cdot t}}{57\cdot e^{0.0305\cdot t} + 97698}\right )} + 0.012\cdot\left(T_{s0} +\frac{\sigma}{\log{\left (2\right )}}\cdot\log{\left (\frac{284}{285} +\frac{343\cdot e^{0.0305\cdot t}}{57\cdot e^{0.0305\cdot t} + 97698}\right )} - 25\right)^{2} + 0.700000000000003\right)\cdot\log{\left (\frac{284}{285} +\frac{343\cdot e^{0.0305\cdot t}}{57\cdot e^{0.0305\cdot t} + 97698}\right )}}{\left(- 1.68\cdot T_{s0} +\rho\cdot\left(284 +\frac{1715\cdot e^{0.0305\cdot t}}{e^{0.0305\cdot t} + 1714}\right) -\frac{1.68\cdot\sigma}{\log{\left (2\right )}}\cdot\log{\left (\frac{284}{285} +\frac{343\cdot e^{0.0305\cdot t}}{57\cdot e^{0.0305\cdot t} + 97698}\right )} - 0.012\cdot\left(T_{s0} +\frac{\sigma}{\log{\left (2\right )}}\cdot\log{\left (\frac{284}{285} +\frac{343\cdot e^{0.0305\cdot t}}{57\cdot e^{0.0305\cdot t} + 97698}\right )} - 25\right)^{2} - 0.700000000000003\right)\cdot\left(3.36\cdot T_{s0} +\rho\cdot\left(284 +\frac{1715\cdot e^{0.0305\cdot t}}{e^{0.0305\cdot t} + 1714}\right) +\frac{3.36\cdot\sigma}{\log{\left (2\right )}}\cdot\log{\left (\frac{284}{285} +\frac{343\cdot e^{0.0305\cdot t}}{57\cdot e^{0.0305\cdot t} + 97698}\right )} + 0.024\cdot\left(T_{s0} +\frac{\sigma}{\log{\left (2\right )}}\cdot\log{\left (\frac{284}{285} +\frac{343\cdot e^{0.0305\cdot t}}{57\cdot e^{0.0305\cdot t} + 97698}\right )} - 25\right)^{2} + 1.40000000000001\right)} + 1\right)\)
\(x_{1}: x_{1}\cdot\left(b_{11} - b_{41} - b_{51}\right)\)
\(x_{2}: x_{2}\cdot\left(b_{22} - b_{42} - b_{52}\right)\)
\(x_{3}: x_{3}\cdot\left(b_{33} - b_{63}\right)\)
\(x_{4}: x_{4}\cdot\xi_{b}^{\frac{1}{\log{\left (2\right )}}\cdot\left(0.1\cdot\sigma\cdot\log{\left (\frac{1999\cdot e^{0.0305\cdot t} + 486776}{285\cdot e^{0.0305\cdot t} + 488490}\right )} +\left(0.1\cdot T_{s0} - 1.5\right)\cdot\log{\left (2\right )}\right)}\cdot\left(b_{44} - b_{74}\right)\)
\(x_{5}: - x_{5}\cdot\xi_{b}^{\frac{1}{\log{\left (2\right )}}\cdot\left(0.1\cdot\sigma\cdot\log{\left (\frac{1999\cdot e^{0.0305\cdot t} + 486776}{285\cdot e^{0.0305\cdot t} + 488490}\right )} +\left(0.1\cdot T_{s0} - 1.5\right)\cdot\log{\left (2\right )}\right)}\cdot\left(- b_{55} + b_{75} + b_{85}\right)\)
\(x_{6}: - x_{6}\cdot\xi_{b}^{\frac{1}{\log{\left (2\right )}}\cdot\left(0.1\cdot\sigma\cdot\log{\left (\frac{1999\cdot e^{0.0305\cdot t} + 486776}{285\cdot e^{0.0305\cdot t} + 488490}\right )} +\left(0.1\cdot T_{s0} - 1.5\right)\cdot\log{\left (2\right )}\right)}\cdot\left(- b_{66} + b_{76} + b_{86}\right)\)
\(x_{7}: - x_{7}\cdot\xi_{b}^{\frac{1}{\log{\left (2\right )}}\cdot\left(0.1\cdot\sigma\cdot\log{\left (\frac{1999\cdot e^{0.0305\cdot t} + 486776}{285\cdot e^{0.0305\cdot t} + 488490}\right )} +\left(0.1\cdot T_{s0} - 1.5\right)\cdot\log{\left (2\right )}\right)}\cdot\left(- b_{77} + b_{87} + b_{97}\right)\)
\(x_{8}: - x_{8}\cdot\xi_{b}^{\frac{1}{\log{\left (2\right )}}\cdot\left(0.1\cdot\sigma\cdot\log{\left (\frac{1999\cdot e^{0.0305\cdot t} + 486776}{285\cdot e^{0.0305\cdot t} + 488490}\right )} +\left(0.1\cdot T_{s0} - 1.5\right)\cdot\log{\left (2\right )}\right)}\cdot\left(b_{78} - b_{88} + b_{98}\right)\)
\(x_{9}: - x_{9}\cdot\xi_{b}^{\frac{1}{\log{\left (2\right )}}\cdot\left(0.1\cdot\sigma\cdot\log{\left (\frac{1999\cdot e^{0.0305\cdot t} + 486776}{285\cdot e^{0.0305\cdot t} + 488490}\right )} +\left(0.1\cdot T_{s0} - 1.5\right)\cdot\log{\left (2\right )}\right)}\cdot\left(b_{79} + b_{89} - b_{99}\right)\)
\(x_{1} \rightarrow x_{4}: b_{41}\cdot x_{1}\)
\(x_{1} \rightarrow x_{5}: b_{51}\cdot x_{1}\)
\(x_{2} \rightarrow x_{4}: b_{42}\cdot x_{2}\)
\(x_{2} \rightarrow x_{5}: b_{52}\cdot x_{2}\)
\(x_{3} \rightarrow x_{6}: b_{63}\cdot x_{3}\)
\(x_{4} \rightarrow x_{7}: b_{74}\cdot x_{4}\cdot\xi_{b}^{\frac{1}{\log{\left (2\right )}}\cdot\left(0.1\cdot\sigma\cdot\log{\left (\frac{1999\cdot e^{0.0305\cdot t} + 486776}{285\cdot e^{0.0305\cdot t} + 488490}\right )} +\left(0.1\cdot T_{s0} - 1.5\right)\cdot\log{\left (2\right )}\right)}\)
\(x_{5} \rightarrow x_{7}: b_{75}\cdot x_{5}\cdot\xi_{b}^{\frac{1}{\log{\left (2\right )}}\cdot\left(0.1\cdot\sigma\cdot\log{\left (\frac{1999\cdot e^{0.0305\cdot t} + 486776}{285\cdot e^{0.0305\cdot t} + 488490}\right )} +\left(0.1\cdot T_{s0} - 1.5\right)\cdot\log{\left (2\right )}\right)}\)
\(x_{5} \rightarrow x_{8}: b_{85}\cdot x_{5}\cdot\xi_{b}^{\frac{1}{\log{\left (2\right )}}\cdot\left(0.1\cdot\sigma\cdot\log{\left (\frac{1999\cdot e^{0.0305\cdot t} + 486776}{285\cdot e^{0.0305\cdot t} + 488490}\right )} +\left(0.1\cdot T_{s0} - 1.5\right)\cdot\log{\left (2\right )}\right)}\)
\(x_{6} \rightarrow x_{7}: b_{76}\cdot x_{6}\cdot\xi_{b}^{\frac{1}{\log{\left (2\right )}}\cdot\left(0.1\cdot\sigma\cdot\log{\left (\frac{1999\cdot e^{0.0305\cdot t} + 486776}{285\cdot e^{0.0305\cdot t} + 488490}\right )} +\left(0.1\cdot T_{s0} - 1.5\right)\cdot\log{\left (2\right )}\right)}\)
\(x_{6} \rightarrow x_{8}: b_{86}\cdot x_{6}\cdot\xi_{b}^{\frac{1}{\log{\left (2\right )}}\cdot\left(0.1\cdot\sigma\cdot\log{\left (\frac{1999\cdot e^{0.0305\cdot t} + 486776}{285\cdot e^{0.0305\cdot t} + 488490}\right )} +\left(0.1\cdot T_{s0} - 1.5\right)\cdot\log{\left (2\right )}\right)}\)
\(x_{7} \rightarrow x_{8}: b_{87}\cdot x_{7}\cdot\xi_{b}^{\frac{1}{\log{\left (2\right )}}\cdot\left(0.1\cdot\sigma\cdot\log{\left (\frac{1999\cdot e^{0.0305\cdot t} + 486776}{285\cdot e^{0.0305\cdot t} + 488490}\right )} +\left(0.1\cdot T_{s0} - 1.5\right)\cdot\log{\left (2\right )}\right)}\)
\(x_{7} \rightarrow x_{9}: b_{97}\cdot x_{7}\cdot\xi_{b}^{\frac{1}{\log{\left (2\right )}}\cdot\left(0.1\cdot\sigma\cdot\log{\left (\frac{1999\cdot e^{0.0305\cdot t} + 486776}{285\cdot e^{0.0305\cdot t} + 488490}\right )} +\left(0.1\cdot T_{s0} - 1.5\right)\cdot\log{\left (2\right )}\right)}\)
\(x_{8} \rightarrow x_{7}: b_{78}\cdot x_{8}\cdot\xi_{b}^{\frac{1}{\log{\left (2\right )}}\cdot\left(0.1\cdot\sigma\cdot\log{\left (\frac{1999\cdot e^{0.0305\cdot t} + 486776}{285\cdot e^{0.0305\cdot t} + 488490}\right )} +\left(0.1\cdot T_{s0} - 1.5\right)\cdot\log{\left (2\right )}\right)}\)
\(x_{8} \rightarrow x_{9}: b_{98}\cdot x_{8}\cdot\xi_{b}^{\frac{1}{\log{\left (2\right )}}\cdot\left(0.1\cdot\sigma\cdot\log{\left (\frac{1999\cdot e^{0.0305\cdot t} + 486776}{285\cdot e^{0.0305\cdot t} + 488490}\right )} +\left(0.1\cdot T_{s0} - 1.5\right)\cdot\log{\left (2\right )}\right)}\)
\(x_{9} \rightarrow x_{7}: b_{79}\cdot x_{9}\cdot\xi_{b}^{\frac{1}{\log{\left (2\right )}}\cdot\left(0.1\cdot\sigma\cdot\log{\left (\frac{1999\cdot e^{0.0305\cdot t} + 486776}{285\cdot e^{0.0305\cdot t} + 488490}\right )} +\left(0.1\cdot T_{s0} - 1.5\right)\cdot\log{\left (2\right )}\right)}\)
\(x_{9} \rightarrow x_{8}: b_{89}\cdot x_{9}\cdot\xi_{b}^{\frac{1}{\log{\left (2\right )}}\cdot\left(0.1\cdot\sigma\cdot\log{\left (\frac{1999\cdot e^{0.0305\cdot t} + 486776}{285\cdot e^{0.0305\cdot t} + 488490}\right )} +\left(0.1\cdot T_{s0} - 1.5\right)\cdot\log{\left (2\right )}\right)}\)
Rasmussen, M., Hastings, A., Smith, M. J., Agusto, F. B., Chen-Charpentier, B. M., Hoffman, F. M., … Luo, Y. (2016). Transit times and mean ages for nonautonomous and autonomous compartmental systems. J. Math. Biol., 73(6-7), 1379–1398. http://doi.org/10.1007/s00285-016-0990-8