This report presents a general overview of the model Century , 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 10/03/2016. The entry was processed by the python package bgc-md to produce symbolic output.
The model was originally described by Parton, Schimel, Cole, & Ojima (1987).
| Name | Description |
|---|---|
| \(C_{1}\) | structural soil surface litter pool |
| \(C_{2}\) | metabolic soil surface litter pool |
| \(C_{3}\) | structural soil litter pool |
| \(C_{4}\) | metabolic soil litter pool |
| \(C_{5}\) | active soil organic matter pool |
| \(C_{6}\) | slow soil organic matter pool |
| \(C_{7}\) | passive soil organic matter pool |
| Name | Description | Expression |
|---|---|---|
| \(C\) | carbon content | \(C=\left[\begin{matrix}C_{1}\\C_{2}\\C_{3}\\C_{4}\\C_{5}\\C_{6}\\C_{7}\end{matrix}\right]\) |
| \(I\) | input vector | \(I=\left[\begin{matrix}F_{s}\cdot J_{1}\\F_{m}\cdot J_{1}\\F_{s}\cdot J_{2}\\F_{m}\cdot J_{2}\\0\\0\\0\end{matrix}\right]\) |
| \(\xi\) | environmental effects multiplier (DEFAG) | \(\xi=f_{T}\cdot f_{W}\) |
| \(A\) | decomposition operator | \(A=\left[\begin{matrix}- k_{1} & 0 & 0 & 0 & 0 & 0 & 0\\0 & - K_{2} & 0 & 0 & 0 & 0 & 0\\0 & 0 & - k_{3} & 0 & 0 & 0 & 0\\0 & 0 & 0 & - K_{4} & 0 & 0 & 0\\\alpha_{51}\cdot k_{1} & 0.45\cdot K_{2} &\alpha_{53}\cdot k_{3} & 0.45\cdot K_{4} & - k_{5} & 0.42\cdot K_{6} & 0.45\cdot K_{7}\\\alpha_{61}\cdot k_{1} & 0 &\alpha_{63}\cdot k_{3} & 0 &\alpha_{65}\cdot k_{5} & - K_{6} & 0\\0 & 0 & 0 & 0 & 0.004\cdot k_{5} & 0.03\cdot K_{6} & - K_{7}\end{matrix}\right]\) |
| \(f_{s}\) | the right hand side of the ode | \(f_{s}=\xi A C + I\) |
\(C_{1}: J_{1}\cdot\left(0.018\cdot LN + 0.15\right)\)
\(C_{2}: J_{1}\cdot\left(- 0.018\cdot LN + 0.85\right)\)
\(C_{3}: J_{2}\cdot\left(0.018\cdot LN + 0.15\right)\)
\(C_{4}: J_{2}\cdot\left(- 0.018\cdot LN + 0.85\right)\)
\(C_{1}: - C_{1}\cdot K_{1}\cdot f_{T}\cdot f_{W}\cdot\left(0.15\cdot A_{l} - 0.45\right)\cdot e^{- 3\cdot Ls}\)
\(C_{2}: 0.55\cdot C_{2}\cdot K_{2}\cdot f_{T}\cdot f_{W}\)
\(C_{3}: - C_{3}\cdot K_{3}\cdot f_{T}\cdot f_{W}\cdot\left(0.25\cdot A_{l} - 0.55\right)\cdot e^{- 3\cdot Ls}\)
\(C_{4}: 0.55\cdot C_{4}\cdot K_{4}\cdot f_{T}\cdot f_{W}\)
\(C_{5}: C_{5}\cdot K_{5}\cdot f_{T}\cdot f_{W}\cdot\left(0.51\cdot Tx^{2} - 1.3175\cdot Tx + 0.85\right)\)
\(C_{6}: 0.55\cdot C_{6}\cdot K_{6}\cdot f_{T}\cdot f_{W}\)
\(C_{7}: 0.55\cdot C_{7}\cdot K_{7}\cdot f_{T}\cdot f_{W}\)
\(C_{1} \rightarrow C_{5}: - 0.55\cdot C_{1}\cdot K_{1}\cdot f_{T}\cdot f_{W}\cdot\left(A_{l} - 1\right)\cdot e^{- 3\cdot Ls}\)
\(C_{1} \rightarrow C_{6}: 0.7\cdot A_{l}\cdot C_{1}\cdot K_{1}\cdot f_{T}\cdot f_{W}\cdot e^{- 3\cdot Ls}\)
\(C_{2} \rightarrow C_{5}: 0.45\cdot C_{2}\cdot K_{2}\cdot f_{T}\cdot f_{W}\)
\(C_{3} \rightarrow C_{5}: - 0.45\cdot C_{3}\cdot K_{3}\cdot f_{T}\cdot f_{W}\cdot\left(A_{l} - 1\right)\cdot e^{- 3\cdot Ls}\)
\(C_{3} \rightarrow C_{6}: 0.7\cdot A_{l}\cdot C_{3}\cdot K_{3}\cdot f_{T}\cdot f_{W}\cdot e^{- 3\cdot Ls}\)
\(C_{4} \rightarrow C_{5}: 0.45\cdot C_{4}\cdot K_{4}\cdot f_{T}\cdot f_{W}\)
\(C_{5} \rightarrow C_{6}: C_{5}\cdot K_{5}\cdot f_{T}\cdot f_{W}\cdot\left(- 0.51\cdot Tx^{2} + 0.5705\cdot Tx + 0.146\right)\)
\(C_{5} \rightarrow C_{7}: C_{5}\cdot K_{5}\cdot f_{T}\cdot f_{W}\cdot\left(- 0.003\cdot Tx + 0.004\right)\)
\(C_{6} \rightarrow C_{5}: 0.42\cdot C_{6}\cdot K_{6}\cdot f_{T}\cdot f_{W}\)
\(C_{6} \rightarrow C_{7}: 0.03\cdot C_{6}\cdot K_{6}\cdot f_{T}\cdot f_{W}\)
\(C_{7} \rightarrow C_{5}: 0.45\cdot C_{7}\cdot K_{7}\cdot f_{T}\cdot f_{W}\)
\(C_1 = \frac{0.006\cdot J_{1}\cdot e^{3.0\cdot Ls}}{K_{1}\cdot f_{T}\cdot f_{W}}\cdot\left(3.0\cdot LN + 25.0\right)\)
\(C_2 = -\frac{0.002\cdot J_{1}\cdot\left(9.0\cdot LN - 425.0\right)}{K_{2}\cdot f_{T}\cdot f_{W}}\)
\(C_3 = \frac{0.006\cdot J_{2}\cdot e^{3.0\cdot Ls}}{K_{3}\cdot f_{T}\cdot f_{W}}\cdot\left(3.0\cdot LN + 25.0\right)\)
\(C_4 = -\frac{0.002\cdot J_{2}\cdot\left(9.0\cdot LN - 425.0\right)}{K_{4}\cdot f_{T}\cdot f_{W}}\)
\(C_5 = \frac{1}{K_{5}\cdot f_{T}\cdot f_{W}\cdot\left(884340.0\cdot Tx^{2} - 3983847.0\cdot Tx + 3739636.0\right)}\cdot\left(- 17751.6\cdot A_{l}\cdot J_{1}\cdot LN - 147930.0\cdot A_{l}\cdot J_{1} - 10551.6\cdot A_{l}\cdot J_{2}\cdot LN - 87930.0\cdot A_{l}\cdot J_{2} + 7200.0\cdot J_{1}\cdot LN + 1860000.0\cdot J_{1} + 1800000.0\cdot J_{2}\right)\)
\(C_6 = \frac{1}{K_{6}\cdot f_{T}\cdot f_{W}\cdot\left(294780.0\cdot Tx - 934909.0\right)}\cdot\left(6732.0\cdot A_{l}\cdot J_{1}\cdot LN\cdot Tx - 11131.92\cdot A_{l}\cdot J_{1}\cdot LN + 56100.0\cdot A_{l}\cdot J_{1}\cdot Tx - 92766.0\cdot A_{l}\cdot J_{1} + 5508.0\cdot A_{l}\cdot J_{2}\cdot LN\cdot Tx - 11394.72\cdot A_{l}\cdot J_{2}\cdot LN + 45900.0\cdot A_{l}\cdot J_{2}\cdot Tx - 94956.0\cdot A_{l}\cdot J_{2} - 1224.0\cdot J_{1}\cdot LN\cdot Tx - 262.8\cdot J_{1}\cdot LN - 316200.0\cdot J_{1}\cdot Tx - 67890.0\cdot J_{1} - 306000.0\cdot J_{2}\cdot Tx - 65700.0\cdot J_{2}\right)\)
\(C_7 = \frac{1}{K_{7}\cdot f_{T}\cdot f_{W}\cdot\left(294780.0\cdot Tx - 934909.0\right)}\cdot\left(201.96\cdot A_{l}\cdot J_{1}\cdot LN\cdot Tx - 316.206\cdot A_{l}\cdot J_{1}\cdot LN + 1683.0\cdot A_{l}\cdot J_{1}\cdot Tx - 2635.05\cdot A_{l}\cdot J_{1} + 165.24\cdot A_{l}\cdot J_{2}\cdot LN\cdot Tx - 331.29\cdot A_{l}\cdot J_{2}\cdot LN + 1377.0\cdot A_{l}\cdot J_{2}\cdot Tx - 2760.75\cdot A_{l}\cdot J_{2} - 36.72\cdot J_{1}\cdot LN\cdot Tx - 15.084\cdot J_{1}\cdot LN - 9486.0\cdot J_{1}\cdot Tx - 3896.7\cdot J_{1} - 9180.0\cdot J_{2}\cdot Tx - 3771.0\cdot J_{2}\right)\)
Parton, W. J., Schimel, D. S., Cole, C. V., & Ojima, D. S. (1987). Analysis of factors controlling soil organic matter levels in Great Plains grasslands. Soil Sci. Soc. Am. J., 51(5), 1173–1179. http://doi.org/10.2136/sssaj1987.03615995005100050015x