This report presents a general overview of the model RothC-26.3 , 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 Jenkinson & Rayner (1977).
plot, field, catchment, regional, national, global
| Name | Description | Unit |
|---|---|---|
| \(C_{1}\) | decomposable plant material pool (DPM) | \(t C\cdot ha^{-1}\) |
| \(C_{2}\) | resistant plant material pool (RPM) | \(t C\cdot ha^{-1}\) |
| \(C_{3}\) | microbial biomass pool (BIO) | \(t C\cdot ha^{-1}\) |
| \(C_{4}\) | humified organic matter pool (HUM) | \(t C\cdot ha^{-1}\) |
| \(C_{5}\) | inert organic matter pool (IOM) | \(t C\cdot ha^{-1}\) |
| Name | Description | Expression |
|---|---|---|
| \(C\) | carbon content | \(C=\left[\begin{matrix}C_{1}\\C_{2}\\C_{3}\\C_{4}\\C_{5}\end{matrix}\right]\) |
| \(I\) | input vector | \(I=\left[\begin{matrix}J\cdot\gamma\\J\cdot\left(-\gamma + 1\right)\\0\\0\\0\end{matrix}\right]\) |
| \(\xi\) | environmental effects multiplier | \(\xi=f_{T}\cdot f_{W}\) |
| \(A\) | decomposition operator | \(A=\left[\begin{matrix}- k_{1} & 0 & 0 & 0 & 0\\0 & - k_{2} & 0 & 0 & 0\\a\cdot k_{1} & a\cdot k_{2} & a\cdot k_{3} - k_{3} & a\cdot k_{4} & 0\\b\cdot k_{1} & b\cdot k_{2} & b\cdot k_{3} & b\cdot k_{4} - k_{4} & 0\\0 & 0 & 0 & 0 & 0\end{matrix}\right]\) |
| \(f_{s}\) | the right hand side of the ode | \(f_{s}=\xi A C + I\) |
\(C_{1}: \frac{DR\cdot J}{DR + 1}\)
\(C_{2}: J\cdot\left(-\frac{DR}{DR + 1} + 1\right)\)
\(C_{1}: \frac{C_{1}\cdot f_{T}\cdot f_{W}\cdot k_{1}}{4.0895\cdot e^{0.0786\cdot pClay} + 2.672}\cdot\left(3.0895\cdot e^{0.0786\cdot pClay} + 2.672\right)\)
\(C_{2}: \frac{C_{2}\cdot f_{T}\cdot f_{W}\cdot k_{2}}{4.0895\cdot e^{0.0786\cdot pClay} + 2.672}\cdot\left(3.0895\cdot e^{0.0786\cdot pClay} + 2.672\right)\)
\(C_{3}: \frac{1.0\cdot C_{3}\cdot f_{T}\cdot f_{W}\cdot k_{3}}{4.0895\cdot e^{0.0786\cdot pClay} + 2.672}\cdot\left(3.0895\cdot e^{0.0786\cdot pClay} + 2.672\right)\)
\(C_{4}: \frac{1.0\cdot C_{4}\cdot f_{T}\cdot f_{W}\cdot k_{4}}{4.0895\cdot e^{0.0786\cdot pClay} + 2.672}\cdot\left(3.0895\cdot e^{0.0786\cdot pClay} + 2.672\right)\)
\(C_{1} \rightarrow C_{3}: \frac{0.46\cdot C_{1}\cdot f_{T}\cdot f_{W}\cdot k_{1}\cdot e^{0.0786\cdot pClay}}{4.0895\cdot e^{0.0786\cdot pClay} + 2.672}\)
\(C_{1} \rightarrow C_{4}: \frac{0.54\cdot C_{1}\cdot f_{T}\cdot f_{W}\cdot k_{1}\cdot e^{0.0786\cdot pClay}}{4.0895\cdot e^{0.0786\cdot pClay} + 2.672}\)
\(C_{2} \rightarrow C_{3}: \frac{0.46\cdot C_{2}\cdot f_{T}\cdot f_{W}\cdot k_{2}\cdot e^{0.0786\cdot pClay}}{4.0895\cdot e^{0.0786\cdot pClay} + 2.672}\)
\(C_{2} \rightarrow C_{4}: \frac{0.54\cdot C_{2}\cdot f_{T}\cdot f_{W}\cdot k_{2}\cdot e^{0.0786\cdot pClay}}{4.0895\cdot e^{0.0786\cdot pClay} + 2.672}\)
\(C_{3} \rightarrow C_{4}: \frac{0.54\cdot C_{3}\cdot f_{T}\cdot f_{W}\cdot k_{3}\cdot e^{0.0786\cdot pClay}}{4.0895\cdot e^{0.0786\cdot pClay} + 2.672}\)
\(C_{4} \rightarrow C_{3}: \frac{0.46\cdot C_{4}\cdot f_{T}\cdot f_{W}\cdot k_{4}\cdot e^{0.0786\cdot pClay}}{4.0895\cdot e^{0.0786\cdot pClay} + 2.672}\)
Jenkinson, D. S., & Rayner, J. H. (1977). The turnover of soil organic matter in some of the Rothamsted classical expermiments. Soil Science, 123(5), 298–305. http://doi.org/10.1097/00010694-197705000-00005