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 Holger Metzler (Orcid ID: 0000-0002-8239-1601) on 09/03/2016, and was last modified on lm.
The model depicted in this document considers soil organic matter decomposition. It was originally described by Hénin & Dupuis (1945).
differential equations, linear, time invariant, analytic
mass balance, substrate dependence of decomposition, heterogeneity of speed of decay, internal transformations of organic matter
The following table contains the available information regarding this section:
| Name | Description | Units |
|---|---|---|
| \(A\) | labile pool | \(MgC\cdot ha^{-1}\) |
| \(B\) | stable pool | \(MgC\cdot ha^{-1}\) |
The following table contains the available information regarding this section:
| Name | Description | Type | Units |
|---|---|---|---|
| \(\alpha\) | annual decomposition rate of labile pool | parameter | \(yr^{-1}\) |
| \(\beta\) | annual decomposition rate of stable pool | parameter | \(yr^{-1}\) |
The following table contains the available information regarding this section:
| Name | Description | Type | Units |
|---|---|---|---|
| \(m\) | annual organic matter input | parameter | \(MgC yr^{-1}\) |
The following table contains the available information regarding this section:
| Name | Description | Type |
|---|---|---|
| \(K\) | isohumic coefficient | parameter |
The following table contains the available information regarding this section:
| Name | Description | Expressions |
|---|---|---|
| \(C\) | carbon content | \(C=\left[\begin{matrix}A\\B\end{matrix}\right]\) |
| \(I\) | input vector | \(I=\left[\begin{matrix}m\\0\end{matrix}\right]\) |
| \(A_{GeM}\) | decomposition operator | \(A_{GeM}=\left[\begin{matrix}-\alpha & 0\\K\cdot\alpha & -\beta\end{matrix}\right]\) |
| \(f_{s}\) | the right hand side of the ode | \(f_{s}=I+A_{GeM}\,C\) |
| Flux description | |
|---|---|
 Figure 1: Pool model representation |
Input fluxes\(A: m\) Output fluxes\(A: A\cdot\alpha\cdot\left(- K + 1\right)\) Internal fluxes\(A > B: A\cdot K\cdot\alpha\) |
\(\left[\begin{matrix}- A\cdot\alpha + m\\A\cdot K\cdot\alpha - B\cdot\beta\end{matrix}\right]\)
\(\left[\begin{matrix}-\alpha & 0\\K\cdot\alpha & -\beta\end{matrix}\right]\)
\(A = \frac{m}{\alpha}\)
\(B = \frac{K}{\beta}\cdot m\)
Hénin, S., & Dupuis, M. (1945). Essai de bilan de la matière organique du sol. In Annales agronomiques (Vol. 15, pp. 17–29).