This report presents a general overview of the model AWB , 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 17/03/2016. The entry was processed by the python package bgc-md to produce symbolic output.
The model was originally described by Allison, Wallenstein, & Bradford (2010).
| Name | Description | Unit |
|---|---|---|
| \(S\) | soil organic carbon pool | \(mgC cm^{-3}\) |
| \(D\) | dissolved organic carbon pool | \(mgC cm^{-3}\) |
| \(B\) | microbial biomass pool | \(mgC cm^{-3}\) |
| \(E\) | enzyme pool | \(mgC cm^{-3}\) |
| Name | Description | Expression |
|---|---|---|
| \(C\) | carbon content | \(C=\left[\begin{matrix}S\\D\\B\\E\end{matrix}\right]\) |
| \(I\) | input vector | \(I=\left[\begin{matrix}I_{S}\\I_{D}\\0\\0\end{matrix}\right]\) |
| \(T_{M}\) | transition operator | \(T_{M}=\left[\begin{matrix}-1 & 0 &\frac{a_{BS}\cdot r_{B}}{r_{B} + r_{E}} & 0\\1 & -1 &\frac{r_{B}\cdot\left(- a_{BS} + 1\right)}{r_{B} + r_{E}} & 1\\1 & E_{C} & -1 & 0\\0 & 0 &\frac{r_{E}}{r_{B} + r_{E}} & -1\end{matrix}\right]\) |
| \(N\) | decomposition operator | \(N=\left[\begin{matrix}\frac{E\cdot V}{K + S} & 0 & 0 & 0\\0 &\frac{B\cdot V_{U}}{D + K_{U}} & 0 & 0\\0 & 0 & r_{B} + r_{E} & 0\\0 & 0 & 0 & r_{L}\end{matrix}\right]\) |
| \(f_{s}\) | the right hand side of the ode | \(f_{s}=T_{M} N C + I\) |
\(S: I_{S}\)
\(D: I_{D}\)
\(S: -\frac{E\cdot S\cdot V_{max}\cdot e^{-\frac{E_{a}}{0.008314\cdot T + 2.269722}}}{K_{0} + K_{s}\cdot T + S}\)
\(D: -\frac{B\cdot D\cdot V_{Umax}\cdot e^{-\frac{E_{aU}}{0.008314\cdot T + 2.269722}}}{D + K_{U0} + K_{Us}\cdot T}\cdot\left(T\cdot\epsilon_{s} +\epsilon_{0} - 1\right)\)
\(S \rightarrow D: \frac{E\cdot S\cdot V_{max}\cdot e^{-\frac{E_{a}}{0.008314\cdot T + 2.269722}}}{K_{0} + K_{s}\cdot T + S}\)
\(S \rightarrow B: \frac{E\cdot S\cdot V_{max}\cdot e^{-\frac{E_{a}}{0.008314\cdot T + 2.269722}}}{K_{0} + K_{s}\cdot T + S}\)
\(D \rightarrow B: \frac{B\cdot D\cdot V_{Umax}\cdot e^{-\frac{E_{aU}}{0.008314\cdot T + 2.269722}}}{D + K_{U0} + K_{Us}\cdot T}\cdot\left(T\cdot\epsilon_{s} +\epsilon_{0}\right)\)
\(B \rightarrow S: B\cdot a_{BS}\cdot r_{B}\)
\(B \rightarrow D: B\cdot r_{B}\cdot\left(- a_{BS} + 1\right)\)
\(B \rightarrow E: B\cdot r_{E}\)
\(E \rightarrow D: E\cdot r_{L}\)
Allison, S. D., Wallenstein, M. D., & Bradford, M. A. (2010). Soil-carbon response to warming dependent on microbial physiology. Nature Geoscience, 3(5), 336–340. http://doi.org/10.1038/ngeo846