Models description
Simulations of SOC stocks
Soil organic carbon models represent
SOC with a conventional multi-compartmental structure
that can be summarized with the following matrix equation:
$\frac{d\mathbf{C}}{dt}=\mathbf{I}(t)- ξ(t)\times \mathbf{A} \times \mathbf{K}\times \mathbf{C}(t),\mathbf{\ }\mathbf{\ } \mathbf{\ } \mathbf{\ } \mathbf{C}(t=0)=\mathbf{C}_{0},$
Where:
● $\mathbf{C}(t)$ is a nx1 vector describing the mass of SOC in the n compartments as a function of time (t);
● $\mathbf{I}(t)$ is a nx1 vector representing the C inputs to the soil;
● $ξ(t)$ is the scalar effect of the pedo-climatic conditions on the decomposition of SOC;
● $\mathbf{A}$ is a nxn matrix describing the mass flow among each compartment.
Its elements ${a}_{i,j}$ represent the flow of SOC from compartment j to compartment i, for i, j = 1,...,n;
● $\mathbf{K}$ is a nxn diagonal matrix containing the decomposition coefficients of the n compartments;
● $\mathbf{C}_{0}$ is a nx1 vector representing the initial level of SOC in each compartment at t=0.
Simulations of CO2 fluxes
The CO2 fluxes can also be calculated with the SOC models as:
${r}= \mathbf{R} \times \mathbf{C}(t)$,
where ${r}$ is the instantaneous release of C for all compartments
and $\mathbf{R}$ is a nxn diagonal matrix with the release
coefficients ${r}_{j}$ calculated from matrix $\mathbf{A}$ as:
$\mathbf{r}_{j}= [1-\sum_{i=1}^{n}{(a}_{i,j}{)}]$.
Other greenhouse gases
In addition to the CO2 fluxes,
CH4 uptake and N2O fluxes
are also estimated using the SG models.
These are simple empirical models allowing to estimate GHG fluxes using data on
soil physiochemical properties, water and temperature.
Models in the ensemble
The models currently included in the ensemble are:
Schematization of the SOC models
Figure
Schematization of the SOC models used in the ensemble.
Each box represents a SOC compartment where the C is transferred (black arrows),
or respired (red arrows).
DPM, RPM BIO, HUM, IOM = decomposable plant material, resistant plant material,
microbial biomass, humified organic matter, inert organic matter;
AM, BM, AS, BS = aboveground metabolic, belowground metabolic;
aboveground structural, and belowground structural.
Models resolution
To solve the equations of the SOC models, the initial partitioning of C in the different pools needs to be estimated.
To do that, we run the models with constant inputs until all the SOC pools reach a steady-state.
That is, the annual variation of SOC in all pools is lower than 0.1% for at least 10 years.
As forcing, we use the average climate and environmental conditions of the decades preceding the onset of the simulations.
Finally, we solve the matrix differential equation for the specified simulation length.
