Fig 1.
The compounds and processes involved within the microbial decomposition of organic matter in soil: DOM comes from the decomposition of SOM (slow decomposition) and FOM (fast decomposition).
The microorganisms grow by assimilating DOM, breathe by producing CO2 and when they die, they are recycled into DOM and SOM.
Fig 2.
Voxel representation of a 3D binary image (left) and its corresponding graph of connected pore space voxels (right).
The blue cubes represent void voxels (pore space), while the white cubes represent solid voxels. The graph shows the adjacency of the void voxels (pore space), where node 2 is connected to nodes 1, 3, 4, and 5, indicating geometrical proximity in the 3D space.
Fig 3.
Graph representation of the microbial activity model.
Each node represents a spatial unit, with links indicating geometrical adjacency between nodes. Microbial processes are split into diffusion and transformation, where transformation occurs within nodes and diffusion is modeled as mass exchange between connected nodes according to Fick’s law.
Fig 4.
Random cross-sections of the 3D binary image depicting pore space (black) and solid matrix (white).
These slices are taken from random depths within the 3D structure, highlighting the spatial variability and heterogeneity of the pore network. The image illustrates the complexity of the porous medium involved in simulating microbial activity in soil.
Fig 5.
Three-dimensional visualization of the binary image, illustrating the spatial distribution and morphology of two distinct phases within a cubic volume. The black regions represent the void (pore space), while the white regions represent the solid phase.
Fig 6.
3D plot of the spheres set approximating the pore space of the 3D binary image with centers located within the region bounded by [50,100] on the x-axis, [50,100] on the y-axis, and [150,200] on the z-axis.
Fig 7.
Comparison of diffusion simulations: implicit scheme of the GDE with a 30-second time step (blue line), implicit scheme of the PNGM with α = 0.6 and a 15-second time step (green line), and LBM with a 0.43-second time step (red line).
Fig 8.
Comparison of diffusion simulation using the implicit and explicit schemes of the graph diffusion equation: the implicit scheme time step was set to 30 seconds, while the explicit scheme time step was set to 0.1 seconds.
Fig 9.
LBM-based approach using synchronous transformation with a time step of 0.43s, PNGM-based method using asynchronous transformation with a 5s time step, VGA using explicit scheme with a 0.1s time step and asynchronous transformation with a 0.43s time step.
Fig 10.
Training History: The x-axis represents the number of epochs, and the y-axis represents the L2 error for the four selected data points.
Fig 11.
Diffusion simulation comparison: VGA-based simulation (red curve), PNGM-based simulation calibrated by LBM-based simulation (green curve), and PNGM-based simulation with the approximated diffusional conductance coefficients (blue curve).
Fig 12.
Microbial decomposition simulation: VGA-based simulation (solid lines), PNGM-based simulation calibrated by LBM-based simulation (dash-dotted lines), and PNGM-based simulation with the approximated diffusional conductance coefficients (dotted lines).
Table 1.
Pros and Cons of discussed numerical approaches for simulating microbial decomposition of organic matter in soil.