Using Complex Networks to Model Two- and Three-Dimensional Soil Porous Architecture

The ability to quantify three dimensional (3-D) soil porous architecture is a key requirement in the advanced understanding of soil functioning. Recent developments in the visualization of soil structure using tools such as x-ray Computed Tomography (CT) provide new opportunities for pore-scale modeling. Here we apply a novel complex network approach to examine soil pore architecture in both two (2-D) and three dimensions (3-D). Using images of soil structure obtained by x-ray CT; we constructed and successfully validated a complex network derived from a simple measure for network links between two pores in 2-D. We were able to illustrate that the soil comprised a spatially embedded scale-free network characterized by a power-law degree distribution. Computation of the degree dependent clustering coefficient of the constructed networks showed the hierarchical organization of the soil pore architecture. Finally, we derived an algorithm to generate a soil structure model built on the underlying scale-free network which was in close agreement with an actual 3-D reconstructed soil structure. Considering the soil system as a complex network with scale-free properties is likely to have important consequences for the further understanding of function, in particular transport in soils.